ABAQUS/Explicit User's Manual
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The information in this document is subject to change without notice and should not be construed as a
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General conversion factors (to five significant digits)
Quantity
U.S. unit
SI equivalent
Length
1 in
0.025400 m
1 ft
0.30480 m
1 mile
1609.3 m
2
Area
1 in
0.64516 ´ 10-3 m2
1 ft2
0.092903 m 2
1 acre
4046.9 m2
Volume
1 in3
0.016387 ´ 10-3 m3
3
1 ft
0.028317 m 3
1 US gallon
3.7854 ´ 10-3 m3
Quantity
Density
Energy
Force
Mass
Power
Pressure, Stress
Conversion factors for stress analysis
U.S. unit
SI equivalent
1 slug/ft3 = 1 lbf s2/ft4
515.38 kg/m3
1 lbf s2/in4
10.687 ´ 106 kg/m3
1 ft lbf
1.3558 J (N m)
1 lbf
4.4482 N (kg m/s2)
2
1 slug = 1 lbf s /ft
14.594 kg (N s2/m)
175.13 kg
1 lbf s2/in
1 ft lbf/s
1.3558 W (N m/s)
2
1 psi (lbf/in )
6894.8 Pa (N/m2)
Conversion factors for heat transfer analysis
Quantity
U.S. unit
SI equivalent
Conductivity
1 Btu/ft hr °F
1.7307 W/m °C
1 Btu/in hr °F
20.769 W/m °C
Density
1 lbm/in3
27680. kg/m3
Energy
1 Btu
1055.1 J
Heat flux density
1 Btu/in 2 hr
454.26 W/m2
Power
1 Btu/hr
0.29307 W
Specific heat
1 Btu/lbm °F
4186.8 J/kg °C
Temperature
1 °F
5/9 °C
Temp °F
9/5 ´ Temp °C + 32°
9/5 ´ Temp °K - 459.67°
Constant
Absolute zero
Acceleration of gravity
Atmospheric pressure
Stefan-Boltzmann
constant
Important constants
U.S. unit
-459.67 °F
32.174 ft/s 2
14.694 psi
0.1714 ´ 10-8 Btu/hr ft2
°R4
where °R = °F + 459.67
SI unit
-273.15 °C
9.8066 m/s2
0.10132 ´ 106 Pa
5.669 ´ 10-8 W/m2 °K4
where °K = °C + 273.15
Approximate properties of mild steel at room temperature
Quantity
U.S. unit
SI unit
Conductivity
28.9 Btu/ft hr °F
50 W/m °C
2.4 Btu/in hr °F
Density
15.13 slug/ft3 (lbf s2/ft4)
7800 kg/m3
0.730 ´ 10-3 lbf s2/in4
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Elastic modulus
Specific heat
Yield stress
0.282 lbm/in 3
30 ´ 106 psi
0.11 Btu/lbm °F
30 ´ 103 psi
207 ´ 109 Pa
460 J/kg °C
207 ´ 106 Pa
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This section lists various resources that are available for help with using ABAQUS, including
technical and systems support, training seminars, and documentation.
Support
HKS offers both technical (engineering) support and systems support for ABAQUS. Technical and
systems support are provided through the nearest local support office. You can contact our offices by
telephone, fax, electronic mail, or regular mail. Information on how to contact each office is listed in
the front of each ABAQUS manual. Support information is also available by visiting the ABAQUS
Home Page on the World Wide Web (details are given below). When contacting your local support
office, please specify whether you would like technical support (you have encountered problems
performing an ABAQUS analysis) or systems support (ABAQUS will not install correctly, licensing
does not work correctly, or other hardware-related issues have arisen).
We welcome any suggestions for improvements to the support program or documentation. We will
ensure that any enhancement requests you make are considered for future releases. If you wish to file a
complaint about the service or products provided by HKS, refer to the ABAQUS Home Page.
Technical support
HKS technical support engineers can assist in clarifying ABAQUS features and checking errors by
giving both general information on using ABAQUS and information on its application to specific
analyses. If you have concerns about an analysis, we suggest that you contact us at an early stage, since
it is usually easier to solve problems at the beginning of a project rather than trying to correct an
analysis at the end.
Please have the following information ready before calling the technical support hotline, and include it
in any written contacts:
· The version of ABAQUS that are you using.
- The version numbers for ABAQUS/Standard and ABAQUS/Explicit are given at the top of the
data (.dat) file.
- The version numbers for ABAQUS/CAE and ABAQUS/Viewer can be found by selecting
Help->On version from the main menu bar.
- The version number for ABAQUS/CAT is given at the top of the input ( .inp) file as well as
the data file.
- The version numbers for ABAQUS/ADAMS and ABAQUS/C-MOLD are output to the
screen.
- The version number for ABAQUS/Safe is given under the ABAQUS logo in the main
window.
· The type of computer on which you are running ABAQUS.
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· The symptoms of any problems, including the exact error messages, if any.
· Workarounds or tests that you have already tried.
When calling for support about a specific problem, any available ABAQUS output files may be helpful
in answering questions that the support engineer may ask you.
The support engineer will try to diagnose your problem from the model description and a description
of the difficulties you are having. Frequently, the support engineer will need model sketches, which
can be faxed to HKS or sent in the mail. Plots of the final results or the results near the point that the
analysis terminated may also be needed to understand what may have caused the problem.
If the support engineer cannot diagnose your problem from this information, you may be asked to send
the input data. The data can be sent by means of e-mail, tape, or disk. Please check the ABAQUS
Home Page at www.abaqus.com for the media formats that are currently accepted.
All support calls are logged into a database, which enables us to monitor the progress of a particular
problem and to check that we are resolving support issues efficiently. If you would like to know the log
number of your particular call for future reference, please ask the support engineer. If you are calling to
discuss an existing support problem and you know the log number, please mention it so that we can
consult the database to see what the latest action has been and, thus, avoid duplication of effort. In
addition, please give the receptionist the support engineer's name (or include it at the top of any e-mail
correspondence).
Systems support
HKS systems support engineers can help you resolve issues related to the installation and running of
ABAQUS, including licensing difficulties, that are not covered by technical support.
You should install ABAQUS by carefully following the instructions in the ABAQUS Site Guide. If
you encounter problems with the installation or licensing, first review the instructions in the ABAQUS
Site Guide to ensure that they have been followed correctly. If this does not resolve the problems, look
on the ABAQUS Home Page under Technical Support for information about known installation
problems. If this does not address your situation, please contact your local support office. Send
whatever information is available to define the problem: error messages from an aborted analysis or a
detailed explanation of the problems encountered. Whenever possible, please send the output from the
abaqus info=env and abaqus info=sys commands.
ABAQUS Web server
For users connected to the Internet, many questions can be answered by visiting the ABAQUS Home
Page on the World Wide Web at
http://www.abaqus.com
The information available on the ABAQUS Home Page includes:
· Frequently asked questions
· ABAQUS systems information and machine requirements
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· Benchmark timing documents
· Error status reports
· ABAQUS documentation price list
· Training seminar schedule
· Newsletters
Anonymous ftp site
For users connected to the Internet, HKS maintains useful documents on an anonymous ftp account on
the computer ftp.abaqus.com. Simply ftp to ftp.abaqus.com. Login as user anonymous, and type your
e-mail address as your password. Directions will come up automatically upon login.
Writing to technical support
Address of HKS Headquarters:
Hibbitt, Karlsson & Sorensen, Inc.
1080 Main Street
Pawtucket, RI 02860-4847, USA
Attention: Technical Support
Addresses for other offices and representatives are listed in the front of each manual.
Support for academic institutions
Under the terms of the Academic License Agreement we do not provide support to users at academic
institutions unless the institution has also purchased technical support. Please see the ABAQUS Home
Page, or contact us for more information.
Training
All HKS offices offer regularly scheduled public training classes.
The Introduction to ABAQUS/Standard and ABAQUS/Explicit seminar covers basic usage and
nonlinear applications, such as large deformation, plasticity, contact, and dynamics. Workshops
provide as much practical experience with ABAQUS as possible.
The Introduction to ABAQUS/CAE seminar discusses modeling, managing simulations, and viewing
results with ABAQUS/CAE. "Hands-on" workshops are complemented by lectures.
Advanced seminars cover topics of interest to customers with experience using ABAQUS, such as
engine analysis, metal forming, fracture mechanics, and heat transfer.
We also provide training seminars at customer sites. On-site training seminars can be one or more days
in duration, depending on customer requirements. The training topics can include a combination of
material from our introductory and advanced seminars. Workshops allow customers to exercise
ABAQUS on their own computers.
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For a schedule of seminars see the ABAQUS Home Page, or call HKS or your local HKS
representative.
Documentation
The following documentation and publications are available from HKS, unless otherwise specified, in
printed form and through our online documentation server. For more information on accessing the
online books, refer to the discussion of execution procedures in the user's manuals.
In addition to the documentation listed below, HKS publishes two newsletters on a regular schedule:
ABAQUS/News and ABAQUS/Answers. ABAQUS/News includes topical information about program
releases, training seminars, etc. ABAQUS/Answers includes technical articles on particular topics
related to ABAQUS usage. These newsletters are distributed at no cost to users who wish to subscribe.
Please contact your local ABAQUS support office if you wish to be added to the mailing list for these
publications. They are also archived in the Reference Shelf on the ABAQUS Home Page.
Training Manuals
Getting Started with ABAQUS/Standard: This document is a self-paced tutorial designed to
help new users become familiar with using ABAQUS/Standard for static and dynamic stress
analysis simulations. It contains a number of fully worked examples that provide practical
guidelines for performing structural analyses with ABAQUS.
Getting Started with ABAQUS/Explicit: This document is a self-paced tutorial designed to help
new users become familiar with using ABAQUS/Explicit. It begins with the basics of modeling in
ABAQUS, so no prior knowledge of ABAQUS is required. A number of fully worked examples
provide practical guidelines for performing explicit dynamic analyses, such as drop tests and metal
forming simulations, with ABAQUS/Explicit.
Lecture Notes: These notes are available on many topics to which ABAQUS is applied. They are
used in the technical seminars that HKS presents to help users improve their understanding and
usage of ABAQUS (see the "Training" section above for more information about these seminars).
While not intended as stand-alone tutorial material, they are sufficiently comprehensive that they
can usually be used in that mode. The list of available lecture notes is included in the
Documentation Price List.
User's Manuals
ABAQUS/Standard User's Manual: This volume contains a complete description of the
elements, material models, procedures, input specifications, etc. It is the basic reference document
for ABAQUS/Standard.
ABAQUS/Explicit User's Manual: This volume contains a complete description of the elements,
material models, procedures, input specifications, etc. It is the basic reference document for
ABAQUS/Explicit.
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ABAQUS/CAE User's Manual: This reference document for ABAQUS/CAE includes three
comprehensive tutorials as well as detailed descriptions of how to use ABAQUS/CAE for model
generation, analysis, and results evaluation.
ABAQUS/Viewer User's Manual: This basic reference document for ABAQUS/Viewer includes
an introductory tutorial as well as a complete description of how to use ABAQUS/Viewer to
display your model and results.
ABAQUS/ADAMS User's Manual: This document describes how to install and how to use
ABAQUS/ADAMS, an interface program that creates ABAQUS models of ADAMS components
and converts the ABAQUS results into an ADAMS modal neutral file that can be used by the
ADAMS/Flex program. It is the basic reference document for the ABAQUS/ADAMS program.
ABAQUS/CAT User's Manual: This document describes how to install and how to use
ABAQUS/CAT, an interface program that creates an ABAQUS input file from a CATIA model
and postprocesses the analysis results in CATIA. It is the basic reference document for the
ABAQUS/CAT program.
ABAQUS/C-MOLD User's Manual: This document describes how to install and how to use
ABAQUS/C-MOLD, an interface program that translates finite element mesh, material property,
and initial stress data from a C-MOLD analysis to an ABAQUS input file.
ABAQUS/Safe User's Manual: This document describes how to install and how to use
ABAQUS/Safe, an interface program that calculates fatigue lives and fatigue strength reserve
factors from finite element models. It is the basic reference document for the ABAQUS/Safe
program. The theoretical background to fatigue analysis is contained in the Modern Metal Fatigue
Analysis manual (available only in print).
Using ABAQUS Online Documentation: This online manual contains instructions on using the
ABAQUS online documentation server to read the manuals that are available online.
ABAQUS Release Notes: This document contains brief descriptions of the new features available
in the latest release of the ABAQUS product line.
ABAQUS Site Guide: This document describes how to install ABAQUS and how to configure
the installation for particular circumstances. Some of this information, of most relevance to users,
is also provided in the user's manuals.
Examples Manuals
ABAQUS Example Problems Manual: This volume contains more than 75 detailed examples
designed to illustrate the approaches and decisions needed to perform meaningful linear and
nonlinear analysis. Typical cases are large motion of an elastic-plastic pipe hitting a rigid wall;
inelastic buckling collapse of a thin-walled elbow; explosive loading of an elastic, viscoplastic thin
ring; consolidation under a footing; buckling of a composite shell with a hole; and deep drawing of
a metal sheet. It is generally useful to look for relevant examples in this manual and to review
them when embarking on a new class of problem.
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ABAQUS Benchmarks Manual: This volume (available online and, if requested, in print)
contains over 200 benchmark problems and standard analyses used to evaluate the performance of
ABAQUS; the tests are multiple element tests of simple geometries or simplified versions of real
problems. The NAFEMS benchmark problems are included in this manual.
ABAQUS Verification Manual: This online-only volume contains more than 5000 basic test
cases, providing verification of each individual program feature (procedures, output options,
MPCs, etc.) against exact calculations and other published results. It may be useful to run these
problems when learning to use a new capability. In addition, the supplied input data files provide
good starting points to check the behavior of elements, materials, etc.
Reference Manuals
ABAQUS Keywords Manual: This volume contains a complete description of all the input
options that are available in ABAQUS/Standard and ABAQUS/Explicit.
ABAQUS Theory Manual: This volume (available online and, if requested, in print) contains
detailed, precise discussions of all theoretical aspects of ABAQUS. It is written to be understood
by users with an engineering background.
ABAQUS Command Language Manual: This online manual provides a description of the
ABAQUS Command Language and a command reference that lists the syntax of each command.
The manual describes how commands can be used to create and analyze ABAQUS/CAE models,
to view the results of the analysis, and to automate repetitive tasks. It also contains information on
using the ABAQUS Command Language or C++ as an application programming interface (API).
ABAQUS Input Files: This online manual contains all the input files that are included with the
ABAQUS release and referred to in the ABAQUS Example Problems Manual, the ABAQUS
Benchmarks Manual, and the ABAQUS Verification Manual. They are listed in the order in which
they appear in the manuals, under the title of the problem that refers to them. The input file
references in the manuals hyperlink directly to this book.
Quality Assurance Plan: This document describes HKS's QA procedures. It is a controlled
document, provided to customers who subscribe to either HKS's Nuclear QA Program or the
Quality Monitoring Service.
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Introduction, Spatial Modeling, and Execution
Part I: Introduction, Spatial Modeling, and
Execution
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Introduction
1. Introduction
1.1 Introduction
1.1.1 Introduction: general
Overview of the ABAQUS finite element system
The ABAQUS finite element system includes:
· ABAQUS/Standard, a general-purpose finite element program;
· ABAQUS/Explicit, an explicit dynamics finite element program;
· ABAQUS/CAE, an interactive preprocessor that can be used to create finite element models and
the associated input file for ABAQUS; and
· ABAQUS/Viewer, a menu-driven interactive postprocessor that provides X-Y plots, animations,
contour plots, and tabular output of results from ABAQUS/Standard and ABAQUS/Explicit.
ABAQUS/Viewer is available only on selected platforms.
Overview of this manual
This manual is a reference guide to using ABAQUS/Explicit. The manual is divided into several parts:
· Part I, "Introduction, Spatial Modeling, and Execution ," discusses basic modeling concepts in
ABAQUS, such as defining nodes, elements, and surfaces; the conventions and input formats that
should be followed when using ABAQUS; and the ABAQUS execution procedures for
ABAQUS/Explicit, ABAQUS/Viewer, and several utilities that are provided with the ABAQUS
system.
· Part II, "Output," describes how to obtain output from ABAQUS/Explicit, including the output
variable identifiers that are available.
· Part III, "Analysis," describes the analysis types and related options.
· Part IV, "Materials," describes the material modeling options and how to calibrate some of the
more advanced material models.
· Part V, "Elements," describes the elements available in ABAQUS/Explicit.
· Part VI, "Prescribed Conditions," describes the use of prescribed conditions, such as distributed
loads and nodal velocities.
· Part VII, "Constraints and Interactions," discusses the use of constraints and interactions between
structures, such as multi-point constraints or contact, in an ABAQUS/Explicit analysis.
· Part VIII, "User Subroutines," describes the user subroutines that can be used with
ABAQUS/Explicit.
1-16
Introduction
· Part IX, "Parametric Studies," describes the Python scripting functions and commands that are
used to perform parametric studies with ABAQUS/Design.
The manual also includes an index of all of the elements available in ABAQUS/Explicit.
For more information on using the online documentation system, refer to the electronic book Using
ABAQUS Online Documentation.
Using ABAQUS
ABAQUS/Standard and ABAQUS/Explicit run as batch applications (see ``Execution procedure for
ABAQUS/Standard and ABAQUS/Explicit,'' Section 3.2.1, for details). The main input to these
modules is a file containing the options required for the simulation and the data associated with those
options. There may also be supplementary files, such as restart or results files from previous analyses,
or auxiliary data files, such as a file containing an acceleration record. As described in ``Defining a
model in ABAQUS,'' Section 1.3.1, the main input file consists of two sections: model input and
history input.
Reviewing the results of an ABAQUS simulation
Information on requesting output from an ABAQUS/Explicit simulation is discussed in ``Output,''
Section 4.1.1. Requested results from an ABAQUS/Explicit simulation are viewed through
ABAQUS/Viewer.
The use of ABAQUS/Viewer is described in the ABAQUS/Viewer User's Manual (see ``Execution
procedure for ABAQUS/Viewer,'' Section 3.2.3, for details describing how to start ABAQUS/Viewer).
ABAQUS/Viewer reads the output database file to create contour plots, animations, X-Y plots, and
tabular output of ABAQUS results.
1.1.2 An introduction to using ABAQUS/Explicit
This section presents a tutorial introduction to using ABAQUS/Explicit.
References
· ``Input syntax rules,'' Section 1.2.1
· ``Conventions,'' Section 1.2.2
· ``Defining a model in ABAQUS,'' Section 1.3.1
· ABAQUS Keywords Manual
Overview
This volume is the reference manual for using ABAQUS/Explicit. The new user is encouraged to read
this section to learn how to use the program. ABAQUS/Explicit is very easy to use because the input is
organized around a few natural concepts and conventions. After reading this section, a new user will
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Introduction
be able to run quite complicated problems with very little effort.
Since ABAQUS/Explicit is a batch program, the objective is to assemble an "input file" that describes
a problem so that ABAQUS can provide an analysis. Input files for complex simulations can be large
but can be managed without too much difficulty by using the convenience features built into the
program's input structure. In this section we concentrate on simple usage of the program. Extensions to
more realistic cases follow naturally because the problem definition concepts are the same for all
cases--we just use more features in the more complicated cases.
The ABAQUS/Explicit input file
An input file for ABAQUS/Explicit contains model data and history data. Model data (discussed in
``Defining a model in ABAQUS,'' Section 1.3.1) define a finite element model: the elements, nodes,
element properties, contact surface definitions, material definitions, and so on--any data that specify
the model itself. Model data can be organized into parts, which are assembled together to create a
meaningful model (see ``Defining an assembly,'' Section 2.5.1).
History data (discussed in ``Defining a model in ABAQUS,'' Section 1.3.1) define what happens to the
model--the sequence of events or loadings for which the model's response is sought. In ABAQUS this
history is divided by the user into a sequence of steps. Analysis steps define a sequence of events that
follow one another, in the sense that the state of the model at the end of a step provides the initial
conditions for the start of the next step. The definition of a step includes the procedure type (such as
explicit transient dynamics), loading, and output requests. What constitutes a step is a matter of choice
on the part of the user. For example, a dynamic event might be modeled in one step, or, if the
deformations take some time to evolve and the solution is not particularly interesting in the early time,
the same analysis might be broken into two steps so that the output requests can be changed to provide
more frequent writing of the results during the second step.
As an example, consider the axisymmetric cup forming problem shown in Figure 1.1.2-1.
Figure 1.1.2-1 Simple axisymmetric cup forming problem.
1-18
Introduction
In this example a sheet of metal (the blank) is to be drawn into a cup by the motion of the punch. In the
first step the blank holder (the top die) is moved down into the mating die to form a draw bead, which
is used to restrain the motion of the blank. In the next step the punch is moved downward to form the
blank into an axisymmetric cup. This step is followed by a step in which the punch is moved upward to
determine the springback of the blank. The final step involves removing the blank holder to determine
the unconstrained shape of the workpiece. In this case it is clear that each analysis step must use the
state at the end of the previous analysis step as its initial conditions, which introduces a natural order
dependency in the input file.
Option blocks
All ABAQUS/Explicit data are defined in option blocks--sets of data describing a part of the problem
definition. The user chooses those options that are relevant for a particular application. Each option is
introduced by a keyword line. If the option requires data lines, they follow the keyword line. Again, we
see a natural ordering of the input file. The syntax of keyword and data lines is defined in ``Input
syntax rules,'' Section 1.2.1. A brief description, enough for our purposes here, is as follows. Keyword
lines begin with a *, followed by the keyword (for example: *MATERIAL begins the definition of
material properties). Any line beginning with ** is a comment line. Keywords may have parameters,
which are separated by a comma (,). Blanks within keyword lines are ignored.
Some parameters are required (for example, on the *ELEMENT option, which introduces a list of
element definitions, the parameter TYPE is required to tell ABAQUS what type of element--solid,
shell, beam, etc.--is being defined). Many parameters are optional: this allows specification of diverse
models. Parameters may have values: if they do, the = sign is used to associate the value with the
parameter (for example, *MATERIAL, NAME=STEEL associates the name STEEL with a material
1-19
Introduction
definition).
Data lines may be associated with the option--if so, they must follow the keyword line. They are used
to provide data that are more easily given in lists than as parameters on the keyword, usually because
the list might be extensive. For example,
*ELASTIC
200.E3, 0.3, 20.
150.E3, 0.35, 400.
80.E3, 0.42, 700.
defines a part of a material behavior: isotropic, linear elasticity, in which the Young's modulus varies
with temperature from 200 £ 103 at 20° to 80 £ 103 at 700°, with a corresponding variation in the
Poisson's ratio from 0.3 to 0.42. As in most options in ABAQUS, as many lines of data can be
associated with an option as are needed.
Sets
One of the most useful features of the ABAQUS data definition method is the availability of sets. A set
can be a set of nodes or a set of elements. The user provides a name (up to 80 characters, the first of
which must be a letter--not a number) for each set. That name then provides a means of referencing all
of the members of the set. As an example, suppose that, for the structure shown in Figure 1.1.2-2, we
wish to apply symmetry boundary conditions at all of the nodes in the set MIDDLE and pin the nodes
in the set SUPPORT. We assemble the relevant nodes into sets and then specify the boundary
conditions by:
*BOUNDARY
MIDDLE, ZSYMM
SUPPORT, PINNED
Figure 1.1.2-2 Example of the use of sets.
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Introduction
The use of sets, which are the basic reference throughout ABAQUS, is recommended. Choosing
meaningful set names makes it simple to identify which data belong to which part of the model.
Further discussion of sets is provided in ``Node definition,'' Section 2.1.1, and ``Element definition,''
Section 2.2.1.
A simple example
Probably the simplest way for a new user to understand how to use ABAQUS/Explicit is to follow an
example. The example we will use for this purpose is a very simple structure--a cantilever beam
modeled using shell elements, shown in Figure 1.1.2-3. The beam is 500 mm long and 100 mm wide
and has a thickness of 2.5 mm.
Figure 1.1.2-3 Cantilever beam.
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Introduction
Mesh definitions
We model only half of the beam with shell elements using a symmetry boundary condition along the
centerline of the beam. The following paragraphs discuss how the model for this structure is defined.
While the structure is very simple, it allows some of the input options to be introduced; the analyst will
find that even the most complex problem can be set up following the same ideas.
The first option is usually the header for the analysis, which is given on the *HEADING option. (You
should follow the example by looking up the detailed definitions of the various options being
introduced. The keywords are arranged alphabetically in the ABAQUS Keywords Manual.) Any
number of data lines can follow the *HEADING option. Thus,
*HEADING
CANTILEVER BEAM MODELED USING SHELL ELEMENTS
The model data now follow. There is no particular order for defining a model, but we choose to begin
with the mesh--the nodes and elements. Our beam is modeled with 60 4-node shell elements and with
84 nodes. We give the nodes first:
*NODE
1, 0., 0., 0.
21, .50, 0., 0.
301, 0., .05, 0.
321, .50, .05, 0.
*NGEN, NSET=FREE
1, 21, 1
*NGEN, NSET=CENTER
301, 321, 1
*NFILL, NSET=ALLN
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Introduction
FREE, CENTER, 3, 100
*NSET, NSET=CLAMP, GENERATE
1, 301, 100
The *NODE option begins the reading of nodes and their coordinates. ABAQUS contains several
simple mesh generation capabilities. Here we have used the *NGEN option to generate the nodes along
the free edge of the beam and along the centerline of the beam. The NSET parameter has been
included, with the values FREE and CENTER to assign the nodes to node sets along the edges of the
beam. Next, we use the *NFILL option to fill in the nodes between the two edges. We have defined a
node set ( CLAMP), which we will use below to define the boundary conditions at the fixed end of the
cantilever beam. Likewise, we define the elements:
*ELEMENT, TYPE=S4R
1, 1, 2, 102, 101
*ELGEN, ELSET=BEAM
1, 20, 1, 1, 3, 100, 20
The *ELEMENT option includes the TYPE parameter with the value S4R. Element type S4R is a
uniform strain 4-node shell element for three-dimensional problems. It is described in
``Three-dimensional shell element library,'' Section 14.4.6. All of the elements in ABAQUS/Explicit
are described in Part V, "Elements." There is an index to the element types at the end of Volume II of
the manual.
We have again used a simple mesh generation option: the *ELGEN option. The ELSET parameter has
been used on the *ELGEN option, with the value BEAM, introducing an element set named BEAM and
adding all 60 elements generated in the option to the set. The same parameter ELSET=BEAM could
have also been used on the *ELEMENT option, but it would be redundant in this case because the use
of the ELSET parameter on the *ELGEN option adds all of the elements used and generated in the
option to the set.
We now have 84 nodes and 60 elements. Element and node numbers in ABAQUS must be positive
integers and must not exceed 7 digits (9999999 is, thus, the largest number that can be used as a node
or element number). These numbers are purely labels, and any convenient numbering system can be
used. In our example the node numbers were incremented by 100 for each "row" across the width of
the beam and by 1 along its length. The element numbers were incremented by 20 for each "row"
across the width of the beam and by 1 along its length.
Next, we define the properties associated with the elements:
*SHELL SECTION, ELSET=BEAM, MATERIAL=STEEL
0.0025,
This option gives the name of the material of which the beam is made ( STEEL) and associates this
property definition with a set of elements. The material named STEEL is defined in the next option.
The (required) data line following the *SHELL SECTION option contains the thickness of the shell
element. The *SHELL SECTION option also has an optional parameter COMPOSITE, which allows
the user to define multiple layers, with different materials through the shell thickness. Properties for
solid elements would be defined by using the *SOLID SECTION option; for beams, by using the
*BEAM SECTION option; for rigid elements, by using the *RIGID BODY option; and for springs, by
1-23
Introduction
using the *SPRING option.
Material definition
The material definition for our example is:
*MATERIAL, NAME=STEEL
*DENSITY
7800.,
*ELASTIC
200.E9, .3
*PLASTIC
250.E6,
Following the *MATERIAL option another natural order dependence comes into play. All keywords
that follow the *MATERIAL option and introduce material behavior (such as the *ELASTIC option)
define the properties of this material, until a keyword appears that does not define material properties
(such as the *BOUNDARY option or another *MATERIAL option). The material behavior definition
can, thus, be as complex as needed--plasticity (the *PLASTIC option), rate dependence (the *RATE
DEPENDENT option), and so on might be added, as required. In this case we have defined an elastic,
perfectly plastic material with a yield stress of 250 MPa. We could define material hardening by giving
yield stress as a function of plastic strain. ``Material library: overview,'' Section 8.1.1, contains a
discussion of defining material properties as functions of independent variables in ABAQUS. For
ABAQUS/Explicit the material density (the *DENSITY option) is required for all materials in the
model.
Boundary conditions
The model definition is completed by giving the fixed boundary conditions:
*BOUNDARY
CLAMP, ENCASTRE
CENTER, YSYMM
Here the displacements and rotations of all nodes in node set CLAMP are fully restrained by the
ENCASTRE specification. Also, the degrees of freedom of all nodes in node set CENTER have been
constrained to model symmetry about a plane defined by Y =constant by the YSYMM "type"
specification.
ABAQUS/Explicit uses conventional numbering for the degrees of freedom at nodes of structural
elements: 1, 2, 3 are displacement components, and 4, 5, 6 are rotation components. See
``Conventions,'' Section 1.2.2, for details of these and other ABAQUS conventions.
Step definition
We now specify the history data describing the sequence of loadings and identifying the response
variables we wish to see. As was explained previously, the history data are divided into steps. In the
simplest case we wish to apply a load to the model and record its dynamic response: one step suffices.
1-24
Introduction
*STEP
*DYNAMIC, EXPLICIT
, 1.0E-02
*DLOAD
BEAM, P, -0.1E6
*END STEP
The *STEP option begins the step; the *END STEP option ends it. In a more complicated history we
would have several steps and might use the *RESTART option to divide up the analysis. The
*DYNAMIC, EXPLICIT option specifies that the procedure type is explicit dynamics. The first data
item on the following line is not used by default; the second item indicates that the duration of the step
is .01 seconds. The *DLOAD option introduces distributed loads--in this case, a pressure of magnitude
¡0:1 MPa, applied to the face of the shell elements in the element set BEAM. In ABAQUS pressures
applied to shell elements are positive in the direction of the positive outward normal. The shell
elements were defined such that the positive normal points upward (see ``Three-dimensional shell
element library,'' Section 14.4.6) and, in this case, we want the load to be a constant downward
pressure, applied instantaneously to the model at the beginning of the step. We, therefore, use a
negative sign on the pressure magnitude.
ABAQUS offers very extensive and flexible loading options: various other types of distributed loads
can be applied with the *DLOAD option, concentrated loads can be given with the *CLOAD option,
or nonzero boundary conditions can be given with the *BOUNDARY option. In a more complicated
case we may wish to define loads that vary with time. One way ABAQUS allows the user to handle
this complexity is the *AMPLITUDE option, which defines an amplitude variation as a function of
time. This amplitude variation is then referred to by the loading options. For example, we can ramp the
load from zero to the final magnitude over a time of 2 milliseconds by
*AMPLITUDE, NAME=RAMP
0., 0., 2.E-3, 1., 12.E-3, 1.
*STEP
*DYNAMIC, EXPLICIT
, 1.0E-02
*DLOAD, AMPLITUDE=RAMP
BEAM, P, -0.1E6
This example defines a time variation that rises linearly from a value of 0.0 at zero time to 1.0 at a time
of 2 milliseconds and remains at that value (see Figure 1.1.2-4).
Figure 1.1.2-4 RAMP amplitude variation.
1-25
Introduction
This time variation is called RAMP and is referred to on the *DLOAD option, where it controls the
behavior of a pressure load applied on the face (load type P) of a set of elements called BEAM. The
nominal pressure magnitude is ¡0.1E6. This magnitude will vary through time according to the
amplitude definition, so that, for example, at a time of 1 millisecond the pressure will be ¡0.05E6.
Any amplitude definition can be used in any loading option in any step. The combination of
*AMPLITUDE references, the various loading options, and multiple steps provides the flexibility to
cover a wide range of applications.
Output
So far we have not asked for any output. ABAQUS includes default output requests; however, in any
real application the user is likely to want to modify these defaults. Output control is described in
``Output,'' Section 4.1.1. For our case we might request
*OUTPUT, FIELD, NUMBER INTERVAL=10
*NODE OUTPUT
U,
*ELEMENT OUTPUT
PEEQ,
*OUTPUT, HISTORY, VARIABLE=PRESELECT
*FILE OUTPUT, NUMBER INTERVAL=30
*EL FILE
S, LE
*NODE FILE
COORD, U, V, A, RF
The *OUTPUT option produces the output database file for postprocessing with ABAQUS/Viewer.
The option is used with the FIELD and HISTORY parameters to request field and history output,
respectively, to the output database file. In general, field output is used to generate contour plots,
symbol plots, and deformed shape plots while history output is used for X-Y plotting. The parameter
NUMBER INTERVAL=10 on the *OUTPUT, FIELD option causes ABAQUS to write 11 frames of
field data to the output database file. ABAQUS/Explicit always writes the first output database frame
at the beginning of the step, the remaining frames are written at the time marks dictated by the
NUMBER INTERVAL parameter. Specific field output requests follow the *OUTPUT, FIELD option.
1-26
Introduction
For this analysis ABAQUS will record nodal displacement (output variable U) and element equivalent
plastic strain (output variable PEEQ) to the output database file. The parameter
VARIABLE=PRESELECT on the *OUTPUT, HISTORY option causes ABAQUS to write the default
history data for a *DYNAMIC, EXPLICIT procedure to the output database file. Additional field
output requests may follow the *OUTPUT, HISTORY option for analyses that require more specific
history output along with the default output.
The *EL FILE and *NODE FILE options are used to write results to the selected results file
(job-name.sel), which can be converted to the standard ABAQUS results file (job-name.fil). The
results file is the storage medium for results that can be saved for external postprocessing. (Standard
commercial postprocessors use this file to obtain data from ABAQUS.) With this definition
ABAQUS/Explicit will provide the stresses and logarithmic strains for all the elements and the current
coordinates, displacements, velocities, accelerations, and reactions for all the nodes at 31 evenly
spaced times during the step. The format for the results file is described in ``Results file output
format,'' Section 5.1.2, and accessing the results stored in the file is described in ``Accessing the results
file information,'' Section 5.1.3.
Running the analysis
We now have an input file for the analysis of the simply supported beam:
*HEADING
CANTILEVER BEAM MODELED USING SHELL ELEMENTS
*NODE
1, 0., 0., 0.
21, .50, 0., 0.
301, 0., .05, 0.
321, .50, .05, 0.
*NGEN, NSET=FREE
1, 21, 1
*NGEN, NSET=CENTER
301, 321, 1
*NFILL, NSET=ALLN
FREE, CENTER, 3, 100
*NSET, NSET=CLAMP, GENERATE
1, 301, 100
*ELEMENT, TYPE=S4R
1, 1, 2, 102, 101
*ELGEN, ELSET=BEAM
1, 20, 1, 1, 3, 100, 20
*SHELL SECTION, ELSET=BEAM, MATERIAL=STEEL
0.0025,
*MATERIAL, NAME=STEEL
*DENSITY
7800.,
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Introduction
*ELASTIC
200.E9, .3
*PLASTIC
250.E6,
*BOUNDARY
CLAMP, ENCASTRE
CENTER, YSYMM
*STEP
*DYNAMIC, EXPLICIT
, 1.0E-02
*DLOAD
BEAM, P, -0.1E6
*OUTPUT, FIELD, NUMBER INTERVAL=10
*NODE OUTPUT
U,
*ELEMENT OUTPUT
PEEQ,
*OUTPUT, HISTORY, VARIABLE=PRESELECT
*FILE OUTPUT, NUMBER INTERVAL=30
*EL FILE
S, LE
*NODE FILE
COORD, U, V, A, RF
*END STEP
If we name this input file beam_xpl.inp, we can run this example by typing the command
abaqus job=beam_xpl
Chapter 3, "Execution Procedures," discusses the full syntax of the abaqus command, as well as
environment variables that are used to control various aspects of job execution.
Output files
When the analysis is complete, several new files will have been created. The names of the files will all
start with the job identifier (in this case beam_xpl) but will have different extensions.
The data file beam_xpl.dat is a text file that can be viewed in an editor or printed. It contains any
error or warning messages issued by ABAQUS during the preprocessing stage.
The status file beam_xpl.sta is a text file that can be printed or viewed in an editor. It contains a
summary of the time incrementation used in the analysis, a record of when the results were written to
the selected results file ( beam_xpl.sel), and a record of when the results were written to the output
database file (beam_xpl.odb). The *MONITOR option allows the user to monitor the solution
during execution by writing the value of one degree of freedom to this file.
The message file beam_xpl.msg is a text file that can be printed or viewed in an editor. It contains
warning and error messages to help the user to diagnose problems if the analysis fails.
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Introduction
Postprocessing using ABAQUS/Viewer
In this tutorial we will display the results of the analysis graphically using ABAQUS/Viewer.
ABAQUS/Viewer reads the results of the analysis from the file beam_xpl.odb. To start
ABAQUS/Viewer, use the command
abaqus viewer odb=beam_xpl
The odb parameter specifies the output database file to be used. Detailed information and a complete
tutorial on postprocessing using ABAQUS/Viewer can be found in the ABAQUS/Viewer User's
Manual. Here we will use some of the most common options.
Displaying and customizing an undeformed model shape plot
To begin this exercise, you will display the undeformed model shape and use the plot options to enable
the display of node and element numbering in the plot.
To plot the undeformed model shape:
1. From the main menu bar, select Plot->Undeformed Shape ; or use the
tool in the toolbox.
ABAQUS/Viewer displays the undeformed model shape in the current viewport.
Several options are available for choosing which edges will be visible in the model display. By
default, only feature edges are visible. Use the undeformed plot options to display element edges
on the undeformed model shape.
To display element edges on the undeformed model shape:
1. From the main menu bar, select Options->Undeformed.
The Undeformed Plot Options dialog box appears.
2. Click the Basic tab if it is not already selected.
3. From the Visible Edges options, choose Exterior.
4. Click Apply.
ABAQUS/Viewer applies the change and keeps the dialog box open. You can also display node
symbols on the undeformed model shape to view model node locations.
To display node symbols on the undeformed model shape:
1. In the Undeformed Plot Options dialog box, click the Labels tab.
2. Toggle on Show node symbols .
3. Click OK.
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Introduction
ABAQUS/Viewer applies the change and closes the dialog box.
Changing the view
The default view is isometric. You can change the view by using the options in the View menu or the
view tools in the toolbar.
To rotate the view:
1. From the main menu bar, select View->Rotate; or use the tool in the toolbar.
2. Drag the mouse over the virtual trackball in the viewport.
The view rotates interactively.
You can also specify a view by entering values for rotation angles, viewpoint, zoom factor, or fraction
of viewport to pan.
To specify the view:
1. From the main menu bar, select View->Specify.
The Specify View dialog box appears.
2. From the list of available methods, select Viewpoint .
In the Viewpoint method, you enter three values representing the X-, Y-, and Z-position of an
observer. You can also specify an up vector. ABAQUS positions your model so that this vector
points upward.
3. Enter the X-, Y-, and Z-coordinates of the viewpoint vector as 0.5, -1.0, 0.5 and the
coordinates of the up vector as 0, 0, 1.
4. Click OK.
ABAQUS/Viewer displays your model in the specified view, as shown in Figure 1.1.2-5.
Figure 1.1.2-5 Undeformed cantilever beam.
To disable the display of node symbols in the undeformed shape plot, repeat the above procedure to
display node symbols and, under Labels, toggle off Show node symbols .
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Introduction
Displaying and customizing a deformed model shape plot
You will now display the deformed model shape with all edges visible and overlay the undeformed
model shape on the deformed model shape.
To plot the deformed model shape with exterior edges visible:
1. From the main menu bar, select Options->Deformed.
2. In the Deformed Plot Options dialog box, click the Basic tab if it is not already selected.
3. From the Visible Edges options, choose Exterior.
4. Click Apply.
5. From the main menu bar, select Plot->Deformed Shape; or use the
tool in the toolbox.
ABAQUS/Viewer displays the deformed model shape with all edges visible. If necessary, click
to fit the model in the viewport.
To overlay the undeformed model shape on the deformed model shape:
1. In the Basic options in the Deformed Plot Options dialog box, toggle on Superimpose
undeformed plot.
2. Click OK.
ABAQUS/Viewer displays both the deformed and undeformed model shapes. The plot is shown in
Figure 1.1.2-6. By default, the undeformed model shape is colored green and the deformed model
shape is colored white.
Figure 1.1.2-6 Deformed cantilever beam.
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Introduction
Creating a contour plot
Contour plots display the variation of a variable across the surface of a model. You can contour plots
of field output results from the output database. Equivalent plastic strain ( PEEQ) was included in the
output database results requests for this analysis. Plot equivalent plastic strain contours on the
cantilever beam.
To plot the contours of equivalent plastic strain:
1. From the main menu bar, select Result->Field Output.
ABAQUS/Viewer displays the list of the available field variables in the Field Output dialog box.
2. Select PEEQ from the Output Variable list if it is not already selected.
3. Click OK.
The Select Plot Mode dialog box appears.
4. Select Contour, and click OK.
ABAQUS displays a contour plot of equivalent plastic strain on the deformed model shape.
By default, ABAQUS/Viewer automatically computes the minimum and maximum values shown in
your contour plots and evenly divides the range between these values into 12 intervals. In this model
the value of equivalent plastic strain near the fixed end of the cantilever beam is much higher than in
the rest of the beam. Consequently, the equivalent plastic strain variation that occurs away from the
fixed end of the beam is not visible with the default contour settings. You can modify the minimum
and maximum contour values ABAQUS/Viewer displays, as well as the number of intervals to display
more contours on the beam.
To generate a customized contour plot:
1. From the main menu bar, select Options->Contour.
The Contour Plot Options dialog box appears.
In the Contour Plot Options dialog box, click the Basic tab if it is not already selected.
2. Under Contour Limits, choose Specify beside Max; then, enter a maximum value of 4.5E-3.
3. Drag the Contour Intervals slider to change the number of contour intervals to eight.
4. To display the mesh on the contour plot, select Exterior visible edges.
5. Click OK.
ABAQUS/Viewer displays your model with the specified contour option settings ( Figure 1.1.2-7).
These settings remain in effect for all subsequent contour plots until you change them or reset
them to their default values.
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Introduction
Figure 1.1.2-7 Equivalent plastic strain plotted on deformed shape of the cantilever beam.
Exiting ABAQUS/Viewer
From the main menu bar, select File->Exit to exit ABAQUS/Viewer.
Introducing contact
Now, suppose we want to analyze the impact of the beam onto a rigid circular cylinder of radius 40
mm, as shown in Figure 1.1.2-8.
Figure 1.1.2-8 Cantilever beam and rigid cylinder.
We can model the rigid cylinder by defining a rigid body and adding appropriate nodes and rigid
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Introduction
elements to the model definition:
*NODE
999, .30, .035, -.07
1000, .30, -.01, -.07
1001, .30, -.01, -.11
1010, .34, -.01, -.07
1019, .30, -.01, -.03
1028, .26, -.01, -.07
1037, .30, -.01, -.11
1100, .30, .06, -.07
1101, .30, .06, -.11
1110, .34, .06, -.07
1119, .30, .06, -.03
1128, .26, .06, -.07
1137, .30, .06, -.11
*NGEN, NSET=RIGID, LINE=C
1001, 1010, 1, 1000
1010, 1019, 1, 1000
1019, 1028, 1, 1000
1028, 1037, 1, 1000
1101, 1110, 1, 1100
1110, 1119, 1, 1100
1119, 1128, 1, 1100
1128, 1137, 1, 1100
*ELEMENT, TYPE=R3D4, ELSET=CYLINDER
1001, 1001, 1101, 1102, 1002
1036, 1036, 1136, 1101, 1001
*ELGEN, ELSET=CYLINDER
1001, 35, 1, 1
*RIGID BODY, ELSET=CYLINDER, REF NODE=999
*BOUNDARY
999, ENCASTRE
Element type R3D4 (``Rigid elements,'' Section 15.3.1) is a 4-node surface element that must be part of
a rigid body. Elements that are part of a rigid body can move only according to the rigid body motion
of its rigid body reference node (node 999). By fixing node 999 with the ENCASTRE boundary
condition, the entire rigid cylinder is fully restrained.
It is important to refine the mesh of the beam so that it will be able to follow the geometric detail of the
cylinder it contacts. For this simulation the number of elements used to model the beam has been
increased from 60 to 120.
Contact surface definitions must be added to the model definition:
*SURFACE, NAME=OUTSIDE
1-34
Introduction
CYLINDER, SPOS
*SURFACE, NAME=BOTTOM
BEAM, SNEG
The *SURFACE option defines individual surfaces. In the *SURFACE option the surface is given a
name and is defined by giving a list of element sets (or element numbers) and face identifiers. Shells,
membranes, and rigid elements have identifiers SPOS and SNEG. SPOS is the face that is defined by
the positive normal, and SNEG is the opposite face of the element. In this example the rigid elements
are defined such that their positive normals point radially outward. Thus, the surface OUTSIDE uses
the SPOS designation with the element set CYLINDER. The shell elements (element set BEAM) have
positive normals pointing upward. Thus, the surface BOTTOM uses the SNEG designation with the
element set BEAM.
All that remains is to include the contact definition. Contact is defined in ABAQUS/Explicit as part of
the history data, which allows new contact specifications to be introduced in later steps if necessary.
Add the following option block to the history portion of your input file:
*CONTACT PAIR
OUTSIDE, BOTTOM
The *CONTACT PAIR option specifies how surfaces can contact each other. Here we have paired the
surface named BOTTOM with the surface named OUTSIDE. Any of the element surfaces in surface
BOTTOM can contact any element surface in surface OUTSIDE.
We now have an input file for the analysis of the simply supported beam impacting the rigid cylinder:
*HEADING
CANTILEVER BEAM MODELED USING SHELL ELEMENTS
CONTACT WITH RIGID CYLINDER
*NODE
1, 0., 0., 0.
41, .50, 0., 0.
301, 0., .05, 0.
341, .50, .05, 0.
*NGEN, NSET=FREE
1, 41, 1
*NGEN, NSET=CENTER
301, 341, 1
*NFILL, NSET=ALLN
FREE, CENTER, 3, 100
*NSET, NSET=CLAMP, GENERATE
1, 301, 100
*ELEMENT, TYPE=S4R
1, 1, 2, 102, 101
*ELGEN, ELSET=BEAM
1, 40, 1, 1, 3, 100, 40
*SHELL SECTION, ELSET=BEAM, MATERIAL=STEEL
1-35
-
Introduction
0.0025,
*MATERIAL, NAME=STEEL
*DENSITY
7800.,
*ELASTIC
200.E9, .3
*PLASTIC
250.E6,
*BOUNDARY
CLAMP, ENCASTRE
CENTER, YSYMM
*NODE
999, .30, .035, -.07
1000, .30, -.01, -.07
1001, .30, -.01, -.11
1010, .34, -.01, -.07
1019, .30, -.01, -.03
1028, .26, -.01, -.07
1037, .30, -.01, -.11
1100, .30, .06, -.07
1101, .30, .06, -.11
1110, .34, .06, -.07
1119, .30, .06, -.03
1128, .26, .06, -.07
1137, .30, .06, -.11
*NGEN, NSET=RIGID, LINE=C
1001, 1010, 1, 1000
1010, 1019, 1, 1000
1019, 1028, 1, 1000
1028, 1037, 1, 1000
1101, 1110, 1, 1100
1110, 1119, 1, 1100
1119, 1128, 1, 1100
1128, 1137, 1, 1100
*ELEMENT, TYPE=R3D4, ELSET=CYLINDER
1001, 1001, 1101, 1102, 1002
1036, 1036, 1136, 1101, 1001
*ELGEN, ELSET=CYLINDER
1001, 35, 1, 1
*RIGID BODY, ELSET=CYLINDER, REF NODE=999
*BOUNDARY
999, ENCASTRE
*SURFACE, NAME=OUTSIDE
1-36
Introduction
CYLINDER, SPOS
*SURFACE, NAME=BOTTOM
BEAM, SNEG
*STEP
*DYNAMIC, EXPLICIT
, 1.0E-02
*DLOAD
BEAM, P, -0.1E6
*CONTACT PAIR
OUTSIDE, BOTTOM
*OUTPUT, FIELD, NUMBER INTERVAL=10
*NODE OUTPUT
U,
*ELEMENT OUTPUT
PEEQ,
*OUTPUT, HISTORY, VARIABLE=PRESELECT
*FILE OUTPUT, NUMBER INTERVAL=30
*EL FILE
S, LE
*NODE FILE
COORD, U, V, A, RF
*END STEP
Save the input file as beamContact_xpl.inp, and run the analysis.
Additional postprocessing using ABAQUS/Viewer
Start ABAQUS/Viewer by typing
abaqus viewer odb=beamContact_xpl
at the operating system prompt.
Creating a contour plot
To begin this exercise, plot equivalent plastic strain contours on the cantilever beam. Start by setting
the contour options to display exterior edges and eight contour intervals.
To plot the contours of equivalent plastic strain:
1. From the main menu bar, select Options->Contour.
2. In the Contour Plot Options dialog box, click the Basic tab if it is not already selected.
3. From the Visible Edges options, choose Exterior.
4. Drag the Contour Intervals slider to 8.
5. Click OK.
1-37
Introduction
6. From the main menu bar, select Result->Field Output.
The Field Output dialog box appears.
7. Select PEEQ from the Output Variable list if it is not already selected.
8. Click OK.
The Select Plot Mode dialog box appears.
9. Select Contour, and click OK.
ABAQUS displays a contour plot of equivalent plastic strain on the deformed model shape.
Change the view to see the contour plot from a more appropriate angle.
To specify the view:
1. From the main menu bar, select View->Specify.
The Specify View dialog box appears.
2. Enter the X-, Y-, and Z-coordinates of the viewpoint vector as 0.5, -1.0, 0.5 and the
coordinates of the up vector as 0, 0, 1.
3. Click OK.
ABAQUS/Viewer displays your model in the specified view, as shown in Figure 1.1.2-9.
Figure 1.1.2-9 Equivalent plastic strain on the cantilever beam impacting the rigid cylinder.
Using results from other frames
During the analysis ABAQUS wrote field output results to the output database file for eleven evenly
1-38
Introduction
spaced increments. By default, ABAQUS/Viewer uses the data for the last available increment saved
on the output database file. You can evaluate the results from other increments saved to the output
database file by selecting the appropriate frame.
To select a new frame:
1. From the main menu bar, select Result->Frame.
The Frame Selector dialog box appears.
ABAQUS/Viewer displays the list of the available frames in the Frame Selector dialog box. The
list tabulates the steps and increments for which field data are stored.
2. Select the frame at step time 6.0E-3 from the Frame menu.
3. Click OK to apply your changes and to close the Frame Selector dialog box.
The resulting plot is shown in Figure 1.1.2-10. Any plots requested from now on will use results from
analysis time 0.006 s until a different frame is selected. Repeat this procedure, substituting the
increment number of interest, to evaluate results at different simulation times. When you have
completed viewing the results of the analysis, exit ABAQUS/Viewer.
Figure 1.1.2-10 Equivalent plastic strain on the cantilever beam impacting the rigid cylinder at time
0.006 s.
Exiting ABAQUS/Viewer
From the main menu bar, select File->Exit to exit ABAQUS/Viewer.
Conclusion
The reader has now been introduced to the fundamentals of setting up an ABAQUS/Explicit input file
for a simple analysis involving large deformations, plasticity, and contact and should know how to use
1-39
Introduction
this manual as a reference. The next step is to read the rest of Part I, "Introduction, Spatial Modeling,
and Execution," and Part III, "Analysis," to review the details of what has been covered very briefly in
this section. After that, the best method of learning is to gain experience by running cases.
The Example Problems Manual is intended to help in that phase of the learning process. It contains
many worked examples of illustrations of typical ABAQUS applications, each of which is written up
in detail to show why the various analysis decisions were made. Input files are listed for all of the
examples; these files, as well as the other input files mentioned but not listed in the manual, are all
available with the ABAQUS release.
The Verification Manual and the Benchmarks Manual are two other sources of example ABAQUS
analyses. The Verification Manual contains basic test problems that provide quality assurance testing
of each individual program feature. The Benchmarks Manual contains benchmark and standard
analyses used to evaluate the performance of ABAQUS; results are compared against exact
calculations and other published results. Frequently, these test cases are good starting points for
learning about new elements, materials, or other special features.
The input data files for the Example, Verification, and Benchmarks problems can be copied to the
user's working directory by using the ABAQUS fetch utility:
abaqus fetch job=job-name
where job-name.inp is the name listed in the ABAQUS Example Problems, Verification, or
Benchmarks manuals (see ``Execution procedure for ABAQUS/Fetch,'' Section 3.2.9).
1.2 ABAQUS syntax and conventions
1.2.1 Input syntax rules
This section describes the syntax rules that govern an ABAQUS input file.
Reference
· ``Defining a model in ABAQUS,'' Section 1.3.1
Overview
Three types of input lines are used in an ABAQUS input file: keyword lines, data lines, and comment
lines. A carriage return is required at the end of each line in an input file.
· Keyword lines introduce options and often have parameters, which appear as words or phrases
separated by commas on the keyword line. Parameters are used to define the behavior of an option.
Parameters can stand alone or have a value, and they may be required or optional.
· Data lines, which are used to provide numeric or alphanumeric entries, follow most keyword lines.
· Any line that begins with stars in columns 1 and 2 (**) is a comment line. Such lines can be placed
anywhere in the file. They are ignored by ABAQUS, so they will be printed only in the initial
listing of the file. There is no restriction on how many or where such lines occur in the file.
1-40
Introduction
Relevant parameters and data lines are described in the sections of the ABAQUS Keywords Manual
describing each option. This section describes the general rules that apply to all keyword and data
lines.
Keyword lines
The following rules apply when entering a keyword line:
· The first non-blank character of each keyword line must be a star (*).
· The keyword must be followed by a comma (,) if any parameters are given.
· Parameters must be separated by commas.
· Blanks on a keyword line are ignored.
· A line can include no more than 256 characters, including blanks.
· Keywords and parameters are not case sensitive.
· Parameter values usually are not case sensitive. The only exceptions to this rule are those imposed
externally to ABAQUS, such as file names on case-sensitive operating systems.
· Keywords, parameters, and, in most cases, parameter values need not be spelled out completely,
but there must be enough characters given to distinguish them from other keywords, parameters,
and parameter values that begin in the same way. ABAQUS first searches each associated text
string for an exact match. If an exact match is not found, ABAQUS then searches based upon the
minimum number of unique characters in each keyword, parameter, or parameter value, as the case
may be. Embedded blanks can be omitted from any item in a keyword line. If a parameter value is
used to provide a number or a file name, the complete value should be provided.
· The whole parameter need not be spelled out, but there must be enough characters given to
distinguish it from other parameters that begin in the same way.
· If a parameter has a value, the equal sign (=) is used. The value can be an integer, a floating point
number, or a character string, depending on the context. For example,
*ELASTIC, TYPE=ISOTROPIC, DEPENDENCIES=1
· Continuation of a keyword line is sometimes necessary; for example, because of a large number of
parameters. If the last character on a keyword line is a comma, the next line is interpreted as a
continuation of the line. For example, the *ELASTIC keyword line above could also be given as
*ELASTIC, TYPE=ISOTROPIC,
DEPENDENCIES=1
· Some options allow the INPUT or FILE parameter to be set equal to the name of an alternate input
file. Such file names can include a full path name or a relative path name. Relative path names
must be with respect to the directory from which the job was submitted. If no path is specified, the
1-41
Introduction
file is assumed to be in the directory from which the job was submitted.
For files referenced by the INPUT parameter, the file name must include any extension (e.g.,
elem.inp). For files referenced by the FILE parameter, the name must be given without an extension
since ABAQUS assumes that the file to be read has the correct extension for the file type that is
relevant to the option: .res for restart files (``Restarting an analysis,'' Section 7.1.1) and .fil for
results files (``Output,'' Section 4.1.1).
The file must have the correct case on computers with case-sensitive operating systems. The complete
name can have a maximum of 32 characters.
Data lines
Data lines are used to provide data that are more easily given in lists than as parameters on an option.
Most options require one or more data lines; if they are required, the data lines must immediately
follow the keyword line introducing the option. The following rules apply when entering a data line:
· A data line can include no more than 256 characters, including blanks. Trailing blanks are ignored.
· All data items must be separated by commas (,). An empty data field is specified by omitting data
between commas. ABAQUS will use values of zero for any required numeric data that are omitted
unless a default value is specified. If a data line contains only a single data item, the data item
should be followed by a comma to distinguish the data line from a fixed format data line used in
previous versions of ABAQUS.
· A line must contain only the number of items specified.
· Empty data fields at the end of a line can be ignored.
· Floating point numbers can occupy a maximum of 20 spaces including the sign, decimal point, and
any exponential notation.
Floating point numbers can be given with or without an exponent. Any exponent, if input, must be
preceded by E or D and an optional (¡) or (+). The following line shows four acceptable ways of
entering the same floating point number:
-12.345
-1234.5E-2
-1234.5D-2
-1.2345E1
· Integer data items can occupy a maximum of 10 digits.
· Character strings can be up to 80 characters long and are not case sensitive.
· Continuation lines are allowed in specific instances (see ``Element definition,'' Section 2.2.1). If
allowed, such lines are indicated by a comma as the last character of the preceding line. A single
data item cannot be entered over multiple lines.
In many cases the choice of parameters used with an option determines the type of data lines required.
For example, there are five different ways to define a linear elastic material (``Elastic behavior:
overview,'' Section 9.1.1). The data lines given by the user must be consistent with the value of the
TYPE parameter given on the *ELASTIC option.
1-42
Introduction
Labels
Labels such as set names, surface names, and rebar names are case insensitive and can be up to 80
characters long. All spaces within a label are ignored unless the label is enclosed in quotation marks, in
which case all spaces within the label are maintained. A label that is not enclosed within quotation
marks may not include a period ( . ) and should not contain characters such as commas and equal signs.
These restrictions do not apply to labels enclosed within quotation marks.
If a label is defined using quotation marks, the quotation marks are stored as part of the label. Any
subsequent use of the label should also be enclosed in quotation marks. Embedded quotation marks are
not allowed.
Labels cannot begin and end with a double underscore (e.g., __STEEL__). This label format is
reserved for internal use by ABAQUS.
The following are examples of labels entered with and without the use of quotation marks:
*ELEMENT, TYPE=SPRINGA, ELSET="One element"
1,1,2
*SPRING, ELSET="One element"
1.0E-5,
*NSET, ELSET="One element", NSET=NODESET
*BOUNDARY
nodeset,1,2
Repeating data lines
Some options list only a single data line. In cases where only one data line is allowed, this is indicated
by the data line title "First (and only) line." An example of this is the *DYNAMIC option. In many
cases the single data line shown can be repeated to define one variable as a function of another; this
choice is indicated by a note after the data line. For example, a table of biaxial test data can be given to
define a hyperelastic material:
*BIAXIAL TEST DATA
TB1 , ²1B
TB2 , ²2B
TB3 , ²3B
Etc.
There is no limit on the number of data lines allowed, but the data must be given in a certain order, as
explained below.
Many options require more than one data line; these are indicated by the data line titles "First line:",
"Second line:", etc. For example, exactly two data lines must be used to define a local orientation for a
shell element (*ORIENTATION), and at least three data lines are required to define anisotropic
elasticity (*ELASTIC).
In many cases the data lines can be repeated, which is indicated by a note after the data lines. As with
1-43
Introduction
repetition of a single data line, it is important that sets of data lines be given in the correct order so that
ABAQUS can interpolate the data properly.
Example: Multiple data lines due to field variable dependence
Any time an option can be defined as a function of field variables, the number of data lines required to
define the option completely must be determined by the user. (See ``Using the DEPENDENCIES
parameter to define field variable dependence'' in ``Material data definition,'' Section 8.1.2, for more
information.) For example, two data lines are required if stress-based failure criteria ( *FAIL STRESS)
are defined as a function of two field variables. This pair of data lines is repeated as often as necessary
to define the failure criteria completely:
(In this example the last field on the first data line of each pair was left blank, which means that the
stress-based failure criteria are not temperature dependent.)
If the stress-based failure criteria were defined as a function of nine field variables, a set of three data
lines would be repeated as often as necessary:
Ordering the data lines
Whenever one variable is defined as a function of another, the data must be given in the proper order
so that ABAQUS can interpolate for intermediate values correctly. The variable being defined is
assumed to be constant outside the range of independent variables given.
If the property being defined is a function of only one variable (such as the *BIAXIAL TEST DATA
shown above), the data should be given in the order of increasing value of the independent variable.
If the property being defined is a function of multiple independent variables, the variation of the
property with respect to the first variable must be given at fixed values of the other variables, in
1-44
Introduction
ascending values of the second variable, then of the third variable, and so on. The data lines must
always be ordered so that the independent variables are given increasing values. This process ensures
that the value of the material property is completely and uniquely defined at any values of the
independent variables upon which the property depends.
As an example, consider isotropic elasticity defined as a function of three field variables (but not of
temperature):
*ELASTIC,
E1 , º1 ,
E2 , º2 ,
E3 , º3 ,
E4 , º4 ,
E5 , º5 ,
E6 , º6 ,
E7 , º7 ,
E8 , º8 ,
E9 , º9 ,
E10 , º10 ,
E11 , º11 ,
E12 , º12 ,
E13 , º13 ,
E14 , º14 ,
E15 , º15 ,
E16 , º16 ,
E17 , º17 ,
E18 , º18 ,
DEPENDENCIES=3
, 1, 1, 1
, 2, 1, 1
, 1, 2, 1
, 2, 2, 1
, 1, 3, 1
, 2, 3, 1
, 1, 1, 2
, 2, 1, 2
, 1, 2, 2
, 2, 2, 2
, 1, 3, 2
, 2, 3, 2
, 1, 1, 3
, 2, 1, 3
, 1, 2, 3
, 2, 2, 3
, 1, 3, 3
, 2, 3, 3
1.2.2 Conventions
The conventions that are used throughout ABAQUS/Explicit are defined in this section.
References
· Chapter 2, "Spatial Modeling"
· Part II, "Output"
· ``Boundary conditions,'' Section 18.3.1
Overview
The following topics are discussed in this section:
· Degrees of freedom
· Coordinate systems
1-45
Introduction
· Self-consistent units
· Time measures
· Local directions on surfaces in space
· Stress and strain conventions
· Stress and strain measures
· Conventions for finite rotations
Degrees of freedom
Except for axisymmetric elements, the degrees of freedom are always referred to as follows:
1: x-displacement
2: y-displacement
3: z-displacement
4: Rotation about the x-axis, in radians
5: Rotation about the y-axis, in radians
6: Rotation about the z-axis, in radians
8: Fluid pressure
11: Temperature
Here the x-, y-, and z-directions coincide with the global X-, Y -, and Z-directions, respectively;
however, if the *TRANSFORM option is used at the node, they coincide with the local directions
defined in the *TRANSFORM option (see ``Transformed coordinate systems,'' Section 2.1.4).
Axisymmetric elements
The displacement and rotation degrees of freedom in axisymmetric elements are referred to as follows:
1: r-displacement
2: z-displacement
6: Rotation in the r-z plane (for axisymmetric shells), in radians
Here the r- and z-directions coincide with the global X- and Y -directions, respectively; however, if
the *TRANSFORM option is used at the node, they coincide with the local directions defined in the
*TRANSFORM option.
Activation of degrees of freedom
ABAQUS activates only those degrees of freedom needed at a node. Thus, some of the degrees of
1-46
Introduction
freedom listed above may not be used at all nodes in a model, because some elements do not use all of
them. For example, two-dimensional solid (continuum) stress/displacement elements use only degrees
of freedom 1 and 2. The degrees of freedom actually used at any node are the envelope of those needed
in each element that shares the node.
Coordinate systems
The basic coordinate system in ABAQUS is a right-handed, rectangular Cartesian system. The user can
choose other systems locally for input (see the *NODE, the *NGEN, and the *SYSTEM options), for
output of nodal variables (displacements, velocities, etc.) and point load or boundary condition
specification (see the *TRANSFORM option), and for material specification (see the
*ORIENTATION option). All coordinate systems must be right-handed.
Units
ABAQUS has no units built into it except for rotation measures. Therefore, the units chosen must be
self-consistent, which means that derived units of the chosen system can be expressed in terms of the
fundamental units without conversion factors.
Rotation measures
In ABAQUS rotational degrees of freedom are expressed in radians.
International System of units (SI)
The International System of units (SI) is an example of a self-consistent set of units. The fundamental
units in the SI system are length in meters (m), mass in kilograms (kg), time in seconds (s),
temperature in degrees Kelvin (K), and electric current in Amperes (A). The units of secondary or
derived quantities are based on these fundamental units. An example of a derived unit is the unit of
force. A unit of force in the SI system is called a Newton (N):
1 Newton = 1 kg m=s2 :
Similarly, a unit of electrical charge in the SI system is called a Coulomb (C):
1 Coulomb = 1 A s:
Another example is the unit of energy, called a Joule (J):
1 Joule = 1 N m = 1 A Volt s = 1 kg m2 =s2 :
The unit of electrical potential in the SI system is the Volt, which is chosen such that
1 Joule = 1 Volt C = 1 Volt A s :
Sometimes the standard units are not convenient to work with. For example, Young's modulus is
frequently specified in terms of MegaPascals (MPa) (or, equivalently, N=mm2 ), where
1-47
Introduction
1 Pascal = 1 N=m2 . In this case the fundamental units could be tonnes (1 tonne = 1000 kilograms),
millimeters, and seconds.
American or English units
American or English units can cause confusion since the naming conventions are not as clear as in the
SI system. For example, 1 pound force (lbf) will give 1 pound mass (lbm) an acceleration of g ft=sec2 ,
where g is the value of acceleration due to gravity. If pounds force, feet (ft), and seconds are taken as
fundamental units, the derived unit of mass is lbf sec2 =ft. Since density is commonly given in
handbooks as lbm=in3 , it must be converted to lbf sec2 =ft4 by
1 lbm=in3 =
123
lbf sec2 =ft4 :
g
Frequently it is not made clear in handbooks whether lb stands for lbm or lbf. The user needs to check
that the values used make up a consistent set of units.
Two other units that cause difficulty are the slug, defined as the mass that will be accelerated at
1 ft=sec2 by 1 lbf, and the poundal, defined as the force required to accelerate 1 lbm at 1 ft=sec2 .
Useful conversions are
1 slug = g lbm
and
1 lbf = g poundals ;
where g is the magnitude of the acceleration due to gravity in ft=sec2 .
Symbols used in ABAQUS for units
Units are indicated for the value to be given on load and flux types as follows:
Dimension
Indicato Example (S.I. units)
r
length
L
meter
mass
M
kilogram
time
T
second
µ
temperature
degree Celsius
electric current
A
Ampere
force
F
Newton
energy
J
Joule
electric charge
C
Coulomb
'
electric potential
volt
mass concentration
P
Parts per million
Time
ABAQUS/Explicit has two measures of time--step time and total time. Step time is measured from the
1-48
Introduction
beginning of each step. Total time starts at zero and is the total accumulated time over all of the steps
(including *RESTART steps, see ``Restarting an analysis,'' Section 7.1.1).
Local directions on surfaces in space
Local directions are needed on surfaces in space; for example, to define stress and strain components
in a shell. The convention used in ABAQUS for such directions is as follows.
The default local 1-direction is the projection of the global x-axis onto the surface. If the global x-axis
is within 0.1° of being normal to the surface, the local 1-direction is the projection of the global z-axis
onto the surface. The local 2-direction is then at right angles to the local 1-direction, so that the local
1-direction, local 2-direction, and the positive normal to the surface form a right-handed set (see
Figure 1.2.2-1). The positive normal direction is defined in an element by the right-hand rotation rule
going around the nodes of the element. The local surface directions can be redefined by using the
*ORIENTATION option.
Figure 1.2.2-1 Default local surface directions.
Stress and strain components in shells and membranes are given with respect to these surface
coordinate directions, which rotate with the average rigid body rotation of the surface.
Convention used for stress and strain components
ABAQUS/Explicit stores the stress and strain components in the following order internally: ¾11 , ¾22 ,
¾33 , ¿12 , ¿23 , ¿13 . This distinction is important when user subroutine VUMAT is used (see ``VUMAT,''
Section 21.2.3). However, when defining material properties, the convention used for stress and strain
1-49
Introduction
components in ABAQUS/Explicit is that they are ordered:
¾11 : Direct stress in the 1-direction
¾22 : Direct stress in the 2-direction
¾33 : Direct stress in the 3-direction
¿12 : Shear stress in the 1-2 plane
¿13 : Shear stress in the 1-3 plane
¿23 : Shear stress in the 2-3 plane
For example, a fully anisotropic, linear elasticity matrix is
1 2
¾11
D1111
B ¾22 C 6
C 6
B
B ¾33 C 6
C=6
B
B ¿12 C 6
A 4
@
¿13
¿23
0
D1122
D2222
symm.
D1133
D2233
D3333
D1112
D2212
D3312
D1212
D1113
D2213
D3313
D1213
D1313
30
1
D1123
"11
D2223 7 B "22 C
7B
C
D3323 7 B "33 C
7B
C:
D1223 7 B °12 C
5@
A
D1323
°13
D2323
°23
The 1-, 2-, and 3-directions depend on the element type chosen. For solid elements the defaults for
these directions are the global spatial directions. For shell and membrane elements the defaults for the
1- and 2-directions are local directions in the surface of the shell or membrane, as defined in Part V,
"Elements." In both cases the 1-, 2-, and 3-directions can be changed by using the *ORIENTATION
option (``Orientations,'' Section 2.2.3).
Shear strains
ABAQUS always reports shear strain as engineering shear strain, °:
°ij = "ij + "ji :
Stress and strain measures
The stress measure used in ABAQUS is Cauchy or "true" stress, which corresponds to the force per
current area. See ``Stress measures,'' Section 1.5.2 of the ABAQUS Theory Manual, and ``Stress rates,''
Section 1.5.4 of the ABAQUS Theory Manual, for more details on stress measures.
Unlike "true" stress, there is no clearly preferred "true" strain. For the same physical deformation
different strain measures will report different values in large-strain analysis. The optimal choice of
strain measure depends on analysis type, material behavior, and (to some degree) personal preference.
See ``Strain measures,'' Section 1.4.2 of the ABAQUS Theory Manual, for more details on strain
measures.
The user can request that strain be given as logarithmic strain (output variable LE) and nominal strain
(output variable NE). Both are derived from the total deformation gradient, F . By default, in
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Introduction
ABAQUS/Explicit the logarithmic strains are output when strains are requested.
Nominal strain
The nominal strain, NE, is
N
"
=V¡I=
3
X
i=1
(¸i ¡ 1) ni ni T ;
p
where V = F ¢ FT is the left stretch tensor, ¸i are the principal stretches, and ni are the principal
stretch directions in the current configuration. The principal values of nominal strain are, therefore, the
ratios of length in the current configuration to length in the reference configuration in the principal
directions, thus giving a direct measure of deformation.
Logarithmic strain
The logarithmic strain, LE, is
L
" = ln V =
3
X
ln ¸i ni ni T ;
i=1
where the variables are as defined earlier for nominal strain.
Finite rotations
The following convention is used for finite rotations in space: Define Áx , Áy , Áz as "rotations" about
the global X, Y , and Z-axes (that is, degrees of freedom 4, 5, and 6 at a node). Then define
px = Áx =Á;
py = Áy =Á;
pz = Áz =Á;
where
Á=
q
Á2x + Á2y + Á2z :
The direction p is then the axis of rotation, and Á is the angular rotation (in radians) about the axis p
according to the right-hand rule (see Figure 1.2.2-2). The value of Á is not uniquely determined. In
large-rotation problems where the overall rotation exceeds 2¼, any multiple of 2¼ can be added or
subtracted, which may lead to discontinuous output values for the rotation components.
Figure 1.2.2-2 Definition of finite rotation.
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Introduction
This convention provides straightforward input of kinematic boundary conditions and moments in
most cases and simple interpretation of the output. The rotations output by ABAQUS represent a
single rotation from the reference configuration to the current configuration about a fixed axis. The
output does not follow the history of rotation at a node. In addition, this convention reduces to the
usual convention for small rotations, even in the case of small rotations superposed on an initial finite
rotation (such as might be considered in the study of small vibrations about a predeformed state).
Compound rotations
Because finite rotations are not additive, the way they must be specified is a bit different from the way
other boundary conditions are specified: the increment in rotation specified over a step must be the
rotation needed to rotate the node from the configuration at the beginning of the step to that desired at
the end of the step. It is not enough to rotate the node over this step to a total rotation vector that would
have taken the node into its final configuration if applied on the node in some other initial reference
configuration. If an increment of rotation (¢Áx ; ¢Áy ; ¢Áz ) is needed to rotate from the rotation
boundary condition (Áx ; Áy ; Áz )t at the beginning of the step (and at the end of the previous step) to its
final position at the end of the step, the boundary condition must be specified such that the rotation
vector is (Átx + ¢Áx ; Áty + ¢Áy ; Átz + ¢Áz ) at the end of step. If the direction of the rotation vector is
constant, this method of specifying rotation boundary conditions and the total rotation vector will be
the same.
As an example of how to specify compound finite rotations and to interpret finite rotation output,
consider the following example of the rotation of a beam.
The beam initially lies along the x-axis. We want to perform the compound rotation, where (Step 1)
1-52
Introduction
the beam is rotated by 60° about the z-axis, followed by (Step 2) a 90° spin of the beam about itself,
followed by (Step 3) a 90° rotation of the beam about an axis perpendicular to the beam in the x-y
plane, such that the beam finishes on the z-axis.
This compound rotation is achieved in three steps with applied rotation vectors Á1 , Á2 , and Á3 , where
Á 1 = Á1 ez = f 0
0
T
1:047198 g ;
Á2 = Á2 (cos Á1 ex + sin Á1 ey ) = f 0:785398
Á 3 = Á3 (sin Á1 ex ¡ cos Á1 ey ) = f 1:360350
1:360350
¡0:785398
T
0g ;
and
T
0g :
For this example Á1 = ¼=3, Á2 = ¼=2, and Á3 = ¼=2. Here Ái represents the magnitude of each finite
rotation about the (unit length) rotation axis. The rotation vectors above are to be applied in each of the
three steps on the configuration at the beginning of that step. It is most straightforward to prescribe
these rotations with the TYPE parameter on the *BOUNDARY option set equal to VELOCITY. The
default in ABAQUS/Explicit, when no amplitude is specified, is to assume a constant value. The
ABAQUS step definition for this example, where node 1 is pinned at the origin and the rotation is
applied to node 2, is as follows:
*STEP
Step 1: Rotate 60 degrees about the z-axis
*DYNAMIC, EXPLICIT
, 0.001
*BOUNDARY, TYPE=VELOCITY
2, 4, 5
2, 6, 6, 1.047198E3
*END STEP
**
*STEP
Step 2: Rotate 90 degrees about the beam axis
*DYNAMIC, EXPLICIT
, 0.001
*BOUNDARY, TYPE=VELOCITY
2, 4, 4, 0.785398E3
2, 5, 5, 1.36035E3
2, 6, 6
*END STEP
**
*STEP
Step 3: Rotate beam onto z-axis
*DYNAMIC, EXPLICIT
, 0.001
*BOUNDARY, TYPE=VELOCITY
2, 4, 4, 1.36035E3
2, 5, 5, -0.785398E3
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Introduction
2, 6, 6
*END STEP
The above method for applying finite-rotation boundary conditions (*BOUNDARY,
TYPE=VELOCITY, with the default constant amplitude definition) is strongly recommended.
However, if the rotation boundary conditions are applied as displacement-type boundary conditions in
ABAQUS/Explicit, references to amplitude definitions should be used such that there are no jumps in
displacement across the steps. It is often convenient to use *AMPLITUDE, TIME=TOTAL TIME
option for this purpose. The displacement boundary conditions will be applied incrementally based on
the increment in the value of amplitude curve over the time increment. Due to this reason any sudden
jumps in displacement at the beginning of a step introduced either without the amplitude curves or
with two amplitude curves will be ignored (see ``Boundary conditions,'' Section 18.3.1). The
ABAQUS step definitions from above would change to:
*AMPLITUDE, TIME=TOTAL TIME, NAME=RAMPUR1
0., 0., 0.001, 0., 0.002, 0.785398, 0.003, 2.145748
*AMPLITUDE, TIME=TOTAL TIME, NAME=RAMPUR2
0., 0., 0.001, 0., 0.002, 1.36035, 0.003, 0.574952
*AMPLITUDE, TIME=TOTAL TIME, NAME=RAMPUR3
0., 0., 0.001, 1.047198, 0.002, 1.047198, 0.003, 1.047198
*STEP
Step 1: Rotate 60 degrees about the z-axis
*DYNAMIC, EXPLICIT
, 0.001
*BOUNDARY, AMP=RAMPUR1
2, 4, 4, 1.0
*BOUNDARY, AMP=RAMPUR2
2, 5, 5, 1.0
*BOUNDARY, AMP=RAMPUR3
2, 6, 6, 1.0
*END STEP
**
*STEP
Step 2: Rotate 90 degrees about the beam axis
*DYNAMIC, EXPLICIT
, 0.001
*END STEP
**
*STEP
Step 3: Rotate beam onto z-axis
*DYNAMIC, EXPLICIT
, 0.001
*END STEP
The boundary conditions in Steps 2 and 3 are the sum of the incremental rotation components plus the
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Introduction
rotation boundary conditions specified in the previous steps.
The ABAQUS output of the rotation field at the end of Step 3 is
UR1 = 1:927 ; UR2 = ¡0:5163 ; UR3 = 1:927 :
We see that none of the individual components of the specified boundary conditions appears in the
final rotation output. The final rotation output represents the rotation vector required to obtain the final
orientation in a single step.
Suppose that in Step 3 of the previous example we want to apply the rotation vector Á3 at node 1
instead of at node 2. If the rotation is applied incrementally, the ABAQUS step definition is as follows:
*STEP
Step 3: Rotate beam onto z-axis
*DYNAMIC, EXPLICIT
, 0.001
*BOUNDARY, TYPE=VELOCITY, OP=NEW
1, 1, 3
1, 4, 4, 1.36035E3
1, 5, 5, -0.785398E3
1, 6, 6
*END STEP
The OP=NEW parameter is needed to remove the rotation boundary conditions that are in effect at
node 2. As mentioned previously, TYPE=VELOCITY is the preferred method for applying
finite-rotation boundary conditions. If the rotation boundary condition is to be applied as a
displacement-type boundary condition, we must first retrieve the rotation field at node 1 at the end of
Step 2 from the output database file using ABAQUS/Viewer. The ABAQUS/Viewer output of this
rotation field is
UR1 = 1:412 ; UR2 = 0:8155 ; UR3 = 0:8155 :
These rotation vector components must then be added to the incremental rotation vector components
we wish to prescribe in Step 3. The ABAQUS step definition would change to
*STEP
Step 3: Rotate beam onto z-axis
*DYNAMIC, EXPLICIT
, 0.001
*AMPLITUDE, TIME=STEP TIME, NAME=NODE1UR1
0., 1.412, 0.001, 2.772
*AMPLITUDE, TIME=STEP TIME, NAME=NODE1UR2
0., 0.8155, 0.001, 0.0301
*AMPLITUDE, TIME=STEP TIME, NAME=NODE1UR3
0., 0.8155, 0.001, 0.8155
*BOUNDARY, OP=NEW
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Introduction
1, 1, 3
*BOUNDARY, OP=NEW, AMP=NODE1UR1
1, 4, 4, 1.
*BOUNDARY, OP=NEW, AMP=NODE1UR2
1, 5, 5, 1.
*BOUNDARY, OP=NEW, AMP=NODE1UR3
1, 6, 6, 1.
*END STEP
Note that the boundary conditions are specified above using amplitude curves in order to avoid any
sudden jump in their values at the beginning of the step. As stated in ``Boundary conditions,'' Section
18.3.1, any jumps in the displacement values will be ignored and the boundary will be maintained at
the previous values. As this last procedure clearly demonstrates, it is simpler to apply finite-rotation
boundary conditions with *BOUNDARY, TYPE=VELOCITY rather than as displacement-type
boundary conditions. For further discussion of how finite rotations are accumulated, see ``Rotation
variables,'' Section 1.3.1 of the ABAQUS Theory Manual.
1.3 Defining an ABAQUS model
1.3.1 Defining a model in ABAQUS
This section describes how to define a finite element model in ABAQUS/Explicit.
References
· ``Input syntax rules,'' Section 1.2.1
· ABAQUS Keywords Manual
Overview
A finite element analysis in ABAQUS/Explicit is defined by an input file, which
· contains keyword lines and data lines; and
· is divided into model data and history data.
The input file
An ABAQUS input file is an ASCII data file. It can be created by using a text editor or by using a
graphical preprocessor such as ABAQUS/CAE. The input file consists of a series of lines containing
ABAQUS options (keyword lines) and data (data lines). The input syntax for keyword and data lines is
described in ``Input syntax rules,'' Section 1.2.1.
Most input files have the same basic structure. All three of the following portions of the input file are
specified, in the order listed, to define a finite element model:
1. An input file must begin with the *HEADING option, which is used to define a title for the
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Introduction
analysis. Any number of data lines can be used to give the title; they will appear at the beginning
of the output files (``Output,'' Section 4.1.1). The first heading line will appear as a heading at the
top of each page of the output.
2. After the heading the input file usually contains a model data section to define nodes, elements,
materials, initial conditions, etc. The model data section is explained below.
3. Finally, the input file contains history data to define the analysis type, loading, output requests,
etc. The *STEP option divides the model data from the history data in an input file: everything
appearing before the first occurrence of the *STEP option is model data, and everything appearing
after the *STEP option is history data. The history data section is explained below.
The input file is processed by the "solver input file processor" prior to executing the appropriate
solver, ABAQUS/Standard or ABAQUS/Explicit. The functions of the solver input file processor are
to interpret the ABAQUS options, to perform the necessary consistency checking, and to prepare the
data for the solvers.
Model data
Model data define the nodes, elements, materials, initial conditions, etc.
Required model data
The following model data must be included in an input file to define a finite element model:
Geometry: The geometry of a model is described by elements and their nodes. The rules and
methods for defining nodes and elements are described in ``Node definition,'' Section 2.1.1;
``Element definition,'' Section 2.2.1; and ``Defining an assembly,'' Section 2.5.1. Cross-sections for
structural elements (such as beams) must be defined. Special features can be defined with special
elements such as springs, dashpots, point masses, etc. The element types available for modeling
are described in Part V, "Elements," along with explanations of how to define the elements. The
user can view the initial mesh or the configuration after adjustment for initial overclosure in
ABAQUS/Viewer after a datacheck run (see ``Execution procedure for ABAQUS/Standard and
ABAQUS/Explicit,'' Section 3.2.1).
Material definitions: A material type must be associated with most portions of the geometry. The
material library is described in Part IV, "Materials." Special elements such as springs or dashpots
do not have an associated material, but their properties must be defined.
Optional model data
The following model data can be included as necessary:
Parts and an assembly: The geometry of a model can be defined by organizing it into parts,
which are positioned relative to one another in an assembly ( ``Defining an assembly,'' Section
2.5.1).
Initial conditions: Nonzero initial conditions such as initial stresses, temperatures, or velocities
1-57
Introduction
can be specified (``Initial conditions,'' Section 18.2.1).
Boundary conditions: Zero-valued boundary conditions (including symmetry conditions) can be
imposed on individual solution variables such as displacements or rotations ( ``Boundary
conditions,'' Section 18.3.1).
Kinematic constraints: Equations involving several of the fundamental solution variables in the
model (``Linear constraint equations,'' Section 19.2.1) or multi-point constraints (``General
multi-point constraints,'' Section 19.2.2) can be defined.
Amplitude definitions: Amplitude curves can be defined for later use in specifying
time-dependent loading or boundary conditions ( ``Amplitude curves,'' Section 18.1.2).
Output control: Options for controlling model definition output to the data file can be included.
See ``Output,'' Section 4.1.1.
Analysis continuation: It is possible to write restart data or to use the results from a previous
analysis and continue the analysis with new model or history data (see ``Restarting an analysis,''
Section 7.1.1) or with a different ABAQUS program (see ``Transferring results between
ABAQUS/Explicit and ABAQUS/Standard,'' Section 7.3.1).
History data
The purpose of an analysis is to predict the response of a model to some form of external loading or to
some nonequilibrium initial conditions. An ABAQUS/Explicit analysis is based on the concept of
steps, which are described in the history data portion of the input file. (For more information on steps,
see ``Procedures: overview,'' Section 6.1.1.) The history input options are combined within a step as
needed to define the history of the analysis.
Multiple steps can be defined in an analysis; each step begins with the *STEP option and ends with the
*END STEP option. Steps can be introduced simply to change the output requests or to change the
loads, boundary conditions, etc. There is no limit on the number of steps in an analysis.
Each step in an analysis involves the response to a set of transient loading conditions. Each analysis
step is thus a portion or period of the history. Typically, a step is simply a change from one load to
another. The user can also add or delete contact conditions, boundary conditions, etc. from step to step.
The state at the end of a step provides the initial conditions for the next step, making it easy to simulate
consecutive loadings of a model.
The optional history data described below prescribing the loading, boundary conditions, and the output
controls are continued to all subsequent steps until they are modified or reset.
Required history data
The following history data must be included in an input file to define an analysis procedure:
Response type: An option to define the analysis procedure type must appear immediately after the
*STEP option.
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Introduction
There are two procedures available. Dynamic transient analysis is performed using the
*DYNAMIC, EXPLICIT procedure (``Explicit dynamic analysis,'' Section 6.2.1). This procedure
can also be used to perform an adiabatic thermal analysis ( ``Adiabatic analysis,'' Section 6.3.2).
The annealing of a metallic structure or reinitialization of state variables in a user-defined material
model can be modeled using the *ANNEAL procedure (``Annealing procedure,'' Section 6.2.2).
Optional history data
The following history data can be included as necessary:
Loading: Usually some form of external loading is defined. For example, concentrated or
distributed loads can be applied ( ``Applying loads: overview,'' Section 18.4.1), temperature
changes leading to thermal expansion can be prescribed ( ``Thermal expansion,'' Section 11.1.2), or
contact conditions can be used to apply loads ( ``Contact analysis: overview,'' Section 20.1.1).
The loading can be prescribed as a function of time (``Amplitude curves,'' Section 18.1.2). This
feature can be used to prescribe loadings such as known accelerations or pressure transients. If an
amplitude variation is not defined, ABAQUS/Explicit assumes that the load is applied
instantaneously at the beginning of the step and held constant throughout the step.
Boundary conditions: Zero-valued or nonzero boundary conditions can be added, modified, or
removed during an analysis (``Boundary conditions,'' Section 18.3.1).
Output control: Quantities such as stress, strain, reaction force, temperature, and energy are
available as output. The output options are described in ``Output to the results file,'' Section 4.1.2;
and all of the output variables are listed in ``Output variable identifiers,'' Section 4.2.1. The
available output files are described in ``Output,'' Section 4.1.1.
Contact: Contact surfaces and contact interactions can be added, modified, or removed during an
analysis (see ``Contact analysis: overview,'' Section 20.1.1).
Including model or history data from an external file
The *INCLUDE option can be used to specify an external file that contains a portion of the ABAQUS
input file. This file can include model and history definition data, comment lines, and other
*INCLUDE references. When the option is encountered, ABAQUS will immediately process the input
data within the file specified by the INPUT parameter. When the end-of-file is reached, ABAQUS will
return to processing the original file.
A maximum of five levels of nested *INCLUDE references can be used. The option supports UNIX
environment variables.
Usage: *INCLUDE, INPUT=file_name
1.4 Parametric modeling
1.4.1 Parametric input
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Introduction
This section describes how to parametrize an ABAQUS input file so as to allow greater flexibility in
building and manipulating models.
References
· ``Scripting parametric studies,'' Section 23.1.1
· ``Parametric shape variation,'' Section 2.1.2
· *PARAMETER
· *PARAMETER DEPENDENCE
· *PARAMETER SHAPE VARIATION
Overview
The parametric input capability allows the user to create an ABAQUS input file in which:
· Any number of input parameters is defined by assigning a value to each one of them.
· The parameters defined in the input file are used in place of input quantities.
· The parameters are evaluated according to their definition and are substituted for the parametrized
input quantities before an analysis is run.
The different kinds of parameters and the different ways of parametrizing the ABAQUS input
quantities are discussed in this section.
Introduction
All parameter definitions must be given under *PARAMETER options. For example,
*PARAMETER
width = 2.5
height = width*2
defines the two parameters width and height.
The Python language (Lutz, 1996) is used to perform parameter evaluation and substitution; hence,
parameter definitions are required to follow the Python syntax rules discussed later in this section.
The parameters can then be used in place of input quantities by delimiting them with < >. For example,
*BEAM SECTION, SECTION=RECT, ELSET=name, MATERIAL=name
<width>, <height>
In this simple example models with beams of different cross-sections can be obtained simply by
changing the values of the parameters.
Parameters
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Introduction
Parameters are user-named variables to which the user assigns values. When a parameter is used
instead of a value, the value of that parameter is substituted. There are two basic types of parameters:
independent parameters and dependent parameters.
Independent parameters
Independent parameters are those that do not depend on any other parameters. The following are
examples of the definition of independent parameters:
*PARAMETER
thickness = 10.0
area = 5.0**2
length = 3.0*sin(45*pi/180.0) # convert degrees to radians
Python expressions using numbers and numerical operations (such as addition, multiplication, and
exponentiation) can be used to define independent parameters. Arithmetic support in Python is
discussed later in this section.
Dependent parameters
Dependent parameters are those that depend on other parameters (dependent or independent).
Dependent parameters can be defined in one of two ways: using a mathematical expression or using a
tabular dependence.
Expressional dependence
Python parametric expressions involving operations between numbers and parameters are used to
define expressionally dependent parameters. In the following example area and mom_inertia are
dependent parameters:
*PARAMETER
width = 2.0
height = 5.0
area = width*height
mom_inertia = area*height**3/12.0
Tabular dependence
Tabular dependence between parameters is defined by specifying the dependent and independent
parameters as well as a dependence table. The dependent and independent parameters are specified on
the *PARAMETER option. They are given inside parentheses as a sequence of parameter names
separated by commas. The name of the table that defines the dependence between the parameters is
given with the TABLE parameter. The table is specified using the *PARAMETER DEPENDENCE
option. It must have as many values per line as the number of dependent parameters plus the number of
independent parameters for which it is going to be used. This number must be specified with the
NUMBER VALUES parameter. The table must contain only real values; dependent parameter values
are given first, followed by independent parameter values. Parameter names and character strings
cannot be used in a table.
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Introduction
The evaluation of tabularly dependent parameters by interpolation between values in a table will result
in these parameters being assigned real values. If it is necessary that the tabularly dependent
parameters be integer numbers, the real numbers must be converted to integer numbers as described
later in the Python language section.
When the tabularly dependent parameters are functions of only one independent parameter, the tabular
data must be given in order of increasing values of the independent parameter. ABAQUS then
interpolates linearly for values between those given. The dependent parameters are assumed to be
constant outside the range of the independent parameters used in a table. When the tabularly dependent
parameters depend on several independent parameters, the variation of the dependent parameters with
respect to the first independent parameter must be given at fixed values of the other independent
parameters, in ascending values of the second independent parameter, then of the third independent
parameter, and so on. The table lines must always be ordered so that the independent parameters are
given increasing values. This process ensures that the value of each dependent parameter is completely
and uniquely defined for all values of the independent parameters.
The fact that the definition of the dependence table is separate from the assignment of the dependence
to particular parameters means that the same table can be used for multiple sets of
dependent/independent parameters. This is useful when there are different instances of the same kind
of input data; for example, multiple material definitions that use the same dependence but different sets
of parameters.
Because the evaluation of parameters is procedural (see "Parameter evaluation" under "Rules for
parameters"), a parameter dependence table must always be defined with the *PARAMETER
DEPENDENCE, TABLE option before it is used to specify tabular parameter dependencies.
Independent parameters in tabular dependence definitions are treated as independent for the purpose of
defining this dependency; however, these "independent" parameters can be defined to depend on other
parameters in a preceding parameter definition.
Usage: Use both of the following options:
*PARAMETER DEPENDENCE, TABLE=name, NUMBER VALUES=number
table with NUMBER VALUES values per line
*PARAMETER, TABLE=name, DEPENDENT=(parList), INDEPENDENT=(parList)
Rules for parameters
Some general rules apply to all parameters used in ABAQUS input files. These rules are described in
the following subsections.
Parameter evaluation
Parameters are evaluated by ordered execution of the parameter definitions as they appear in the input
file. For example, the input
*PARAMETER
x = 2
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Introduction
y = x + 3
x = 4
gives x=4 and y=5, not x=4 and y=7. The input
*PARAMETER
y = x + 3
x = 4
is flagged as an error because y cannot be evaluated by ordered execution of the input. In other words,
there is no deferred execution of the *PARAMETER options.
It is possible to define parameters anywhere in the input file, even after parameters have been used in
place of input quantities, since the *PARAMETER options are always processed before any other
input options are processed.
Parameters can also be defined and used in place of input quantities in an input file used for a restart
analysis. However, parameters defined in the input file for the original analysis (from which the restart
run is continued) are not available in the restart analysis.
Parameter substitution
When the parameterized data are processed, ABAQUS assigns the parameter values as determined at
the end of parameter evaluation. An error is reported if a parameter used in place of input quantities
has not been assigned a value. Later, the solver input file processor performs its usual checks on the
validity of the parameter values with respect to the options in which they are being used.
Data types
The data type of a parameter is deduced from its definition in the *PARAMETER option. An integer
parameter results from assigning an integer literal value to the parameter. Similarly, a real parameter
arises from assigning a real literal value to the parameter. Integers are promoted to reals if they are
used in operations containing reals. A character string parameter results from assigning a character
string literal value to the parameter.
The input option context in which the parameter is used dictates the data type that the parameter must
have. Parameters of real data type should be used in place of real ABAQUS input quantities.
Parameters of integer (or character string) type should be used in place of integer (or character string)
type input quantities, respectively. In some instances, mismatches between the input context and the
type of the substituted parameter will cause the solver input file processor to flag these instances as
input errors. For example, the input
*PARAMETER
int_pts = 5.0
*SHELL SECTION
10.0, <int_pts>
will cause the solver input file processor to report an error because the number of integration points in
the *SHELL SECTION option must be an integer. However, the input
*PARAMETER
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Introduction
thick = 5/4
*SHELL SECTION
<thick>,
which, as a result of doing integer division, gives a shell thickness of one (not 1.25) will be accepted
by the solver input file processor without a warning being flagged. In conclusion, the user can rely on
the solver input file processor to catch only some data type errors.
Auxiliary input files
Parameters can be defined in *INCLUDE input files but not in any other auxiliary input files. Names
of auxiliary input files can be parameterized, except those used in the *INCLUDE option.
Parametrization of input quantities
ABAQUS treats parametrization of "size" and "shape" quantities somewhat differently.
Parametrization of shape input quantities is discussed in a separate section (see ``Parametric shape
variation,'' Section 2.1.2).
Size input quantities are understood to include all ABAQUS input quantities except those that relate to
shape. Size input quantities include section properties, material properties, orientation properties,
prescribed conditions, interaction definitions and properties, and analysis procedure data.
Parametrizing individual input quantities
The following example shows the parametrization of shell section input using three independent
parameters of differing data types.
*ELSET, ELSET=<shell_set>, GEN
1, 111, 10
*PARAMETER
shell_set = 'lining'
shell_thick = 1.E2
num_int_pts = 5
*SHELL SECTION, ELSET=<shell_set>, MATERIAL=name
<shell_thick>, <num_int_pts>
Parametrizing groups of input quantities (expressional
dependence)
The following example shows the parametrization of a three-layer composite shell section using
expressional-dependent parameters. In this example the thickness parameter can be used to change
the thickness of the layers of the composite section uniformly.
*PARAMETER
thickness = 10.
layer1_thick = 0.15*thickness
layer2_thick = 0.6*thickness
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Introduction
layer3_thick = 0.25*thickness
*SHELL SECTION, ELSET=, COMPOSITE
<layer1_thick>,num int pts, material name, orientation
<layer2_thick>,num int pts, material name, orientation
<layer3_thick>,num int pts, material name, orientation
This parametrization requires that dependent parameters be created for the three input quantities
(layer1_thick, layer2_thick, layer3_thick) that each depend on the independent
parameter (thickness).
Parametrizing groups of input quantities (tabular dependence)
The following example shows the parametrization of the section properties of a box beam. The height
and wall thicknesses of the beam section are parameters that depend tabularly on the section width.
*PARAMETER
a = 60.
*PARAMETER DEPENDENCE, TABLE=sectprop, NUMBER VALUES=6
25.0, 1.04, 1.04, 1.04, 1.04, 50.0
50.0, 4.17, 3.13, 2.08, 2.50, 100.0
75.0, 9.38, 6.24, 3.13, 4.90, 150.0
*PARAMETER, TABLE=sectprop, DEPENDENT=(b, t1, t2, t3, t4),
INDEPENDENT=(a)
*BEAM SECTION, SECTION=BOX, ELSET=beams, MATERIAL=steel
<a>, <b>, <t1>, <t2>, <t3>, <t4>
The above parametrization creates dependent parameters ( b, t1, t2, t3, t4) that each depend on the
independent parameter ( a). Usage of tabular dependence allows the definition of the dependencies of
input quantities on parameters to be confined to the *PARAMETER options; i.e., separate from the
options where parametrization of input quantities is done. An advantage of this method of
parametrization is that the same parameter dependence table can be used for different parameters in
different input options. For example, the user may wish to use beams of different cross-section
dimensions in different parts of the structure being modeled. The parameter dependence table can be
reused with new dependent ( bb, tt1, tt2, tt3, tt4) and independent ( aa) parameters.
*PARAMETER
aa = 65.
*PARAMETER, TABLE=sectprop, DEPENDENT=(bb, tt1, tt2, tt3, tt4),
INDEPENDENT=(aa)
*BEAM SECTION, SECTION=BOX, ELSET=columns, MATERIAL=steel
<aa>, <bb>, <tt1>, <tt2>, <tt3>, <tt4>
In options where predefined field variable dependence is supported, this method of parametrization
provides a clear separation between predefined field variable dependence and parameter dependence;
therefore, field variable and parameter dependence can never be confused. Consider, for example, the
case of perfect plasticity properties for a metal where the yield stress depends on a field variable and is
also parametrized to depend tabularly on the carbon content of the metal alloy.
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Introduction
*PARAMETER
carbon = 0.01
*PARAMETER DEPENDENCE, TABLE=yield_data, NUMBER=4
ys_fv1 val 1, ys_fv2 val 1, ys_fv3 val 1, carbon val 1
ys_fv1 val 2, ys_fv2 val 2, ys_fv3 val 2, carbon val 2
ys_fv1 val 3, ys_fv2 val 3, ys_fv3 val 3, carbon val 3
ys_fv1 val 4, ys_fv2 val 4, ys_fv3 val 4, carbon val 4
*PARAMETER, TABLE=yield_data, DEPENDENT=(ys_fv1, ys_fv2, ys_fv3),
INDEPENDENT=(carbon)
*MATERIAL, NAME=alloy
*PLASTIC, DEPENDENCIES=1
<ys_fv1>, , , fv val 1
<ys_fv2>, , , fv val 2
<ys_fv3>, , , fv val 3
This example shows that any combination of dependencies on predefined field variables and/or
dependent parameters can be defined.
Python language
Parameter statements in *PARAMETER options are required to follow the syntax and semantics of the
Python language (note that the *PARAMETER DEPENDENCE and *PARAMETER SHAPE
VARIATION options follow the usual ABAQUS input syntax rules). The subset of the Python
language that is endorsed is documented here.
Statement length and continuation lines
Python statements in *PARAMETER keyword blocks can be continued over multiple lines by
terminating each line with a backslash character (\). The *PARAMETER type keyword lines can be
continued onto the following line using a trailing comma since they are treated like other ABAQUS
keyword lines.
Comments
Comments in the *PARAMETER option start with the number character (#) and continue to the end of
the line. However, comments in the *PARAMETER DEPENDENCE and *PARAMETER SHAPE
VARIATION options are indicated by the usual ABAQUS input syntax convention (**).
Parameter names
Parameter names must begin with a letter and can contain the underscore character (_) and numbers.
Parameter names are case sensitive.
Data types
Data types are limited to character strings, integers, and reals.
Strings are delimited with single or double quotation marks (' ' or " "). Backward single quotation
marks (` `) are not permitted. Character strings should not contain the backslash character (\).
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Introduction
Integers are created by assignment to integer literals (for example, aInt = 2).
Reals are created by assignment to real literals (for example, aReal = 1.0). Real numbers can be given
with or without an exponent. Any exponent must be preceded by E or e. The following line shows five
acceptable ways of entering the same real number:
-12.345, -1234.5E-2, -0.12345E+2, -0.12345E2, -0.12345e2
The syntax
-0.12345D+2
(allowed elsewhere in the ABAQUS input file) is not valid in Python.
Type conversion
If integers and reals are mixed in expressions, integers are promoted automatically to reals. Explicit
type conversion can be obtained using:
int(aReal): aReal converted to integer type
float(anInt): anInt converted to real type (float is the same as real)
str(anIntOrReal): anIntOrReal converted to character string type
'anIntOrReal': anIntOrReal converted to character string type
Numeric operators
Standard support for operators is provided:
- x: x negated
+ x: x unchanged
x + y: sum of x and y
x - y: difference of x and y
x * y: product of x and y
x / y: quotient of x and y
x**y: x to the power y
Functions
The following utility functions are supported:
abs(x): absolute value of x
acos(x): arc cosine of x (x is in radians)
asin(x): arc sine of x (x is in radians)
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Introduction
atan(x): arc tangent of x (x is in radians)
cos(x): cosine of x (x is in radians)
log(x): natural logarithm of x
log10(x): base 10 logarithm of x
pow(x,y): x to the power y (equivalent to x**y)
sin(x): sine of x (x is in radians)
sqrt(x): square root of x
tan(x): tangent of x (x is in radians)
Character string operators
'abc' + 'def': concatenation of character string 'abc' and character string 'def'
Execution of parametrized input
Jobs with parametrized input files are submitted to ABAQUS in the usual way; for example,
abaqus job=job-name input=input-file
where it is assumed that an input file named input-file.inp exists.
ABAQUS searches input-file.inp and any *INCLUDE input files for the *PARAMETER,
*PARAMETER DEPENDENCE, and *PARAMETER SHAPE VARIATION (``Parametric shape
variation,'' Section 2.1.2) options, as well as parameter names inside < > that may have been used in
place of input quantities. If any of the above are found, ABAQUS will interpret the parametrized input
file and perform the tasks of parameter evaluation and substitution.
As a result, a modified input file that is free of *PARAMETER options, *PARAMETER
DEPENDENCE options, and <parameter> instances is produced. This file is named job-name.pes
and is subsequently submitted for execution of an analysis. The execution procedure of a parametrized
input file, except for the additional processing of *PARAMETER SHAPE VARIATION options in the
solver input file processor, does not differ from that of a non-parametrized input file. All the files
generated by the parametrized input job will be named job-name with the appropriate extension
appended to it.
parametercheck and continue jobs
An execution mode in which only parameter processing (evaluation and substitution) is carried out is
invoked with the parametercheck option; for example,
abaqus job=job-name input=input-file parametercheck
The parametercheck execution option is mutually exclusive of the analysis, datacheck, continue,
convert, and recover execution options.
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Introduction
A parametercheck run is useful in situations where the user has defined complex parametrization in
the input. In these cases the user may want to study the results of parameter evaluation and substitution
before proceeding further.
A parametercheck run does not permit continuation of the execution by using the continue option in
a subsequent run; the job must be rerun from the beginning.
Display of parametric input
Display of the results of parameter evaluation and substitution in the data file is described in this
section. Visualization of parameter shape variations is described in ``Parametric shape variation,''
Section 2.1.2.
Data file display
The data (.dat) file contains information about the model definition generated by the solver input file
processor. The amount of output generated by the solver input file processor is controlled by the
*PREPRINT option. In particular, the option *PREPRINT, ECHO=YES or NO (default) specifies
whether or not the original input ( .inp) file is echoed to the data file.
In the case of parametric input this file will generally contain a number of *PARAMETER,
*PARAMETER DEPENDENCE, and *PARAMETER SHAPE VARIATION options, as well as a
number of <parameter> instances. To verify the definition of parametric input, two keyword
parameters, PARVALUES and PARSUBSTITUTION, are available on the *PREPRINT option.
PARVALUES=YES is used to create a modified version of the original input file showing the
parameters and their values (this file is named job-name.par). PARSUBSTITUTION=YES is used
to create the job-name.pes file, which is the modified version of the original input file that is free
of *PARAMETER options, *PARAMETER DEPENDENCE options, and <parameter> instances.
Usage: Use one of the following options:
*PREPRINT, PARVALUES=YES or NO
*PREPRINT, PARSUBSTITUTION=YES or NO
Additional reference
· Lutz, M., Programming Python, O'Reilly & Associates, Inc., 1996.
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2. Spatial Modeling
2.1 Defining nodes
2.1.1 Node definition
This section describes the methods for defining nodes in ABAQUS.
References
· *NCOPY
· *NFILL
· *NGEN
· *NMAP
· *NODE
· *NSET
· *SYSTEM
Overview
Node definition consists of:
· assigning a node number to the node;
· optionally specifying a local coordinate system in which to define nodes;
· defining individual nodes by specifying their coordinates;
· grouping nodes into node sets;
· creating nodes from existing nodes by generating them incrementally, by copying existing nodes,
or by filling in nodes between the bounds of a region; and
· mapping a set of nodes from one coordinate system to another.
If any node is specified more than once, the last specification given is used.
ABAQUS/Explicit will eliminate all unnecessary nodes before proceeding with the analysis. This
feature is useful because it allows points to be defined as nodes for mesh generation purposes only.
Assigning a node number to the node
Each individual node must have a numeric label called the node number, which is assigned when the
node is defined. The node number must be a positive integer, and the maximum node number allowed
is 9999999 (for information on integer input, see ``Input syntax rules,'' Section 1.2.1). The nodes do
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not need to be numbered continuously.
An ABAQUS model can be defined in terms of an assembly of part instances (see ``Defining an
assembly,'' Section 2.5.1). In such a model all nodes must belong to either a part, part instance, or, in
the case of reference nodes, to the assembly. Node numbers must be unique within a part, part
instance, or the assembly, but they can be repeated in different parts or part instances.
Specifying a local coordinate system in which to define nodes
Sometimes it is convenient to define nodal coordinates in a local coordinate system and then transform
these coordinates to the global coordinate system. Use the *SYSTEM option to translate and rotate the
local (X 1 ; Y 1 ; Z 1 ) coordinate values into the global coordinate system. The transformation is done
immediately after input and will be applied to all nodal coordinates entered or generated after the
*SYSTEM option.
The transformation affects only the input of nodal coordinates with the *NODE and *NGEN options.
The *SYSTEM option cannot be used
· to specify a local coordinate system for applying loads and boundary conditions--use the
*TRANSFORM option instead (``Transformed coordinate systems,'' Section 2.1.4), or
· to define a local coordinate system for output of components of stress, strain, and element section
forces--use the *ORIENTATION option instead (``Orientations,'' Section 2.2.3).
The *SYSTEM option can be used in addition to the SYSTEM parameter on the *NODE and *NGEN
options. If the *SYSTEM option is in effect and the SYSTEM parameter has been used on the *NODE
or *NGEN options, the input coordinates are first transformed according to the SYSTEM parameter
and then according to the *SYSTEM specification.
Defining the local coordinate system
Set up the system specification by specifying the global coordinates of three points in the local system:
the origin of the local system (point a in Figure 2.1.1-1), a point on the local X 1 -axis (point b in Figure
2.1.1-1), and a point in the (X 1 ; Y 1 ) plane of the local system on (or near) the local Y 1 -axis (point c
in Figure 2.1.1-1). Enter these values on the data lines of the *SYSTEM option. If only one point (the
origin) is given, ABAQUS assumes that the user needs a translation only. If only two points are given,
the direction of the Z 1 -axis will be the same as that of the Z-axis.
Figure 2.1.1-1 Local coordinate system.
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Spatial Modeling
Use another *SYSTEM definition to change the local coordinate system, and use a *SYSTEM option
without any associated data lines to revert to input in the global coordinate system.
Usage: *SYSTEM
Using the *SYSTEM option within part definitions
When the *SYSTEM option is used within a part (or part instance) definition, it is in effect only within
that part (or part instance) definition. Nodes defined in other parts are not affected.
The *SYSTEM option is used to specify the local (X 1 ; Y 1 ; Z 1 ) coordinate values relative to the part
coordinate system, which subsequently may be translated and/or rotated according to the positioning
data given for the instance (see ``Defining an assembly,'' Section 2.5.1).
Defining individual nodes by specifying their coordinates
Use the *NODE option to define individual nodes. Specify the node number and the coordinates that
define the node on the data lines. ABAQUS/Explicit uses a right-handed, rectangular Cartesian
coordinate system for all nodes except for axisymmetric models, when the coordinates of the nodes
must be given as the radial and axial positions. For more information about direction definitions, see
``Conventions,'' Section 1.2.2.
In a model defined in terms of an assembly of part instances, give nodal coordinates in the local
coordinate system of the part (or part instance). See ``Defining an assembly,'' Section 2.5.1.
Usage: *NODE
Reading node definitions from a file
Node definitions can be read into ABAQUS from an alternate input file. The syntax of such file names
is described in ``Input syntax rules,'' Section 1.2.1. Use the INPUT parameter to specify the name of
the alternate input file.
Usage: *NODE, INPUT=file_name
Defining the nodal coordinates in a local coordinate system
Use the SYSTEM parameter to define a local coordinate system in which to specify the nodal
coordinates. The SYSTEM parameter can be set equal to the following:
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Spatial Modeling
· R to give coordinates in a rectangular Cartesian system (this is the default),
· C to give coordinates in a cylindrical system, or
· S to give coordinates in a spherical system.
These coordinate systems are shown in Figure 2.1.1-2.
Usage: *NODE, SYSTEM=R or C or S
Figure 2.1.1-2 Coordinate systems.
The SYSTEM parameter is entirely local to the *NODE option. As the data lines are read, the
coordinates are transformed to rectangular Cartesian coordinates immediately. If the *SYSTEM option
is also in effect, these are local rectangular Cartesian coordinates as defined by the *SYSTEM option,
which are subsequently transformed to global Cartesian coordinates. For example, the following lines
define node number 1 with coordinates ( 10 cos 20± , 10 sin 20± , 5.). These coordinates are defined in a
local cylindrical system (R, µ, Z) as indicated by SYSTEM=C.
*NODE, NSET=DISC, SYSTEM=C
1, 10., 20., 5.
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Spatial Modeling
Grouping nodes into node sets
Node sets are used as convenient cross-references when defining loads, constraints, properties, etc.
Node sets are the fundamental references of the model and should be used to assist the input definition.
The members of a node set can be individual nodes or other node sets. An individual node can belong
to several node sets.
Nodes can be grouped into node sets when they are created or after they have already been defined. In
either case, each node set is assigned a name. Node set names can be up to 80 characters long.
The same name can be used for a node set and for an element set.
By default, the nodes within a node set will be arranged in ascending order, and duplicate nodes will
be removed. Such a set is called a sorted node set. The user may choose to create an unsorted node set
as described later, which is often useful for options that match two or more node sets. For example, if
the user defines multi-point constraints ( ``General multi-point constraints,'' Section 19.2.2) between
two node sets, a constraint will be created between the first node in Set 1 and the first node in Set 2,
then between the second node in Set 1 and the second node in Set 2, etc. It is important to ensure that
the nodes are combined in the desired way. Therefore, it is sometimes better to specify that a node set
be stored in unsorted order.
Once nodes are assigned to a node set, additional nodes can be added to the same node set; however,
nodes cannot be removed from a node set.
Creating an unsorted node set
Include the UNSORTED parameter on the *NSET option to assign the nodes in this node set to the set
(or to add the nodes to the set if it already exists) in the order in which they are given. The node
numbers will not be rearranged, and duplicates will not be removed.
Usage: *NSET, NSET=name, UNSORTED
This unsorted node set will affect the *NCOPY option, the *NFILL option, the *EQUATION option,
and the *MPC option. An unsorted node set can be created only by using the *NSET, UNSORTED
option or by using the *NCOPY option to copy an unsorted node set. Any additions or modifications
to the node set using other means will result in a sorted node set.
Assigning nodes to a node set as they are created
There are several ways that nodes can be assigned to node sets as they are created.
Usage: Use any of the following options:
*NODE, NSET=name
*NCOPY, NEW SET=name
*NFILL, NSET=name
*NGEN, NSET=name
*NMAP, NSET=name
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Assigning previously defined nodes to a node set
Use the *NSET option to assign nodes that have been defined previously (by using the *NODE, the
*NFILL, or the *NGEN options) to a node set by listing the nodes forming the set directly, by
generating the node set, or by generating a node set from an element set. Use the NSET parameter to
assign these nodes to a node set.
Listing the nodes that define the set directly
List the nodes that form the node set directly on the data lines of the *NSET option. Node sets, as well
as individual nodes, can be assigned to node sets.
Usage: *NSET, NSET=name
For example, the following lines add nodes 1, 3, 10, 11, and all of the nodes in set A11 to set A12:
*NSET, NSET=A12
1, 3
10, 11,
A11
All of the nodes in node set A12 will be sorted into ascending numerical order. If the UNSORTED
parameter was included on the *NSET option in the above example, node set A12 would contain the
nodes in the order in which they were specified on the data lines.
Generating the node set
To generate the node set, specify a first node, n1 ; a last node, n2 ; and the increment in node numbers
between these nodes, i, on the data line of the *NSET option. All nodes going from n1 to n2 in
increments of i will be added to the set. Therefore, i must be an integer such that (n2 ¡ n1 )=i is a
whole number (not a fraction). The default is i = 1.
Usage: *NSET, NSET=name, GENERATE
For example, the following lines add all nodes from 100 to 120 in increments of 10 to set A13:
*NSET, NSET=A13, GENERATE
100, 120, 10
Generating a node set from an element set
Use the ELSET parameter to specify the name of an element set (``Element definition,'' Section 2.2.1).
The nodes that define the elements contained in this element set will be assigned to the node set
specified. This option can be used only to define sorted node sets.
Usage: *NSET, NSET=name, ELSET=name
For example, the following lines add all nodes that define elements 50 and 100 (nodes 1, 2, 3, and 4) to
node set A14:
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Spatial Modeling
*ELEMENT, TYPE=B21
50, 1, 2
100, 3, 4
*ELSET, ELSET=B1
50, 100
*NSET, NSET=A14, ELSET=B1
Defining part and assembly sets
In a model defined in terms of an assembly of part instances, all node sets must be defined within a
part, part instance, or the assembly definition. If a node set is defined within a part (or part instance)
definition, refer to the node numbers directly:
*PART, NAME=PartA
...
*NSET, NSET=set1
1,3,26,500
*END PART
Node set set1 belongs to part PartA and will be inherited by every instance of PartA.
To define an assembly-level node set, identify the nodes to be added to the set by prefixing each node
number with the part instance name and a "." (as explained in ``Defining an assembly,'' Section 2.5.1):
*ASSEMBLY, NAME=Assembly-1
*INSTANCE, NAME=PartA-1, PART=PartA
...
*END INSTANCE
*INSTANCE, NAME=PartA-2, PART=PartA
...
*END INSTANCE
*NSET, NSET=set1
PartA-1.1, PartA-1.3, PartA-1.26, PartA-1.500
PartA-2.1, PartA-2.3, PartA-2.26, PartA-2.500
*END ASSEMBLY
An assembly-level node set can have the same name as a part-level node set. In this example
assembly-level node set set1 contains all the nodes from node sets set1 belonging to part instances
PartA-1 and PartA-2. Therefore, the nodes are assigned to two separate node sets: one at the part
instance level and one at the assembly level. An assembly-level node set called set1 could be created
with entirely different nodes than those that belong to the part set; part- and assembly-level node sets
are independent. However, since in this example the same nodes are assigned to both the part- and
assembly-level node sets set1, the assembly-level set could alternatively be defined by:
*ASSEMBLY, NAME=Assembly-1
*INSTANCE, NAME=PartA-1, PART=PartA
...
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*END INSTANCE
*INSTANCE, NAME=PartA-2, PART=PartA
...
*END INSTANCE
*NSET, NSET=set1
PartA-1.set1, PartA-2.set1
*END ASSEMBLY
This node set definition is equivalent to the previous example, where the nodes were listed
individually.
Sometimes it is not convenient to define an assembly-level node set by referring to part-level node
sets. In such cases a set definition containing many nodes can get quite lengthy. Therefore, the
INSTANCE parameter is provided on the *NSET option as an alternative. The following example
shows two equivalent ways to define an assembly-level node set; once by prefixing each node number
with a part instance name (as shown above) and once using the more compact INSTANCE notation:
*ASSEMBLY, NAME=Assembly-1
*INSTANCE, NAME=PartA-1, PART=PartA
...
*END INSTANCE
*INSTANCE, NAME=PartA-2, PART=PartA
...
*END INSTANCE
*NSET, NSET=set2
PartA-1.101, PartA-1.102, PartA-1.103, PartA-1.104,
PartA-2.201, PartA-2.202, PartA-2.203, PartA-2.204
*NSET, NSET=set3, INSTANCE=PartA-1
101, 102, 103, 104
*NSET, NSET=set3, INSTANCE=PartA-2
201, 202, 203, 204
*END ASSEMBLY
When the *NSET option is used more than once with the same name, as it is with set3, the nodes in
the second use of *NSET are appended to the set created by the first use of *NSET.
Usage: *NSET, NSET=NsetName, INSTANCE=InstanceName
Internal node sets created by ABAQUS/CAE
In ABAQUS/CAE many modeling operations are performed by picking geometry with the mouse. For
example, a concentrated load can be applied by picking a point on a geometric part instance. Since the
*CLOAD option refers to a node set, this "picked" geometry must be translated into a node set in the
input file. Such sets are assigned a name by ABAQUS/CAE, and the set is marked with the
INTERNAL parameter on the *NSET option. These and other internal sets created by ABAQUS/CAE
will not appear in ABAQUS/Viewer.
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Usage: *NSET, NSET=NsetName, INTERNAL
Transferring of node sets
If the results of an ABAQUS/Explicit analysis are imported into an ABAQUS/Standard analysis (or
vice versa) with the *IMPORT option, all node sets in the original analysis are imported by default.
Selected node sets can be imported with the *IMPORT NSET option. See ``Transferring results
between ABAQUS/Explicit and ABAQUS/Standard,'' Section 7.3.1, for details.
Creating nodes from existing nodes by generating them
incrementally
Use the *NGEN option to generate nodes incrementally from existing nodes. All of the nodes along a
straight or curved line can be generated by giving the coordinates of the two end nodes and defining
the type of curve.
The two end nodes must already be defined, usually by using the *NODE option, but it is also possible
to have them defined by an earlier generation.
Defining a straight line between the two end nodes
To define a straight line between the two end nodes, omit the LINE parameter from the *NGEN option.
Specify the number of the first end node, n1 ; the number of the last end node, n2 ; and the increment in
node numbers between each node along the line, i, on the data lines of the *NGEN option. Therefore, i
must be an integer such that (n2 ¡ n1 )=i is a whole number (not a fraction). The default is i = 1.
Usage: *NGEN
For example, the following lines define node number 1 with coordinates (0:; 0:; 0:) and node number 6
with coordinates (10:; 0:; 0:) . Nodes 2, 3, 4, and 5 with coordinates (2:; 0:; 0:) , (4:; 0:; 0:) , (6:; 0:; 0:) ,
and (8:; 0:; 0:) , respectively, are generated automatically using the *NGEN option.
*NODE
1, 0., 0., 0.
6, 10., 0., 0.
*NGEN
1, 6, 1
Defining a circular arc between the two end nodes
To define a circular arc between the two end nodes, set LINE=C. Specify the number of the first end
node, n1 ; the number of the last end node, n2 ; and the increment in node numbers between each node
along the arc, i, on the data lines of the *NGEN option. Therefore, i must be an integer such that
(n2 ¡ n1 )=i is a whole number (not a fraction). The default is i = 1.
In addition, the coordinates of one extra point, the center of the circle, must be specified on the data
lines of the *NGEN option by giving the node number of a node that has already been defined or by
giving the nodal coordinates directly. The user may choose either option. If both are supplied, the node
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number will take precedence over the coordinates.
If the coordinates are defined directly, they can be specified in a local coordinate system as described
later.
Usage: *NGEN, LINE=C
The coordinates of the end nodes will be adjusted radially if the circle cannot be passed through both
points. An arc of a circle of 180° through 360° will require more extensive definition. For this case the
user must define the plane of the circular disc by giving the normal to the disc; the nodes will then be
numbered according to the right-hand rule about this normal.
Defining a parabola between the two end nodes
To define a parabola between the two end nodes, set LINE=P. Specify the number of the first end
node, n1 ; the number of the last end node, n2 ; and the increment in node numbers between each node
along the parabola, i, on the data lines of the *NGEN option. Therefore, i must be an integer such that
(n2 ¡ n1 )=i is a whole number (not a fraction). The default is i = 1.
In addition, the coordinates of one extra point, the midpoint on the arc between the two end points,
must be specified on the data lines of the *NGEN option by giving the node number of a node that has
already been defined or by giving the nodal coordinates directly. The user can choose either option. If
both are supplied, the node number will take precedence over the coordinates.
If the coordinates are defined directly, they can be specified in a local coordinate system as described
later.
Usage: *NGEN, LINE=P
Defining the extra point and the normal direction in a local
coordinate system
The SYSTEM parameter can be used to define a local coordinate system in which to enter the
coordinates of the extra point that is required for a circle or a parabola. The SYSTEM parameter can be
set equal to the following:
· RC to define the extra node in a rectangular Cartesian system (this is the default),
· C to define the extra node in a cylindrical system, or
· S to define the extra node in a spherical system.
These coordinate systems are shown in Figure 2.1.1-2.
If the *SYSTEM option is in effect, the coordinates and normal direction specified with the *NGEN
option are assumed to be in the local coordinate system. If the *SYSTEM option is in effect and the
SYSTEM parameter has been used on the *NGEN option, the input is first transformed according to
the SYSTEM parameter and subsequently according to the *SYSTEM specification.
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Creating nodes by copying existing nodes
Use the *NCOPY option to create new nodes by copying existing nodes. The coordinates of the new
nodes can be translated and rotated, reflected from the nodes being copied, or projected from the nodes
being copied by using a polar projection with respect to a pole node.
Use the OLD SET parameter to identify the existing node set. Use the CHANGE NUMBER parameter
to specify an integer constant that will be added to the node numbers of existing nodes to define node
numbers for the nodes being created.
Use the NEW SET parameter to assign the newly created nodes to a node set. If the NEW SET
parameter is omitted, the newly created nodes are not assigned to a node set.
Usage: *NCOPY, OLD SET=name, CHANGE NUMBER=n, NEW SET=new_name
Translating and rotating the coordinates of the old nodes
Use the SHIFT parameter to create new nodes by translating or rotating the nodes in the old node set
(see Figure 2.1.1-3). Specify the value of the translation in the X-, Y -, and Z-directions on the first
data line of the *NCOPY option.
Figure 2.1.1-3 *NCOPY, SHIFT option.
Enter the coordinates of the first point defining the rotation axis (point a in Figure 2.1.1-3), the
coordinates of the second point defining the rotation axis (point b in Figure 2.1.1-3), and the angle of
rotation (in degrees) about the axis a-b on the second data line of the *NCOPY option. The rotation
can be applied multiple times as described later.
If both translation and rotation are specified, the translation is applied once before the rotation.
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Usage: *NCOPY, OLD SET=name, CHANGE NUMBER=n, SHIFT
Applying the rotation multiple times
Use the MULTIPLE parameter to define the number of times the rotation should be applied. For
example, if nodes are to be created at angles of 30°, 60°, and 90°, set MULTIPLE=3. The identifiers of
the nodes created are incremented sequentially by the value of the CHANGE NUMBER parameter.
Usage: *NCOPY, OLD SET=name, CHANGE NUMBER=n, SHIFT, MULTIPLE=n
Reflecting the coordinates of the old nodes
Use the REFLECT parameter to create new nodes by reflecting the coordinates of the old nodes
through a line, a plane, or a point.
Reflecting the coordinates through a line
To reflect the old nodal coordinates through a line, specify the coordinates of points a and b (see
Figure 2.1.1-4) on the data lines of the *NCOPY option.
Usage: *NCOPY, OLD SET=name, CHANGE NUMBER=n, REFLECT=LINE
Figure 2.1.1-4 *NCOPY, REFLECT=LINE option.
Reflecting the coordinates through a plane
To reflect the old nodal coordinates through a plane, specify the coordinates of points a, b, and c (see
Figure 2.1.1-5) on the data lines of the *NCOPY option.
Usage: *NCOPY, OLD SET=name, CHANGE NUMBER=n, REFLECT=MIRROR
Figure 2.1.1-5 *NCOPY, REFLECT=MIRROR option.
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Reflecting the coordinates through a point
To reflect the old nodal coordinates through a point, specify the coordinates of point a (see Figure
2.1.1-6) on the data lines of the *NCOPY option.
Usage: *NCOPY, OLD SET=name, CHANGE NUMBER=n, REFLECT=POINT
Figure 2.1.1-6 *NCOPY, REFLECT=POINT option.
Projecting the nodes in the old set from a pole node
Use the POLE parameter to create new nodes by projecting the nodes in the old set from a pole node.
Each new node will be located such that the corresponding old node is equidistant between the pole
node and the new node. The pole node (see Figure 2.1.1-7) is identified by giving its number or,
alternatively, its coordinates on the data line of the *NCOPY option.
This option is particularly useful for creating nodes that are associated with infinite elements ( ``Infinite
elements,'' Section 13.2.1). In this case the pole node should be located at the center of the far-field
solution.
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Usage: *NCOPY, OLD SET=name, CHANGE NUMBER=n, POLE
Figure 2.1.1-7 *NCOPY, POLE option.
Creating nodes by filling in nodes between two bounds
Use the *NFILL option to create nodes by filling in nodes between two bounds. On the data line
specify the two node sets whose members form the bounds, the number of intervals along each line
between the bounding nodes, and the increment in node numbers from the node number at the first
bound set end.
Let l equal the number of lines of nodes to be created between the two bounding node sets; the number
of intervals along each line between the bounding nodes is then given by l + 1.
Let n equal the increment in node numbers from the node number at the first bound set end; for each
node (nAi ) in the first bounding node set, the corresponding node in the other bounding node set ( nBi )
must be numbered such that (nBi ¡ nAi ) =n is a whole number.
The node sets that define the bounds of the region are used as they exist at the time the *NFILL option
appears in the input file: only those nodes that have been added to the sets prior to the *NFILL option
are used. Both sorted and unsorted node sets can be used with this option. Nodes that have not yet
been given coordinates are assumed to be at the origin, (0:; 0:; 0:) .
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The nodes created by the *NFILL option lie on straight lines between corresponding nodes in the two
sets. If the sets do not have the same number of nodes, the extra nodes in the longer set are ignored. By
default, the spacing between nodes along the lines is uniform.
Usage: *NFILL
For example, Figure 2.1.1-8 shows a simple quarter-cylinder model. The quarter circles INSIDEA
(nodes 1101-1105), OUTSIDEA (nodes 1501-1505), INSIDEB (nodes 6101-6105), and OUTSIDEB
(6501-6505) have already been defined using the *NODE and the *NGEN options. The region is filled
by first filling the end planes and placing the nodes on those planes into sets A and B and then filling
between those sets by the following options:
*NFILL, NSET=A
INSIDEA, OUTSIDEA, 4, 100
*NFILL, NSET=B
INSIDEB, OUTSIDEB, 4, 100
*NFILL
A, B, 5, 1000
Figure 2.1.1-8 *NFILL used to fill a three-dimensional region.
Concentrating the nodes toward one bound or the other
Use the BIAS parameter to concentrate the nodes toward one bound or the other. Specify the ratio of
adjacent distances between nodes along each line of nodes generated, as the nodes go from the first
bounding node set to the second.
Thus, if the BIAS parameter is less than one, the nodes are concentrated toward the first bounding
node set; if the BIAS parameter is greater than one, the nodes are concentrated toward the second
bounding set. The value of the parameter must be positive.
Usage: *NFILL, BIAS=b
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The bias intervals along the line from the first bounding node are L, L=b, L=b2 , L=b3 , L=b4 , L=b5 , ...
(where L is the length of the first interval).
For example, suppose the lines of nodes shown in Figure 2.1.1-9 have already been generated by the
*NODE or the *NGEN options and placed into node sets INSIDE and OUTSIDE. The following
option will fill the region as shown in Figure 2.1.1-10:
*NFILL, BIAS=0.6
INSIDE, OUTSIDE, 5, 100
Figure 2.1.1-9 Node sets defining *NFILL, BIAS example.
Figure 2.1.1-10 Result of *NFILL, BIAS example.
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Mapping a set of nodes from one coordinate system to another
Use the *NMAP option to map a set of nodes from one coordinate system to another. This capability is
useful for many geometric situations: a mesh can be generated quite easily in a local coordinate system
(for example, on the surface of a cylinder), using the *NGEN and *NFILL options, and then mapped
into the global (X, Y , Z) system using this option.
The *NMAP option cannot be used in a model defined in terms of an assembly of part instances.
Five different mappings are provided: a simple shift and/or rotation, skewed Cartesian, cylindrical,
spherical, and toroidal. These mappings are shown in Figure 2.1.1-11.
Figure 2.1.1-11 Coordinate systems; angles are in degrees.
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In all cases the coordinates of the nodes in the set are assumed to be defined in the local system when
this option is used: these local coordinates at each node are replaced with the global Cartesian ( X, Y ,
Z) coordinates defined by the mapping. All angular coordinates should be given in degrees.
The *NMAP option can be used several times in succession on the same nodes, if required.
Scaling the local coordinates before they are mapped
The local coordinates can be scaled by a factor before they are mapped. Specify the scaling factor on
the data line of the *NMAP option.
This facility is useful for "stretching" some of the coordinates that are given. For example, in cases
where the local system uses some angular coordinates and some distance coordinates (cylindrical,
spherical, etc.), it may be preferable to generate the mesh in a system that uses distance measures in the
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angular directions and then scale onto the angular coordinate system for the mapping.
Introducing a simple shift and/or rotation
To introduce a simple shift and/or rotation, set TYPE=RECTANGULAR.
Usage: *NMAP, NSET=name, TYPE=RECTANGULAR
Mapping from cylindrical coordinates
To map from cylindrical coordinates, set TYPE=CYLINDRICAL.
Usage: *NMAP, NSET=name, TYPE=CYLINDRICAL
Mapping from skewed Cartesian coordinates
To map from skewed Cartesian coordinates, set TYPE=DIAMOND.
Usage: *NMAP, NSET=name, TYPE=DIAMOND
Mapping from toroidal coordinates
To map from toroidal coordinates, set TYPE=TOROIDAL.
Usage: *NMAP, NSET=name, TYPE=TOROIDAL
2.1.2 Parametric shape variation
This section describes how to introduce shape parametrization in an ABAQUS input file.
References
· ``Parametric input,'' Section 1.4.1
· *PARAMETER SHAPE VARIATION
Overview
Shape parametrization can be accomplished by:
· parametrizing nodal coordinates; or
· relating nodal coordinates to shape parameters using shape variations.
The different approaches to shape parametrization are described in this section.
Parametrization of nodal coordinates
Any individual nodal coordinates can be parametrized directly. This is usually of limited value because
it often leads to designs with irregular shape that cannot be manufactured easily. In addition,
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parametrization of individual nodal coordinates generally requires an excessive number of parameters
to define the parametrized shape.
Parametrization of nodal coordinates used in conjunction with the node generation options in
ABAQUS provides a more practical method of shape parametrization. However, this method is still of
somewhat limited practical use because the simple node generation capabilities available in ABAQUS
cannot describe complex shapes.
Direct parametrization of individual nodal coordinates
The simplest form of parametrization of nodal coordinates is to define individual parameters and use
them in place of the nodal coordinates to be parametrized; for example,
*PARAMETER
x_coord_node_1 = 10.
y_coord_node_1 = 20.
*NODE
1, <x_coord_node_1>, <y_coord_node_1>
Parametrization of nodal coordinates using node generation
options
Shape parametrization can be accomplished by parametrizing the coordinates of some nodes, then
using these nodes to generate other nodes and their coordinates. For example:
*PARAMETER
x_coord_node_1 = 10.
x_coord_node_11 = 20.
*NODE
1, <x_coord_node_1>, 50.
11, <x_coord_node_11>, 50.
*NGEN
1, 11, 1
This method of shape parametrization reduces the number of user-defined parameters necessary for
shape parametrization by implicitly making the nodal coordinates of the generated nodes dependent on
the shape parameters.
Shape change by linear combination of shape variations
The definition of shape in ABAQUS includes a basic shape plus any number of additional shape
variations that are added to the basic shape using a linear combination. Mathematically, we can
express the nodal coordinates, x, as
x = x0 +
N
X
si pi ;
i=1
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where x0 is the basic shape, si is the ith shape variation, and pi is the value of the ith shape parameter.
This calculation is always done in the global rectangular Cartesian coordinate system. Although it is
not necessarily so, it is frequently the case that the data input to define a shape variation is simply the
gradient of the basic shape x0 taken with respect to the corresponding shape parameter.
The basic shape of a model is specified in the ABAQUS input file by providing nodal definitions using
a combination of the following options: *NODE, *NGEN, *NCOPY, *NFILL, and *NMAP.
The shape variations and associated shape parameters are specified using the *PARAMETER SHAPE
VARIATION option.
In addition, the *IMPERFECTION option provides the ability to specify perturbations of the shape as
a linear combination of other shapes (for example, buckling mode shapes).
The definition of the nodal coordinates for a model in the ABAQUS input file is then possible using a
combination of four types of options:
· The *NODE option must be used to define individual nodes and their respective coordinates; these
coordinates are part of the definition of the basic shape, x0 , and can be parametrized.
· The node generation options (*NGEN, *NCOPY, *NFILL, and *NMAP) can be used to create
nodes and their coordinates according to geometrically simple mappings that rely on existing
*NODE definitions; these generated coordinates are also part of the definition of the basic shape,
x0 . If necessary, the node generation options themselves can be parametrized.
· *PARAMETER SHAPE VARIATION options can be used to vary the coordinates of nodes
defined using the above options.
· The *IMPERFECTION option can be used to perturb nodal coordinates previously defined using
any combination of the above three types of options.
Shape parametrization using shape variations
Instead of parametrizing nodal coordinates directly, the user specifies shape variations by repeatedly
using the *PARAMETER SHAPE VARIATION option. Each shape variation must be associated with
a single shape parameter. This is accomplished by using PARAMETER=name. The names of the
parameters associated with the shape variations must be chosen such that the names remain unique
when interpreted in a case-insensitive manner. The values of the shape parameters are assigned using
the *PARAMETER option.
The *PARAMETER SHAPE VARIATION option can be used more than once for the same parameter
so that different parts of a shape variation can be specified separately. In these cases if the same node is
specified in multiple *PARAMETER SHAPE VARIATION options, the last definition for the node
prevails.
A node that is specified under a *PARAMETER SHAPE VARIATION option that has not also been
defined using the *NODE option or using the node generation options will be ignored.
The user can specify the shape variation using a combination of three possibilities: directly specifying
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them in the input file, reading them from an alternate input file, and reading them from the results files
of auxiliary analyses. These options are described in the following sections.
Defining shape variations directly in the input file or reading
them from an alternate input file
The shape variation data are specified as data lines of the *PARAMETER SHAPE VARIATION
option. Each data line gives the node number and corresponding variations of coordinate components.
The data lines can be given in an ASCII file that is specified by the INPUT parameter or, if no input
file is specified, as data that immediately follow the *PARAMETER SHAPE VARIATION option.
By default, the shape variation data are interpreted in the global rectangular Cartesian coordinate
system. The optional SYSTEM keyword parameter can be used to specify the shape variation data in
cylindrical or spherical coordinate systems. In such cases the computation of the shape variation is
done as follows. The nodal coordinate components that define the basic shape are first transformed
from the global rectangular Cartesian coordinate system in which they are stored to the specified
coordinate system. The shape variation coordinate components are then added to give updated
coordinate components, which are transformed back to the global rectangular Cartesian coordinate
system. Finally, the shape variation is taken as the difference between the updated coordinate
components and the original coordinate components, using the components expressed in the global
rectangular Cartesian coordinate system. The value of the shape parameter associated with the shape
variation is not used at any point in the calculation of the shape variation.
Usage: *PARAMETER SHAPE VARIATION, PARAMETER=name, INPUT=input file,
SYSTEM=name
Using auxiliary analyses to generate shape variations
Auxiliary models are additional finite element models that are used to generate shape variations for a
primary model. Rather than defining shape variations directly on a node-by-node basis, auxiliary
models can be used to simplify this process. Auxiliary analyses are finite element analyses of these
auxiliary models.
An auxiliary model usually has the same geometry, element connectivity, and material type as the
primary model. However, the boundary conditions are usually different. Applying loading to an
auxiliary model results in sets of displacements that we may interpret as shape variations. For example,
we may be interested in studying the sensitivity of the nonlinear buckling behavior of a structure with
respect to imperfections in the structure. In this case we could perform an auxiliary eigenvalue linear
buckling analysis and then use the resulting mode shapes as shape variations to be added to the basic
geometry of the primary model. (This particular problem could also be addressed by using the
*IMPERFECTION option.)
ABAQUS reads the shape variation data from auxiliary analyses through the user node labels.
ABAQUS does not check model compatibility between both analysis runs. Shape variation data cannot
be read from the results file for models defined in terms of an assembly of part instances ( ``Defining an
assembly,'' Section 2.5.1).
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Reading shape variations from a static analysis results file
To define a shape variation based on the deformed geometry of a previous static analysis, specify the
results file and step from a previous *STATIC analysis. The optional INC parameter defines the
increment number from which displacement data are read. (If this parameter is omitted, ABAQUS will
read data from the last increment available for the specified step on the results file.) The optional
NSET parameter can be used to read shape variation data for a specified node set.
Usage: *PARAMETER SHAPE VARIATION, PARAMETER=name, FILE=results file, STE
INC=inc, NSET=name
Reading shape variations from an eigenvalue analysis results file
To define a shape variation based on a mode shape from a previous eigenvalue analysis, specify the
results file and step from a previous *FREQUENCY or *BUCKLE analysis. The optional MODE
parameter defines the mode number from which eigenvector data are read. (If this parameter is omitted,
ABAQUS will read data from the first eigenvector available for the specified step on the results file.)
The optional NSET parameter can be used to read eigenmode data for the specified node set.
Usage: *PARAMETER SHAPE VARIATION, PARAMETER=name, FILE=results file, STE
MODE=mode, NSET=name
Visualization of shape variations
Shape variations can be visualized only after the parametrized input file has been processed by the
solver input file processor. Therefore, at least a datacheck run must be executed before parameter
shape variations can be visualized using ABAQUS/Viewer.
The shape variations associated with each individual shape parameter can be visualized as displaced
shape plots at step zero of the analysis. The basic shape is interpreted as the undeformed shape, and the
shape generated by adding the ith shape variation to the basic shape is interpreted as the ith displaced
shape.
The combination of all shape variations added to the basic shape represents the true undeformed shape
of the analysis.
2.1.3 Nodal thicknesses
The spatial variation of the thickness of a shell or membrane is defined using the *NODAL
THICKNESS option. The thickness values are assigned to the nodes that define the shell or membrane
elements.
References
· *NODAL THICKNESS
· *MEMBRANE SECTION
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· *SHELL GENERAL SECTION
· *SHELL SECTION
· ``Membrane elements,'' Section 14.1.1
· ``Using the *SHELL SECTION option to define the section behavior, '' Section 14.4.4
· ``Using the *SHELL GENERAL SECTION option to define the section behavior, '' Section 14.4.5
Overview
The *NODAL THICKNESS option is used to define continuously varying thicknesses for:
· shell structures; or
· membrane structures.
Defining nodal thicknesses
Use the *NODAL THICKNESS option to specify the thickness of a shell or membrane at a particular
node or node set.
Usage: *NODAL THICKNESS
node_number or node_set_name, thickness
Reading nodal thicknesses from an alternate input file
The data lines for the *NODAL THICKNESS option can be stored in a file other than the input file
and read from there at the start of the analysis. Use the INPUT parameter to identify the name of the
alternate input file containing the data lines defining the nodal thicknesses. For details on the syntax of
such file names, see ``Input syntax rules,'' Section 1.2.1. No data lines are needed in the input file when
the INPUT parameter is used.
Usage: *NODAL THICKNESS, INPUT=file_name
Generating continuously varying thicknesses between two nodes
or node sets
ABAQUS can linearly interpolate the thickness between two bounding nodes or node sets. The
thicknesses at the bounding nodes must be defined in a separate *NODAL THICKNESS option that
appears earlier in the input file. Use the GENERATE parameter to indicate that the nodal thickness
should be interpolated linearly from the thicknesses at the bounding nodes.
Usage: *NODAL THICKNESS, GENERATE
Specifying a continuously varying thickness for shell, membrane,
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and rigid elements
Specify that a shell or membrane element is going to have a continuously varying thickness rather than
a homogeneous thickness by using the NODAL THICKNESS parameter on the element property
option (*SHELL SECTION, *SHELL GENERAL SECTION, or *MEMBRANE SECTION). Specify
that a rigid element is going to have a continuously varying thickness by using the NODAL
THICKNESS parameter on the *RIGID BODY option. The usage of this parameter is described in the
sections referenced above.
Every node that is part of a shell, membrane, or rigid element using a continuously varying thickness
must have a thickness defined with the *NODAL THICKNESS option. ABAQUS will issue an error
message if there is a node with no nodal thickness in an element that is using a continuously varying
thickness.
Specifying a continuously varying thickness for a composite
shell
When a composite shell structure has a continuously varying thickness, the total thickness of the shell
at any node is defined by the value given on the *NODAL THICKNESS option. The total thickness at
an integration point is interpolated from the nodal thicknesses. The layer thicknesses given on the shell
section option are used as relative thicknesses and are scaled proportionally such that the sum of the
layer thicknesses equals the total thickness at the integration point.
For example, if a composite shell section were defined with the following input
*SHELL SECTION, COMPOSITE, NODAL THICKNESS, ELSET=name
1.5, 3, STEEL
2.5, 3, FOAM
1.0, 3, STEEL
and the total thickness at a point was only 1.0, the thicknesses of the individual layers at the point
would be 0.3 for the first steel layer, 0.5 for the foam layer, and 0.2 for the second steel layer.
Creating a discontinuity in the shell, membrane, or rigid element
thicknesses
The *NODAL THICKNESS option allows only a single thickness to be specified at each node.
Therefore, use separate nodes along the interface on shell, membrane, or rigid elements where there is
a discontinuity in the thickness and assign the appropriate thickness to each group of nodes. For
elements that are not part of a rigid body, multi-point constraints must be used to make the
displacements (and rotations, for shells) the same at corresponding nodes.
2.1.4 Transformed coordinate systems
Use the *TRANSFORM option to specify a local coordinate system at a node for input of boundary
conditions and concentrated loads.
References
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· *TRANSFORM
· ``Prescribed conditions: overview,'' Section 18.1.1
Overview
The *TRANSFORM option is used to define a local coordinate system for:
· the definition of concentrated forces and moments; and
· the definition of displacement and rotation boundary conditions.
The *TRANSFORM option cannot be used to specify a local coordinate system for defining:
· nodal coordinates--use the SYSTEM parameter on the *NODE option or the *SYSTEM option
(see ``Node definition,'' Section 2.1.1) instead; or
· material properties--use the *ORIENTATION option (see ``Orientations,'' Section 2.2.3) instead.
Defining a local coordinate system
Normally displacement and rotation components are associated with the global, rectangular Cartesian
axis system. When the *TRANSFORM option is associated with a node, all input data for concentrated
forces and moments and for displacement and rotation boundary conditions at the node are given in the
local system. The following transformations are available:
· Rectangular Cartesian
· Cylindrical
· Spherical
The coordinate transformation defined at a node must be consistent with the degrees of freedom that
exist at the node.
Use the NSET parameter on the *TRANSFORM option to identify the node set for which the local
transformed system is given.
Usage: *TRANSFORM, NSET=name
Defining a local coordinate system in a model that contains an
assembly of part instances
In a model defined in terms of an assembly of part instances, the *TRANSFORM option can be used to
define a local coordinate system at the part, part instance, or assembly level. A *TRANSFORM
defined at the part or part instance level will be rotated according to the positioning data given for each
instance of that part (or for the part instance). See ``Defining an assembly,'' Section 2.5.1. Multiple
*TRANSFORM definitions are not allowed at a node, even if one of them is at the part level and
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another is at the assembly level.
Defining displacement components
The transformed coordinate system is always a set of fixed Cartesian axes at a node (even for
cylindrical or spherical transforms). These transformed directions are fixed in space; the directions do
not rotate as the node moves. Therefore, in ABAQUS/Explicit the displacement components must
always be given with respect to these fixed directions in space.
Defining a rectangular Cartesian coordinate transformation
In a rectangular Cartesian transformation the transformed directions are parallel at all nodes of the set.
The coordinates of two points must be given, as shown in Figure 2.1.4-1.
Figure 2.1.4-1 Cartesian transformation option.
The first point, a, must be on a line through the global origin; this point defines the transformed
X 1 -direction. The second point, b, must be in the plane containing the global origin and the
transformed X 1 - and Y 1 -directions. This second point should be on or near the positive Y 1 -axis.
Set TYPE=R (default) on the *TRANSFORM option to define a rectangular Cartesian system.
Usage: *TRANSFORM, NSET=name, TYPE=R
Defining a cylindrical coordinate transformation
The radial, tangential, and axial directions must be defined based on the original coordinates of each
node in the node set for which the transformation is invoked. The global ( X; Y; Z ) coordinates of the
two points defining the axis of the cylindrical system (points a and b as shown in Figure 2.1.4-2) must
be given.
Figure 2.1.4-2 Cylindrical transformation option.
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The origin of the local coordinate system is at the node of interest. The local X 1 -axis is defined by a
line through the node, perpendicular to the line through points a and b. The local Z 1 -axis is defined by
a line that is parallel to the line through points a and b. The local Y 1 -axis forms a right-handed
coordinate system with X 1 and Z 1 .
Set TYPE=C on the *TRANSFORM option to define a cylindrical system.
Usage: *TRANSFORM, NSET=name, TYPE=C
Defining a spherical coordinate transformation
The radial, circumferential, and meridional directions must be defined based on the original
coordinates of each node in the node set for which the transformation is invoked. The global ( X; Y; Z )
coordinates of the center of the spherical system, a, and of a point on the polar axis, b, must be given
as shown in Figure 2.1.4-3.
Figure 2.1.4-3 Spherical transformation option.
The origin of the local coordinate system is at the node of interest. The local X 1 -axis is defined by a
line through the node and point a. The local Z 1 -axis lies in a plane containing the polar axis (the line
between points a and b) and is perpendicular to the local X 1 -axis. The local Y 1 -axis forms a
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right-handed coordinate system with X 1 and Z 1 .
Set TYPE=S on the *TRANSFORM option to define a spherical system.
Usage: *TRANSFORM, NSET=name, TYPE=S
2.2 Defining elements
2.2.1 Element definition
This section describes the methods for defining elements in ABAQUS.
References
· *ELCOPY
· *ELEMENT
· *ELGEN
· *ELSET
Overview
Element definition consists of:
· assigning an element number to the element;
· defining individual elements by specifying their nodes;
· grouping elements into element sets; and
· creating elements from existing elements by generating them incrementally or by copying existing
elements.
If any element is specified more than once, the last specification given is used.
Assigning an element number to the element
Each individual element must have a numeric label called the element number, which is assigned when
the element is defined. The element number must be a positive integer, and the maximum element
number allowed is 9999999 (for information on integer input, see ``Input syntax rules,'' Section 1.2.1).
The elements do not need to be numbered continuously.
An ABAQUS model can be defined in terms of an assembly of part instances (see ``Defining an
assembly,'' Section 2.5.1). In such a model almost all elements must belong to a part or part instance.
The only exceptions are connector, mass, rotary inertia, and capacitance elements, which can belong to
a part or to the assembly. Element numbers must be unique within a part, part instance, or the
assembly, but they can be repeated in different parts or part instances.
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Defining individual elements by specifying their nodes
Use the *ELEMENT option to define individual elements. Use the TYPE parameter to specify the
element type. The element must be chosen from one of the element types specified in Part V,
"Elements." Specify the element number and the nodes that define the element on the data lines.
Usage: *ELEMENT, TYPE=name
For example, the following lines create element number 11, which is of type C3D8R, by defining its
nodes (2, 3, 9, 7, 5, 8, 12, 16):
*ELEMENT, TYPE=C3D8R
11, 2, 3, 9, 7, 5, 8, 12, 16
Reading element definitions from a file
Element definitions can be read into ABAQUS from an alternate input file. The syntax of such file
names is described in ``Input syntax rules,'' Section 1.2.1. Use the INPUT parameter to specify the
name of the alternate input file.
Usage: *ELEMENT, INPUT=file_name
Grouping elements into element sets
Element sets are used as convenient cross-references for defining loads, properties, etc. Element sets
are the fundamental references of the model and should be used to assist the input definition. The
members of an element set can be individual elements or other element sets. An individual element can
belong to several element sets.
Elements can be grouped into element sets when they are created or after they have already been
defined. In either case each element set is assigned a name. Element set names can be up to 80
characters long.
The same name can be used for a node set and for an element set.
All elements within an element set will be arranged in ascending order of their element number, and
duplicates will be removed.
Once elements are assigned to an element set, additional elements can be added to the same element
set; however, elements cannot be removed from an element set.
Assigning elements to an element set as they are created
There are several ways that elements can be assigned to element sets as they are created.
Usage: Use any one of the following options:
*ELEMENT, ELSET=name
*ELGEN, ELSET=name
*ELCOPY, NEW SET=name
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Assigning previously defined elements to an element set
Use the *ELSET option to assign elements that have been defined previously (by using the
*ELEMENT, the *ELGEN, or the *ELCOPY options) to an element set by listing the elements
forming the set directly or generating the element set. In either case use the ELSET parameter to assign
these elements to an element set.
Listing the elements that form the set directly
List the elements that form the element set directly on the data lines of the *ELSET option. Element
sets, as well as individual elements, can be assigned to element sets.
Usage: *ELSET, ELSET=name
For example, the following lines add elements 3, 13, and 20 to set LEFT:
*ELSET, ELSET=LEFT
20
3, 13
The following lines add elements 5 and 16 to the existing set LEFT:
*ELSET, ELSET=LEFT
5, 16
** The above data line is equivalent to specifying 5, 16, LEFT
The following lines add elements 22, 14, and all elements in set LEFT to set B:
*ELSET, ELSET=B
22, 14, LEFT
Thus, element set B contains the following elements: 3, 5, 13, 14, 16, 20, and 22.
Generating the element set
To generate the element set, specify a first element, e1 ; a last element, e2 ; and the increment in element
numbers between these elements, i, on the data line of the *ELSET option. All elements going from e1
to e2 in steps of i will be added to the set. Therefore, i must be an integer such that (e2 ¡ e1 )=i is a
whole number (not a fraction). The default is i = 1.
Usage: *ELSET, ELSET=name, GENERATE
For example, the following lines add elements 1, 3, 5, ..., 19, 21 and elements 39, 49, 59, ..., 129, 139
to set UP:
*ELSET, ELSET=UP, GENERATE
1, 21, 2
39, 139, 10
Defining part and assembly sets
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In a model defined in terms of an assembly of part instances, all element sets must be defined within a
part, part instance, or the assembly definition. If an element set is defined within a part (or part
instance), refer to the element numbers directly:
*PART, NAME=PartA
...
*ELSET, ELSET=set1
1,3,26,500
*END PART
Element set set1 belongs to part PartA and will be inherited by every instance of PartA.
To define an assembly-level element set, identify the nodes to be added to the set by prefixing each
node number with the part instance name and a "." (as explained in ``Defining an assembly,'' Section
2.5.1):
*ASSEMBLY, NAME=Assembly-1
*INSTANCE, NAME=PartA-1, PART=PartA
...
*END INSTANCE
*INSTANCE, NAME=PartA-2, PART=PartA
...
*END INSTANCE
*ELSET, ELSET=set1
PartA-1.1, PartA-1.3, PartA-1.26, PartA-1.500
PartA-2.1, PartA-2.3, PartA-2.26, PartA-2.500
*END ASSEMBLY
An assembly-level element set can have the same name as a part-level element set. In this example
assembly-level element set set1 contains all the elements from element sets set1 belonging to part
instances PartA-1 and PartA-2. Therefore, the elements are assigned to two separate element sets:
one at the part instance level and one at the assembly level. An assembly-level element set called
set1 could be created with entirely different elements than those that belong to the part set; part- and
assembly-level element sets are independent. However, since in this example the same elements are
assigned to both the part- and assembly-level element sets set1, the assembly-level set could
alternatively be defined by:
*ASSEMBLY, NAME=Assembly-1
*INSTANCE, NAME=PartA-1, PART=PartA
...
*END INSTANCE
*INSTANCE, NAME=PartA-2, PART=PartA
...
*END INSTANCE
*ELSET, ELSET=set1
PartA-1.set1, PartA-2.set1
*END ASSEMBLY
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This element set definition is equivalent to the first example, where the elements were listed
individually.
Sometimes it is not convenient to define an assembly-level element set by referring to part-level
element sets. In such cases a set definition containing many elements can get quite lengthy. Therefore,
the INSTANCE parameter is provided on the *ELSET option as an alternative. The following example
shows two equivalent ways to define an assembly-level element set; once by prefixing each element
number with a part instance name (as shown above) and once using the more compact INSTANCE
notation:
*ASSEMBLY, NAME=Assembly-1
*INSTANCE, NAME=PartA-1, PART=PartA
...
*END INSTANCE
*INSTANCE, NAME=PartA-2, PART=PartA
...
*END INSTANCE
*ELSET, ELSET=set2
PartA-1.101, PartA-1.102, PartA-1.103, PartA-1.104,
PartA-2.201, PartA-2.202, PartA-2.203, PartA-2.204
*ELSET, ELSET=set3, INSTANCE=PartA-1
101, 102, 103, 104
*ELSET, ELSET=set3, INSTANCE=PartA-2
201, 202, 203, 204
*END ASSEMBLY
When the *ELSET option is used more than once with the same name, as it is with set3, the elements
in the second use of *ELSET are appended to the set created by the first use of *ELSET.
Usage: *ELSET, ELSET=ElsetName, INSTANCE=InstanceName
Internal element sets created by ABAQUS/CAE
In ABAQUS/CAE many modeling operations are performed by picking geometry with the mouse. For
example, a surface can be created by picking a face on a geometric part instance. Since the
*SURFACE option refers to an element set, this "picked" geometry must be translated into an element
set in the input file. Such sets are assigned a name by ABAQUS/CAE, and the set is marked with the
INTERNAL parameter on the *ELSET option. These and other internal sets created by ABAQUS/CAE
will not appear in ABAQUS/Viewer.
Usage: *ELSET, ELSET=ElsetName, INTERNAL
Transferring of element sets
If the results of an ABAQUS/Explicit analysis are imported into an ABAQUS/Standard analysis (or
vice versa) with the *IMPORT option, all element sets in the original analysis are imported by default.
Selected element sets can be imported with the *IMPORT ELSET option. See ``Transferring results
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between ABAQUS/Explicit and ABAQUS/Standard,'' Section 7.3.1, for details.
Creating elements from existing elements by generating them
incrementally
Use the *ELGEN option to generate elements incrementally from existing elements. The newly created
elements are always the same element type as that of the master element.
The *ELGEN option first generates a row of elements by copying the node pattern of a given element
with prescribed increments in the node and element numbers. This row can then be repeated to form a
layer, which can also be repeated to form a block.
To generate a row of elements, specify the following on the data line of the *ELGEN option:
· The master element number. The master element must exist at the time that this option is
encountered, although it can be an element that has just been defined by a previous data line in this
same *ELGEN option.
· The number of elements to be defined in the first row generated, including the master element.
· The increment in node numbers of corresponding nodes from element to element in the row. The
default is 1. All element node numbers (except special-purpose nodes, discussed later) will
increase by the same value.
· The increment in element numbers in the row. The default is 1.
To copy this newly created master row to create a layer of elements, specify the following additional
information:
· The number of rows to be defined, including the master row.
· The increment in node numbers of corresponding nodes from row to row.
· The increment in element numbers of corresponding elements from row to row.
To copy this newly created master layer to create a block of elements, specify the following additional
information:
· The number of layers to be defined, including the master layer.
· The increment in node numbers of corresponding nodes from layer to layer.
· The increment in element numbers of corresponding elements from layer to layer.
Usage: *ELGEN
For example, the elements forming the quarter cylinder shown in Figure 2.2.1-1 can be generated by
the following lines:
*ELGEN
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1, 3, 1, 1, 5, 10, 10, 6, 100, 100
Figure 2.2.1-1 *ELGEN example.
Incrementing special-purpose nodes
By default, the nodes used to define the direction of the first cross-section axis for beams in space are
not incremented. To increment these nodes, include the ALL NODES parameter on the *ELGEN
option. The increment between node numbers is defined by the user as described above.
Usage: *ELGEN, ALL NODES
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Creating elements by copying existing elements
Use the *ELCOPY option to create new elements by copying existing elements. Use the OLD SET
parameter to identify the existing element set. Use the NEW SET parameter to assign the newly created
elements to an element set. If the NEW SET parameter is omitted, the newly created elements are not
assigned to an element set.
Use the SHIFT NODES parameter to specify an integer constant that will be added to the node
numbers of the existing elements to define the node numbers of the new elements. Likewise, use the
ELEMENT SHIFT parameter to specify an integer constant that will be added to the element numbers
of existing elements to define element numbers for the elements being created.
Usage: *ELCOPY, OLD SET=name, NEW SET=new_name, SHIFT NODES=number,
ELEMENT SHIFT=number
For example, the following data lines will generate new elements in set B that are copies of all
elements in set A at the time this option is processed, with 1000 added to each element number and to
each node number in the definitions of the new elements. The members of set A at the time the line is
processed are those elements defined to be in set A by all element generation and element set definition
lines that appear in the input file prior to this *ELCOPY option.
*ELCOPY, OLD SET=A, NEW SET=B, ELEMENT SHIFT=1000,
SHIFT NODES=1000
Special considerations for continuum elements
Use the REFLECT parameter to avoid creating continuum elements that violate the ABAQUS
convention for counterclockwise element numbering. The REFLECT parameter is normally required
when the nodes have been generated using the *NCOPY option (``Node definition,'' Section 2.1.1).
Usage: *ELCOPY, REFLECT
For example, assume element 1 is in element set A and is defined by nodes 1, 2, 3, 4. The following
data line will generate element number 11, also in set A, with nodes 11, 14, 13, and 12.
*ELCOPY, OLD SET=A, NEW SET=A, ELEMENT SHIFT=10, SHIFT NODES=10,
REFLECT
If the REFLECT parameter is not used, the new element will be defined by the node sequence 11, 12,
13, 14 and will violate the counterclockwise element numbering convention used with continuum
elements (see Figure 2.2.1-2).
Figure 2.2.1-2 *ELCOPY, REFLECT example.
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2.2.2 Reinforcing in elements
Reinforcing in elements is defined by using the *REBAR option. Examples include the definition of
steel reinforcing bars in concrete and the reinforcing belts in tires.
Reference
· *REBAR
Overview
Rebars:
· are used to define uniaxial reinforcement in solid, membrane, and shell elements;
· have material properties that are distinct from those of the underlying element;
· can be defined as individual reinforcing bars in solid elements;
· can be defined as layers of uniformly spaced reinforcing bars in shell, membrane, and solid
elements (such layers are treated as a smeared layer with a constant thickness equal to the area of
each reinforcing bar divided by the reinforcing bar spacing);
· can be used with coupled temperature-displacement elements but do not contribute to the
material's thermal conductivity and specific heat; and
· cannot be used with triangular shell and membrane elements or with triangular, triangular prism,
and tetrahedral solid elements.
Defining the rebar material
The material properties of the rebars are distinct from those of the underlying element and are defined
by using a *MATERIAL data block (``Material data definition,'' Section 8.1.2). Use the MATERIAL
parameter to associate these material properties with the rebars.
Usage: *REBAR, ELEMENT=CONTINUUM, MATERIAL=mat
The following material options cannot be used to define rebar materials:
· *BRITTLE CRACKING (``Cracking model for concrete,'' Section 10.4.1);
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· *CAP PLASTICITY (``Modified Drucker-Prager/Cap model,'' Section 10.3.2);
· *DRUCKER PRAGER (``Extended Drucker-Prager model,'' Section 10.3.1);
· *ELASTIC, TYPE=ANISOTROPIC (``Linear elastic behavior,'' Section 9.2.1);
· *ELASTIC, TYPE=ORTHOTROPIC (``Linear elastic behavior,'' Section 9.2.1);
· *EOS (``Equation of state,'' Section 9.5.1);
· *FOAM (``Crushable foam plasticity model,'' Section 10.3.3);
· *POROUS METAL PLASTICITY (``Porous metal plasticity,'' Section 10.2.6); or
· *POTENTIAL (``Anisotropic yield,'' Section 10.2.3).
Assigning a name to the rebar set
Use the NAME parameter to assign a name to the rebar set. This name can be used in defining rebar
prestress and output requests.
Usage: *REBAR, ELEMENT=elem, MATERIAL=mat, NAME=name
Defining rebars in three-dimensional shell and membrane
elements
Both isoparametric and skew rebars can be defined in three-dimensional shell and membrane elements.
Rebars cannot be used with triangular shells or membranes.
If triangular-shaped shells or membranes are needed, collapsed quadrilateral shells or membranes can
be used. The resulting rebar directions will depend on the type of rebar ( ISOPARAMETRIC or SKEW)
used. The rebar must be defined carefully since the element is distorted. This technique should be used
only in regions of the mesh where results are not critical and stress gradients are not high.
Defining isoparametric rebars in three-dimensional shell and
membrane elements
Isoparametric rebars are aligned along the mapping of constant isoparametric lines in the element (see
Figure 2.2.2-1).
Figure 2.2.2-1 "Isoparametric" rebar in an undistorted three-dimensional shell or membrane element.
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The spacing of the rebar will be fixed in physical space. The spacing, s, and the area of the rebar, A,
are used to determine the thickness of the equivalent smeared layer, t = A=s. If the edges of the
element containing the rebar are not parallel, the number of actual rebar with this spacing passing
through one edge will be different than the number passing through the opposite edge (opposite in
isoparametric space).
Set the parameters ELEMENT=SHELL and GEOMETRY=ISOPARAMETRIC to define isoparametric
rebars in three-dimensional shell elements. Set the parameter ELEMENT=MEMBRANE and the
parameter GEOMETRY=ISOPARAMETRIC to define isoparametric rebars in membrane elements.
On the data line of the *REBAR option, specify the elements that contain the rebars; the
cross-sectional area, A, of each rebar; the rebar spacing in the plane of the shell, s; and the edge
number to which the rebars are parallel when plotted in isoparametric space (see Figure 2.2.2-1). In
addition, for shell elements specify the position of the rebars in the shell thickness direction measured
from the midsurface of the shell (positive in the direction of the positive normal to the shell). If the
NODAL THICKNESS parameter is included on the *SHELL SECTION option of the underlying
element, this distance will be scaled by the ratio of the thickness defined by the *NODAL
THICKNESS option to the thickness defined by the *SHELL SECTION option.
Usage: Use either of the following options:
*REBAR, ELEMENT=SHELL, MATERIAL=mat, GEOMETRY=ISOPARAMETRIC
*REBAR, ELEMENT=MEMBRANE, MATERIAL=mat,
GEOMETRY=ISOPARAMETRIC
Defining skew rebars in three-dimensional shell and membrane
elements
Skew rebars need not be similar to an element edge; they can lie at any prescribed angle from the local
1-axis. The direction of the rebars must be defined in one of two ways, as indicated in Figure 2.2.2-2:
1. The rebars can be defined relative to the default projected local coordinate system (see
``Conventions,'' Section 1.2.2).
2. The rebars can be defined relative to a local coordinate system defined by the *ORIENTATION
option (see ``Orientations,'' Section 2.2.3).
If the rebar cross-sectional area is A, the rebar spacing, s, should be given so that the thickness of the
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equivalent "smeared" layer of reinforcing is t = A=s.
Figure 2.2.2-2 "Skew" rebar in a three-dimensional shell or membrane.
Defining skew rebars relative to the default projected local
coordinate system
To define skew rebars relative to the default projected local coordinate system, include the
GEOMETRY=SKEW parameter on the *REBAR option (but omit the ORIENTATION parameter).
See ``Conventions,'' Section 1.2.2, for a definition of the default projected local directions on a surface
in space. On the data line of the *REBAR option, specify the elements that contain the rebars; the
cross-sectional area, A, of each rebar; the rebar spacing in the plane of the shell, s; the position of the
rebars in the thickness direction (for shell elements only), measured from the midsurface of the shell
(positive in the direction of the positive normal to the shell); and the angle ®, in degrees, between the
default local 1-direction and the rebars. If the NODAL THICKNESS parameter is included on the
*SHELL SECTION option for the underlying element, the rebar position in the thickness direction will
be scaled by the ratio of the thickness defined by the *NODAL THICKNESS option to the thickness
defined by the *SHELL SECTION option. A positive angle ® defines a rotation from local direction 1
to local direction 2 around the element's normal direction. For example, in a membrane the following
input would result in the rebar definition shown in Figure 2.2.2-3:
*REBAR, ELEMENT=MEMBRANE, MATERIAL=MAT1, NAME=REBARA,
GEOMETRY=SKEW
ELSET1, 0.05, 0.1, 45.
Figure 2.2.2-3 Skew rebar defined relative to default local coordinate directions.
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When the ORIENTATION parameter is not used and the normal to the shell is nearly perpendicular to
the global 1-axis, the local 1-axis may change significantly within an element or from one element to
the next (see ``Conventions,'' Section 1.2.2).
Usage: Use either of the following options:
*REBAR, ELEMENT=SHELL, MATERIAL=mat, GEOMETRY=SKEW
*REBAR, ELEMENT=MEMBRANE, MATERIAL=mat, GEOMETRY=SKEW
Defining skew rebars relative to a local coordinate system
defined by *ORIENTATION
To define skew rebars relative to a local coordinate system defined by the *ORIENTATION option,
include the GEOMETRY=SKEW parameter on the *REBAR option and set the ORIENTATION
parameter equal to the orientation name. See ``Orientations,'' Section 2.2.3, for a description of how
the local coordinate system is calculated from the *ORIENTATION-defined directions for definition
of rebar in shells and membranes.
On the data line of the *REBAR option, specify the elements that contain the rebars; the
cross-sectional area, A, of each rebar; the rebar spacing in the plane, s; the position of the rebars in the
thickness direction (for shell elements only), measured from the midsurface of the shell (positive in the
direction of the positive normal to the shell); and the angle, ®, in degrees, between the
*ORIENTATION-defined 1-direction and the rebars. A positive angle ® defines a rotation from local
direction 1 to local direction 2 around the *ORIENTATION-defined normal direction. For example, in
a shell the following input would result in the skew rebar definition shown in Figure 2.2.2-4:
*REBAR, ELEMENT=SHELL, MATERIAL=MAT1, NAME=REBARB,
GEOMETRY=SKEW, ORIENTATION=ORIENT
ELSET1, 0.01, 0.1, 0.0, 30.
*ORIENTATION, SYSTEM=RECTANGULAR, NAME=ORIENT
-0.7071, 0.7071, 0.0, -0.7071, -0.7071, 0.0
3, 0.0
Usage: Use either of the following options:
*REBAR, ELEMENT=SHELL, MATERIAL=mat, GEOMETRY=SKEW,
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ORIENTATION=name
*REBAR, ELEMENT=MEMBRANE, MATERIAL=mat, GEOMETRY=SKEW,
ORIENTATION=name
Figure 2.2.2-4 Skew rebar defined relative to *ORIENTATION-defined local coordinate directions.
Defining rebars in axisymmetric shell elements
Rebars in an axisymmetric shell can lie in the shell reference surface or can be offset from the
midsurface. Rebars in axisymmetric shells can be defined to have any orientation with respect to the
r-z plane. See Figure 2.2.2-5 for an example of circumferential rebars and Figure 2.2.2-6 for an
example of radial rebars in axisymmetric shells.
Figure 2.2.2-5 Example of circumferential rebars in axisymmetric shell elements.
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Figure 2.2.2-6 Example of radial rebars in axisymmetric shell elements.
On the data lines of the *REBAR option specify the cross-sectional area, A, of each rebar; the rebar
spacing, s; the position of the rebars in the shell thickness direction, measured from the midsurface of
the shell (positive in the direction of the positive normal to the shell); the angular orientation with
respect to the r-z plane, ®, measured in degrees; and the radial position at which the rebar spacing is
measured. The angular orientation is measured positive about the positive normal to the shell. If the
NODAL THICKNESS parameter is included on the *SHELL SECTION option for the underlying
element, the distance from the midsurface will be scaled by the ratio of the thickness defined by the
*NODAL THICKNESS option to the thickness defined by the *SHELL SECTION option.
If an orientation angle other than 0 or 90° is specified for rebar in an axisymmetric shell, ABAQUS
assumes that the rebars are balanced (i.e., half of the rebar lie at the specified angle ® and the other
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half at an angle of ¡®) and internal calculations are handled accordingly. See ``Rebar modeling in two
dimensions,'' Section 3.7.1 of the ABAQUS Theory Manual, for details.
If the radial position for the rebar spacing is given, the total cross-sectional area of rebar will remain
constant as the radial position changes; this behavior corresponds to the number of rebar in the
circumferential direction remaining constant and implies that the thickness of the smeared layer of
rebar decreases and that the spacing of the rebars increases as r increases (see Figure 2.2.2-6). If the
radial position for the rebar spacing is omitted (or is set to zero), ABAQUS assumes that the spacing of
the rebar remains constant; the thickness of the corresponding smeared layer is held fixed such that
t = A=s.
Usage: *REBAR, ELEMENT=AXISHELL, MATERIAL=mat
Defining rebars in continuum elements
Two- or three-dimensional continuum (solid) elements can contain rebars; rebars cannot be defined in
triangular, prism, tetrahedral, or infinite elements. If triangular or wedge-shaped elements are needed,
collapsed quadrilateral or brick elements can be used. Be careful when collapsing elements that
contain rebar. It is important to check that the location and orientation of the rebar are correct.
Rebars are defined as single bars or in layers. In the latter case the layer is a surface in each element;
the rebar orientation in the surface is given by the user.
Defining layers of rebars in planar and axisymmetric continuum
elements
The rebars form a layer that lies in a surface that is at right angles to the plane of the model if the
SINGLE parameter is omitted. The line where this rebar surface intersects the plane of the model is
defined by specifying the value of the GEOMETRY parameter and providing the appropriate data.
The orientation of the rebars within the rebar surface is defined by giving an angle, in degrees, between
the line of intersection in the plane of the model and the rebars. This angle is measured in physical
three-dimensional space, not in isoparametric space. See ``Rebar modeling in two dimensions,'' Section
3.7.1 of the ABAQUS Theory Manual, for details. The positive direction along the line of intersection
is from the lower to the higher numbered element edge that is intersected, and a positive angle
indicates rebars oriented down into the plane of the model (where the plane is parallel to the z-axis in
plane strain analysis or the µ-axis for axisymmetric analysis), as shown in Figure 2.2.2-7.
Figure 2.2.2-7 Orientation of rebars in plane and axisymmetric solid elements.
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If an orientation angle other than 0 or 90° is specified for rebar in an axisymmetric element, it is
assumed that the rebar in the element are balanced (i.e., half of the rebar lie at the specified angle ®
and the other half at the angle ¡®).
Defining isoparametric rebars
Set the GEOMETRY parameter on the *REBAR option equal to ISOPARAMETRIC to define
isoparametric rebars. The intersection of the rebar layer with the plane of the model will lie along the
mapping of a constant isoparametric line in the element.
On the data line of the *REBAR option, specify the elements that contain the rebars; the
cross-sectional area, A, of each rebar; the rebar spacing, s; the rebar orientation, ® (as described
above); the fractional distance from the edge, f (the ratio of the distance between the edge and the
rebar to the distance across the element); and the edge number from which the rebars are defined. In
addition, for axisymmetric elements specify the radial position at which the rebar spacing is measured.
If the radial position for the rebar spacing is given for rebar in axisymmetric elements, the total
cross-sectional area of rebar will remain constant as the radial position changes; this behavior
corresponds to the number of rebar remaining constant as r increases; that is, the thickness of the
smeared layer of rebar decreases as r increases. If the radial position for the rebar spacing is omitted
(or is set to zero), ABAQUS assumes that the spacing of the rebar remains constant; the thickness of
the corresponding smeared layer is held fixed such that t = A=s.
Usage: *REBAR, ELEMENT=CONTINUUM, MATERIAL=mat,
GEOMETRY=ISOPARAMETRIC
Figure 2.2.2-8 shows an example of rebar defined with GEOMETRY=ISOPARAMETRIC.
Figure 2.2.2-8 Rebar layer definition in solid elements with GEOMETRY=ISOPARAMETRIC.
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In the isoparametric mapping of the element, the line of rebars is parallel to one of the edges of the
element. In this figure the line for rebar layer A can be defined using edges 1 or 3 and rebar layer B
can be defined by edges 2 or 4. The fractional distance from edge 1 for rebar layer A is the ratio
f1 = LA2 =L2 = LA4 =L4 ; alternatively, layer A can be defined from edge 3, so that
f3 = 1: ¡ LA2 =L2 = 1: ¡ LA4 =L4 .
Defining skew rebars
Set the GEOMETRY parameter on the *REBAR option equal to SKEW to define skew rebars. The
intersection of the rebar layer with the plane of the model can intersect any two edges of an element.
On the first data line of the *REBAR option, specify the elements that contain the rebars; the
cross-sectional area, A, of each rebar; the rebar spacing, s; and the rebar orientation, ® (as described
above). In addition, for axisymmetric elements specify the radial position at which the rebar spacing is
measured. On the second data line of the *REBAR option, specify the fractional distance along the
element edge, from the first node of the edge (as listed in Figure 2.2.2-9) to where the rebar layer
intersects the edge, for all edges. Only the two values corresponding to the two edges that the rebar
intersects can be nonzero.
Figure 2.2.2-9 Rebar layer definition in solid elements with GEOMETRY=SKEW.
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Defining skew rebars in continuum elements can increase the run time for an analysis significantly.
The element's stable time increment will, in most cases, be determined by the stable time increment of
the rebar, which is proportional to the rebar length. If a skew rebar in a continuum element is defined
such that it intersects two adjacent element edges, the resulting rebar length could be considerably less
than the average element edge length, thus, resulting in a very small element stable time increment.
Usage: *REBAR, ELEMENT=CONTINUUM, MATERIAL=mat, GEOMETRY=SKEW
Figure 2.2.2-9 shows an example of rebar defined with GEOMETRY=SKEW. In the isoparametric
mapping of the element, the line of rebars intersects two of the element edges. The intersection points
are located by defining a fractional distance along each intersected edge. In this figure rebar layer A is
defined by the ratio f1 = LA1 =L1 along edge 1 and the ratio f2 = LA2 =L2 along edge 2. Rebar layer
B is defined by the ratio f3 = LB3 =L3 along edge 3 and the ratio f4 = LB4 =L4 along edge 4.
Defining single rebars in axisymmetric continuum elements
Use the SINGLE parameter on the *REBAR option to define single rebars in axisymmetric continuum
elements. In this case the rebar is assumed to be at right angles to the plane of the model (the hoop
direction).
The intersection of the rebar with the plane of the model is defined by the fractional distances along
edges 1 and 2 of the intersections of constant isoparametric lines that pass through the rebar location
(see Figure 2.2.2-10). The fractional distances are measured from the first edge node listed in Figure
2.2.2-10.
Figure 2.2.2-10 SINGLE rebar in a solid element.
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On the data line of the *REBAR option, specify the elements that contain the rebars; the
cross-sectional area, A, of each rebar; and the fractional distances locating the rebar's position in the
element, f1 and f2 .
Usage: *REBAR, ELEMENT=CONTINUUM, MATERIAL=mat, SINGLE
Defining layers of rebars in three-dimensional continuum
elements
If the SINGLE parameter is omitted from the *REBAR option, the rebars in three-dimensional
continuum elements are defined as layers lying in surfaces. The surfaces are most easily defined with
respect to the isoparametric mapped cube of the element. Therefore, the user must consider how the
rebar will be defined before generating the mesh; if the rebar surfaces are not taken into account in
designing the mesh, the rebar input can be very inefficient.
In the isoparametric mapped cube the rebar surface always has two edges (opposite to one another) that
are parallel to an isoparametric direction. The isoparametric directions are defined in Figure 2.2.2-11.
The user provides this isoparametric direction (1, 2, or 3) as input.
Figure 2.2.2-11 Isoparametric direction and edge definitions for three-dimensional elements.
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A particular face of the element, which is perpendicular to this isoparametric direction in the
isoparametric mapped cube, is used to define the position of the other two edges of the surface; the
faces are defined in Figure 2.2.2-11, where the edges of the faces are also defined.
If the rebars are defined with the GEOMETRY=ISOPARAMETRIC parameter, the two edges of the
rebar surface that are not parallel to the isoparametric direction given by the user will be parallel to one
of the other two isoparametric directions; in the isoparametric-mapped cube one isoparametric
coordinate is constant on the rebar surface. Figure 2.2.2-13 illustrates this concept with an element
containing two layers of isoparametric rebars. The position of each surface is given by the fractional
distance f from an edge of the face defined in Figure 2.2.2-11 for the isoparametric direction chosen;
the user must input the edge from which the fractional distance is measured.
If the rebars are defined with the GEOMETRY=SKEW parameter, the two edges of the rebar surface,
which are not parallel to the isoparametric direction given by the user, are generally not parallel to one
of the other isoparametric directions. The positions of these two edges of the rebar surface are
specified by the intersection of the rebar surface with edges of the intersecting face, defined in Figure
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2.2.2-11, for the isoparametric direction chosen; the intersections are given by the fractional distance f
along each edge of the face. (Note that the fractional distance is along the edge for
GEOMETRY=SKEW; for GEOMETRY=ISOPARAMETRIC the fractional distances are measured
from an edge.) The fractional distance along an edge is measured from the first node of the edge. All
four fractional distances must be given, but only two can be nonzero.
The orientation angle, ®, of the rebars within the rebar layer is defined in the isoparametric-mapped
cube; it is measured in degrees and is the angle between the line of intersection of the rebar surface
with the face for the isoparametric direction chosen and the rebar. The positive direction of the line of
intersection is from the lower numbered edge to the higher numbered edge; the positive direction for
the rebars points into the elements. An example is shown in Figure 2.2.2-12.
Figure 2.2.2-12 Orientation example for three-dimensional rebar modeling: defined by
GEOMETRY=SKEW, isoparametric direction 2. Shown in the mapped isoparametric element.
The orientation angle is defined in the rebar layer in the isoparametric-mapped cube; therefore, the
definition is the same for GEOMETRY=ISOPARAMETRIC and GEOMETRY=SKEW.
If the rebar layer is not flat in physical space, the orientation angle at each integration point may be
different. Since it is possible to define only one orientation angle per element, an average value
orientation angle for the element must be used; for reasonable meshes this approximation should not
affect the results significantly.
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Defining isoparametric rebars
On the data line of the *REBAR option, specify the elements that contain the rebars; the
cross-sectional area, A, of each rebar; the rebar spacing, s; the rebar orientation, ® (as described
above); the fractional distance, f , from the edge; the number of the edge from which the fractional
distance is measured; and the isoparametric direction of the rebar surface.
Usage: *REBAR, ELEMENT=CONTINUUM, MATERIAL=mat,
GEOMETRY=ISOPARAMETRIC
For example, the following input defines the isoparametric rebar shown in Figure 2.2.2-13:
Figure 2.2.2-13 Element with two layers of isoparametric rebar.
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*HEADING
ISOPARAMETRIC REBAR
*NODE
1, 0., 0.
2, 10., 0.
3, 10., 5.
4, 0., 5.
5, 0., 0., 7.5
6, 10., 0., 12.5
7, 10., 5., 12.5
8, 0., 5., 7.5
*ELEMENT, TYPE=C3D8R, ELSET=ONE
1,1,2,3,4,5,6,7,8
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*REBAR, ELEMENT=CONTINUUM, MATERIAL=STEEL,
GEOMETRY=ISOPARAMETRIC, NAME=LAYER_A
ONE,.04,2.5,49.32628,0.25,4,2
*REBAR, ELEMENT=CONTINUUM, MATERIAL=STEEL,
GEOMETRY=ISOPARAMETRIC, NAME=LAYER_B
ONE,.04,1.,63.43494,0.5,3,2
*MATERIAL, NAME=STEEL
*ELASTIC
30.E6,
...
Rebar layers A and B are defined using isoparametric direction 2. From Figure 2.2.2-11 the position of
the layers must be given with respect to the face with nodes 1-5-6-2.
The fractional distance defining the position of intersection of layer A with this face can be measured
from edge 4 (edge with nodes 2-1) along edge 3 (edge with nodes 6-2), as shown in Figure 2.2.2-13.
For layer A, f4 = :25 . It could also be given from edge 2 (edge with nodes 5-6), so that
f2 = 1:0 ¡ f4 = :75 .
The orientation of rebar for layer A in physical space is defined by an angle, ¯, equal to 30° for layer
A. This angle must be transformed into the corresponding angle in the isoparametric-mapped cube.
This transformation can be done as follows: consider a single rebar that intersects the intersecting line
(described above) and an adjacent edge (see Figure 2.2.2-14).
Figure 2.2.2-14 Example defining isoparametric rebar.
From the figure tan ¯ = X=S. The length of the rebar layer along the intersecting line is L, and the
length of the opposite edge is W . Consider the same rebar in the rebar layer in the
isoparametric-mapped cube. The orientation angle, ®, is given by tan ® = x=s, where x = 2X=W and
s = 2S=L. (The 2 is included because the isoparametric-mapped cube is a 2 £ 2 £ 2 cube.) This
expression can be simplified to give
tan ® =
X L
L
=
tan ¯:
W S
W
For layer A, L = 10:0778 , W = 5:, ¯ = 30± , and ® = 49:33± , where ® is the orientation angle that
must be input.
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The fractional distance defining the position of the intersection of layer B with this face can be
measured from edge 3 (edge with nodes 6-2); f3 = :5. It could also be measured from edge 1 (edge
with nodes 1-5), such that f1 = 1:0 ¡ f3 . The orientation angle for layer B in the rebar layer is 45± . In
the isoparametric-mapped cube L = 10:, W = 5:, ¯ = 45± , and ® = 63:43± .
Since a rebar layer using GEOMETRY=ISOPARAMETRIC always lies in two of the isoparametric
directions, an alternative but equivalent definition can be given. For example, layer A also lies in
isoparametric direction 1, with the intersecting face having nodes 1-4-8-5. The fractional distance for
layer A, measured from edge 1 (edge with nodes 1-4), is f1 = :25 . The positive sense of the line of
intersection is from edge 2 (edge with nodes 4-8) to edge 4 (edge with nodes 5-1); therefore, ¯ = 120± ,
L = 5:, W = 10:077 , and ® = 139:32± .
Layer B also lies in isoparametric direction 3, with the intersecting face having nodes 1-2-3-4. The
fractional distance for layer B, measured from edge 2 (edge with nodes 2-3), is f2 = :5. The positive
sense of the intersecting line is from edge 1 (edge with nodes 1-2) to edge 3 (edge with nodes 3-4);
therefore, the orientation angle of the rebar in physical space is ¯ = 135± , L = 5:, W = 10:, and in the
isoparametric-mapped cube ® = 153:43± .
Defining skew rebars
On the first data line of the *REBAR option, specify the elements that contain the rebars; the
cross-sectional area, A, of each rebar; the rebar spacing, s; the rebar orientation, ® (as described
above); and the isoparametric direction. On the second data line of the *REBAR option, specify the
fractional distance f along the element edge for each edge of the intersecting face defined in Figure
2.2.2-11. Only the values corresponding to the two edges that the rebar intersects can be nonzero.
Usage: *REBAR, ELEMENT=CONTINUUM, MATERIAL=mat, GEOMETRY=SKEW
For example, the following input defines the skew rebar shown in Figure 2.2.2-15:
Figure 2.2.2-15 Example defining skew rebar.
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*HEADING
*NODE
1, 0., 0.
2, 10., 0.
3, 10., 5.
4, 0., 5.
5, 0., 0., 7.5
6, 10., 0., 12.5
7, 10., 5., 12.5
8, 0., 5., 7.5
*ELEMENT, TYPE=C3D8R, ELSET=ONE
1,1,2,3,4,5,6,7,8
*REBAR, ELEMENT=CONTINUUM, MATERIAL=STEEL, GEOMETRY=SKEW,
NAME=LAYER_A
ONE, .04, 2.5, 55.28, , 2
.2, 0., .4, .0
*MATERIAL, NAME=STEEL
*ELASTIC
30.E6,
...
The rebar layer is defined using isoparametric direction 2. The intersecting face is defined in Figure
2.2.2-11 and has nodes 1-5-6-2. The position of the rebar layer is given by its intersection with the
edges of this face; the fractional distances, f1 and f3 , are shown in Figure 2.2.2-15. The orientation
angle ¯ of the rebar in physical space is 30°. Following the same procedure for calculating ® as was
described for isoparametric rebar, L = 12:5 , W = 5:, and the orientation angle in the
isoparametric-mapped cube ® is 55.28°.
Defining single rebars in three-dimensional continuum elements
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If the SINGLE parameter is used, the rebar is assumed to be placed along one of the element's
isoparametric directions. The rebar is then located by its intersection with the intersecting face (defined
in Figure 2.2.2-11). The intersections of constant isoparametric lines with edges 1 and 2 of the
intersecting face are given by fractional distances along edges 1 and 2, measured from the first node of
each edge, as shown in Figure 2.2.2-10.
On the data line of the *REBAR option, specify the elements that contain the rebars; the
cross-sectional area, A, of each rebar; the fractional distances locating the rebar's position in the
element, f1 and f2 ; and the isoparametric direction. Give the fractional distances with respect to edge
1 and edge 2 for the isoparametric direction chosen, as defined in Figure 2.2.2-11.
Usage: *REBAR, ELEMENT=CONTINUUM, MATERIAL=mat, SINGLE
Initial conditions
Initial conditions (``Initial conditions,'' Section 18.2.1) can be used to define rebar prestress or
solution-dependent values for rebars.
Defining prestress in rebar
For structures in which reinforcing is defined (such as reinforced concrete structures), use the
*INITIAL CONDITIONS option to define the prestress in the rebars. Include the REBAR parameter
and set the TYPE parameter equal to STRESS. On the data line specify the element number or element
set name, the rebar name, and the prestress value.
Usage: *INITIAL CONDITIONS, TYPE=STRESS, REBAR
Defining the initial values of solution-dependent state variables
for rebars
Use the *INITIAL CONDITIONS option to define the initial values of solution-dependent state
variables for rebars within elements. Include the REBAR parameter and set the TYPE parameter equal
to SOLUTION. See ``Initial conditions,'' Section 18.2.1, for details about specifying initial
conditions.
Usage: *INITIAL CONDITIONS, TYPE=SOLUTION, REBAR
Output
Rebar force output is available at the rebar integration locations with output variable RBFOR. The
rebar force is equal to the rebar stress times the current rebar cross-sectional area. The current
cross-sectional area of the rebar is calculated by assuming the rebar is made of an incompressible
material, regardless of the actual material definition. For rebars in membrane or shell elements output
variables RBANG and RBROT identify the current orientation of isoparametric or skew rebar within
the element and the relative rotation of the rebar as a result of finite deformation, respectively. These
quantities are measured with respect to the isoparametric direction in the element specified with the
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ISODIRECTION parameter, not the default local element system or the orientation-defined system.
See ``Rebar modeling in shell and membrane elements,'' Section 3.7.3 of the ABAQUS Theory
Manual.
See ``Output variable identifiers,'' Section 4.2.1, for additional output options such as stress and
strain.
Specifying the direction for rebar angle output in shell and
membrane elements
The output quantities RBANG and RBROT can be measured from either of the isoparametric
directions in the plane of the shell or the membrane. Set the ISODIRECTION parameter on the
*REBAR option equal to the desired isoparametric direction from which the rebar angle will be
measured (1 or 2). In axisymmetric shells the first isoparametric direction coincides with the
meridional direction, and the second isoparametric direction coincides with the hoop direction. The
rebar angle is measured from the isoparametric direction to the rebar with a positive angle defined as a
counterclockwise rotation around the element's normal direction. The default direction is the first
isoparametric direction.
Usage: Use any of the following options:
*REBAR, ELEMENT=SHELL, MATERIAL=mat, ISODIRECTION=n
*REBAR, ELEMENT=AXISHELL, MATERIAL=mat, ISODIRECTION=n
*REBAR, ELEMENT=MEMBRANE, MATERIAL=mat, ISODIRECTION=n
As an example, an *ORIENTATION-defined local coordinate system is used to define skewed rebar in
a shell element (skew angle ® = 30± ), and the output value of RBANG is 75°, as illustrated in Figure
2.2.2-16:
*REBAR, ELEMENT=SHELL, MATERIAL=MAT1, NAME=REBARB,
GEOMETRY=SKEW, ORIENTATION=ORIENT, ISODIRECTION=2
ELSET1, 0.01, 0.1, 0.0, 30.
*ORIENTATION, SYSTEM=RECTANGULAR, NAME=ORIENT
-0.7071, 0.7071, 0.0, -0.7071, -0.7071, 0.0
3, 0.0
Figure 2.2.2-16 RBANG measurement for skew rebar defined relative to *ORIENTATION-defined
local coordinate directions.
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The rebars are located at the midsurface of the shell. Output variable RBANG is measured from the
second isoparametric direction to the rebar. If the ISODIRECTION parameter were set to 1, output
variable RBANG would report an angle of 165°.
Visualizing rebar and results in rebar
ABAQUS/Viewer does not yet support rebar.
2.2.3 Orientations
Use the *ORIENTATION option to define a local coordinate system.
References
· *ORIENTATION
· ``Material library: overview,'' Section 8.1.1
· ``Material data definition,'' Section 8.1.2
Overview
The *ORIENTATION option is used to define a local coordinate system for:
· definition of material properties--for example, orthotropic or anisotropic materials;
· material calculations at integration points;
· output of components of stress and strain; and
· definition of inertial elements.
The *ORIENTATION option is required if material properties are non-isotropic. It cannot be used:
· to specify a local coordinate system for defining nodal coordinates--use the SYSTEM parameter
on the *NODE option or the *SYSTEM option instead; or
· to specify a local coordinate system for applying loads and boundary conditions--use the
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*TRANSFORM option instead.
Considerable generality is provided in the way the local system can be defined, since this system must
often change from point to point because of the shape and construction of the structure being modeled.
Assigning a name to an orientation
A name is assigned to each orientation definition. This name is used to refer to the orientation
definition when creating element properties for continuum or shell elements or when specifying local
directions for rotary inertia elements.
Usage: *ORIENTATION, NAME=name
Defining a local coordinate system in a model that contains an
assembly of part instances
In a model defined in terms of an assembly of part instances, the *ORIENTATION option can be used
to define a local coordinate system at the part, part instance, or assembly level. An *ORIENTATION
defined at the part or part instance level is rotated according to the positioning data given for each
instance of that part (or for the part instance). See ``Defining an assembly,'' Section 2.5.1.
Defining a local coordinate system
A two-stage process is used to define the local system through data lines.
1. The local coordinate system is defined at the particular location at which it is required. Two
independent parameters, SYSTEM and DEFINITION, are used. The SYSTEM parameter is used
to select between rectangular, cylindrical, and spherical coordinate systems. The coordinate system
is defined in terms of two points, a and b, as shown in Figure 2.2.3-1. The DEFINITION parameter
is used to select the method for defining points a and b.
Usage: *ORIENTATION, NAME=name, SYSTEM=type, DEFINITION=method
Figure 2.2.3-1 Material/element orientation systems.
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2. An additional rotation can be specified on the second data line by identifying one of these local
directions (X 0 , Y 0 , or Z 0 ) as a rotation axis and giving a rotation, in degrees, about that axis. The
local system is then rotated through this angle about the specified axis. This method of defining a
local system is required for shells and membranes. The additional rotation is illustrated in Figure
2.2.3-2.
Figure 2.2.3-2 Specifying rotation about a local axis for shells or membranes.
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Available coordinate systems
Rectangular, cylindrical, and spherical coordinate systems are available.
Defining a rectangular coordinate system
A rectangular Cartesian coordinate system is defined by its origin and the two points, a and b, shown
in Figure 2.2.3-1, SYSTEM=RECTANGULAR. Point a must be on the local X 0 -axis, and point b must
be in the X 0 -Y 0 plane. Although it is not necessary, it is intuitive to select point b such that it is on or
near the local Y 0 -axis. The rectangular coordinate system is the default.
Usage: *ORIENTATION, NAME=name, SYSTEM=RECTANGULAR
Defining a cylindrical coordinate system
A cylindrical coordinate system is defined by giving the two points, a and b, on the polar axis of the
cylindrical system, as shown in Figure 2.2.3-1. The local axes are X 0 =radial, Y 0 =tangential, Z 0 =axial.
Usage: *ORIENTATION, NAME=name, SYSTEM=CYLINDRICAL
Defining a spherical coordinate system
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A spherical coordinate system is defined by giving the center of the sphere, a, and point b on the polar
axis as shown in Figure 2.2.3-1. The local axes are X 0 =radial, Y 0 =circumferential, Z 0 =meridional.
Usage: *ORIENTATION, NAME=name, SYSTEM=SPHERICAL
Methods for defining points a and b
Points a and b can be defined by giving their coordinates, by specifying the locations of points a and b
relative to global node numbers, or by specifying the locations of points a and b relative to local node
numbers.
Defining points a and b by giving their coordinates
The coordinates of points a and b can be given directly. These coordinates should be appropriate to the
system chosen. For a rectangular coordinate system the origins of the local and global systems are the
same using this method. The coordinates method is the default.
Usage: *ORIENTATION, NAME=name, DEFINITION=COORDINATES
Defining points a and b by giving global node numbers
Points a and b can be located at nodes by specifying two global node numbers. For a rectangular
coordinate system the origins of the local and global systems are the same using this method.
Usage: *ORIENTATION, NAME=name, DEFINITION=NODES
Defining points a and b by giving local node numbers
Points a and b can be located by specifying the local node numbers of an element. For a rectangular
coordinate system neither point a nor point b can be located at local node number one since the origin
of the local system is the first node of the element. For example, if local node number two is given as
the location of point a, the local X 0 -direction is defined to be parallel to the (1; 2) side of the element.
Usage: *ORIENTATION, NAME=name, DEFINITION=OFFSET TO NODES
Using an orientation definition multiple times
Because the orientation is independent of the material definition and they can both be referenced in
any element property definition option, the ability to describe complex structural components (such as
laminated composite shells) is quite general and straightforward to use.
An orientation definition can be used as often as needed and with different material or element type
definitions; for example, it can be used for different layers of a shell where the orientation is the
same.
Large-displacement considerations
The local coordinate system defined by the *ORIENTATION option rotates with the average rigid
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body motion of the material point or the rigid body when the option is used with ROTARYI elements.
Use with two-dimensional solid elements
When the *ORIENTATION option is used with two-dimensional solid elements such as plane stress,
plane strain, or axisymmetric elements, the orientation must redefine only the X- and Y -directions: the
third direction must remain unchanged (Z-direction for plane strain and plane stress elements,
µ-direction for axisymmetric elements). For axisymmetric elements the global 1-, 2-, and 3-directions
are the radial, axial, and hoop directions, respectively. The use of SYSTEM=CYLINDRICAL or
SPHERICAL may be appropriate for axisymmetric elements only if the local Z 0 -direction is in the
global 3-, or hoop, direction.
Use with shell or membrane elements
When the *ORIENTATION option is used with shell or membrane elements, one of the
*ORIENTATION-defined directions must be identified on the second data line. This direction should
be as close to the surface normal as possible. The user can then specify an additional rotation by which
the other two orientation directions are rotated about this local orientation direction. After being
rotated, the other two *ORIENTATION-defined directions are projected onto the surface of the shell
or membrane as follows:
1. From these two *ORIENTATION-defined directions ABAQUS selects the one that most closely
lies in the plane of the element. This direction is projected onto the element and normalized (so
that it is a unit vector). This will be local direction 1 or 2 for shells and membranes.
2. An orthonormal, right-handed local coordinate system is calculated by taking the cross product of
the projected direction and the element normal.
The positive element normal is the local 3-direction for shells and membranes. This may result in a
local coordinate system in which one direction is reversed with respect to the
*ORIENTATION-defined directions; see Figure 2.2.3-3. (This does not apply in the case of an
*ORIENTATION used to define rebars; see below.)
Figure 2.2.3-3 The local 3-direction will be in the same direction as the element normal.
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If ABAQUS finds in Step 1 that the axis about which the additional rotation can be given lies in the
plane of the element, an error message will be printed in the message ( .msg) file and the analysis will
not continue.
As an example, the orientation of the spiral wound layer of the cylindrical shell shown in Figure
2.2.3-4 would be given by using *ORIENTATION, SYSTEM=CYLINDRICAL and then specifying
the rotation axis as the 1-axis and giving the rotation angle ® (in degrees) on the data line. The local 1and 2-directions for material property specification and material calculations are then those indicated
in the figure.
Figure 2.2.3-4 Spiral wound cylindrical shell layer: material orientation example.
Defining skew rebars in shells and membranes
The orientation of skew rebars in shells and membranes can be defined relative to a local coordinate
system defined by the *ORIENTATION option (see ``Reinforcing in elements,'' Section 2.2.2). When
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the *ORIENTATION option is used for rebar definition, the local coordinate system is calculated as
follows:
1. ABAQUS finds the *ORIENTATION-defined direction (not including the axis identified on the
second data line) that most closely lies in the plane of the element. This direction is projected onto
the element and normalized (so that it is a unit vector).
2. The axis specified on the second data line (about which the additional rotation can be given) is
made orthogonal to the element to create the local 3-direction. This local 3-direction need not be
in the same direction as the element normal.
3. An orthonormal, right-handed local coordinate system is calculated by taking the cross product of
the projected direction and the local 3-direction.
Since the local 3-direction may be opposite to the element normal, the definition of rebars is
independent of the element connectivity.
Use with laminated shells
When the *ORIENTATION option is used with laminated shells, one of the local directions must be
identified on the second data line of the *ORIENTATION option. There are two ways in which this
*ORIENTATION option can be used in the section definition of a laminated shell ( *SHELL SECTION
or *SHELL GENERAL SECTION). In each case the name referenced in the shell section definition is
the name of the local coordinate system defined by the *ORIENTATION option.
The first is to specify a section orientation using *SHELL SECTION (or *SHELL GENERAL
SECTION), COMPOSITE, ORIENTATION=name. In this case the orientation reference refers to the
entire shell section. Then each layer's orientation angle can be given on the data lines relative to this
section orientation (or the default shell coordinate directions if no section orientation is used). The
angle is given as an additional rotation about the local direction defined on the second data line of the
*ORIENTATION option. If the directions defined on the first data line of the *ORIENTATION option
are not in the surface of the shell, the layer angle is applied after the *ORIENTATION directions have
been projected onto the shell surface.
The second is to specify the name of each layer's orientation separately on the data lines for the
laminate; this method allows different orientation definitions to be referenced for the different layers.
Section forces and strains are still reported in the section orientation defined by the ORIENTATION
parameter (or the default shell coordinate directions if no section orientation is used). The individual
layer orientations are used for material calculations and for output of stress and strain.
Use with beam and truss elements
The *ORIENTATION option cannot be used to define material directions for beams or trusses.
Use with inertial elements
The *ORIENTATION option can be used with ROTARYI elements to define the local coordinate
system in which the six components of the inertia tensor have been defined.
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Output
When the *ORIENTATION option is used in the section definition for an element set, the stress, the
strain, and the element section force components are output in the local system.
Material directions can be visualized in ABAQUS/Viewer by selecting Plot->Material Orientations.
Material directions are written automatically to the output database.
2.3 Defining surfaces
2.3.1 Surfaces: overview
This section describes the general rules that apply when creating surfaces in ABAQUS.
References
· ``Defining element-based surfaces,'' Section 2.3.2
· ``Defining node-based surfaces,'' Section 2.3.3
· ``Defining analytical rigid surfaces,'' Section 2.3.4
· ``Contact analysis: overview,'' Section 20.1.1
· ``Defining contact pairs,'' Section 20.2.1
· ``Concentrated and distributed loads, '' Section 18.4.2
Overview
In ABAQUS/Explicit surfaces:
· can be used as contact surfaces in contact simulations;
· can define regions on which a distributed surface load is prescribed;
· are geometric entities that have an area associated with them but have zero volume; and
· have an identifiable orientation defined by their normals;
· are defined by specifying element faces, specifying nodes or node sets, or by specifying an analytic
curve or surface; and
· can be deformable, rigid, or partially deformable and partially rigid.
Why use surfaces?
In an ABAQUS/Explicit simulation both rigid and deformable surfaces can be used when defining
interactions between bodies. Deformable surfaces can also be used to define self-contact
(single-surface contact) for a structure that can interact with itself.
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Element-based surfaces, node-based surfaces, and analytical rigid surfaces are available in
ABAQUS/Explicit. However, element-based surfaces contain more intrinsic information than either
node-based surfaces or analytical rigid surfaces. ABAQUS/Explicit can associate a surface area with
each node and calculate the contact pressure acting on the surface when it contacts another body only
when an element-based surface is used. In addition, when a surface formed by shell, membrane, or
rigid elements is used, ABAQUS/Explicit can consider the current thickness and offset of the reference
surface of these elements in the contact calculations.
When contact occurs between two bodies, at least one body must use an element-based surface or an
analytical rigid surface, since contact between two node-based surfaces or a node-based surface with
itself is not allowed.
Surfaces can be used to define a region on which a distributed surface load is prescribed; this can
facilitate user input of distributed surface loads for complex models.
Restrictions on surfaces to be used in contact analyses
The following restrictions for surfaces must be adhered to because the surfaces will be used as contact
surfaces during the simulation:
· The surface normals of a surface must point toward the other surface that it may contact except
when the surface is double-sided (see ``Defining element-based surfaces,'' Section 2.3.2).
· The surface must be continuous.
Orienting the surface's normal
The orientation of a surface's normal is critical for the proper detection of contact between two
contacting surfaces. At the point of closest proximity the normals of a single-sided master surface
forming the contact pair should always point toward the slave surface. If, in the initial configuration of
the model, a single-sided master surface's normal points away from its slave surface,
ABAQUS/Explicit will detect that the slave surface penetrates the master surface. ABAQUS/Explicit
will attempt to resolve this initial overclosure of the contact pair with strain-free displacements before
the start of the simulation. ABAQUS/Explicit may have difficulty with the simulation if the
overclosure is too severe. In most of these cases the analysis will terminate immediately, and an error
message about severely distorted elements will be issued.
The user must give particular attention to checking that analytical rigid surfaces or single-sided
surfaces created on shell, membrane, or rigid elements have the proper orientation. Surface orientation
errors can often be quickly and easily detected by running a datacheck analysis (``Execution
procedure for ABAQUS/Standard and ABAQUS/Explicit,'' Section 3.2.1) and inspecting the deformed
configuration in ABAQUS/Viewer. If large displacements have occurred, they may be due to an
incorrect surface orientation.
The proper and improper orientation of a rigid and deformable surface is shown in Figure 2.3.1-1.
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Figure 2.3.1-1 Example of proper and improper surface orientation with a rigid surface.
Defining a continuous surface
A surface cannot be made up of two or more disconnected regions. The definition of analytical rigid
surfaces automatically ensures that these surfaces are continuous. However, care must be taken to
define surfaces formed with elements so that they are continuous across element edges in
three-dimensional models or through nodes in two-dimensional models. This continuity requirement
has several implications for what constitutes a valid or invalid surface definition. In two dimensions
the surface must be either a simple, nonintersecting curve with two terminal ends or a closed loop.
Figure 2.3.1-2 shows examples of valid and invalid two-dimensional surfaces.
Figure 2.3.1-2 Valid and invalid 2-D surfaces.
In three dimensions an edge of an element face belonging to a valid surface may be either on the
perimeter of the surface or shared by one other face. Two element faces forming a contact surface
cannot be joined just at a shared node; they must be joined across a common element edge. An element
edge cannot be shared by more than two surface facets. Figure 2.3.1-3 illustrates valid and invalid
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three-dimensional surfaces.
Figure 2.3.1-3 Valid and invalid 3-D surfaces.
The continuity requirement applies to both automatically generated free surfaces and surfaces defined
with element face identifiers (see ``Defining element-based surfaces,'' Section 2.3.2). Figure 2.3.1-4
shows an automatically generated free surface resulting from the specification of an element set
consisting of two disjointed groups of elements. The resulting surface is not continuous since it is
composed of two disjoint open curves.
Figure 2.3.1-4 Automatic free surface generation.
Surface discretization
For element-based surfaces, ABAQUS/Explicit uses the faceted geometry defined by the finite element
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mesh as the surface definition. The surface in a coarse finite element model may not be a very good
approximation if the physical surface is curved. Therefore, sufficient mesh refinement must be used to
ensure that the faceted surface is a reasonable approximation of the curved physical surface.
Alternatively, some curved surface geometries may be more effectively modeled with analytical rigid
surfaces (see ``Defining analytical rigid surfaces,'' Section 2.3.4).
Internal surfaces created by ABAQUS/CAE
In ABAQUS/CAE many modeling operations are performed by picking geometry with the mouse. For
example, a contact pair can be defined by picking faces on geometric part instances. Each such face
must be translated into a surface in the input file. Such a surface is assigned a name by
ABAQUS/CAE, and the surface is marked with the INTERNAL parameter on the *SURFACE option.
These and other internal surfaces created by ABAQUS/CAE will not appear in ABAQUS/Viewer.
Usage: *SURFACE, NAME=SurfaceName, INTERNAL
2.3.2 Defining element-based surfaces
Use the *SURFACE, TYPE=ELEMENT option to define a surface on elements.
References
· *SURFACE
· *RIGID BODY
· ``Surfaces: overview,'' Section 2.3.1
· ``Contact analysis: overview,'' Section 20.1.1
· ``Defining contact pairs,'' Section 20.2.1
· ``Concentrated and distributed loads, '' Section 18.4.2
Overview
An element-based surface:
· can be defined on solid elements;
· can be defined on shell, membrane, or rigid elements;
· can be deformable or rigid; and
· can be either an open surface (has end points or edges) or a closed surface .
For details about defining analytical rigid surfaces, see ``Defining analytical rigid surfaces,'' Section
2.3.4. For details about defining node-based surfaces, see ``Defining node-based surfaces,'' Section
2.3.3.
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Defining element-based surfaces
Use the *SURFACE, TYPE=ELEMENT option to specify the element faces that form the surface. Use
the NAME parameter to assign a label to the surface. This name can be used with the *CONTACT
PAIR option (``Defining contact pairs,'' Section 20.2.1) to indicate that this surface will be a contact
boundary in a contact analysis or with the *DSLOAD option to prescribe a distributed surface load in
the model.
In models that are defined in terms of an assembly of part instances, all surfaces must belong to a part,
part instance, or the assembly. All of the general restrictions on surfaces described in ``Surfaces:
overview,'' Section 2.3.1, still apply in such models. Additional rules are given in ``Defining an
assembly,'' Section 2.5.1.
In models without an assembly definition, surfaces are given as model data; thus, surface definitions
cannot change from step to step.
Usage: *SURFACE, NAME=surface_name, TYPE=ELEMENT
General restrictions on element-based surfaces
Element-based surfaces can be defined only on compatible element types. Elements defining a single
surface must satisfy the following rules:
· Deformable elements cannot be combined with elements that are part of a rigid body to define a
single surface.
· Two-dimensional, axisymmetric, and three-dimensional elements cannot be mixed in the same
surface definition.
· Continuum and structural elements cannot be mixed in the same surface definition.
· Surfaces in plane stress or plane strain models must have the same out-of-plane thickness.
· A surface cannot be created on beam or truss elements.
In models that are defined in terms of an assembly of part instances, all surfaces must belong to a part,
part instance, or the assembly (see ``Defining an assembly,'' Section 2.5.1).
Creating surfaces on solid (continuum) elements
There are two ways to define a surface on solid elements:
1. by generating the free surface automatically from the exposed faces of elements or element sets,
and
2. by specifying the element numbers (or element sets) and the corresponding face identifiers of the
elements.
The automatic free surface generation approach is the simplest method of defining external surfaces on
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solid elements. Specifying the element faces gives the user exact control over which element faces
form the surface.
It is possible to use both approaches in the same surface definition option when creating a single
surface. The automatic surface generation capability can be used only to define surfaces on the exterior
of a model. It cannot be used to define surfaces that are in the interior of a model.
Generating the free surface automatically
Define the surface by specifying a series of element sets or element numbers on the data lines of the
*SURFACE option. The faces of these elements that are on the exterior (free) surface of the model
form the surface.
Usage: *SURFACE, NAME=surface_name, TYPE=ELEMENT
element number or element set,
For example, if the name of the shaded element set in Figure 2.3.2-1 is ESETA, the surface named
ASURF is specified by
*SURFACE, NAME=ASURF, TYPE=ELEMENT
ESETA,
Figure 2.3.2-1 Automatic free surface generation.
The elements used to generate the surface must conform to the restrictions outlined in ``Surfaces:
overview,'' Section 2.3.1. An additional restriction to consider is that multi-point constraints ( ``General
multi-point constraints,'' Section 19.2.2) involving nodes on exposed surfaces are not taken into
account during free surface generation, which can produce incorrect surface definitions.
For example, the nodes of the elements in element set REFINED shown in Figure 2.3.2-2 are used in
linear, mesh-refinement constraints. The surfaces generated with and without multi-point constraints
are shown in Figure 2.3.2-2.
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Figure 2.3.2-2 Effect of multi-point constraints on automatic surface generation.
Creating surfaces by specifying solid element faces
Define the surface by identifying the element faces that form the surface. The face identifiers used with
this approach all begin with the letter S, followed by the face number of the element. (Element face
numbers are defined in Part V, "Elements.") Table 2.3.2-1 contains a list of valid face identifiers for all
deformable elements. The face identifier can refer to individual elements or to entire element sets.
Surfaces internal to bodies can be defined only by using this approach.
Usage: *SURFACE, NAME=surface_name, TYPE=ELEMENT
element number or set, face identifier
Table 2.3.2-1. Surface definition face identifier labels.
Elements
Face Labels
B31
B21
T2D2
T3D2
must use node-based
surfaces.
S3R
S3RS
S4R
S4RS
SPOS SNEG
S4RSW SAX1
M3D3
M3D4
R
RAX2
R3D3
R3D4
CPS3
CPE3
CAX3
CPS6M
S1 S2 S3
CPE6M CAX6
M
CPS4R
CPE4R CAX4R C3D4
S1 S2 S3 S4
C3D10
M
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C3D6
C3D8R
S1 S2 S3 S4 S5
S1 S2 S3 S4 S5 S6
Creating surfaces on structural and rigid elements
ABAQUS/Explicit allows surfaces on structural elements to be either single-sided or double-sided.
Double-sided surfaces can be defined only on three-dimensional shell, membrane, or rigid elements
and consist of two single-sided surfaces separated by the thickness of the underlying elements.
Double-sided surfaces recognize contact from both sides. Single-sided surfaces can be defined on all
shell and membrane elements and require the user to specify a face identifier ( SPOS or SNEG) to
select the side of the element on which contact may occur.
Double-sided surfaces should be avoided when the surface is used to prescribe a distributed surface
load; in such a case the distributed load will be applied to both faces of the element resulting in a net
zero load being prescribed.
Defining double-sided surfaces on three-dimensional shells,
membranes, and rigid elements
To define a double-sided surface on shell, membrane, or rigid elements, use input similar to
*SURFACE, NAME=BSURF,TYPE=ELEMENT
SHELL,
It is not necessary for the normals of all of the underlying shell or membrane elements to have a
consistent positive orientation for a double-sided surface: ABAQUS/Explicit will define the surface
such that its facets have consistent normals, even if the underlying elements do not have consistent
normals. The facet normals will be the same as the element normals if the element normals are all
consistent; otherwise, an arbitrary positive orientation is chosen for the surface. For double-sided
surfaces the positive orientation is significant only with respect to the sign of the contact pressure
output variable, CPRESS (see the discussion of "Visualizing contact pressures" later in this
section).
Because of the lack of a unique outward direction from double-sided facets, the primary limitation for
double-sided surfaces is associated with resolving large initial penetrations. Initial penetration will be
detected only when a slave node lies within the thickness of the underlying element (between the two
single-sided surfaces comprising the double-sided surface), and the initial penetration will be resolved
by moving the slave node to the nearest free surface as shown in Figure 2.3.2-3. A warning message
will be issued to the status ( .sta) file if two adjacent slave nodes (connected by a facet edge) are
detected on opposite sides of a double-sided master surface. No such warning will be issued for
node-based surface nodes on opposite sides at a double-sided master surface, because adjacency
cannot be determined among the node-based surface nodes. If the master surface is a single-sided
surface, initial overclosures will be resolved using the surface normal of the master surface, as shown
in Figure 2.3.2-4.
Figure 2.3.2-3 Correction of initial overclosure for a contact pair involving two double-sided
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surfaces.
Figure 2.3.2-4 Correction of initial overclosure for a contact pair involving a single-sided and a
double-sided surface.
Having slave nodes trapped on opposite sides of a double-sided master surface will often lead to
serious problems which may not became apparent until later in an analysis. Therefore, a datacheck
analysis (see ``Execution procedure for ABAQUS/Standard and ABAQUS/Explicit,'' Section 3.2.1) is
recommended prior to running a large analysis so that the user can check for warning messages in the
status file ( .sta) and check for mislocated adjacent slave nodes on opposite sides of the master
surface.
Defining single-sided surfaces on shells, membranes, and rigid
elements
In most cases double-sided surfaces are preferred for three-dimensional structural elements, but in two
dimensions only single-sided surfaces are available and in some three-dimensional cases a single-sided
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surface may be desired. To obtain a single-sided surface, the SPOS or SNEG face identifier must be
specified. For structural or rigid elements the positive face ( SPOS) of the element is the one in the
direction of the positive element normal. The definition of the element normal for all shell or
membrane elements is given in Part V, "Elements." The SNEG face on all shell or membrane elements
is defined as the face in the direction opposite to the element normal. Table 2.3.2-1 contains a list of
valid face identifiers for structural elements.
To define single-sided surfaces on shell, membrane, or rigid elements, use input similar to
*SURFACE, NAME=BSURF,TYPE=ELEMENT
SHELL, SPOS
In this case the user must ensure that all of the elements in element set SHELL have their normals
oriented consistently. If they are oriented as shown in Figure 2.3.2-5, the surface normals will reverse
direction as the surface is traversed, resulting in an invalid surface. An error message will be issued,
and the analysis will terminate if this condition is detected. The correct method to define the surface,
given the orientation of the elements in this figure, is either to list each element and face identifier
separately or to create two separate element sets.
Figure 2.3.2-5 Inconsistent orientation of structural element normals can result in an invalid
surface.
Single-sided contact is generally more limiting than double-sided contact because it may cause an
analysis to fail due to excessive element distortion if a slave node unexpectedly moves behind a master
surface. This condition can occur, for example, due to large deformations or rigid-body motions or due
to complex tool shapes in a forming analysis. If the analyst knows that such behavior will not occur,
single-sided contact can be selected since the resolution of large initial overclosures is more robust
with single-sided surfaces than with double-sided surfaces. A surface defined as a self-contact surface
will always recognize self-contact from both sides regardless of whether or not a face identifier is
used.
Defining surfaces on beam or truss elements
The nodes forming the beam or truss elements can be included in a node-based surface definition
(``Defining node-based surfaces,'' Section 2.3.3). Contact can then be defined between this node-based
surface and an element-based surface or an analytical rigid surface. Element-based surfaces cannot be
defined on beam and truss elements in ABAQUS/Explicit.
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Visualizing contact pressures on deformable surfaces made from
shell and membrane elements
Contours of contact pressure will be displayed using the convention that a positive pressure represents
compressive contact on the positive side of the surface. The positive side of the surface can be
determined by drawing the surface normals in ABAQUS/Viewer. Following this convention, negative
values of CPRESS may be seen in the case of tied contact if the surfaces are being pulled away from
each other. The sign of CPRESS will also be reversed for contact on the negative (back) side of a
double-sided surface, so negative values of CPRESS may be seen if contact occurs on the back side of
a double-sided surface. Conversely, tied contact on the back side of a double-sided surface will result
in positive CPRESS values if the surfaces are pulled away from each other. If contact occurs on both
sides of the double-sided surface at the same point, the value of CPRESS is given for each contact pair
separately.
Shell, membrane, or rigid element thickness and shell or rigid
element offset
A shell, membrane, or rigid element's reference surface, which contains the nodes of these elements, is
assumed to be midway between its outer surfaces unless a shell or rigid offset is used, in which case
the reference surface (the surface on which the nodes lie) may be different from the midsurface. By
default, the current thickness of a shell or a membrane element and its specified offset are taken into
account in the contact calculations when the surface containing the element is used in a contact pair in
ABAQUS/Explicit. The thickness or offset of a rigid element is also accounted for if a thickness or
offset is given on the *RIGID BODY option (see ``Rigid elements,'' Section 15.3.1).
To define surfaces on these elements such that they are in contact at the start of the analysis, the shell,
membrane, or rigid element thicknesses must be considered when defining the nodal coordinates;
otherwise, the surfaces in the contact pair will be overclosed. Effects of contact surface thickness and
offsets, as well as methods for modifying the contact thickness and for avoiding contact surface offsets,
are discussed below.
Effects of contact surface thickness and offsets
By default, the nodal contact thickness equals the average of the current thickness of the surrounding
elements (see Figure 2.3.2-6 and Table 2.3.2-2). The contact thickness within a facet is interpolated
from the nodal values. If the *NODAL THICKNESS option is used, the nodal contact thickness may
not correspond exactly to the specified nodal thickness (see Figure 2.3.2-7 and Table 2.3.2-3). The
nodal contact thickness distribution will tend to be more diffuse than the specified nodal thickness
distribution (because the specified nodal thicknesses are first averaged to compute the element
thicknesses, which are then averaged to compute the nodal contact thicknesses).
Accounting for thickness in contact problems will cause the contact surface to extend past the parent
element boundary in the plane of the element by an amount equal to one-half its thickness. This surface
extension, which is semi-circular in shape, will cause contact to be established between the edge of a
shell and an opposing surface before the node on the shell boundary reaches the opposing surface. The
extension is present for both single-sided and double-sided surfaces. Figure 2.3.2-8 demonstrates this
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concept.
Figure 2.3.2-6 Continuous variation of contact thickness across facet boundaries.
Table 2.3.2-2. Thicknesses corresponding to Figure 2.3.2-6.
node
element
specified element
nodal contact
thickness
thickness (average
of element
thickness)
1
0.5
a
0.5
2
0.5
b
0.5
3
0.7
c
0.9
4
0.9
d
0.9
5
0.9
Figure 2.3.2-7 Small discrepancy between the nodal contact thickness and the thickness specified
with *NODAL THICKNESS.
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Table 2.3.2-3. Thicknesses corresponding to Figure 2.3.2-7.
nodal contact
element
node
element
specified
thickness
thickness
(*NODAL
(average of
(average of
THICKNES
element
*NODAL
S)
thickness)
THICKNESS)
1
0.5
0.5
a
0.5
2
0.5
0.5
b
0.5
3
0.5
0.6
c
0.7
4
0.9
0.8
d
0.9
5
0.9
0.9
e
0.9
6
0.9
0.9
Figure 2.3.2-8 Extension of contact surface for edge contact without the NO THICK parameter.
The effect of a shell or rigid offset on a surface is shown in Figure 2.3.2-9. Poorly defined surfaces can
result near corners if large offsets are present, as shown in Figure 2.3.2-10. The user should consider
this when defining a model. A warning message will be issued if the offset magnitude is greater than
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one-half of any of the parent shell element edge lengths. However, at acute corners it is possible for an
offset less than one-half of the parent element size to result in a poorly defined contact surface (and in
this case no warning will be given).
Figure 2.3.2-9 Extension of contact surface if a shell offset is present.
Figure 2.3.2-10 Example of a poorly defined surface near a corner when a large shell offset is
present.
Ignoring the contact thickness and offset
The optional NO THICK parameter can be used to cause the contact algorithm to ignore the thickness
and offset of shell, membrane, or rigid elements entirely. In this case the contact surface is taken as the
reference surface (see Figure 2.3.2-11).
Figure 2.3.2-11 Contact surface with NO THICK parameter.
The NO THICK parameter cannot be used if a surface will be used as a contact surface for
single-surface (self) contact. If one of the surfaces in a contact pair is a double-sided surface, the NO
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THICK parameter can be used only on one of the two surfaces: at least one surface in a contact pair
involving double-sided surfaces must have a nonzero thickness. The NO THICK parameter is useful
for performing parameter studies on the thickness or offset of a model since the user can change the
thickness and offset without also having to move the mesh to control the initial separation between the
surfaces.
Usage: *SURFACE, NAME=name, NO THICK
Controlling the effects of contact thickness and offset
Two additional parameters for controlling the effects of contact thickness and offset are provided for
all surfaces. However, they are primarily intended for self-contact surfaces since the NO THICK
parameter cannot be used with these surfaces.
Self-contact surfaces should not contain facets that are thicker than their edge or diagonal lengths.
Extremely large thicknesses will cause nodes to appear to be penetrating nearby facets in even a flat
self-contact surface due to the algorithmic use of a semi-circular tube with a radius of half the contact
thickness around the edge of each facet (see Figure 2.3.2-12).
Figure 2.3.2-12 Undesired penetration resulting from a large thickness in a self-contact surface.
The effective thickness used for contact can be modified using either the SCALE THICK or MAX
RATIO parameters. The SCALE THICK parameter can be used to scale all of the facets by a single
factor. The MAX RATIO parameter will only adjust the thicknesses for facets in which the thickness
to minimum edge or diagonal length ratio exceeds the specified value. The amount by which a facet
thickness is adjusted as a result of using MAX RATIO may vary during an analysis because of changes
in the facet size. If the thickness to element size ratio exceeds 1.0 in the initial configuration for a
self-contact surface, an error message recommending that MAX RATIO be used will be issued.
The user should not specify extremely small values for SCALE THICK or MAX RATIO for
double-sided surfaces or surfaces that will be involved in self-contact since these surfaces must have a
contact thickness that is significant compared to the facet size. For surfaces involved only in
two-surface contact it is acceptable to set SCALE THICK=0.0; however, it is computationally more
efficient to use NO THICK.
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Usage: Use either of the following options:
*SURFACE, NAME=name, SCALE THICK=value
*SURFACE, NAME=name, MAX RATIO=value
Ignoring the offset but modeling the contact thickness
Use the NO OFFSET parameter for situations in which it is desirable to ignore the effect of the offset
but when it is still necessary to model the thickness in the contact calculations. With this parameter the
contact surface is the outside surface of an imaginary shell, membrane, or rigid element whose
midsurface is at the reference surface (see Figure 2.3.2-13). This parameter could be used for a
self-contact surface that would be poorly defined if the offset were enforced (thickness must be
enforced for self-contact surfaces). It is also possible to enforce the offset but not the thickness in the
surface model by setting the SCALE THICK parameter equal to zero.
Usage: *SURFACE, NAME=name, NO OFFSET
Figure 2.3.2-13 Contact surface with NO OFFSET parameter.
Contact calculations are generally most accurate with the default treatment of thickness and offset.
However, when a shell offset of half the original shell thickness has been specified, the NO THICK
parameter will give an accurate representation of one side of the surface. This approach can be more
accurate near a corner (especially on the exterior side of a corner) than if the offset and thickness are
enforced for the surface, as shown in Figure 2.3.2-14.
Figure 2.3.2-14 Use of NO THICK when the shell offset is half the original shell thickness.
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2.3.3 Defining node-based surfaces
Use the *SURFACE, TYPE=NODE option to define a set of nodes that can be used as a slave surface
in a contact analysis.
References
· *SURFACE
· ``Surfaces: overview,'' Section 2.3.1
· ``Contact analysis: overview,'' Section 20.1.1
· ``Defining contact pairs,'' Section 20.2.1
· ``Contact surface interactions: overview,'' Section 20.3.1
Overview
A node-based surface:
· can be used as a "slave surface";
· is convenient in three-dimensional cases where ABAQUS cannot construct a unique physical
surface on the elements, such as a pipe modeled with beam elements contacting the ocean floor or
cables modeled with trusses contacting the ground after they break;
· cannot contain nodes that are part of a rigid body if the node-based surface is to be used in a
kinematic contact pair because in this approach to enforcing contact a surface on a rigid body is
always a master surface and a node-based surface is always a slave surface;
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· must either contain nodes that are all part of the same rigid body or not contain any nodes that are
part of a rigid body if the node-based surface is to be used in a penalty contact pair;
· should not be used to model a shell or membrane surface if the thickness and midsurface offset of
a shell or membrane element needs to be considered in the problem; and
· should not be used if contact output on the slave surface is needed.
Alternatives to node-based surfaces are element-based surfaces (see ``Defining element-based
surfaces,'' Section 2.3.2) and, in the case of rigid surfaces, analytical rigid surfaces (see ``Defining
analytical rigid surfaces,'' Section 2.3.4).
Normally ABAQUS/Explicit accounts for the current thickness and the midsurface offset of shell or
membrane elements in surfaces defined on these elements. However, when the nodes of these elements
are used in a node-based surface, the thickness and midsurface offset of the shell or membrane at each
node is not considered.
Creating a node-based surface
Use the *SURFACE, TYPE=NODE option to create a node-based surface by specifying the nodes or
node sets that form the surface. Use the NAME parameter to assign a label to the node-based surface;
this label will be used when defining contact pairs that contain the surface. The area associated with a
node in a node-based surface is always 1.0 in ABAQUS/Explicit.
In models that are defined in terms of an assembly of part instances, all surfaces must belong to a part,
part instance, or the assembly. Additional rules are given in ``Defining an assembly,'' Section 2.5.1.
Usage: *SURFACE, NAME=name, TYPE=NODE
node number or node set
Interpreting contact pressure values when using node-based
surfaces
ABAQUS/Explicit can calculate accurate contact pressures only when it can determine the current
surface area associated with each node on the surface. When node-based surfaces are used as contact
surfaces, ABAQUS/Explicit cannot determine the surface contact area for the nodes. Therefore, the
contact pressure output variable in ABAQUS/Viewer should be interpreted as the contact force when a
node-based surface is used.
2.3.4 Defining analytical rigid surfaces
Use the *RIGID BODY and *SURFACE options to define an analytical rigid surface as part of a rigid
body.
References
· *RIGID BODY
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· *SURFACE
· ``Surfaces: overview,'' Section 2.3.1
· ``Contact analysis: overview,'' Section 20.1.1
Overview
An analytical rigid surface:
· can be two-dimensional or three-dimensional;
· can be used with the infinitesimal-sliding, small-sliding, or finite-sliding mechanical contact
formulations;
· should be oriented such that the analytical rigid surface's outward normal points toward any body
it may contact; and
· is associated with a node, known as the rigid body reference node, whose motion governs the
motion of the surface.
What are analytical rigid surfaces and why use them?
Analytical rigid surfaces are geometric surfaces with profiles that can be described with straight and
curved line segments. These profiles can be swept along a generator vector or rotated about an axis to
form a three-dimensional surface. An analytical rigid surface is associated with a rigid body reference
node, whose motion governs the motion of the surface. An analytical rigid surface does not contribute
to the rigid body's mass or inertia properties (see ``Rigid body definition,'' Section 2.4.1).
Advantages
Using analytical rigid surfaces instead of defining element-based rigid surfaces provides two important
advantages in contact modeling.
· Many curved geometries can be modeled exactly with analytical rigid surfaces because of the
ability to parameterize the surface with curved line segments. The result is a smoother surface
description, which can reduce contact noise and provide a better approximation to the physical
contact constraint.
· Using analytical rigid surfaces instead of rigid surfaces formed by element faces may result in
decreased computational cost incurred by the contact algorithm. In both two-dimensional and
three-dimensional geometries the use of curved line segments instead of many linear facets will
decrease the time spent in contact tracking operations. Additional computational savings may be
realized in three dimensions because of the intrinsic two-dimensional descriptions of the analytical
surfaces.
Disadvantages
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There are also some disadvantages to using analytical rigid surfaces for contact modeling.
· Contact forces and pressures cannot be contoured on an analytical rigid surface. However, contact
forces and pressures can be plotted on the slave surface.
· Reaction force output for a rigid body containing an analytical rigid surface is calculated only for
constraints that are active at the reference node (e.g., constraints specified with the *BOUNDARY
option). If the net contact force on the rigid body corresponding to an unconstrained degree of
freedom is desired, it must be calculated from the rigid body's acceleration and mass.
· An analytical rigid surface must always act as a master surface in a contact pair. Therefore, contact
cannot be modeled between two analytical rigid surfaces.
· An analytical rigid surface does not contribute to the mass and rotary inertia properties of the rigid
body with which it is associated. Therefore, if the mass distribution on an analytical rigid surface
needs to be accounted for, equivalent mass and rotary inertia properties must be defined for the
rigid body by using MASS and ROTARYI elements or a finite element discretization (see ``Rigid
body definition,'' Section 2.4.1).
· Finally, analytical rigid surfaces are always single-sided with their orientation specified through
their definition. Therefore, contact interaction is recognized only on the outer boundary of an
analytical rigid surface. To model contact on both sides of a thin structure, use an analytical rigid
surface that wraps around the boundary of the thin structure.
Creating an analytical rigid surface
Use the *SURFACE option to define simple, two- or three-dimensional, geometric surfaces. Three
different types of analytical surfaces can be created with this option:
· planar (two-dimensional) surfaces,
· three-dimensional cylindrical (swept) surfaces, and
· three-dimensional surfaces of revolution.
Analytical rigid surfaces are useful when the cross-sections of the surfaces can be represented by
straight and curved line segments. The curved segments can be either circular or parabolic arcs. In
two-dimensional simulations the line segments are defined in the global coordinate system of the
deformable model. In three-dimensional simulations a local, two-dimensional coordinate system must
be created, and the line segments are then defined in that system. The two standard types of
three-dimensional, analytical rigid surfaces available are shown in Figure 2.3.4-1.
Figure 2.3.4-1 Examples of three-dimensional analytical rigid surfaces.
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Use the TYPE parameter to indicate which type of analytical surface (SEGMENTS, CYLINDER, or
REVOLUTION) is being created. Use the NAME parameter to assign a label to this surface, which is
referenced in the *CONTACT PAIR option.
Usage: *SURFACE, TYPE=analytical_surface_type, NAME=name
An analytical surface must be defined as part of a rigid body by assigning the name of the analytical
surface to the ANALYTICAL SURFACE parameter on the *RIGID BODY option. Use the REF
NODE parameter to specify the rigid body reference node that will control the motion of the surface.
Usage: *RIGID BODY, ANALYTICAL SURFACE=name, REF NODE=n
An ABAQUS model can be defined in terms of an assembly of part instances (see ``Defining an
assembly,'' Section 2.5.1). A part can contain only one analytical surface. A part containing an
analytical surface definition cannot also contain elements.
Two-dimensional rigid surfaces
Set TYPE=SEGMENTS to define a planar rigid surface. Define the line segments forming the rigid
surface's cross-section in the global coordinate system on the data lines of the *SURFACE option. If
the analytical surface is being defined inside a part, define the line segments in the local part
coordinate system.
Usage: Use both of the following options:
*SURFACE, TYPE=SEGMENTS, NAME=name
*RIGID BODY, ANALYTICAL SURFACE=name, REF NODE=n
For example, the definition of the two-dimensional rigid surface depicted in Figure 2.3.4-2 is
*SURFACE, TYPE=SEGMENTS, NAME=BSURF
START, xa , ya
CIRCL, xb , yb , xc , yc
LINE, xd , yd
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CIRCL, xe , ye , xf , yf
*RIGID BODY, ANALYTICAL SURFACE=BSURF, REF NODE=101
where xi and yi are the global coordinates of the points shown in Figure 2.3.4-2. The user must
provide the end point of each line segment; the starting point is always the end point of the previous
segment, or, in the case of the first segment, the point specified as the START. The centers of the
circular arcs, points c and f in Figure 2.3.4-2, must be given. ABAQUS can define only arcs that are
less than, but not equal to, 180°; thus, it will use the shorter arc defined by the data provided (use two
adjacent arcs to define a longer arc). For parabolic arcs the user must give a third point that lies on the
parabola and within the arc.
Figure 2.3.4-2 Two-dimensional analytical rigid surface contacting a deformable body.
Three-dimensional cylindrical rigid surfaces
To define a cylindrical rigid surface in a model that is not defined in terms of an assembly of part
instances, specify the points a, b, and c shown in Figure 2.3.4-3 that define the local coordinate system.
Figure 2.3.4-3 Rigid surface, TYPE=CYLINDER.
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Give the coordinates of these points--( Xa ; Ya ; Za ), (Xb ; Yb ; Zb ), and (Xc ; Yc ; Zc )--in the default global
coordinate system. As shown in Figure 2.3.4-3, point a defines the origin of the local system; point b
defines the local x-axis; and point c defines the generator vector, which is the negative local z-axis. If
the segment ac is not perpendicular to ab, ABAQUS will automatically adjust point c within the plane
defined by points a, b, and c, such that they become perpendicular. The line segments forming the
cross-section of the rigid surface are defined in the local x-y plane. The three-dimensional surface is
formed by sweeping this cross-section along the generator vector. The resulting surface extends to
infinity in both the positive and negative directions of the generator vector.
To define a cylindrical rigid surface within a part, leave the first two data lines on the *SURFACE
option blank, and specify the line segments forming the cross-section of the rigid surface in the part
coordinate system. For an analytical surface defined within a part (or part instance), point a is located
at the origin of the part coordinate system, point b is located on the part x-axis, and point c is located
on the negative part z-axis. If the segment ac is not perpendicular to ab, ABAQUS will automatically
adjust point c within the plane defined by points a, b, and c, such that they become perpendicular. This
analytical surface coordinate system cannot be redefined by the user; instead, position the surface in
the model by giving positioning data on the data lines of the *INSTANCE option.
Usage: Use both of the following options:
*SURFACE, TYPE=CYLINDER, NAME=name,
*RIGID BODY, ANALYTICAL SURFACE=name, REF NODE=n
For example, the following input, where xi and yi are points in the local coordinate system, would
define the rigid surface shown in Figure 2.3.4-3 in a model that is not defined in terms of an assembly
of part instances (the reference node is not shown in the figure):
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*SURFACE, TYPE=CYLINDER, NAME=CSURF
Xa , Ya , Za , Xb , Yb , Zb
Xc , Yc , Zc
START, xs , ys
LINE, x1 , y1
CIRCL, ...
...
*RIGID BODY, ANALYTICAL SURFACE=CSURF, REF NODE=n
Three-dimensional surfaces of revolution
To define a rigid surface of revolution in a model that is not defined in terms of an assembly of part
instances, specify the two points a and b shown in Figure 2.3.4-4 that define the local coordinate
system.
Figure 2.3.4-4 Rigid surface, TYPE=REVOLUTION.
Give the coordinates of these points--( Xa ; Ya ; Za ) and (Xb ; Yb ; Zb )--in the default global coordinate
system. As shown in Figure 2.3.4-4, point a defines the origin of the local system, and the vector from
a to b defines the local y-axis, which is the axis of a cylindrical coordinate system. The line segments
forming the profile of the surface of revolution are defined in the local x-y plane, where the local
x-axis aligns with the radial axis of the cylindrical coordinate system. The three-dimensional surface is
formed by revolving this profile about the axis of the cylindrical system, the local y-axis.
To define a rigid surface of revolution within a part, leave the first data line on the *SURFACE option
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blank, and specify the line segments forming the cross-section of the rigid surface in the local part
coordinate system. For an analytical surface defined within a part (or part instance), point a is located
at the origin of the part coordinate system, the part x-axis aligns with the radial axis of the cylindrical
coordinate system, and point b is located on the part y-axis. This local axis cannot be redefined by the
user; instead, position the surface in the model by giving positioning data on the data lines of the
*INSTANCE option.
Usage: Use both of the following options:
*SURFACE, TYPE=REVOLUTION, NAME=name
*RIGID BODY, ANALYTICAL SURFACE=name, REF NODE=n
For example, the following input would define the rigid surface shown in Figure 2.3.4-4 (the reference
node is not shown in the figure):
*SURFACE, TYPE=REVOLUTION, NAME=REVSURF
Xa , Ya , Za , Xb , Yb , Zb
START, xs , ys
LINE, ...
CIRCL, ...
...
*RIGID BODY, ANALYTICAL SURFACE=REVSURF, REF NODE=999
Defining the surface normals
The outward surface normal for analytical rigid surfaces is determined by the direction of the line
segments forming the cross-section of the surface. The sequence of line segments defines a vector s
along the rigid surface; Figure 2.3.4-5 shows this vector for a two-dimensional rigid surface
(TYPE=SEGMENTS).
Figure 2.3.4-5 Orientation of surface normals for a two-dimensional rigid surface.
The outward surface normal is created by taking the cross product of the local z-axis and the vector s
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that is tangent to the surface: n = z £ s. The line segments for the two-dimensional rigid surface
shown in Figure 2.3.4-5 are in the global X-Y plane, so the local z-axis is normal to the figure. For a
planar surface the local z-axis corresponds to the global Z-axis.
ABAQUS uses the same procedure to define the outward surface normals for cylindrical rigid surfaces
(TYPE=CYLINDER) and rigid surfaces of revolution (TYPE=REVOLUTION). Figure 2.3.4-3 and
Figure 2.3.4-4 show the outward normals for each of these types of rigid surfaces, respectively. The
vector s is not shown in either figure, but it is defined as the vector from the starting point to the
ending point of each line segment. The local z-axis in Figure 2.3.4-4 is orthogonal to the local x-y
plane that is shown.
If the line segments are given in the wrong order, the surface normals of a rigid surface will appear in
exactly the opposite direction to what was intended. Such a mistake can be corrected only by defining
the line segments in the opposite sequence.
Smoothing analytical rigid surfaces
Smooth transitions between adjacent line segments can always be created by manually inserting
additional curved line segments. Alternatively, smooth surfaces can be generated automatically by
ABAQUS by using the FILLET RADIUS parameter on the *SURFACE option. The value of the
FILLET RADIUS parameter is the radius of curvature, in the units of length used in the model, that
ABAQUS will use to construct a smooth transition between any discontinuous line segments forming
the rigid surface. The default value of zero provides no smoothing of the surface.
Usage: Use both of the following options:
*SURFACE, TYPE=analytical_surface_type, NAME=name, FILLET RADIUS=r
*RIGID BODY, ANALYTICAL SURFACE=name, REF NODE=n
The effect of the FILLET RADIUS parameter on adjoining line segments and on adjoining line and
circular arc segments is illustrated in Figure 2.3.4-6.
Figure 2.3.4-6 Effect of FILLET RADIUS parameter on an analytical rigid surface.
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The sharp corners have been smoothed using the fillet radius so that the normal and tangent surface
vectors are continuous along the entire master surface. Any value r can be used in a model. However,
if r is greater than the length of either of the two adjacent segments, no smoothing will occur.
Therefore, a practical limit on the size of r is the length of the smallest line segment in forming the
surface.
Surface tangent conventions
ABAQUS forms the analytical rigid surfaces such that the outward surface normal and the two surface
tangents form a right-handed orthonormal system as shown in Figure 2.3.4-7.
Figure 2.3.4-7 Surface tangent and outward normal definitions for three-dimensional analytical rigid
surfaces.
The first surface tangent t1 is always along the direction of the line segments forming the surface, s.
The second surface tangent is the negative local z-axis, which for two-dimensional rigid surfaces is the
global (0; 0; ¡1) vector. For three-dimensional analytical rigid surfaces the local z-axis is defined
when the user specifies the local plane for the line segments. The first surface tangent t1 and the
surface normal n shown in Figure 2.3.4-7(b) lie in this local x-y plane, where the surface cross-section
was defined, and the second surface tangent t2 is orthogonal to this plane.
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2.4 Defining rigid bodies
2.4.1 Rigid body definition
Use the *RIGID BODY option to define a rigid body.
References
· *RIGID BODY
· ``Surfaces: overview,'' Section 2.3.1
· ``Defining element-based surfaces,'' Section 2.3.2
· ``Defining analytical rigid surfaces,'' Section 2.3.4
· ``Rigid elements,'' Section 15.3.1
Overview
A rigid body:
· can be two-dimensional planar, axisymmetric, or three-dimensional;
· is associated with a node, called the rigid body reference node, whose motion governs the motion
of the entire rigid body;
· can consist of nodes, elements, and surfaces;
· can act as a method of constraint;
· can be used with connector elements in multibody dynamic simulations;
· can be used to prescribe the motion of a rigid surface for contact modeling;
· can be computationally efficient and does not affect the global time increment; and
· can have temperature gradients or be isothermal in a coupled temperature-displacement analysis
where thermal interactions are considered.
What is a rigid body?
A rigid body is a collection of nodes, elements, and/or surfaces whose motion is governed by the
motion of a single node, called the rigid body reference node. The relative positions of the nodes and
elements that are part of the rigid body remain constant throughout a simulation. Therefore, the
constituent elements do not deform but can undergo large rigid body motions. The mass and inertia of
a rigid body can be calculated based on contributions from its elements or can be assigned specifically.
Analytical surfaces can also be made part of the rigid body, whereas any surfaces based on the nodes
or elements of a rigid body are associated automatically with the rigid body.
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The motion of a rigid body can be prescribed by applying boundary conditions at the rigid body
reference node. Loads on a rigid body are generated from concentrated loads applied to nodes and from
distributed loads applied to elements that are part of the rigid body. Rigid bodies interact with the
remainder of the model in several ways. Rigid bodies can connect at the nodes to deformable elements,
and surfaces defined on rigid bodies can continue on these deformable elements, provided that
compatible element types are used. Rigid bodies can also be connected to other rigid bodies by
connector elements (see ``Connectors,'' Section 16.1.1). Surfaces defined on rigid bodies can contact
surfaces defined on other bodies in the model.
Determining when to use a rigid body
In dynamic analysis rigid bodies can be used to model very stiff components, either fixed or
undergoing large dynamic motions. They can also be used to model constraints between deformable
components, and they provide a convenient method of specifying certain contact interactions. Rigid
bodies can be used with connector elements to model a wide variety of multibody dynamic problems.
When ABAQUS/Explicit is used for quasi-static analysis, rigid bodies are ideally suited for modeling
tooling (i.e., punch, die, drawbead, blank holder, roller, etc.) and can also be effective as a method of
constraint.
It may be useful to make parts of a model rigid for model verification purposes. For example, in
complex models where all potential contact conditions cannot be anticipated, elements far away from
the contact region could be included as part of a rigid body, resulting in faster run times at the model
development stage. When the user is satisfied with the model and contact pair definitions, rigid body
definitions can be removed and an accurate deformable finite element representation can then be
incorporated throughout.
In multibody dynamic simulations rigid bodies are useful for many reasons. Although the motion of the
rigid body is governed by the six degrees of freedom at the reference node, rigid bodies allow accurate
representation of the geometry, mass, and rotary inertia of the rigid body. Furthermore, rigid bodies
provide accurate visualization and postprocessing of the model.
The principal advantage to representing portions of a model with rigid bodies rather than deformable
finite elements is computational efficiency. Element-level calculations are not performed for elements
that are part of a rigid body. Although some computational effort is required to update the motion of
the nodes of the rigid body and to assemble concentrated and distributed loads, the motion of the rigid
body is determined completely by a maximum of six degrees of freedom at the reference node.
Rigid bodies are particularly effective for modeling relatively stiff parts of a model for which tracking
waves and stress distributions are not important. Element stable time increment estimates in the stiff
region can result in a very small global time increment. Since rigid bodies and elements that are part of
a rigid body do not affect the global time increment, using a rigid body instead of a deformable finite
element representation in a stiff region can result in a much larger global time increment, without
significantly affecting the overall accuracy of the solution.
Creating a rigid body
To create a rigid body, use the *RIGID BODY option. Use the REF NODE parameter to assign a rigid
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body reference node to the rigid body.
Usage: *RIGID BODY, REF NODE=n
The rigid body reference node
A rigid body reference node has both translational and rotational degrees of freedom and must be
defined for every rigid body. If the reference node has not been assigned coordinates, ABAQUS will
assign it the coordinates of the global origin by default. In coupled temperature-displacement analysis
where a rigid body is considered as isothermal, a single temperature degree of freedom describing the
temperature of the rigid body exists at the rigid body reference node. The rigid body reference node:
· can be connected to mass, rotary inertia, capacitance, or deformable elements;
· cannot be connected to any elements that are part of any rigid body;
· cannot be contained in a node set that is associated with any rigid body;
· cannot be a rigid body reference node for another rigid body; and
· can have a temperature degree of freedom if the body is an isothermal rigid body.
The collection of nodes that constitute the rigid body
In addition to the rigid body reference node, rigid bodies consist of a collection of nodes that is
generated by assigning elements and nodes to the rigid body. These nodes provide a connection to
other elements. Nodes that are part of a rigid body are one of two types:
· pin nodes, which have only translational degrees of freedom associated with the rigid body, or
· tie nodes, which have both translational and rotational degrees of freedom associated with the rigid
body.
The rigid body node type is determined by the type of elements on the rigid body to which the node is
attached. The node type can also be specified or modified when assigning nodes directly to a rigid
body. For pin nodes only the translational degrees of freedom are part of the rigid body, and the motion
of these degrees of freedom is constrained by the motion of the rigid body reference node. For tie
nodes both the translational and rotational degrees of freedom are part of the rigid body and are
constrained by the motion of the rigid body reference node.
The node type has important implications when the node is connected to rotary inertia elements,
deformable structural elements, connector elements or when the node has concentrated moments or
follower loads applied to it. Rotary inertia elements and applied concentrated moments affect the rigid
body only when associated with a tie node. Although connections to deformable elements always act
through their translational degrees of freedom, connections to deformable shell, beam, and connector
elements also act through their rotational degrees of freedom if the connection is at a tie node. The
behavior of the two types of connections is illustrated in Figure 2.4.1-1, which shows an octagonal
rigid body connected to two deformable shell elements through nodes at opposite ends subjected to an
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applied rotational velocity.
Figure 2.4.1-1 Rigid body with tie node and pin node connections.
The shell elements are assumed to be stiff when compared to their inertia. When the nodes common to
the rigid body and the shell elements are tie nodes, the rotation applied to the rigid body is transmitted
directly to the shell elements. When the common nodes are pin nodes, the rigid body rotation is not
transmitted directly to the shell elements, which can result in large relative motions between the rigid
body and the adjacent shell structure.
Assigning elements to a rigid body
To include elements in the rigid body definition, create an element set containing all of the elements
that are part of the rigid body. Elements in this element set or nodes connected to this element set
cannot be part of any other rigid body. Use the ELSET parameter to identify the element set on the
*RIGID BODY option.
Usage: *RIGID BODY, REF NODE=n, ELSET=name
Table 2.4.1-1 lists the continuum, structural, and rigid element types that can be included in a rigid
body.
Table 2.4.1-1. List of valid elements that can be included in a rigid body.
Rigid Body
Elements
Nodal Degrees of
Geometry
Freedom
Generate Pin Generate Tie Pin Nodes
Tie Nodes
Nodes
Nodes
ux ; uy
ux ; uy ; Áz
Planar
CPE3,
B21
CPE3T,
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Axisymmetric
Three-dimensiona
l
CPE4R,
CPE4RT,
CPS3,
CPS3T,
CPS4R,
CPS4RT,
CPS6M,
CPE6M,
T2D2, R2D2
CAX3,
CAX3T,
CAX4R,
CAX4RT,
CAX6M,
RAX2
C3D4,
C3D4T,
C3D6,
C3D6T,
C3D8R,
C3D8RT,
C3D10M,
T3D2, M3D3,
M3D4R,
R3D3, R3D4
SAX1
ur ; uz
ur ; uz ; Á
B31, S3R,
S4R, S4RS,
S3RS,
S4RSW
ux ; uy ; uz
ux ; uy ; uz ;Áx ; Áy ; Áz
If elements of more than one type or section definition are part of a rigid body, the ELSET definition
used with the *RIGID BODY option will contain elements with different section definitions. When
continuum or structural elements are assigned to a rigid body using the ELSET parameter, they are no
longer deformable and their motion is governed by the motion of the rigid body reference node.
Element stiffness calculations are not performed for these elements , and they do not affect the global
time increment. However, the mass and inertia of the rigid body includes contributions from these
elements as calculated from their section and material density definitions (see Part V, "Elements").
Mass and rotary inertia elements, as well as point heat capacitance elements, should not be included in
the element set specified by the ELSET parameter. Contributions to a rigid body from mass, rotary
inertia, and heat capacitance elements are accounted for automatically when these elements are
connected to nodes that are part of the rigid body.
A list of nodes that are part of a rigid body is generated automatically when assigning elements to a
rigid body using the ELSET parameter. The node list is constructed as a unique list including all of the
nodes that are connected to elements in the element set. Nodes in this list cannot be part of any other
rigid body. The type of each node, pin or tie, is determined by the type of elements on the rigid body to
which it is connected. Shell and beam elements generate tie nodes; solid, membrane, truss, and rigid
elements generate pin nodes (see Table 2.4.1-1). For nodes that are connected to both elements that
generate pin nodes and elements that generate tie nodes, the common node is defined as the tie type.
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All elements that are part of a rigid body must be of like geometry. Therefore, elements contained in
the element set must be either planar, axisymmetric, or three-dimensional. The geometry of the
elements determines the geometry of the rigid body as shown in Table 2.4.1-1.
Assigning nodes to a rigid body
To assign nodes directly to a rigid body, define a node set containing all of the desired pin nodes and a
node set containing all of the tie nodes. Use the PIN NSET and TIE NSET parameters on the *RIGID
BODY option to indicate which node sets contain the pin and tie nodes to be included in the rigid body
definition. Each of these parameters is optional.
Usage: *RIGID BODY, REF NODE=n, PIN NSET=name, TIE NSET=name
The nodes contained in these node sets become part of the rigid body in addition to any nodes that
have been generated from elements using the ELSET parameter. The following rules apply when
assigning nodes directly with the PIN NSET and TIE NSET parameters:
· The rigid body reference node cannot be contained in either a PIN NSET or TIE NSET.
· Nodes that are part of the PIN NSET cannot also be contained in the TIE NSET.
· Nodes that are contained in the PIN NSET or TIE NSET cannot be part of any other rigid body
definition.
· Nodes that are generated automatically from elements defined by the ELSET parameter that are
also contained in the PIN NSET are classified as pin nodes, regardless of their element
connections.
· Nodes that are generated automatically from elements defined by the ELSET parameter that are
also contained in the TIE NSET are classified as tie nodes, regardless of their element
connections.
The types of nodes generated by elements included in a rigid body can, therefore, be overridden by
using the PIN NSET or TIE NSET parameters, thereby allowing the user greater flexibility to define a
constraint with a rigid body by easily specifying the type of connection the rigid body makes with its
attached deformable finite elements. ABAQUS/Explicit will delete nodes that are part of the PIN
NSET or TIE NSET if these nodes are not connected to any continuum, structural, rigid, point mass,
rotary inertia, or connector element; and any concentrated loads specified at these nodes will be
ignored.
Assigning an analytical surface to a rigid body
To assign an analytical surface to a rigid body, use the ANALYTICAL SURFACE parameter on the
*RIGID BODY option to specify the name of the analytical surface. The procedure to create and name
an analytical rigid surface is described in ``Defining analytical rigid surfaces,'' Section 2.3.4.
Usage: *RIGID BODY, REF NODE=n, ANALYTICAL SURFACE=name
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Only one analytical surface can be defined as part of the rigid body definition.
Defining a rigid body in a model that is defined in terms of an
assembly of part instances
An ABAQUS model can be defined in terms of an assembly of part instances (see ``Defining an
assembly,'' Section 2.5.1). A rigid body in such a model can be created from deformable elements at
either the part level or the assembly level. In either case, all node and element definitions must belong
to one or more parts. If all nodes making up the rigid body belong to the same part, create a rigid part
by using the *RIGID BODY option at the part level.
Multiple deformable part instances can be combined into a single rigid body by creating an
assembly-level node or element set that spans the part instances, then using the *RIGID BODY option
at the assembly level to refer to that set. The rigid body reference node can also be defined at the
assembly level, if necessary.
Rigid body mass and inertial properties
When a rigid body is not constrained fully, the mass and inertia properties of the rigid body are
important to its dynamic response. An error message will be issued if there is no mass (or rotary
inertia) corresponding to an unconstrained degree of freedom. ABAQUS automatically calculates the
mass, center of mass, and rotary inertia of each rigid body and prints the results to the data ( .dat) file
if *PREPRINT, MODEL=YES is included in the input file . The following rules are used to determine
the mass and inertia of a rigid body:
· The mass of each continuum, structural, and rigid element that is part of the rigid body contributes
to both the rigid body's mass, center of mass, and rotary inertia properties.
· Point mass elements that are connected to any node that is part of a rigid body or the rigid body
reference node contribute to the rigid body's mass, center of mass, and rotary inertia properties.
· Rotary inertia elements that are connected to any tie node or to the rigid body reference node
contribute to the rigid body's rotary inertia properties.
Since the rotational degrees of freedom at a pin node are not part of a rigid body, rotary inertia
elements connected to a pin node do not contribute to the rigid body inertia but are rather associated
with the independent rotation of the node.
Defining mass and inertia properties by discretization
In many cases it is desirable to model rigid components for which the mass, center of mass, and rotary
inertia are not readily available. In ABAQUS it is not necessary to define the mass and inertia
properties of the rigid body directly using MASS and ROTARYI elements. Instead, a finite element
discretization can be used to model the rigid components, and ABAQUS will automatically calculate
the properties from the discretization. Rigid structures with one-dimensional rod or beam geometries
can be modeled with beam or truss elements, structures containing two-dimensional surface geometries
can be modeled with shell or membrane elements, and solid geometries can be modeled with solid
elements. The mass contributions to the rigid body for each of these elements are based on that
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element's section properties (see Part V, "Elements") and the material density (see ``Density,'' Section
8.2.1). Although both shell and membrane elements in a rigid body can yield similar mass
contributions given similar section and density definitions, they will generate different node types (tie
nodes for shells and pin nodes for membranes), which may affect the overall results. The same holds
true for beam and truss elements.
In situations where one portion of a rigid component can be modeled with a finite element
discretization but it is not convenient to do so for other portions, point mass and rotary inertia elements
can be used to represent the mass distribution of these other portions. The mass, center of mass, and
rotary inertia for the rigid body will then include the contributions from both the finite elements and
the MASS and ROTARYI elements.
Positioning the reference node at the center of mass
The specific location of the rigid body reference node relative to the rest of the rigid body or to its
center of mass is important if nonzero boundary conditions are to be applied to the rigid body or
concentrated loads are to be applied at the reference node. In many problems of rigid body dynamics, it
may be desirable to apply loads and boundary conditions to the rigid body at its center of mass. In
addition, it may be useful to monitor the configuration of the rigid body at its center of mass for output
purposes. However, it may be difficult to locate the center of mass a priori when the rigid body mass
and inertia properties contain contributions from a finite element discretization or a complex
arrangement of MASS and ROTARYI elements.
Use the POSITION parameter on the *RIGID BODY option to reposition the rigid body reference node
at the calculated center of mass.
Usage: *RIGID BODY, REF NODE=n, POSITION=CENTER OF MASS
The default value of POSITION is INPUT, which indicates that the reference node will not be
repositioned. If the value of the POSITION parameter is CENTER OF MASS and if a MASS element
is defined at the rigid body reference node, the calculated center of mass used for repositioning
includes all mass contributions except the mass at the reference node. The MASS element is then
repositioned at the center of mass and included in the mass properties of the rigid body. If the only
mass contribution to the rigid body is from a MASS element defined at the rigid body reference node,
the reference node will not be repositioned.
Defining mass and inertia properties directly
When mass, center of mass, and rotary inertia properties of the actual rigid component are known or
can be approximated, it is not necessary to use a finite element discretization or to use an array of point
masses to generate the rigid body properties. These properties can be assigned directly by locating the
rigid body reference node at the center of mass and by specifying a MASS element and ROTARYI
element at the reference node to define the rigid body mass and rotary inertia.
It may also be desirable to input mass properties directly at the center of mass but to specify boundary
conditions at a location other than the center of mass. In this case the rigid body reference node should
be placed at the desired boundary condition location. In addition, the user must define a tie node at the
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center of mass of the rigid body by correctly specifying its coordinates to coincide with the coordinates
of the center of mass of the rigid body, and then include the node in a node set referenced by the TIE
NSET parameter on the *RIGID BODY option. A MASS and ROTARYI element can then be assigned
to the tie node to define the rigid body mass and rotary inertia.
For most applications where mass properties are input directly, it may be necessary to assign additional
elements or nodes to a rigid body so that the rigid body can interact with the rest of the model. For
example, contact pair definitions could require rigid surfaces formed with element faces on the rigid
body and additional pin or tie nodes may be necessary to provide the desired constraints with
deformable elements attached to the rigid body. ABAQUS will account for the mass and rotary inertia
contributions from all elements on a rigid body; therefore, if the user wants to assign the rigid body
mass properties directly using MASS and ROTARYI elements, care should be taken to ensure that
contributions from other element types that are part of the rigid body do not affect the desired input
mass properties. If rigid elements are part of the rigid body definition, their mass contribution can be
set to zero by omitting the DENSITY parameter on the *RIGID BODY option. If other element types
are used to define the rigid body, their density should be set to zero.
Kinematics of a rigid body
The motion of a rigid body is defined entirely by the motion of its reference node. The active degrees
of freedom at the reference node depend on the geometry of the rigid body (see ``Conventions,''
Section 1.2.2). The geometry of a rigid body is either planar, axisymmetric, or three-dimensional and is
determined by the type of elements that are assigned to the rigid body. In the case where no elements
are assigned to a rigid body, the geometry of the rigid body is assumed to be three-dimensional.
The calculated mass and rotary inertia properties for each of the active degrees of freedom for all rigid
bodies are printed to the data ( .dat) file if *PREPRINT, MODEL=YES is included in the input file .
These properties include the contributions from elements that are part of the rigid body, as well as
MASS elements and ROTARYI elements at the nodes of the rigid body. Although this calculated mass
represents the true mass of the rigid body, ABAQUS/Explicit actually uses an augmented mass in the
integration of the equation of motion, which is conceptually similar to an added mass formulation.
Essentially, the calculated mass and rotary inertia of the rigid body is augmented with the mass
contributions of all of its attached deformable elements to create a larger, augmented mass and rotary
inertia. Rotary inertia contributions from adjacent deformable elements are also included in the
augmented rotary inertia if the nodal connection is at a tie node.
Rigid body motions
A rigid body can undergo free rigid body motion in each of its active translational degrees of freedom,
as well as, each of its active rotational degrees of freedom.
Boundary conditions
Boundary conditions for rigid bodies should be defined at the rigid body reference node using the
*BOUNDARY and *AMPLITUDE options (see ``Boundary conditions,'' Section 18.3.1). If the
*TRANSFORM option is defined at the rigid body reference node, boundary conditions are applied in
the local system (see ``Transformed coordinate systems,'' Section 2.1.4).
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Boundary conditions applied to any nodes on a rigid body besides the rigid body reference node have
no effect with the exception that symmetry type boundary conditions can affect the contact logic at the
perimeter of a surface (see ``Relative surface motions,'' Section 20.3.4, and ``Common difficulties
associated with contact modeling,'' Section 20.5.1). Reaction forces and moments can be recovered for
all degrees of freedom that are constrained at the reference node.
Constraints
A multi-point constraint (*MPC) or linear constraint (*EQUATION) can be defined for any node on a
rigid body, including the reference node.
Connector elements
Connector elements can be used at any node of a rigid body, including the reference node, to define a
connection between rigid bodies, between a rigid body and a deformable body, or from a rigid body to
ground. Connector elements are convenient for providing multiple points of attachment on rigid
bodies; modeling complex nonlinear kinematic constraints; specifying zero or nonzero boundary
conditions at a point on a rigid body that is not the rigid body reference node; applying force actuation;
and modeling discrete interactions, such as spring, dashpot, node-to-node contact, friction, locking
mechanisms, and failure joints. Unlike multi-point constraints ( *MPC) or linear constraints
(*EQUATION) connector elements retain degrees of freedom in the connection thereby allowing
output of information related to the connection, such as constraint forces and moments; relative
displacements, velocities, accelerations, etc. See ``Connectors,'' Section 16.1.1, for a detailed
description of connector elements.
Planar rigid body
A rigid body with a planar geometry has three active degrees of freedom: 1, 2, and 6 (ux , uy , and Áz ).
Here, the x- and y-directions coincide with the global X- and Y -directions, respectively. If the
*TRANSFORM option is defined at the rigid body reference node, they coincide with the local
directions defined by this option. The coordinate transformation defined at the reference node must be
consistent with the geometry; the local directions must remain in the global X-Y plane. All nodes and
elements that are part of a planar rigid body should lie in the global X-Y plane.
Planar rigid bodies should be connected only to planar deformable elements. To model the connection
of a rigid component with a planar geometry to three-dimensional deformable elements, model the
planar rigid component as a three-dimensional rigid body consisting of the appropriate
three-dimensional elements.
Axisymmetric rigid body
A rigid body with an axisymmetric geometry has three active degrees of freedom: 1, 2, and 6 (ur , uz ,
Á). Here, the r- and z-directions coincide with the global X- and Y -directions, respectively. If the
*TRANSFORM option is defined at the rigid body reference node, the r- and z-directions coincide
with the local directions defined by this option. The coordinate transformation defined at the reference
node must be consistent with the geometry; the local directions must remain in the global X-Y plane.
All nodes and elements that are part of an axisymmetric rigid body should lie in the global X-Y plane.
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Classical axisymmetric theory admits only one rigid body mode, which is displacement in the
z-direction. To maximize the flexibility of using rigid bodies for axisymmetric analysis,
ABAQUS/Explicit allows for three active degrees of freedom, although only the axial displacement is
a rigid body mode. Translation in the r-direction is associated with a radial mode, and rotation in the
r-z plane is associated with a rotary mode (see Figure 2.4.1-2).
Figure 2.4.1-2 Axisymmetric rigid body modes.
For an axisymmetric rigid body in ABAQUS/Explicit each of these modes develop no hoop stress, but
mass and inertia computed for these degrees of freedom represent the modal mass associated with their
modal motion. The mass properties for an axisymmetric rigid body are, therefore, calculated based on
the initial configuration assuming the following:
· Point masses defined on nodes of the rigid body created by the *MASS option are assumed to
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account for the entire mass around the circumference of the body.
· Mass contributions from axisymmetric elements assigned to the rigid body include the integrated
value around the circumference.
· The center of mass of the rigid body is located at the center of mass of the circumferential slice, as
shown in Figure 2.4.1-2.
If the POSITION parameter on the *RIGID BODY option is set to CENTER OF MASS, the reference
node for an axisymmetric rigid body will, thus, be repositioned at the center of mass of the
circumferential slice.
These assumptions are consistent with the manner in which ABAQUS/Explicit handles other
axisymmetric features but are noted here because of the deviation from classical rigid body theory.
Axisymmetric rigid bodies should be connected only to axisymmetric deformable elements. To model
the connection of a rigid component with an axisymmetric geometry to three-dimensional deformable
elements, model the axisymmetric rigid component as a three-dimensional rigid body consisting of the
appropriate three-dimensional elements.
Three-dimensional rigid body
A rigid body with a three-dimensional geometry has six active degrees of freedom: 1, 2, 3, 4, 5, and 6
(ux , uy , uz , Áx , Áy , Áz ). Here, the x-, y-, and z-directions coincide with the global X-, Y - and
Z-directions, respectively. If the *TRANSFORM option is defined at the rigid body reference node,
they coincide with the local directions defined by this option.
In general, three-dimensional rigid bodies will possess a full, nonisotropic inertia tensor and can
behave in a nonintuitive manner when they are spun about an axis that is not one of the principal
inertia axes. Classical phenomena of rigid body dynamics (e.g., precession, gyroscopic moments, etc.)
can be simulated using three-dimensional rigid bodies in ABAQUS/Explicit.
In most cases three-dimensional rigid bodies should be connected only to three-dimensional
deformable elements. If it is physically relevant, a three-dimensional rigid body can be connected to
two-dimensional plane stress, plane strain, or axisymmetric elements; however, the user should always
constrain the z-displacement, x-axis rotation, and y-axis rotation of the rigid body. The above
procedure is useful when incorporating a two-dimensional plane strain approximation in one region of
a model and a three-dimensional discretization in another. Rigid bodies can be used to constrain the
two finite element geometries at their interface as shown in Figure 2.4.1-3. A unique rigid body should
be used at each node in the plane along the interface to handle the constraint properly.
Figure 2.4.1-3 Rigid body node set used to connect a two-dimensional and three-dimensional mesh.
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Defining loads on rigid bodies
Loads on a rigid body are assembled from contributions of all of the loads on nodes and elements that
are part of the rigid body. Loads are defined on nodes and elements that are part of a rigid body in the
same manner that they are specified if the nodes and elements are not part of a rigid body.
Contributions include:
· applied concentrated forces using the *CLOAD option on pin nodes, tie nodes, and the rigid body
reference node,
· applied concentrated moments using the *CLOAD option on tie nodes and the rigid body reference
node, and
· applied distributed loads on all elements and surfaces that are part of the rigid body.
Unless the point of action is through the rigid body center of mass, each of these loads will create both
a force at and a torque about the center of mass, which will tend to rotate an unconstrained rigid body.
If the *TRANSFORM option is defined at any rigid body nodes, concentrated loads defined at these
nodes are interpreted in the local system. The local system defined by the *TRANSFORM option does
not rotate with the rigid body.
Concentrated moments defined on rigid body pin nodes do not contribute load to the rigid body but are
rather associated with the independent rotation of that node. Independent rotation of a pin node exists
only if it is connected to a deformable element with rotational degrees of freedom or a ROTARYI
element. Follower forces defined by the *CLOAD option with the FOLLOWER parameter can be
defined at pin nodes if the independent rotation exists. However, the results may be nonintuitive since
the direction of the force is determined by the independent rotation even though the follower force acts
on the rigid body.
Rigid bodies with temperature degrees of freedom
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If it is reasonable to assume that a rigid body used in a coupled temperature-displacement analysis has
a uniform temperature, set the ISOTHERMAL parameter equal to YES. A transient heat transfer
process involving an isothermal rigid body assumes that the internal resistance of the body to heat is
negligible in comparison with the external resistance. Thus, the body temperature can be a function of
time but cannot be a function of position. The temperature degree of freedom that is created at the rigid
body reference node describes the temperature of the body. This option must be used for rigid bodies
with analytical rigid surfaces if these surfaces are included in contact definitions with thermal
interaction.
If the ISOTHERMAL parameter on the *RIGID BODY option is set to NO (default), all nodes on the
rigid body connected to coupled temperature-displacement elements will have independent
temperature degrees of freedom. The fact that the nodes are part of a rigid body does not affect the
ability of the coupled elements to conduct heat within the rigid body. However, the mechanical
response will be rigid.
The lumped heat capacitance associated with the rigid body reference node of an isothermal body is
calculated automatically if the rigid body is composed of coupled temperature-displacement elements
for which a specific heat and a density property are defined. Otherwise, the *HEATCAP option should
be used to specify the heat capacitance of the rigid body. An error message will be issued if no heat
capacitance is associated with an isothermal rigid body for which temperature is not prescribed at the
reference node.
· The capacitance of each coupled temperature-displacement element that is part of the rigid body
contributes to the isothermal rigid body's capacitance. For an axisymmetric isothermal rigid body,
capacitance contributions from axisymmetric elements assigned to the rigid body include the
integrated value around the circumference.
· HEATCAP elements that are connected to any node that is part of a rigid body or the rigid body
reference node contribute to the isothermal rigid body's capacitance. For an axisymmetric
isothermal rigid body the point capacitances defined on nodes of the rigid body are assumed to
account for the capacitance integrated around the circumference of the body.
Thermal loads acting on the reference node of an isothermal body are assembled from contributions of
all of the thermal loads on nodes and elements that are part of the rigid body. Heat transfer between a
deformable body and an isothermal rigid body can occur during contact, as well as when the bodies are
not in contact if the *GAP CONDUCTANCE and *GAP RADIATION options are specified.
Usage: *RIGID BODY, ISOTHERMAL=YES
Modeling contact with a rigid body
Contact with a rigid body is modeled by specifying a contact pair formed with a rigid surface and with
a surface defined on another body. (see ``Defining contact pairs,'' Section 20.2.1). A rigid surface can
be formed by nodes, element faces, or an analytical surface using the *SURFACE and the *RIGID
BODY options (see ``Defining node-based surfaces,'' Section 2.3.3; ``Defining element-based
surfaces,'' Section 2.3.2; and ``Defining analytical rigid surfaces,'' Section 2.3.4).
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Contact modeling can be a primary factor when choosing the appropriate rigid body geometry. Contact
pairs should be formed with surfaces of like geometry. For example, a planar rigid body should be used
to model contact either with deformable surfaces formed by two-dimensional plane stress or plane
strain elements or via node-based surfaces with two-dimensional beam or truss elements. Similarly, an
axisymmetric rigid body should be used to model contact with surfaces formed by axisymmetric
elements, and a three-dimensional rigid body should be used to model contact either with surfaces
formed by three-dimensional element faces or via node-based surfaces with three-dimensional beam or
truss elements.
Limitations
Contact between two rigid surfaces can be modeled in ABAQUS/Explicit only if penalty contact is
used and at least one of the rigid surfaces is formed by element faces. Kinematic contact cannot be
used for rigid-to-rigid contact. Contact between two analytical rigid surfaces cannot be modeled.
Therefore, when converting two deformable regions of a model to two distinct rigid bodies for the
purpose of model development, any contact pair definitions between these rigid bodies must use
penalty contact.
The penalty contact algorithm, which introduces numerical softening to the contact enforcement
through the use of penalty springs, must be used for all contact pairs involving a rigid body if an
*EQUATION, *MPC, or connector element is defined for a node on the rigid body.
Rigid beams and trusses cannot be included in a kinematic contact pair definition because surfaces
from beams and trusses can be node-based surfaces only. A node-based surface must be a slave
surface, and elements that are part of a rigid body must be part of the master surface in a kinematic
contact pair.
When a rigid surface acts as a slave surface in a penalty contact pair, initial penetrations of the rigid
slave nodes into the master surface will not be corrected with strain-free corrections (see ``Adjusting
initial surface positions and specifying initial clearances in contact pairs, '' Section 20.2.2). Any initial
penetrations of this type may cause artificially large contact forces in the initial increments.
Reaction force output for a rigid body is calculated only for constraints that are active at the reference
node (e.g., constraints specified with the *BOUNDARY option). If the net contact force on the rigid
body corresponding to an unconstrained degree of freedom is desired, it must be calculated either from
the reaction forces distributed on the surface (for a discrete rigid surface only) or from the rigid body's
acceleration and mass.
2.5 Defining an assembly
2.5.1 Defining an assembly
A finite element model in ABAQUS can be defined as an assembly of part instances.
References
· *ASSEMBLY
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· *INSTANCE
· *PART
Overview
A finite element model in ABAQUS can be defined as an assembly of part instances. The organization
of such a model:
· is consistent with models generated by ABAQUS/CAE and presented by ABAQUS/Viewer; and
· allows reuse of part definitions, which is valuable for creating large, complex models.
Input files written by ABAQUS/CAE are written in terms of an assembly of part instances. For input
files not written by ABAQUS/CAE, the use of part and assembly definitions in the input file is
currently optional. However, since ABAQUS/Viewer displays results in terms of an assembly of part
instances, an assembly and at least one part instance will be created automatically by the solver input
file processor if they are not defined in the input file.
Introduction
A physical model is typically created by assembling various components. The assembly interface in
ABAQUS allows analysts to create a finite element mesh using an organizational scheme that parallels
the physical assembly. In ABAQUS the components that are assembled together are called part
instances. This section explains how to organize an ABAQUS finite element model in terms of an
assembly of part instances.
The mesh is created by defining parts, then assembling instances of each part. Each part can be used
(instanced) one or more times, and each part instance has its own position within the assembly. This
organization of the model definition matches the way models are created in ABAQUS/CAE, where the
assembly can be created interactively or imported from an input file (see the ABAQUS/CAE User's
Manual).
Terminology
Assembly
An assembly is a collection of positioned part instances. An analysis is conducted by defining
boundary conditions, constraints, interactions, and a loading history for the assembly.
Part
A part is a finite element idealization of an object. Parts are the building blocks of an assembly
and can be either rigid or deformable. Parts are reusable; they can be instanced multiple times in
the assembly. Parts are not analyzed directly; a part is like a blueprint for its instances.
Part instance
A part instance is a usage of a part within the assembly. All characteristics (such as mesh and
section definitions) defined for a part become characteristics for each instance of that part--they
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are inherited by the part instances. Each part instance is positioned independently within the
assembly.
Example
A hinge can be modeled using two flanges and a pin. The flange geometry is defined by creating a part,
which is instanced twice inside the hinge assembly. Another part, the pin, is created and instanced
once. The pin is modeled as a rigid body created from an analytical surface (see ``Defining analytical
rigid surfaces,'' Section 2.3.4).
Figure 2.5.1-1 The Hinge assembly.
This hinge example is used throughout this section to illustrate the keyword interface for parts and
assemblies. This example is also used in ABAQUS/CAE to illustrate the interactive assembly process
(see the ABAQUS/CAE User's Manual).
Defining parts, part instances, and the assembly
Everything defined within a part, instance, or the assembly is local to that part, instance, or the
assembly. This means that node/element identifiers and names (like set and surface names) need not be
unique throughout a model; they need only be unique within the part, instance, or assembly where they
are being defined. For example, consider Figure 2.5.1-2. In this model the assembly (Hinge) contains
three part instances ( Flange-1, Flange-2, and Pin-1). Multiple sets named top can be defined:
in this case one is defined within the assembly and one is defined within each of the Flange part
instances. The set name top can be reused, and each set named top is independent from the others.
Figure 2.5.1-2 The organization of the Hinge assembly.
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Use the following keywords to begin and end each part, instance, and assembly definition:
· *PART/*END PART,
· *INSTANCE/*END INSTANCE, and
· *ASSEMBLY/*END ASSEMBLY.
If any one of these keywords appears in an input file, they must all appear; the model must be
consistently defined as an assembly of part instances.
Defining a part
A part is defined by using the *PART and *END PART options, which must appear outside of the
assembly definition. Multiple parts can be defined in a model; each part must have a unique name. All
of the options to define the part go between the *PART and *END PART options.
Usage: Use the following options to define a part:
*PART, NAME=PartName
Node, element, section, set, and surface definitions
*END PART
Defining part instances
A part instance is defined by using the *INSTANCE and *END INSTANCE options within the
assembly definition. Each part instance must have a unique name. Set the PART parameter equal to the
name of the part that is being instanced. A part can be instanced multiple times by repeating the
*INSTANCE and *END INSTANCE options, each time referring to the same part name.
The *INSTANCE option has two data lines, which are used to position the instance within the
assembly. Give a translation and rotation for the part instance relative to the origin of the assembly
(global) coordinate system.
Additional sets and surfaces can be defined at the instance level, as explained later in this section.
Usage: Use the following options to instance a part:
*INSTANCE, NAME=InstanceName, PART=PartName
<positioning data>
additional set and surface definitions (optional)
*END INSTANCE
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Defining the assembly
The assembly is defined by using the *ASSEMBLY and *END ASSEMBLY options. Only one
assembly can be defined in a model. All uses of the *INSTANCE option must appear between the
*ASSEMBLY and *END ASSEMBLY options.
Sets and surfaces can be defined at the assembly level by including the appropriate keywords within
the assembly definition.
Usage: Use the following options to create an assembly:
*ASSEMBLY, NAME=name
Part instance definitions
Set and surface definitions
Connector and constraint definitions
Rigid body definitions
*END ASSEMBLY
Example
The hinge assembly shown in Figure 2.5.1-1 can be defined using the following syntax in the input
file:
*PART, NAME=Flange
*NODE, NSET=Flange
1, ...
2, ...
...
360, ...
*ELEMENT, ELSET=Flange
1, ...
2, ...
...
200, ...
*SOLID SECTION, ELSET=Flange, MATERIAL=Steel
*ELSET, ELSET=Flat, GENERATE
176, 200, 1
*SURFACE, NAME=Flat
Flat, S1
*END PART
*PART, NAME=Pin
*NODE, NSET=RefPt
1, ...
*SURFACE, TYPE=REVOLUTION, NAME=Pin
...
*RIGID BODY, REF NODE=1, ANALYTICAL SURFACE=Pin
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*END PART
*ASSEMBLY, NAME=Hinge
*INSTANCE, NAME=Flange-1, PART=Flange
<positioning data>
*END INSTANCE
*INSTANCE, NAME=Flange-2, PART=Flange
<positioning data>
*END INSTANCE
*INSTANCE, NAME=Pin-1, PART=Pin
<positioning data>
*END INSTANCE
*ELSET, ELSET=Top
...
*NSET, NSET=Output
...
*END ASSEMBLY
*MATERIAL, NAME=Steel
...
Notes
· All of the nodes and elements that describe the Flange part are defined between the *PART and
*END PART options. The section definition ( *SOLID SECTION) must also appear within the part
definition.
· At least one element set must be defined within the Flange part so that the section definition can
refer to it. Additional node and element sets can also be defined in the part.
· The Flange part is instanced twice in the Hinge assembly. Therefore, the model contains two
element sets named Flat: one belongs to part instance Flange-1, and the other belongs to part
instance Flange-2.
· When a meshed part is instanced, the node and element numbers are repeated in each part instance.
· The Pin part is instanced once. It is a rigid body created from an analytical surface (see ``Defining
analytical rigid surfaces,'' Section 2.3.4).
· Keywords can be indented to help clarify the definition of each part, part instance, and assembly.
Organizing the model definition
In a traditional ABAQUS model without an assembly definition, keywords fall into one of two
categories: model data (step independent) and history data (step dependent). In an ABAQUS model
that is organized into an assembly of part instances, all options are further categorized and must fall
within the proper level: part, assembly, instance, step, or model. Step-level options correspond to
history data; all step-dependent options must appear between the *STEP and *END STEP options.
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Model-level data include everything that does not fall into part-, assembly-, instance-, or step-level
data (for example, material definitions; see Figure 2.5.1-3).
Figure 2.5.1-3 Organization of a model defined in terms of an assembly of part instances.
Rules for defining an assembly
The organization shown in Figure 2.5.1-3 is achieved by following a few basic rules.
Referring to items between levels
When creating a model, it is often necessary to refer to something outside of the current level; for
example, a section definition within a part must refer to a material, which is defined at the model level.
Loads defined within a step must refer to sets within the assembly. But some references between levels
are not allowed; for example, a set in one part instance cannot refer to nodes in another part instance.
The following references are allowed:
A definition Can refer to
within:
items within:
the assembly an instance
the model
an instance
the model
a part
the model
a step
the assembly
an instance
the model
These rules are illustrated in Figure 2.5.1-4.
Figure 2.5.1-4 Allowable references between levels.
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Naming conventions
The ABAQUS naming conventions have been extended to allow for a model that contains an
assembly. When something defined within a part, instance, or the assembly is referred to from outside
its level, the complete name must be used to identify it (set Flat of instance Flange-2 in assembly
Hinge, for example). A complete name is given in the input file using "dot" notation: each name in
the hierarchy is separated by a "." (period). For example, some complete names in the Hinge
assembly are
Hinge.Flange-2.Flat
An element set that belongs to
part instance Flange-2.
Hinge.Output
A node set that belongs to
assembly Hinge.
Such names would be used to refer to the sets from outside the assembly. The same syntax is used to
refer to individual nodes or elements.
Hinge.Flange-1.3
A node or element that belongs
to part instance Flange-1.
Hinge.Flange-2.11
A node or element that belongs
to part instance Flange-2.
As always, the context determines whether a node or element is being referred to. The "." has special
meaning; it is used to separate the individual names in a complete name. Therefore, the "." cannot be
used in labels such as set and surface names. For example,
ELSET, ELSET=Set.1
Error
ELSET, ELSET=Set1
OK
Complete names are limited to 80 characters, including the periods.
Quoted labels
Labels for set and surface names can be defined by enclosing the label in quotation marks (see ``Input
syntax rules,'' Section 1.2.1). Any subsequent use of the label in a complete name must be enclosed in
quotation marks as well. For example,
*PART, NAME=Flange
...
*ELSET, ELSET="Set 1"
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...
*END PART
...
*ELEMENT OUTPUT, ELSET=Hinge.Flange-1."Set 1"
Example
An assembly node set Top can be defined by the following syntax:
*ASSEMBLY, NAME=Hinge
...
*NSET, NSET=Top
Flange-1.2, Flange-1.5, ...
Flange-2.1, Flange-2.4, ...
*END ASSEMBLY
Since the node set is defined within the assembly level, Hinge. is not part of the complete names
given on the data lines. However, the prefix Hinge. would be required to request output for this node
set, since the output request exists within the step definition, which is outside the assembly level.
*STEP
...
*NODE OUTPUT, NSET=Hinge.Top
*END STEP
Similarly, a boundary condition could be applied to a set defined for part instance Flange-2.
*STEP
...
*BOUNDARY
Hinge.Flange-2.FixedEnd, 1, 3
*END STEP
The mesh (nodes and elements)
· The mesh can be defined either on a part or on an instance of that part (not both). Typically, parts
are meshed and instances inherit that mesh, but it is not required. If, for example, you want to use
fully integrated elements for one part instance and reduced-integration elements for another, or if
you want to define a more refined mesh on one part instance than on another, you must mesh the
instances separately.
- If the mesh is defined on a part, it is inherited by every instance of that part.
- If the mesh is defined on a part, it cannot be redefined (overridden) on an instance of that part.
In other words, if the *NODE and *ELEMENT options appear between the *PART and *END
PART options, they cannot appear between the *INSTANCE and *END INSTANCE options
that are used to instance that part.
- If a mesh is not defined on a part, it must be defined on every instance of that part.
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· The *PART and *END PART options are required even if no keywords are given between them to
mesh the part. In such cases, the empty *PART definition is used only to relate various instances
to each other via the required PART parameter on the *INSTANCE option. This allows
ABAQUS/Viewer to group information by part.
· Rebar must be defined within a part along with the elements that are being reinforced.
· Reference nodes can be created at the assembly level.
· Only connector, mass, rotary inertia, and capacitance elements can be created at the assembly
level. All other element types must be defined within a part (or part instance). To define
assembly-level elements that refer to part-level nodes, include the part name when defining the
element connectivity. For example:
*ELEMENT, TYPE=MASS
1, Instance-1.10
Section definitions
· Sections must be assigned where the mesh is defined (either within a part definition or within each
instance of the part).
· If a part is meshed, all instances of that part have the same element types and are made of the same
materials.
· The set referred to by a section definition must be created at the same level as the mesh and section
definition.
· If the part is meshed, section assignment cannot be overridden at the instance level.
Sets and surfaces
· Sets and surfaces (rigid or deformable) can be created within a part, part instance, or the
assembly.
- Sets and surfaces can be created on a part if a mesh is defined on the part.
- Sets and surfaces defined on a part are inherited by each instance of that part.
- Assembly-level sets can span part instances.
· If the *ELSET or *NSET option is used with the same name more than once at the same level, the
new members are appended to the set.
· New sets and surfaces can be created on a part instance. If a set or surface is defined on a part
instance and a set or surface with that name was not defined on the part, the set or surface is added
to the instance.
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· Sets and surfaces cannot be redefined on a part instance. If a set or surface is defined on a part
instance and a set or surface with that name was also defined on the part, an error will be
generated.
· Sets and surfaces are not step dependent. All sets and surfaces must be defined within a part, part
instance, or the assembly.
Defining assembly-level sets
The INSTANCE parameter on the *ELSET and *NSET options can be used as a shortcut to using the
complete name when defining assembly-level sets. Set the INSTANCE parameter equal to the name of
the instance that contains the elements or nodes listed on the data lines of the *ELSET or *NSET
option. To add elements or nodes from more than one instance to the set, repeat the *ELSET or *NSET
option (see ``Node definition,'' Section 2.1.1, and ``Element definition,'' Section 2.2.1, for more
details).
Usage: Use the following options to define assembly-level sets:
*NSET, NSET=NsetName, INSTANCE=InstanceName
*ELSET, ELSET=ElsetName, INSTANCE=InstanceName
Adding sets and surfaces on restart
· Existing sets and surfaces cannot be redefined on restart.
· New sets and surfaces can be added to part instances or the assembly on restart. To add a set or
surface, give the complete name. As in the original analysis, the INSTANCE parameter can be
used on the *ELSET or *NSET options to define an assembly-level set in the restart analysis. For
example,
*HEADING
*RESTART, READ, STEP=1
** Add element set "Bottom" to assembly "Hinge":
*ELSET, ELSET=Hinge.Bottom
Flange-1.40, Flange-2.99
**
** Add node set "Top" to assembly "Hinge":
*NSET, NSET=Hinge.Top, Instance=Hinge.Flange-1
21, 22, 23, 24, 26, 28, 31
*NSET, NSET=Hinge.Top, Instance=Hinge.Flange-2
21, 22, 23, 24, 26, 28, 31
**
** Add element set "Right" to part instance "Flange-2":
*ELSET, ELSET=Hinge.Flange-2.Right
16, 18, 20, 29
**
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** Add surface "surfR" to part instance "Flange-2":
*SURFACE, TYPE=ELEMENT, NAME=Hinge.Flange-2.surfR
Right, S1
**
*STEP
...
*END STEP
Rigid bodies
Rigid bodies can be defined at the part or assembly level.
· To define a rigid body at the part level, include the *RIGID BODY and rigid body reference node
definitions within the part definition.
- Rigid elements, deformable elements, and analytical surfaces cannot be combined within a
part.
- If a part contains a rigid body definition, all deformable or rigid elements in the part must
belong to the element set given on the *RIGID BODY option. A part-level rigid body that
refers to only some of the deformable or rigid elements within the part is not allowed. Mass,
rotary inertia, and heat capacitance elements can also be defined within a rigid part; these
elements cannot be in the element set that is given on the *RIGID BODY option.
- To create a part-level rigid body from an analytical surface, include the *SURFACE option
within the part definition. Only one analytical surface is allowed per part.
· To define a rigid body at the assembly level, include the *RIGID BODY and reference node
definitions within the assembly definition.
- A rigid body can be created at the assembly level from any combination of rigid elements,
deformable elements, and up to one analytical surface.
- The *RIGID BODY option can refer to assembly-level or part-level sets.
- A part that contains a rigid body definition cannot be included in an assembly-level rigid
body.
· The *SURFACE option can be used to define a discrete surface at the part or assembly level
independent from the *RIGID BODY definition.
· When the *SURFACE option is used to define an analytical surface, it can only appear within a
part definition, even if the rigid body is defined at the assembly level.
Materials
· Materials are defined at the model level so that they can be reused. The *MATERIAL option
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cannot appear within a part, part instance, or the assembly.
· All materials in a model must have unique names.
Interactions
An interaction is a relationship between surfaces or between a surface and its environment.
Interactions in ABAQUS/Explicit include contact and film conditions.
· Interactions are defined within steps; they cannot be defined within a part, assembly, or instance.
Constraints
Constraints are inflexible coupling mechanisms such as MPCs and equations (see ``Kinematic
constraints: overview,'' Section 19.1.1).
· Constraints can be defined within a part or the assembly. They can be defined within a part
instance if the mesh is defined within the part instance. Constraints should be defined at the
assembly level if they constrain the motion of one part instance relative to another.
· Constraints are translated and rotated according to the positioning data given for a part instance.
Examples
In the following examples most parameters and data lines are omitted for clarity.
Example 1
Notes
*PART, NAME=PartA
*NODE ...
The mesh is defined on the
*ELEMENT ...
part.
*SOLID SECTION, ELSET=setA,
Section assignment must
MATERIAL=Mat1
appear within the part level
if the mesh is defined on
the part.
*SURFACE, NAME=surf1 setB, ...
error Element set setB is not
defined at the part level.
*ELSET, ELSET=setA
Sets and surfaces can be
*NSET, NSET=setA
defined on the part since
*SURFACE, NAME=surf2 setA, ...
the mesh is defined on the
part.
*END PART
*ASSEMBLY, NAME=Assembly-1
*INSTANCE, NAME=I1, PART=PartA
*NODE
error Mesh and section
*ELEMENT
error assignment cannot be
*SOLID SECTION
error defined on the instance if
they are defined on the
part.
*ELSET, ELSET=setA
error Sets and surfaces cannot be
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*NSET, NSET=setA
*SURFACE, NAME=surf2
*ELSET, ELSET=setB
*NSET, NSET=setB
*SURFACE, NAME=surf3
error
error
redefined on the instance.
New sets and surfaces can
be defined on the instance.
Set and surface definitions
can refer to inherited sets.
setA, ...
*END INSTANCE
*END ASSEMBLY
In the second example the instances are meshed.
Example 2
*PART, NAME=PartB
*END PART
*PART, NAME=PartC
*SOLID SECTION, ...
*END PART
error
*ASSEMBLY, NAME=Assembly-1
*INSTANCE, NAME=I1, PART=PartB
*NODE ...
*ELEMENT ...
*SOLID SECTION, ELSET=setA,
MATERIAL=Mat1
*ELSET, ELSET=setA
*NSET, NSET=setA
*SURFACE, NAME=surf2
The mesh is defined on the
part instance.
Section assignment must
appear within the same level
as the mesh definition.
Sets and surfaces are defined
on the instance since the
mesh is defined on the
instance.
setA, ...
*END INSTANCE
*INSTANCE, NAME=I3, PART=PartC
<positioning data>
*END INSTANCE
*END ASSEMBLY
Notes
The *PART and *END
PART options are required,
even when the instance is
meshed.
Section cannot be defined on
the part if mesh is not
defined on the part.
error
The mesh and section must
be defined for each instance
since the part is not meshed.
Coordinate system definitions
ABAQUS provides several options for defining local coordinate systems.
*SYSTEM
The *SYSTEM option is used for defining nodal coordinates (see ``Node definition,'' Section
2.1.1). It can be used within a part definition to define the nodes in that part. The *SYSTEM
definition remains in effect until another *SYSTEM option is defined within the same level or
until the level ends.
*TRANSFORM
The *TRANSFORM option is used for applying loads and boundary conditions (see
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Spatial Modeling
``Transformed coordinate systems,'' Section 2.1.4). It can be used at the part or assembly level
to define a local coordinate system for application of loads and boundary conditions or for the
definition of linear constraint equations.
*ORIENTATION
The *ORIENTATION option is used for defining material properties, connectors, and rebar
(see ``Orientations,'' Section 2.2.3). It can be used at the part level for reference from a section
definition, connector, or rebar option. The *ORIENTATION option can also be used at the
assembly level for reference from a connector .
A local coordinate system defined for a part using any of these options is inherited by all instances of
the part.
Translating and rotating a part instance
The assembly's coordinate system is the global coordinate system. Part instances can be positioned
within the assembly by giving a translation and/or rotation relative to the global origin on the data lines
of the *INSTANCE option. Specify a translation by giving a translation vector. Specify a rotation by
giving two points, a and b, to define a rotation axis plus a right-handed angular rotation around that
axis.
Local coordinate systems defined within a part or part instance will be translated and rotated according
to the positioning data given on the data lines of the *INSTANCE option, as shown in Figure 2.5.1-5.
(In this figure details such as element and section definitions are omitted for clarity.) Equations will
also be translated and rotated according to the positioning data for an instance. All data within a part
(or part instance) definition are defined relative to the part's local coordinate system; positioning data
are applied to a part instance after everything within that instance is defined.
Limitations
The following options are not supported in a model defined in terms of an assembly of part instances:
· *IMPERFECTION, FILE=file
· *IMPORT
· *NMAP
· *PARAMETER SHAPE VARIATION, FILE=file
Figure 2.5.1-5 Defining local coordinate systems.
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Template
*HEADING
*PART, NAME=Part-1
Node, element, section, set, and surface definitions
Connector and constraint definitions
*END PART
*PART, NAME=Part-2
**The instance is meshed, so the part definition is empty
*END PART
*MATERIAL, NAME=mat1
Suboptions and data lines to define this material
*ASSEMBLY, NAME=Assembly-1
*INSTANCE, NAME=i1, PART=Part-1
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<positioning data>
Additional set and surface definitions (optional)
*END INSTANCE
*INSTANCE, NAME=i2, PART=Part-2
<positioning data>
Node, element, section, set, and surface definitions
Connector and constraint definitions
*END INSTANCE
Assembly-level set and surface definitions
Assembly-level connectors and constraints
Assembly-level reference node definitions
Assembly-level rigid body definitions
*END ASSEMBLY
*MATERIAL, NAME=mat2
Suboptions and data lines to define this material
*AMPLITUDE
*INITIAL CONDITIONS
*BOUNDARY CONDITIONS
Zero-valued boundary conditions
*PHYSICAL CONSTANTS
*CONNECTOR BEHAVIOR
Suboptions and data lines to define this connector behavior
*STEP
Loads and boundary conditions
Predefined field definitions
Output requests
Contact pair definitions
*END STEP
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3. Execution Procedures
3.1 Execution procedures: overview
3.1.1 Execution procedure for ABAQUS: overview
Overview
ABAQUS is executed by using the ABAQUS execution procedure. In the following discussion the
command to run the execution procedure is assumed to be abaqus. However, you can customize the
execution procedure to run ABAQUS using any alias you choose. (See the ABAQUS Site Guide for
details.) The abaqus command is described in more detail in the following sections:
· ``Execution procedure for ABAQUS/Standard and ABAQUS/Explicit,'' Section 3.2.1
· ``Execution procedure for ABAQUS/CAE,'' Section 3.2.2
· ``Execution procedure for ABAQUS/Viewer,'' Section 3.2.3
· ``Execution procedure for online documentation, '' Section 3.2.4
· ``Execution procedure for licensing,'' Section 3.2.5
· ``Execution procedure for ASCII translation of results (.fil) files,'' Section 3.2.6
· ``Execution procedure for joining results (.fil) files, '' Section 3.2.7
· ``Execution procedure for querying the keyword/problem database,'' Section 3.2.8
· ``Execution procedure for ABAQUS/Fetch,'' Section 3.2.9
· ``Execution procedure for ABAQUS/Make,'' Section 3.2.10
· ``Execution procedure for fixed format conversion utility, '' Section 3.2.11
The following sections contain further information about running ABAQUS jobs:
· ``Examples of using the abaqus command,'' Section 3.3.1
· ``Using the ABAQUS environment settings,'' Section 3.4.1
· ``File extensions used by ABAQUS,'' Section 3.5.1
· ``FORTRAN unit numbers used by ABAQUS,'' Section 3.6.1
Conventions
The following conventions are used in these sections:
· Items in boldface are options. Options can appear in any order and can be abbreviated.
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· Default options are underlined ( ).
· Items enclosed in square brackets ([ ]) are optional.
· Items appearing in a list separated by bars ( j ) are mutually exclusive.
· One value must be selected from a list of values enclosed by curly brackets (f g).
· Values in italics must be supplied by the user.
· Blanks are used as separators between options and must not precede nor follow an equal sign.
· An alternate syntax of -option value can be used instead of the option=value format.
The abaqus procedure will prompt for any information required that is not provided on the command
line. If abaqus is typed with no options, prompts are issued for all options.
Environment settings
The ABAQUS execution procedure uses "environment" settings to customize the execution of a job.
These settings can be changed using the ABAQUS environment file, abaqus_v6.env. The
execution procedure looks for this file in two places other than the installation location when running a
job. The first place it looks is in the user's home directory. If it exists, the settings in this file will be
applied to all jobs run by the user. The second place the execution procedure looks is in the current
directory. If the file exists, the settings defined there will be applied to all jobs run from that
directory.
If the same job parameter is defined in more than one environment file or is defined more than once
within the same environment file, the last definition encountered will be used. Some exceptions to this
rule are noted in ``Using the ABAQUS environment settings,'' Section 3.4.1. These environment files
can be used to customize the behavior of ABAQUS, including modification of the default options. See
``Using the ABAQUS environment settings,'' Section 3.4.1, for further information on the environment
files.
3.2 Execution procedures
3.2.1 Execution procedure for ABAQUS/Standard and
ABAQUS/Explicit
Reference
· ``Execution procedure for ABAQUS: overview,'' Section 3.1.1
Overview
ABAQUS/Standard and ABAQUS/Explicit, the ABAQUS analysis modules, are executed by running
the ABAQUS execution procedure. Several parameters can be set either on the command line or in the
environment file (see ``Using the ABAQUS environment settings,'' Section 3.4.1). In addition, the
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ABAQUS execution procedure can be used to obtain help regarding command syntax or information
about the installation and computing environment.
Command summary
abaqus
job=job-name
[analysis | datacheck | parametercheck | continue | convert={select |
odb | all} | recover | script=[script-file] | suspend | syntaxcheck |
help | information={environment | local | memory | release |
status | system} | whereami]
[input=input-file]
[user={source-file| object-file}]
[oldjob=oldjob-name]
[fil={append | new}]
[globalmodel=results file-name ]
[cpus=number-of-cpus]
[memory=memory-size]
[buffer=buffer-size]
[interactive | background | queue=[queue-name][after=time]]
[double]
[scratch=scratch-dir]
[solver={sparse | wavefront}]
[time=suspend_time]
[startup=startup file-name noenvstartup]
Command line options
Informational options
help
This option prints a summary of the abaqus command syntax.
information
Typing abaqus information=value prints helpful information about the installation and the
environment that is in effect for this job.
whereami
This option prints the location of the ABAQUS release directory. It cannot be used with any other
command line option.
Required option except when script, help, information, or
whereami is the only option used
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Execution Procedures
job
The value of this option specifies the name of all files generated during the run and the name of
files that are read in the continue, convert, and recover phases.
If this option is omitted from the command line, the user will be prompted for its value except for
the informational options.
Mutually exclusive options that determine which phases of an
analysis are performed
All options are order independent. If none of these options is present, the analysis option is assumed.
The convert option is an exception to the mutual exclusion rule: convert can appear with any option
except datacheck, parametercheck, and syntaxcheck.
analysis
This option indicates that a complete ABAQUS analysis (or a restart of an ABAQUS analysis) is
to be performed.
datacheck
This option indicates that the run is for data checking only. No analysis will be performed. If this
option is used, all files necessary to continue the analysis are saved.
parametercheck
This option indicates that the run is for input parameter checking only (the *PARAMETER option
must have been used). No analysis or data checking will be performed.
continue
This option indicates that the run is to begin at the point at which a previous datacheck run ended.
convert
The value of this parameter indicates which files will be postprocessed.
Results can be converted either immediately following an analysis run, as a separate run
subsequent to an analysis run, or while an analysis is running as follows:
1. To run an analysis including a subsequent conversion of the results, use the convert option in
conjunction with the job and analysis options.
2. To convert the results of a previously run analysis, use the convert option in conjunction with
the job option.
3. To convert results from a job that is currently running, use the convert option in conjunction
with the oldjob option (to name the running job) and the job option (to supply a new name for
the files generated by the convert option).
If convert=select, the ABAQUS/Explicit selected results file ( job-name.sel) will be
converted into a standard ABAQUS results file ( job-name.fil).
If convert=odb, the output database ( job-name.odb) will be converted using the
postprocessing calculator (see ``The postprocessing calculator,'' Section 4.3.1). This conversion is
necessary only if the types of output listed in ``The postprocessing calculator,'' Section 4.3.1, are
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requested.
If convert=all, the selected results file and the output database file will be converted.
recover
This option applies only to ABAQUS/Explicit. It indicates that an analysis is to be restarted at the
last available step and increment in the state file. This capability is available to restart after a
catastrophic failure, such as exceeding a CPU limit or a disk quota.
script
This option indicates that Python scripting is to be done (see ``Scripting parametric studies,''
Section 23.1.1). If this option is not given a value, the Python interpreter is initialized. When this
option is set equal to a script file name, the Python interpreter is initialized and the instructions in
the script file are executed. If the script file contains references to other input files, these files must
be located in the same directory as the script file. The files created by the execution of the script
file are placed in the directory from which the ABAQUS execution procedure is run.
suspend
This option is used to suspend an ABAQUS analysis job and temporarily release its license tokens
to the free-token pool. (See the ABAQUS Site Guide for details.)
syntaxcheck
This option indicates that the run is for checking the syntax of the input file only. This option does
not use any license tokens. No analysis will be performed, and the continue option cannot be used
to continue with an analysis. Only the data ( .dat) and output database ( .odb) files are generated
for viewing.
help
This option outputs a short description of the execution procedure and its commands. By default,
the help information is written to the screen. If a job-name is given or if the job is run in the
background, the help summary is written to the file job-name.log.
information
This option specifies that the run includes information extraction. By default, the information is
written to the screen. If a job-name is given or if the job is run in the background, the information
text is written to the file job-name.log. The following information is output for all information
requests: the current version, the support identifier, the directory in which ABAQUS is located,
and the directory in which the information files are located.
If information=environment, the current settings of the environment file options are
displayed.
If information=local, the local installation notes are output.
If information=memory, some suggestions for setting memory parameters for analysis jobs are
output.
If information=release, information is provided about where to locate the current release
notes.
If information=status, information is provided about where to locate the status reports.
If information=system, information is provided about system software and hardware resources
(operating system level, compiler levels, processor type, graphics board, memory, etc).
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Additional options available for the analysis module
input
This option is used to specify the input file name. If this option is not supplied, the procedure will
look for an input file, job-name.inp. If job-name.inp cannot be found, the procedure will
prompt for the input file name. The input file must be located in the directory from which the
ABAQUS execution procedure is run.
user
This option specifies the name of a FORTRAN source or object file that contains any user
subroutines to be used in the analysis. The name of the user routine may contain a path name and
may be given with or without a file extension. If an extension is given, the program will take the
appropriate action based on the file type. If the file name has no extension, the program will search
for a FORTRAN source file. If the source file does not exist, an object file will be searched for
instead. The execution procedure creates a shared library using the user subroutine file that is used
by ABAQUS/Standard or ABAQUS/Explicit during execution.
oldjob
This option specifies the name of the files from a previous run from which a restart or *POST
OUTPUT (ABAQUS/Standard only) run is to be started or from which results are to be imported.
A file extension is not allowed. This option is required when the *RESTART, *POST OUTPUT,
*SYMMETRIC MODEL GENERATION, or *IMPORT option in the input file indicates that data
are to be read from the restart or the results file. The oldjob-name must be different from the
current job-name.
fil
This option specifies whether the data from the results file of the oldjob specified in a restart run
are included at the beginning of the new results file (default). If fil=new is used, the new results
file will contain only the data from the point in the analysis where the restart occurred. This feature
is used for ABAQUS/Standard runs to join the output from restarted analyses into a single,
continuous results file. Non-restart jobs cannot use this feature to append results file output to an
old results file; the ABAQUS/Append utility must be used for this purpose. Setting fil=new is not
allowed for ABAQUS/Explicit runs.
globalmodel
This option is available only for ABAQUS/Standard. It specifies the name of the global model's
results file from which the results are to be interpolated to drive a submodel analysis. The value for
this option cannot exceed 32 characters, and a file extension is not allowed. This option is required
whenever the *SUBMODEL option or the *BOUNDARY, SUBMODEL option in the input file
indicates that data are to be read from the results file.
cpus
This option specifies the number of processors to use during an analysis run. This feature is not
available on all systems. Use information=local to learn about local multiprocessing
capabilities. The default value for this parameter can be set in the environment file (see ``Using the
ABAQUS environment settings,'' Section 3.4.1).
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memory
This option specifies the number of 64-bit words of memory allocated by the solver input file
processor. The default is sufficient for most problems. If an analysis requires more memory than is
currently in use by the solver input file processor, it will issue an error message listing the current
amount of memory in use. Incrementing the memory by 50% is the recommended approach to
increasing memory. The default value for this parameter can be set with the pre_memory
parameter in the environment file (see ``Using the ABAQUS environment settings,'' Section 3.4.1).
buffer
This option specifies the number of 64-bit words that are used for each internal scratch buffer in
the solver input file processor. These scratch buffers are used for internal databases. The default is
sufficient for most problems. Insufficient buffer space will cause the solver input file processor to
use more external (disk) storage and will affect performance. The default value for this parameter
can be set with the pre_buffer parameter in the environment file (see ``Using the ABAQUS
environment settings,'' Section 3.4.1).
interactive
This option will cause the job to run interactively. For ABAQUS/Standard the log file will be
output to the screen; for ABAQUS/Explicit the status file and the log file will be output to the
screen. The default run_mode can be set in the environment file (see ``Using the ABAQUS
environment settings,'' Section 3.4.1).
background
This option will submit the job to run in the background, which is the default. Log file output will
be saved in the file job-name.log in the current directory. The default method for submitting
the job can be set in the environment file by using the run_mode parameter (see ``Using the
ABAQUS environment settings,'' Section 3.4.1).
queue
This option will submit the job to a batch queue. If the option appears with no value, the job will
be submitted to the system default queue. Quoted strings are allowed. The available queues are site
specific. Contact your site administrator to find out more about local queuing capabilities. Use
information=local to see what local queuing capabilities have been installed. The default
method for submitting the job can be set in the environment file by using the run_mode parameter
(see ``Using the ABAQUS environment settings,'' Section 3.4.1).
after
This option is used in conjunction with the queue option to specify the time at which the job will
start in the selected batch queue. This capability is supported for each individual site through the
ABAQUS environment file. (See the ABAQUS Site Guide for details.)
double
This option is used to specify that the double precision executable is to be used for
ABAQUS/Explicit. This option is available only on machines where the default length of a single
precision, floating point word is 32 bits. This option will run the executable for ABAQUS/Explicit
that was built using double precision, floating point word lengths of 64 bits. This capability is also
supported through the ABAQUS environment file with the environment variable
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explicit_precision (see ``Using the ABAQUS environment settings,'' Section 3.4.1).
scratch
This option is used to specify the name of the directory used for scratch files. On UNIX systems
the default value is the value of the $TMPDIR environment variable or /tmp if $TMPDIR is not
defined. On NT the default value is the value of the %TEMP% environment variable or \TEMP if
this variable is not defined. During the analysis a subdirectory will be created under this directory
to hold the analysis scratch files. The default value for this parameter can be set in the environment
file (see ``Using the ABAQUS environment settings,'' Section 3.4.1). If the scratch files are too
large for the scratch directory, auxiliary scratch directories can be specified using the aux_scratch
parameter in the environment file. The scratch file will be split once split_scratch (also set in the
environment file) is exceeded.
solver
This option is used to choose the equation solver for ABAQUS/Standard. If solver=sparse, the
sparse solver is used. If solver=wavefront, the wavefront solver is used. The default is
solver=sparse.
startup
This option is available only for ABAQUS/Design. It specifies the name of the file containing
Python configuration commands to be run at application startup. Commands in this file are run
after any configuration commands that have been set in the environment file.
time
This option is used in conjunction with the suspend option to specify how many minutes the job
should be suspended; the default is 10 minutes. (See the ABAQUS Site Guide for details.)
noenvstartup
This option is available only for ABAQUS/Design. It specifies that all configuration commands in
the environment files should not be run at application startup. This option can be used in
conjunction with the startup command to suppress all configuration commands except for those in
the startup file.
3.2.2 Execution procedure for ABAQUS/CAE
Reference
· ``Execution procedure for ABAQUS: overview,'' Section 3.1.1
Overview
ABAQUS/CAE, an interactive environment for creating, submitting, moinitoring, and evaluating
results from ABAQUS simulations, is executed by running the ABAQUS execution procedure and
specifying the cae parameter.
Command summary
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abaqus cae
[database=database-file ]
[replay=replay-file]
[recover=journal-file ]
[startup=startup-file ]
[noenvstartup]
Command line options
database
This option specifies the name of the model database file or output database file to open. To
specify a model database file, include either the .cae file extension or no file extension in the file
name. To specify an output database file, include the .odb file extension in the file name.
replay
This option specifies the name of the file from which ABAQUS/CAE commands are to be
replayed. The commands in replay-file will execute immediately upon startup of ABAQUS/CAE.
If no file extension is given, the default extension is .rpy.
recover
This option specifies the name of the file from which a model database is to be rebuilt. The
commands in journal-file will execute immediately upon startup of ABAQUS/CAE. If no file
extension is given, the default extension is .jnl.
startup
This option specifies the name of the file containing Python configuration commands to be run at
application startup. Commands in this file are run after any configuration commands that have
been set in the environment file.
noenvstartup
This option specifies that all configuration commands in the environment files should not be run at
application startup. This option can be used in conjunction with the startup command to suppress
all configuration commands except for those in the startup file.
3.2.3 Execution procedure for ABAQUS/Viewer
Reference
· ``Execution procedure for ABAQUS: overview,'' Section 3.1.1
Overview
ABAQUS/Viewer, an interactive postprocessor for ABAQUS, is executed by running the ABAQUS
execution procedure and specifying the viewer parameter.
Command summary
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abaqus viewer
[database=odb-file]
[replay=replay-file]
[startup=startup-file ]
[noenvstartup]
Command line options
database
This option specifies the name of the output database file to use if it is different from job-name.
The procedure searches for odb-file as entered on the command line with the .odb file extension.
replay
This option specifies the name of the file from which ABAQUS/Viewer commands are read. The
commands in replay-file will execute immediately upon startup of ABAQUS/Viewer. If no file
extension is given, the default extension is .rpy.
startup
This option specifies the name of the file containing Python configuration commands to be run at
application startup. Commands in this file are run after any configuration commands that have
been set in the environment file.
noenvstartup
This option specifies that all configuration commands in the environment files should not be run at
application startup. This option can be used in conjunction with the startup command to suppress
all configuration commands except for those in the startup file.
3.2.4 Execution procedure for online documentation
Reference
· ``Execution procedure for ABAQUS: overview,'' Section 3.1.1
Overview
The online documentation consists of the following "electronic books" (unless otherwise indicated, the
online books are identical to the printed manuals):
· ABAQUS/Standard User's Manual
· ABAQUS/Explicit User's Manual
· ABAQUS Keywords Manual
· ABAQUS Example Problems Manual
· ABAQUS Benchmarks Manual
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· ABAQUS Verification Manual: more than 5000 basic test cases, providing verification of each
individual program feature (procedures, output options, MPCs, etc.) against exact calculations and
other published results.
· ABAQUS Input Files: all the input files that are referenced in the ABAQUS Example Problems
Manual, ABAQUS Benchmarks Manual, and ABAQUS Verification Manual.
· ABAQUS Theory Manual
· ABAQUS/CAE User's Manual: all the material in the printed version of the manual, as well as
context-sensitive help sections that do not appear in the printed manual.
· ABAQUS/Viewer User's Manual: all the material in the printed version of the manual, as well as
context-sensitive help sections that do not appear in the printed manual.
· ABAQUS Release Notes
· ABAQUS Site Guide
· Getting Started with ABAQUS/Standard
· Getting Started with ABAQUS/Explicit
· ABAQUS Command Language Manual: a description of the ABAQUS Command Language, a
command reference that lists the syntax of each command, and information on using the ABAQUS
Command Language or C++ as an application programming interface (API).
· Using ABAQUS Online Documentation: a description of how to use the documentation viewing
software.
· ABAQUS/ADAMS User's Manual
· ABAQUS/CAT User's Manual
· ABAQUS/C-MOLD User's Manual
· ABAQUS/Safe User's Manual
Refer to the ABAQUS Site Guide for a list of the platforms on which the online documentation is
available and information on installing the documentation.
Using ABAQUS online documentation
To view the online documentation:
1. Type abaqus doc
The documentation library window appears with a list of the available documentation on the right
side of the window under the heading Book Titles.
2. Double-click the title of the desired book to display it.
A two-pane window appears. The right pane contains the content of the book and is called the
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content view, and the left pane contains the book's Table of Contents and is called the TOC view.
3. Navigate through the book's content in any of the following ways:
· To scroll so that you can view additional book content or Table of Contents entries, use the
scroll bars to the right of the content and TOC views.
· To jump directly to a section whose title is displayed in the TOC, click that title.
· To search for a word or phrase, enter it in the Find text box at the bottom of the book window.
The search engine searches for the precise word or phrase you type; for example, searching for
the word ``element'' yields different results than searching for the word ``elements.'' Use the *
character as a wildcard; for example, searching for ``element*'' will find occurrences of the
words ``element,'' ``elements,'' ``elemental,'' and ``elementary.''
For more detailed information about using the documentation viewing software, refer to the online
book Using ABAQUS Online Documentation.
Command summary
abaqus doc
3.2.5 Execution procedure for licensing
Reference
· ``Execution procedure for ABAQUS: overview,'' Section 3.1.1
Overview
ABAQUS licensing, a toolkit of licensing utilities, is executed by running the ABAQUS execution
procedure and specifying the licensing parameter.
Refer to the ABAQUS Site Guide for a detailed description of the licensing utilities.
Using ABAQUS licensing
To start the licensing toolkit, type abaqus licensing. The licensing toolkit window appears with a
selection of four options:
Monitoring...
This option displays a dialog box for monitoring and controlling active ABAQUS clients
(analysis jobs and interactive sessions).
Reporting...
This option displays a dialog box for generating reports of license usage, based on the selected
server log file.
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Server Control...
This option displays a dialog box for starting and stopping the license server and for changing
license server settings.
Key Installation...
This option displays a dialog box for installing an ABAQUS license key.
Command summary
abaqus licensing
3.2.6 Execution procedure for ASCII translation of results (.fil)
files
Reference
· ``Execution procedure for ABAQUS: overview,'' Section 3.1.1
Overview
The abaqus ascfil translation facility:
· is provided to convert results ( .fil) files (produced by an ABAQUS analysis) to ASCII format
for porting between dissimilar operating systems;
· permits the movement of results data to a different system for postprocessing; and
· can also be used to convert a results file in ASCII format to binary format to save disk space.
Command summary
abaqus ascfil
job=job-name
[input=input-file]
Command line options
job
This option specifies the input and output file names to use during results file translation. The
job-name value is used as the default input file name. The translated output file will have the name
job-name.fin if the input option is not used.
If the input file is in binary format (default), this utility will create the job-name.fin file in
ASCII format. To transfer the results file back to binary format after porting to a dissimilar
operating system, rename the job-name.fin file to job-name.fil, and use this utility again;
the resulting job-name.fin file will be in binary format.
If this option is omitted from the command line, the user will be prompted for this value.
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input
This option specifies the name of the results file if it is different from job-name. The name of the
translated results file is input-file.fin when this option is used.
3.2.7 Execution procedure for joining results (.fil) files
Reference
· ``Execution procedure for ABAQUS: overview,'' Section 3.1.1
Overview
The abaqus append postprocessing facility:
· is provided to join results ( .fil) files into a single file;
· permits two results files that may be either ASCII or binary files, or a combination of ASCII and
binary, to be joined for further postprocessing; and
· will write a results file in the same format as the file specified with the oldjob option.
Command summary
abaqus append
job=job-name
oldjob=oldjob-name
input=input-file
Command line options
job
This option specifies the output file name to use during execution. The job-name value is used as
the output file name. The joined output file will have the name job-name.fil.
If this option is omitted from the command line, the user will be prompted for this value.
oldjob
This option specifies the name of the first input file to use during execution. The oldjob-name
value is used as the input file name.
If this option is omitted from the command line, the user will be prompted for this value.
input
This option specifies the name of the second results file to use during execution. The input-file
results file will be appended to the oldjob-name results file.
If this option is omitted from the command line, the user will be prompted for this value.
3.2.8 Execution procedure for querying the keyword/problem
database
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Reference
· ``Execution procedure for ABAQUS: overview,'' Section 3.1.1
Overview
The abaqus findkeyword utility queries a keyword/problem database that contains information on
ABAQUS/Standard and ABAQUS/Explicit example problems, verification problems, problems used
in training seminars, problems shown in the ABAQUS application briefs, benchmark timing problems,
and those in the tutorial books Getting Started with ABAQUS/Standard and Getting Started with
ABAQUS/Explicit. The user specifies which keywords, parameters, and values are of interest, and this
utility will list the input files that contain those keywords, parameters, and values. The user can specify
multiple keywords, which causes the findkeyword utility to list those input files that contain all of the
specified keywords. The user can then use ABAQUS/Fetch to fetch the input files. See ``Execution
procedure for ABAQUS/Fetch,'' Section 3.2.9, for information on the ABAQUS/Fetch command. The
output is grouped into problem sets; e.g., ABAQUS/Standard example problems or ABAQUS/Explicit
verification problems.
Command summary
abaqus findkeyword [job=job-name]
[maximum=maximum-output]
keyword data lines
Command line options
job
This option is used to specify the output file name for the output listing. If this option is omitted
from the command line, the output will be printed to the standard output device.
maximum
This option is used to limit the number of sample problems that are listed for each set. If this
option is omitted, a maximum of 100 sample problems are listed for each set.
keyword data lines
The keyword data lines specify which ABAQUS keywords, parameters, and values are of interest
to the user. The names of sample problems that contain the specified keywords, parameters, and
values are printed to the standard output device or to the file indicated by the job command line
parameter. The keyword is required, but parameters and values are optional. If a keyword is
specified without a parameter or a value, all sample problems that use that keyword (with or
without parameters and values) will be listed. If a parameter is specified without a value, all
sample problems that use that parameter with any value will be listed. Parameter values that are
user-specified data (e.g., numeric data, set names, orientation names, etc.) are ignored. The end of
the keyword data lines is indicated by an empty line or an end of file.
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3.2.9 Execution procedure for ABAQUS/Fetch
Reference
· ``Execution procedure for ABAQUS: overview,'' Section 3.1.1
Overview
ABAQUS/Fetch is used to extract sample ABAQUS input files, user subroutine files, journal files,
parametric study script files, or postprocessing programs from the compressed archive files provided
with the release (for problems in the ABAQUS Example Problems Manual, the ABAQUS Benchmarks
Manual, and the ABAQUS Verification Manual). File names are specified in the manuals. If no file
extension is specified, all files corresponding to the name given will be extracted.
Command summary
abaqus fetch
job=job-name
[input=input-file]
Command line options
job
This option is used to specify the output file name for the fetched input file or files. It is also the
default name of the input file to fetch.
If this option is omitted from the command line, the user will be prompted for this value.
input
This option is used to specify the name of the input file or files to fetch if it is different from the
job-name.
3.2.10 Execution procedure for ABAQUS/Make
Reference
· ``Execution procedure for ABAQUS: overview,'' Section 3.1.1
Overview
ABAQUS/Make will compile user-supplied postprocessing programs and create executables. The
commands used to compile and link the user-supplied program can be changed using the appropriate
ABAQUS environment file parameters; i.e., compile and link. The user can skip the procedure's
compilation step by providing a precompiled object as input.
Postprocessing executables created using this procedure must be run using the ABAQUS execution
procedure. This is necessary to set the operating system environment variables for finding the
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ABAQUS utility libraries. To run a user postprocessing program, use the following command:
abaqus job-name
Command summary
abaqus make
job=job-name
[user={source-file | object-file}]
Command line options
job
This option is used to specify the name of the executable created by this procedure. It is also used
as the default source file name.
If this option is omitted from the command line, the user will be prompted for this value.
user
This option is used to specify the name of the source or object file containing the user's program if
it is different from job-name. If a file extension is not provided, the option value with a
FORTRAN source file extension will be sought. If a file by this name is not found, the option
value with an object file extension will be sought.
3.2.11 Execution procedure for fixed format conversion utility
Reference
· ``Execution procedure for ABAQUS: overview,'' Section 3.1.1
Overview
The abaqus free utility will convert fixed format input files used with previous versions of ABAQUS
to free format.
Command summary
abaqus free
job=job-name
input=input-file
Command line options
job
This option is used to specify the name of the free format input file to be output by the utility.
input
This option is used to specify the name of the fixed format input file to be converted.
3.3 Execution examples
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3.3.1 Examples of using the abaqus command
This section contains examples of using the abaqus execution procedure.
Reference
· ``Execution procedure for ABAQUS: overview,'' Section 3.1.1
Overview
A few examples illustrate the use of the ABAQUS execution procedure. For clarity abbreviations of
the options are not employed.
ABAQUS/Standard examples
The following command is used to run a heat transfer analysis called "c8" in the background:
abaqus analysis job=c8 background
The follow-up analysis to the heat transfer analysis c8 is "c10," which is a static analysis that uses
temperature data from c8 as input. The temperature data are read in by using *TEMPERATURE,
FILE=c8 in the ABAQUS input file. The execution procedure scans the ABAQUS input file for file
dependencies of this sort. In this example the procedure will look for the c8 results file in the current
directory with the extension .fil. Results file identifiers specified with the FILE parameter can
include a path name (see ``Input syntax rules,'' Section 1.2.1), and the execution procedure will then
look in the directory specified. In either case an error message will be issued if the file does not exist.
The following command is used to run the job c10 in the "long" queue:
abaqus analysis job=c10 queue=long
This job is next restarted as "c11," using the final results from c10 as the starting point for a creep
analysis. The following command is used to run this job in the default queue:
abaqus analysis job=c11 oldjob=c10 queue=
The following command is used to run an ABAQUS/Standard analysis called "draw_imp" that imports
the results from a previously run ABAQUS/Explicit analysis called "draw_exp."
abaqus analysis job=draw_imp oldjob=draw_exp
ABAQUS/Explicit examples
The following command is used to submit an ABAQUS/Explicit analysis, called "beam," to the default
queue:
abaqus analysis job=beam convert=all queue=
Equivalent results would be obtained from a series of commands:
abaqus datacheck job=beam interactive
abaqus continue job=beam queue=
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abaqus convert=restart job=beam interactive
abaqus convert=select job=beam interactive
Note that the CPU-intensive analysis option is run in batch, while the other options are run
interactively.
ABAQUS/Standard and ABAQUS/Explicit parametercheck,
datacheck, and continue examples
Use the following command to perform a parameter check run on an input file called "parmodel":
abaqus job=parmodel parametercheck
Use the following command to perform a data check run on an input file called "parmodel" (the
parameter check is done again if this job is run after the previous one):
abaqus job=parmodel datacheck
The following command will continue the previous datacheck job to execute the analysis:
abaqus job=parmodel continue
ABAQUS/Standard and ABAQUS/Explicit scripting examples
Use the following command to execute the Python script in a file named "parstudy.psf":
abaqus script=parstudy
The following command will initiate a Python scripting session:
abaqus script
In a Python scripting session the following command will execute the Python script in a file named
"scriptfile":
script("scriptfile")
ABAQUS/Viewer example
The following command will execute ABAQUS/Viewer and load the output database file called
"beam":
abaqus viewer odb=beam
ABAQUS/Standard and ABAQUS/Explicit information examples
Use the following command to display the local installation notes:
abaqus information=local
The following command will run the job c8 in the background and output the current environment
settings to the log file:
abaqus analysis job=c8 information=environment background
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The information option can be used alone or in conjunction with any of the other procedures.
Keyword/problem database query examples
The "findkeyword" procedure will list the sample input files that use a specified keyword. For
example, to list the sample problems that use the *RESTART option with the WRITE parameter, type
the following command and data lines:
abaqus findkeyword
*RESTART,WRITE
To generate a list of sample problems that contain two keyword lines in the same file, both keywords
are included as data lines. For example,
abaqus findkeyword
*RESTART,WRITE
*NGEN
To list all sample problems that use a keyword and parameter with a value, the value must be included
on the data line. For example,
abaqus findkeyword job=beam
*BEAM SECTION,SECTION=ARBITRARY
The output is written to the file beam.dat.
User-specified parameter values (e.g., numeric data, set names, orientation names, etc.) are ignored.
The following two examples are equivalent because the value MYSET is an element set name.
abaqus findkeyword
*ELSET,ELSET=MYSET
abaqus findkeyword
*ELSET,ELSET
ABAQUS/Fetch example
The "fetch" procedure will extract an ABAQUS input file from the sample input file archive files. To
fetch the example input file c2.inp from the archive files, use the following command:
abaqus fetch job=c2.inp
To fetch all files associated with job c8 from the archive files, use the command
abaqus fetch job=c8
In this case ABAQUS will extract both the input file ( c8.inp) and the user subroutine file ( c8.f).
To fetch the sample parametric study scripting file parstudy.psf from the archive files, use the
following command:
abaqus fetch job=parstudy.psf
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ABAQUS/Make example
The "make" procedure will compile a user-provided FORTRAN source or object file and link it with
the appropriate ABAQUS object libraries to create an executable postprocessing program. To create an
executable called "pprocess" given a FORTRAN source file of the same name, use the following
command:
abaqus make job=pprocess
This program can then be run using the command:
abaqus pprocess
ABAQUS/Ascfil example
The "ascfil" procedure will convert a results file ( .fil) from binary to ASCII format and vice versa.
To convert the results file c4.fil from binary to ASCII format, use the following command:
abaqus ascfil job=c4
The translated file will have the name c4.fin.
ABAQUS/Append example
The "append" procedure will append the history information of a second results file to the end of a first
results file. The following command will append the history contents of the fjoin003.fil results
file to the end of the fjoin002.fil results file and create the file fjoin001.fil:
abaqus append job=fjoin001 oldjob=fjoin002 input=fjoin003
The same command can be given with the alternative syntax:
abaqus append -job fjoin001 -oldjob fjoin002 -input fjoin003
3.4 Environment file settings
3.4.1 Using the ABAQUS environment settings
The ABAQUS environment settings can be used to customize job execution.
Reference
· ``Execution procedure for ABAQUS: overview,'' Section 3.1.1
Overview
The ABAQUS environment settings allow the user to control various aspects of an ABAQUS job's
execution. For example, the user can
· "Tune" ABAQUS to improve its performance by changing memory-related parameters.
· Control where and how scratch files are written.
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· Provide default values for job parameters that would otherwise have to be given on the command
line.
Many other aspects of a job's execution can be configured through the environment settings. Some of
these are discussed in this section; others, which are mainly of interest to the ABAQUS site manager,
are discussed in detail in the ABAQUS Site Guide.
Environment settings hierarchy
ABAQUS environment settings are processed in the following order:
1. The host-level environment settings. These settings are applied to all ABAQUS jobs run on the
designated computer.
2. The user-level environment settings. These settings are applied to all ABAQUS jobs run in a user's
account.
3. The job-level environment settings. These settings are applied to only the designated ABAQUS
job.
Environment settings can be specified more than once. The last value processed will be the one used
for the setting if it is defined at more than one level or if it is given twice at the same level.
ABAQUS environment settings are set using special files in specific directories. The host-level
settings are set in the site directory in the abaqus account directory. The user can change these
settings by creating an environment file, abaqus_v6.env, in their home directory and/or the current
directory. Settings in the home directory file will be applied to all jobs run by that user. Settings in the
current directory file will be applied only to jobs run from the current directory.
Syntax
The entries given in the environment file must be given using Python language syntax. Entries take the
form:
parameter=value
The following is a brief overview of the Python syntax rules:
· The parameter must always have a value. The value can be any valid Python constant or
expression.
· A string value must be enclosed in a pair of double or single quotes.
· Comments are preceded by a number sign (#). All characters following a number sign on a line are
ignored. Number signs within a quoted string are part of the string, not the beginning of a
comment.
· Blank lines are ignored.
· Embedded single quotes do not require special handling if they are placed within a double quoted
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string. For example, "my value's" is translated as my value's. The same holds true for
double quotes embedded in a single quoted string. Quotes of the same type as the enclosing quotes
can be embedded if they are prefixed by the backslash (\) character.
· Triple quoted (""") strings can span more than one line, and no special treatment of quotes within
the string is necessary. Entries take the form:
parameter="""
multi-line
value
"""
· Lists must be enclosed in parentheses (( )) or square brackets ([ ]). Individual items in the list are
separated by commas. String list items must be enclosed in quotes. Entries take the form:
parameter=(value1, value2, value3)
Troubleshooting
Problems caused by faulty environment settings can be diagnosed by using the command
abaqus information=environment
This command prints all of the current environment settings.
Command line default parameters
The following parameters provide default values for various settings that would otherwise have to be
specified on the command line (see ``Execution procedure for ABAQUS/Standard and
ABAQUS/Explicit,'' Section 3.2.1). Values given on the command line override values specified in the
environment files.
cpus
Number of processors to use if parallel processing is available. The default is 1.
explicit_precision
The default precision version of ABAQUS/Explicit to run. Possible values are "single" or
"double". The default is "single".
pre_buffer
Internal buffer size in 64-bit words for the solver input file processor. The default is
1000000.
pre_memory
Number of 64-bit words for the solver input file processor. The default is 4000000.
run_mode
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Default run mode (interactive, background, or batch) if the user does not specify the run mode
on the abaqus command line. The default for abaqus analysis is "background", while the
default for abaqus viewer is "interactive".
scratch
Directory to be used for scratch files. This directory must be created by the user and given
write permission. On UNIX systems the default value is the value of the $TMPDIR
environment variable or /tmp if $TMPDIR is not defined. On NT the default value is the
value of the %TEMP% environment variable or \TEMP if this variable is not defined. During
the analysis a subdirectory will be created under this directory to hold the analysis scratch
files. The name of the subdirectory is constructed from the user's user name, the job id, and the
job's process identifier. The subdirectory and its contents are deleted upon completion of the
analysis.
solver
ABAQUS/Standard equation solver. Either the sparse solver ( "sparse") or the wavefront
solver ("wavefront") can be used. The default is "sparse".
System resource parameters
The following environment file variables can be set after the code has been installed to change the
resources used by ABAQUS and, therefore, to improve system performance. The variables are defined
as the number of 64-bit words. More detailed information about changing the system resources used by
ABAQUS is given later in this section.
pre_memory
Discussed earlier as command line parameter memory.
pre_buffer
Discussed earlier as command line parameter buffer.
standard_memory
Maximum size of the default workspace used by the ABAQUS/Standard analysis program.
The default is 8000000.
standard_buffer
Maximum size of the internal buffers for the ABAQUS/Standard analysis program. The
default is 2000000.
System customization parameters
The following is a discussion of some additional environment file parameters that are commonly used.
A complete listing of parameters can be found in the ABAQUS Site Guide.
ask_delete
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If this parameter is set equal to "no", the user will not be asked whether old job files of the
same file name should be deleted; the files will be deleted automatically. The default is
"yes".
auto_calculate
If this parameter is set equal to "yes", the postprocessing calculator will be launched
automatically at the end of an analysis if the execution procedure detects that output database
file conversion is necessary. If this parameter is set to "no", the postprocessing calculator will
not run at the end of an analysis even if the execution procedure detects that it is necessary.
The default value is "yes".
odb_output_by_default
If this parameter is set equal to "yes", output database output will be generated
automatically. If this parameter is set equal to "no", output database request keywords must
be placed in an input file to obtain output database output. The default value is "yes".
Scratch file management parameters
In some cases the size of a particular ABAQUS/Standard scratch file may exceed the space available
on an individual disk, or it may exceed a file size or file system limit for a given machine. Therefore,
the following parameters can be used to split the more substantial ABAQUS/Standard scratch files into
separate files either on the same disk or on different disks. For large ABAQUS/Standard jobs using the
wavefront solver, the ABAQUS equation file (unit 2) will usually be the largest file and can, therefore,
be split using the aux_scratch and split_scratch parameters. For large ABAQUS/Standard jobs using
the sparse solver, the factor ( .fct) file will usually be the largest file and can be split using the
split_xxx and spill_list_xxx parameters. This functionality has also been extended to allow the operator
(.opr), solver database ( .sdb), solution ( .sol), Lanczos vector (.lnc), Lanczos eigenvector
(.eig), and Lanczos scratch ( .scr) files to be split.
aux_scratch
List of directories to be used for additional scratch files if the wavefront solver file in
ABAQUS/Standard is to be split, which would be necessary if the ABAQUS equation file
(unit 2) exceeds file system limits. The list must be enclosed in parentheses or square brackets,
each directory must be enclosed in single quotation marks, and each directory must be
separated from the next by a comma. This parameter is used in conjunction with the
split_scratch parameter. If split_scratch is set but aux_scratch is not, one auxiliary scratch
file will be created in the scratch directory.
split_scratch
Size, in 64-bit words, at which to split the ABAQUS/Standard wavefront solver scratch files.
Every solver scratch file but the last will be split at this limit. The last solver scratch file will
be filled with whatever does not fit in all of the previous scratch files. The scratch file
directories are specified using the aux_scratch parameter. The default is to not split the
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scratch files.
split_xxx
List of file sizes to be used in splitting a sparse solver file specified by xxx, which can be set to
fct, opr, sdb, sol, lnc, eig, or scr. The units for the size of a given file can be specified
following the file size. The available units are b (bytes), mb (megabytes), and w (words). If the
units are not specified for a file size, the size is assumed to be in words. If no sizes are
specified with split_xxx, the maximum file size allowed on the platform in question will be
used.
spill_list_xxx
List of directories to be used for pieces of a sparse solver file specified by xxx, which can be
set to fct, opr, sdb, sol, lnc, eig, or scr. If no directories are specified with
spill_list_xxx, the scratch directory will be used for all the sparse solver files. This parameter
is used in conjunction with split_xxx. Please refer to the description below for further
explanation.
The directories specified by the aux_scratch and spill_list_xxx parameters must be created by the user
and given write permission.
Example: Splitting the factor (.fct) file
Consider using the parameters necessary to split the factor ( .fct) file. The syntax of the commands is
as follows:
split_fct=('size0 ','unit0 ','size1 ','unit1 ','¢ ¢ ¢','sizen ','unitn ')
spill_list_fct=('dir0 ','dir1 ','¢ ¢ ¢','dirm ')
The units that are listed for the file sizes for split_fct are optional. The first piece of the factor file (size
size0 ) will be written to the file jobid.fct in the directory dir0 , the second piece (size size1 ) to
jobid.fct.1 in the directory dir1 , the third piece (size size2 ) to jobid.fct.2 in the directory dir2 ,
and so on.
There are three cases that must be considered:
1. The number of file sizes specified is equal to the number of directories specified ( n=m where n is
the number of sizes given by split_fct and m is the number of directories given by spill_list_fct).
In this case a file of each specified size is written to the corresponding directory. If the nth file
requires a size that is greater than sizen , a new file jobid.fct.n+1 of maximum size sizen will
be created in the directory dirn . This process will be repeated as necessary.
2. The number of file sizes specified is greater than the number of directories specified ( n > m). In
this case the first m files will be written to the corresponding directory. All subsequent files will be
written to the directory dirm . If more than n files are required, additional files will be created in
the same fashion as in Case 1.
3. The number of file sizes specified is less than the number of directories specified ( n < m). In this
case the first n files will be written to the corresponding directory. If the nth file requires a size that
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is greater than sizen , the file jobid.fct.n+1 will be written to the directory dirn+1 . This
process will continue as necessary until the directory list is exhausted. All subsequent files will be
written to the dirm directory.
Determining when to split files
An estimate of the size of the scratch files used by ABAQUS/Standard is printed under the heading
"PROBLEM SIZE" at the end of the user input processing section of the data ( .dat) file. A user who
is running a large job in which scratch files may exceed either available disk space for a single disk or
a file system limit should check the file size estimates after running a datacheck analysis. At this point
the user can split files as necessary before continuing the analysis. For information about file size and
file system limits on a given machine, consult your system administrator. The solver database ( .sdb)
file is used during the datacheck portion of an analysis as well as during the subsequent continuation;
therefore, an analysis in which the solver database is to be split cannot be continued following a
datacheck analysis in which the file was not split. It is unlikely that it will be necessary to split the
solver database file, so this limitation should not be of great concern.
Automatic splitting of files for file size limitations
The sparse solver files will be split automatically as necessary for file size limits. Automatic splitting is
not supported for the wavefront solver equation file (unit 2).
Using aux_scratch and split_scratch with the sparse solver
Use of split_scratch and aux_scratch is not recommended for sparse solver jobs. However, if a sparse
solver job is run with aux_scratch and split_scratch set in the environment file, split_fct and
spill_list_fct will be set automatically to corresponding values to split the factor ( .fct) file. For
example, specifying
split_scratch=(size0 )
aux_scratch=('dir0 ','dir1 ')
for a sparse solver job will result in the job being run with
split_fct=(size0 )
spill_list_fct=('dir0 ','dir1 ')
Changing the system resources used by ABAQUS
The system resource parameters described above can be used to control memory use and I/O
performance for a job. For a user running small jobs the default settings for these parameters are
generally sufficient. However, large ABAQUS jobs often require a significant amount of memory and
I/O.
The schemes for handling memory use during input file processing and during analysis in
ABAQUS/Standard are somewhat different and are considered separately.
Memory in ABAQUS/Explicit is allocated as needed during the analysis. The memory requirements
for ABAQUS/Explicit are usually quite low as compared to those for ABAQUS/Standard, and memory
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use is generally not an important concern for the ABAQUS/Explicit user. Therefore, no user control is
provided for memory use in ABAQUS/Explicit.
Memory use during input file processing
There are two parameters that control memory use during input file processing: pre_memory and
pre_buffer. The value of pre_memory determines the basic core memory used. The minimum
required size of pre_memory depends on the job. If the pre_memory setting is too low, the following
error message is printed in the printed results ( .dat) file:
THERE IS NOT ENOUGH MEMORY ALLOCATED TO PROCESS THE INPUT DATA.
THE pre_memory VARIABLE IN THE ENVIRONMENT FILE IS CURRENTLY SET
TO XXX. THIS VARIABLE MUST BE INCREASED BY AT LEAST YYY WORDS
TO SUCCESSFULLY PRE-PROCESS THE MODEL.
Increasing pre_memory by the amount specified in the message above does not guarantee the job will
complete input file processing. Sometimes the solver input file processor will fail again, and you will
have to increase pre_memory even further. Therefore, you should typically increase pre_memory by
more than the amount YYY specified in the message. However, if you are using the sparse solver, you
should use some caution as described below.
pre_buffer provides an upper bound for the memory used to buffer the databases used by the solver
input file processor. I/O performance during input file processing is improved by using larger database
buffers. If you are very concerned about obtaining optimal performance during input file processing,
you should use a large value for pre_buffer. However, in the typical case the run time for input file
processing is relatively small, and the default setting for pre_buffer is sufficient.
The memory required for input file processing for an ABAQUS/Standard job is handled differently for
the wavefront and sparse solvers. The memory requirements for an ABAQUS/Explicit job are similar
to those for an ABAQUS/Standard job using the wavefront solver. The differences are described
below.
Sparse solver
The total memory used during input file processing for the sparse solver is:
``total memory = pre_memory + 5 ´ pre_buffer + additional memory''
The ``additional memory'' in the equation above is memory that is allocated dynamically
during run time. This memory amount is significant, often greater than the memory used for
pre_memory and pre_buffer combined. If the solver input file processor cannot allocate
sufficient additional memory for a job, the following error message is issued in the printed
results (.dat) file:
ERROR ALLOCATING RUN TIME MEMORY. THIS IS MEMORY ALLOCATED
IN ADDITION TO MEMORY SPECIFIED BY PRE_MEMORY AND PRE_BUFFER.
CHECK THAT THE SETTINGS OF PRE_MEMORY AND PRE_BUFFER ARE NOT
EXCESSIVELY HIGH.
As indicated in the error message, a given computer or queue on a computer has a certain
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amount of available memory. If pre_memory and pre_buffer are set so that too much of the
available memory is dedicated to them, there will not be enough free memory on the computer
to allow allocation of the "additional memory," which will cause the job to fail. Therefore, you
must exercise some caution in setting pre_memory and pre_buffer. pre_memory + 5 ´
pre_buffer should not be used to determine the queue to which a job will be submitted on a
computer for which the queues have memory limits. The additional memory must be taken
into account, and the memory limits of the queue must be greater than the total memory
required.
Wavefront solver or ABAQUS/Explicit
The total memory used during input file processing for the wavefront solver or for
ABAQUS/Explicit is:
``total memory = pre_memory + 5 ´ pre_buffer''
In this case you can use less caution in setting pre_memory and pre_buffer, and these
settings can be used to select a queue. However, the amount of memory specified by
pre_memory is allocated whether or not it is necessary. On a computer running a single job
this is not a problem, but for a multi-job or multi-user computer a "greedy" setting for
pre_memory may result in memory contention between jobs.
Recommended memory settings
For typical ABAQUS jobs it is unlikely that a value of pre_memory greater than 5,000,000 will be
required. Very large ABAQUS jobs (typically jobs with more than two million degrees of freedom)
may require pre_memory values of up to 20,000,000. Even if the input file processing phase can
complete, the analysis may be very expensive in terms of memory and time required. If a value larger
than 20,000,000 is required, you should examine the model carefully. The amount of memory in use
can probably be decreased by modifying the model. The following types of problems may use a great
deal of memory:
· Cavity radiation problems with very large cavities
· Problems in which equations or multi-point constraints are used to constrain a large number of
nodes to a single node
· Problems with DCOUP elements that include a very large number of nodes
Typically the default settings for pre_buffer are more than adequate. You should increase the
pre_buffer setting only if you are very concerned about performance during input file processing.
Memory use for analysis in ABAQUS/Standard
Memory use for analysis in ABAQUS/Standard is controlled by the parameters standard_memory
and standard_buffer. The total memory used for an analysis will be less than or equal to
standard_memory. This memory includes the memory used for the database buffers (in contrast to
input file processing, where the memory used for the database buffers is controlled only by pre_buffer
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and not by pre_memory). The setting of standard_buffer provides an upper bound for the database
buffers.
The solver input file processor calculates a minimum amount of core memory that will be required for
a particular ABAQUS/Standard job. This amount of memory is subtracted from standard_memory,
and the remaining memory is allocated to the database buffers with the limitation that a database buffer
cannot be larger than standard_buffer. There are two frequently accessed databases for which the
buffers are not limited by standard_buffer. If possible, these two databases are kept entirely in
memory to improve I/O performance. Generally these databases are very small, and keeping them in
memory will not affect memory use significantly. Large eigenvalue problems, which are discussed
below, are the exception to this rule.
If the setting for standard_memory is too small for a particular job, the solver input file processor
issues an error message. Three possible combinations of standard_memory and standard_buffer
sufficient to run the job are printed: the first gives the best possible performance with the greatest
memory requirement, the second yields a solution at the lowest possible memory requirement with
some penalty in performance, and the third gives good performance at a relatively modest memory
cost. In general, you should use the third combination of standard_memory and standard_buffer
values. This is especially true for large sparse solver jobs where a high value for standard_buffer is
not particularly beneficial.
An error message about memory allocation issued by ABAQUS/Standard indicates that
standard_memory is set to a value that is larger than what is physically available on the computer or
to a value that exceeds the memory limit for the queue in which the job is being run.
The default settings for standard_memory and standard_buffer will be sufficient for the typical
ABAQUS/Standard user.
A user that frequently runs large jobs and is often forced to rerun the solver input file processor for a
job because of an error message about insufficient standard_memory may want to modify the settings
for standard_memory and standard_buffer. Unlike the solver input file processor,
ABAQUS/Standard will not allocate all the memory specified by standard_memory if this memory is
not required by the analysis. As long as standard_buffer is kept to a reasonable value to control the
memory that will be given to the database buffers, you can generally specify a large value for
standard_memory without using unnecessary memory. As noted earlier, one of the databases that is
not limited by standard_buffer is quite large for eigenvalue problems. For such problems
ABAQUS/Standard is likely to use all the memory allowed by standard_memory, so you should use
some care in choosing a setting.
For large sparse solver jobs a large value of standard_buffer does very little for performance. A
setting of 40,960 (which is much smaller than the default) is typically sufficient.
For the wavefront solver a large setting for standard_buffer will improve performance significantly,
although it will increase memory use. If sufficient memory is available, it is recommended that
standard_buffer be set to the same value as standard_memory. Use of the wavefront solver is
recommended only for superelement generation (it is required in this case and will be selected
automatically) since the sparse solver is generally more efficient.
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Superelements and cavity radiation
ABAQUS/Standard requires that every element stiffness matrix (without assuming symmetry) fits in
memory. If there are N degrees of freedom in an element, the size of the full (unsymmetric) stiffness
matrix will be N*N. Most elements in ABAQUS/Standard have a relatively small number of degrees of
freedom; however, there are a few exceptions. Superelements with a large number of retained degrees
of freedom may require a large amount of memory. A similarly high memory requirement may be seen
with the viewfactor calculation in a large cavity radiation problem. Many analyses containing either
very large superelements or very large cavities will run very slowly even if you are able to provide
adequate memory, so some thought should be put into the modeling for these cases.
Environment file examples
Example environment files that use some of the previously discussed parameters are shown below. A
sample environment file, named hks.env, is included in the site subdirectory of the release to
show the options used at HKS.
UNIX environment file:
ask_delete="no"
# The following parameters cause the scratch files for the
# wavefront solver to be split at 5,000,000 64-bit words
# with the first portion going to /tmp and overflow
# portions going first to /ptmp and then to /a/tmp.
scratch="/tmp"
split_scratch=5000000
aux_scratch=("/ptmp", "/a/tmp")
# The following memory settings are appropriate for a
# 128 Mb machine:
# standard_memory = 75% of RAM / 8 bytes per word
# standard_buffer = standard_memory / 10
standard_memory=12000000
standard_buffer=standard_memory/10
NT environment file:
ask_delete="no"
# The following parameters cause the scratch files for the
# wavefront solver to be split at 5,000,000 64-bit words
# with the first portion going to c:\tmp and overflow
# portions going first to c:\ptmp and then to c:\a\tmp.
scratch="c:\tmp"
split_scratch=5000000
aux_scratch=("c:\ptmp", "c:\a\tmp")
# The following memory settings are appropriate for a
# 128 Mb machine:
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# standard_memory = 75% of RAM / 8 bytes per word
# standard_buffer = standard_memory / 10
standard_memory=12000000
standard_buffer=standard_memory/10
3.5 File extension definitions
3.5.1 File extensions used by ABAQUS
This section describes the files that are created by ABAQUS.
Reference
· ``Execution procedure for ABAQUS: overview,'' Section 3.1.1
Overview
The abaqus procedure generates several files. Some of these files exist only while ABAQUS is
executing and are deleted when a run completes. Other files contain analysis, postprocessing, and
translation results and are retained for use by other analysis options, restarting, or postprocessing.
File extensions
abq
State file, only used by ABAQUS/Explicit. It is written by the analysis, continue, and recover
options. It is read by the convert and recover options.
axi
Symmetric model data file, only used by ABAQUS/Standard. It is written during symmetric
model generation by the datacheck and analysis options.
bat
Batch file, created by the ABAQUS execution procedure on Windows NT systems only.
cid
Auto-release file. Contains information needed for license recovery and suspension.
com
Command file, created by the ABAQUS execution procedure except on Windows NT systems.
dat
Printed output file. It is written by the analysis, datacheck, parametercheck, and continue
options. ABAQUS/Explicit does not write analysis results to this file.
eig
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Lanczos eigenvector file. This is a temporary scratch file that is used to store the eigenvectors
calculated by the Lanczos eigensolver during the solution procedure.
f
User subroutine or other special-purpose FORTRAN file.
fct
Sparse solver factor file. This is a temporary scratch file that is used by the sparse solver in
ABAQUS/Standard.
fil
Results file. It is written by the analysis and continue options in ABAQUS/Standard and by
the convert=select and convert=all options in ABAQUS/Explicit.
fin
Results file created when changing the format of the .fil file using the abaqus ascfil
command. It can be in either ASCII or binary format. (See ``Execution procedure for ASCII
translation of results (.fil) files,'' Section 3.2.6.) The ASCII format is convenient for data
transfer between machines that do not have compatible binary data formats.
GRD
Underwater shock analysis NICE file that stores USI element, nodal, and mass data. The file
name is Ujobid.GRD. Only used in ABAQUS/USA.
inp
Analysis input file. It is read when the analysis, datacheck, and parametercheck options are
selected.
ipm
Interprocess message file. It is written when an analysis is run from ABAQUS/CAE, and it
contains a log of all messages sent from ABAQUS/Standard or ABAQUS/Explicit to
ABAQUS/CAE.
lnc
Lanczos vector file. This is a temporary scratch file that is used to store the Lanczos vectors
and weighted Lanczos vectors.
log
Log file, which contains start and end times for modules run by the current ABAQUS
execution procedure.
msg
Message file. It is written by the analysis and continue options in ABAQUS/Standard. It is
written by the analysis, datacheck, and continue options in ABAQUS/Explicit.
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mdl
Model file. It is written by the datacheck option in ABAQUS/Standard and
ABAQUS/Explicit. It is read and can be written by the analysis and continue options in
ABAQUS/Standard. It is read by the analysis and continue options in ABAQUS/Explicit.
Multiple model files may exist if the elements are reordered during an ABAQUS/Standard
analysis. In such a case a sequence identifier is attached to the job name. This file is required
for restart.
odb
Output database. It is written by the analysis and continue options in ABAQUS/Standard and
ABAQUS/Explicit. It is read by ABAQUS/Viewer and by the convert=odb option.
opr
Sparse solver operator file, which is a temporary scratch file used by the sparse solver in
ABAQUS/Standard.
pac
Package file, which contains model information and is used by ABAQUS/Explicit only. It is
written by the analysis and datacheck options. It is read by the analysis, continue, and
recover options.
par
Modified version of original parametrized input file showing input parameters and their
values.
pes
Modified version of original parametrized input file showing input free of parameter
information (after input parameter evaluation and substitution has been performed).
pmg
Parameter evaluation and substitution message file. It is written when the input file is
parametrized.
PRE
Underwater shock analysis NICE file, which stores augmented system matrices. The file name
is Ujobid.PRE. Only used in ABAQUS/USA.
prt
Part file. This file is used to store part and assembly information and is created even if the
input file does not contain an assembly definition. The part file is required for restart, import,
submodeling, sequentially coupled thermal-stress analysis, symmetric model generation, and
underwater shock analysis, even if the model is not defined in terms of an assembly of part
instances.
psf
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Python scripting file. This type of file can be created by the user but is also generated by a
parametric study.
res
Restart file, which contains information necessary to continue a previous analysis. The restart
file is written by the analysis, datacheck, and continue options. It is read by any restarted
analysis.
RSU
Underwater shock analysis NICE file that stores USA-specific restart data. The file name is
Ujobid.RSU. Used only in ABAQUS/USA.
scr
Lanczos scratch file. This is a temporary scratch file that is used to hold temporary information
required by the Lanczos solver.
sdb
Sparse solver database file. This is a temporary file that is used by the sparse solver.
sel
Selected results file, used by ABAQUS/Explicit . It is written by the analysis, continue, and
recover options and is read by the convert=select option.
sol
Sparse solver file used to store the solution vectors for a problem. This file is a temporary file
used by the sparse solver in ABAQUS/Standard.
sta
Status file. ABAQUS writes increment summaries to this file in the analysis, continue, and
recover options.
stt
State file. It is written by the datacheck option in ABAQUS/Standard and ABAQUS/Explicit.
It is read and can be written by the analysis and continue options in ABAQUS/Standard. It is
read by the analysis and continue options in ABAQUS/Explicit. Multiple state files may exist
if the elements are reordered during an ABAQUS/Standard analysis. In such a case a sequence
identifier is attached to the job name. This file is required for restart.
sup
Superelement file, used by ABAQUS/Standard.
var
File containing information about the input file variations generated by a parametric study.
023
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Communications file. It is written by the analysis and datacheck options and is read by the
analysis and continue options.
3.6 FORTRAN unit numbers
3.6.1 FORTRAN unit numbers used by ABAQUS
This section describes the FORTRAN unit numbers that are used by ABAQUS.
Reference
· ``Execution procedure for ABAQUS: overview,'' Section 3.1.1
Overview
ABAQUS uses the FORTRAN unit numbers outlined in the table below. Unless noted otherwise, users
should not try to write to these FORTRAN units from user subroutines. The user should specify unit
numbers 15-18 or unit numbers greater than 100.
FORTRAN unit numbers
Code
Unit Number
ABAQUS/Standar
1
d
2
6
Code
ABAQUS/USA
ABAQUS/Explici
Description
Internal database
Solver file
Printed output ( .dat) file (The user can
write output to this file.)
7
Message (.msg) file (The user can write
output to this file.)
8
Results (.fil) file
10
Internal database
12
Restart (.res) file
13
Plot (.mpl) file
19-30
Internal databases (scratch files). Unit
numbers 21 and 22 are always written to
disk.
61-70
If split_scratch is used in the environment
file, data written to unit 2 are split up into
files using these unit numbers.
Unit Number Description
51-55, 60, 62 Internal databases
64
USA restart (.rsu) file
66
USA AUGMAT mass storage (.pre) file
81
USA FLUMAS input .fluplm
82
USA AUGMAT input .augplm
83
USA TIMINT input .tim00n (n=step
number)
6
Printed output ( .log or .sta) file
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t
Analysis
ABAQUS/Explici
t
Packager
60
61
62
63
64
69
12
Package (.pac) file
State (.abq) file
Temporary file
Selected results ( .sel) file
Message (.msg) file
Internal database; temporary file
Restart (.res) file
23
60
61
62
63
69
Communications (.023) file
Package (.pac) file
State (.abq) file
Temporary file
Selected results ( .sel) file
Internal database; temporary file
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Part II: Output
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Output
4. Output
4.1 Output
4.1.1 Output
This section describes the different types of output that are available for postprocessing and for
monitoring an analysis.
References
· ``Output to the results file,'' Section 4.1.2
· ``Output to the output database, '' Section 4.1.3
· ``Output variable identifiers,'' Section 4.2.1
Overview
ABAQUS/Explicit can create the following output files during an analysis:
· a data file containing printed output of the model and history definitions generated by the solver
input file processor;
· an output database file containing results for postprocessing with ABAQUS/Viewer;
· a selected results file (generated using *FILE OUTPUT);
· a results file (generated by converting the selected results file) containing results for
postprocessing with third-party postprocessors;
· a message file containing diagnostic messages about the solution; and
· a status file containing diagnostic messages and information about the stable time increment and
the status of the analysis.
ABAQUS can create files for restarting an analysis--see ``Restarting an analysis,'' Section 7.1.1. These
files can also be used to extract results output not requested during analysis.
Except for the information in the status and message files, results from an ABAQUS/Explicit analysis
can be obtained only by postprocessing with ABAQUS/Viewer.
The data file
The data file (job-name.dat) is a text file generated by the solver input file processor. It contains
the model definition, the history definition, and any error and warning messages that were detected
while processing the input data.
Controlling the amount of solver input file processor information
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Output
written to the data file
Use the *PREPRINT option in the model definition section of the input file to control the amount of
information written to the data file by the solver input file processor.
Input file echo
By default, the input file will not be echoed to the data file. The ECHO parameter can be used to
activate this printout.
Usage: *PREPRINT, ECHO=YES
or
NO
Input parameter information
For parametrized input files, information about input parameters and their values can be printed in the
data file. By default, the modified version of the original input file showing this information will not be
printed in the data file. Use the PARVALUES keyword parameter to activate this printout.
Usage: *PREPRINT, PARVALUES=YES
or
NO
Parameter-free input file information
For parametrized input files, a parameter-free version (after parameter evaluation and substitution) of
the original input file can be printed in the data file. By default, this modified version of the input file
will not be printed in the data file. Use the PARSUBSTITUTION keyword parameter to activate this
printout.
Usage: *PREPRINT, PARSUBSTITUTION=YES
or
NO
Model and history data summaries
By default, the options defining the model and history data will not be summarized in the data file. Set
the MODEL and/or HISTORY parameters equal to YES to activate this printout.
Usage: *PREPRINT, MODEL=YES
or
NO, HISTORY=YES
or
NO
Viewing part and assembly information in the data file
An ABAQUS model can be defined in terms of an assembly of part instances (see ``Defining an
assembly,'' Section 2.5.1). In such a model node and element numbers can be repeated within the
definitions of different parts. These local numbers are converted internally by ABAQUS to unique
global numbers, and the output written to the data file is given in terms of those internal numbers. A
map between user-defined numbers and internal numbers is printed to the data file if any output that
includes node and element numbers is requested in the data file.
Set and surface names that appear in the data file are prefixed by the assembly and part instance names,
separated by underscores (Assembly_Part1-1_setname, for example).
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Output
Local coordinate systems defined within a part or part instance are translated and rotated according to
the positioning data given on the data lines of the *INSTANCE option.
The output database
The ABAQUS output database ( job-name.odb) is a neutral binary file used to store model
information and analysis results in terms of an assembly of part instances. ABAQUS/Viewer uses the
output database for postprocessing analysis results.
Requesting output to the output database
Variables to be written to the output database are chosen by the user from ``Output variable
identifiers,'' Section 4.2.1, using the *OUTPUT, *ELEMENT OUTPUT, *NODE OUTPUT,
*CONTACT OUTPUT, *ENERGY OUTPUT, and *INCREMENTATION OUTPUT options. See
``Output to the output database, '' Section 4.1.3, for a detailed explanation of how to generate output
database requests.
There are two types of output stored on the output database: "field" output and "history" output. The
type of output written to the output database is controlled by the *OUTPUT option. Field output is
intended to be relatively infrequent output for a large portion of the model. ABAQUS/Viewer uses
field output to generate contour plots, displaced shape plots, and symbol plots. History output is
intended to be output for a small portion of the model requested at a fairly high frequency.
ABAQUS/Viewer uses history output to generate X-Y plots. See ``Output to the output database, ''
Section 4.1.3, for detailed descriptions of field and history output.
Format of the output database
The output database is a neutral binary, platform-independent file. Unlike the restart or results files, it
can be copied directly from one computing platform to another without translation.
The selected results file
The ABAQUS/Explicit selected results file ( job-name.sel) stores user-selected results, which are
converted into the results ( job-name.fil) file for postprocessing by other commercial
postprocessing packages. The variables available for output are listed in ``Output variable identifiers,''
Section 4.2.1.
The *FILE OUTPUT option can be used to write a user-selected subset of the results for a given node
set or element set at more frequent intervals than the restart intervals. The *EL FILE, *ENERGY FILE,
and *NODE FILE options are used with the *FILE OUTPUT option to request particular output
variables (see ``Output to the results file,'' Section 4.1.2). These options are specified within a step
definition and allow the user to be selective about the amount of data written to the selected results file
to avoid using excessive disk storage. For example, when dealing with a very large model, the user
may elect to write only one restart at the end of each step, to write just the current coordinates and the
equivalent plastic strain for the entire model 20 times in the step, and to write the acceleration history
at one node for every increment in the step.
The results file
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The results file ( job-name.fil) is a sequential access file generated from the selected results file by
the convert=select (or convert=all) option of the ABAQUS execution procedure (see ``Execution
procedure for ABAQUS/Standard and ABAQUS/Explicit,'' Section 3.2.1). The results file contains
*FILE OUTPUT results, in the format described in ``Results file output format,'' Section 5.1.2.
Most commercial finite element results-display packages provide translators that use the ABAQUS
results file as their input.
The results file can also be used as a convenient medium for importing analysis results into the user's
own postprocessing program. ``Accessing the results file information,'' Section 5.1.3, provides details
on how to read this file.
Part and assembly information
An ABAQUS model can be defined in terms of an assembly of part instances (see ``Defining an
assembly,'' Section 2.5.1). However, the results file does not contain part and assembly records.
In a model defined in terms of an assembly of part instances, node and element numbers can be
repeated within the definitions of different parts. These local numbers are converted internally by
ABAQUS to unique global numbers, and the output written to the results file is given in terms of the
global (internal) numbers. A map between user-defined numbers and internal numbers is printed to the
data file if any results file output that includes node and element numbers is requested.
Set and surface names that appear in the results file are prefixed by the assembly and part instance
names, separated by underscores (Assembly_Part1-1_setname, for example).
Local coordinate systems defined within a part or part instance are translated and rotated according to
the positioning data given on the data lines of the *INSTANCE option.
Format of the results file
ABAQUS/Explicit always writes the results file output in binary format during file conversion, but the
results file can be converted to ASCII format. ASCII format is necessary if the file is to be read on a
computer system that is different from the one on which the file was written. Use the ascfil facility in
the ABAQUS execution procedure to convert a binary ABAQUS results file ( job-name.fil) to
ASCII format job-name.fin)--see ``Execution procedure for ASCII translation of results (.fil)
files,'' Section 3.2.6. ASCII format allows the results file to be transferred between different computer
systems without having to translate binary data. ASCII format is not needed if the file will always be
used on the same system or on systems that use the same binary format. For large problems a file in
ASCII format will be significantly larger than the same file in binary format.
ASCII format
``Results file output format,'' Section 5.1.2, defines the contents of the records that are written to the
results file; these descriptions also hold if the results file is written in ASCII format. All the data items
in these files are either integers, floating point numbers, or character strings. When ASCII format is
requested, each data item is translated into an equivalent character string before it is written to the file.
These strings are written in 80-character logical records in the order described in the record
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Output
definitions.
Each 80-character logical record is completely filled before the next one is started, so that any data
item can be split, with some of the characters that define the item in one logical record and the
remainder in the next. Each data item usually follows immediately behind its predecessor. The
exception is that for results file record key 2001 ABAQUS will fill out the logical record with blank
characters, so that the record can be written immediately to the physical storage medium. ABAQUS
then inserts a logical record consisting of 80 blanks, which allows the end-of-file to be handled
correctly.
The beginning of each "record" is indicated by an asterisk (*). Each floating point number begins with
the character D, followed by the number in the format E22.15. Each character string begins with the
character A, followed by eight characters (if the character string has fewer than eight characters, the
right part of the string is blank; character strings longer than eight characters are written eight
characters at a time). Each integer begins with the character I, followed by a two digit integer giving
the number of decimal digits in the integer, followed by the integer itself (written as decimal
digits).
For example, record key 1900 for an S4R element with element number 5 and nodes 195, 198, 205,
and 204 would be written
*I 18I 41900I 15AS4R
I 3195I 3198I 3205I 3204
and record key 101 for node 135 and 6 degrees of freedom would be written
*I 19I 3101I 3135D1.280271914214298E-10D1.500000000000036E+00
D-1.074629835784448E-46D 6.983222716550941E-12
D-4.084928798492785E-13D-1.072688441364597E-10
The message file
The message file (job-name.msg) is a text file that contains diagnostic messages if potential
problems are detected during an analysis. The *DIAGNOSTICS option can be used within a step
definition to control the output of diagnostic messages (see ``Explicit dynamic analysis,'' Section 6.2.1,
and ``Adjusting initial surface positions and specifying initial clearances in contact pairs, '' Section
20.2.2).
The status file
The status file ( job-name.sta) is a text file that contains, by default, mass and inertial properties
for the model, initial stable time increment information, a synopsis of the progress of the analysis
including total accumulated CPU usage and the current time increment size, and an estimate of the
memory required to process each step. The *PRINT option can be used to control additional output
including the total kinetic energy, the energy balance, the identifier of the element with the smallest
stable time increment, and the percent change in total mass of the model due to mass scaling.
The frequency at which summary increments are written to the status file depends on the duration of
the analysis in CPU minutes and the amount of output specified in the analysis. The following list
provides general guidelines for when a summary increment will be written to the status file.
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Summary information will generally be written:
· Each time restart information or results file output is written.
· Once per increment if the problem requires fewer than 20 increments.
· 20 times during the step for a short analysis (less than 40 CPU minutes).
· Every 2 CPU minutes for an analysis between 40 CPU minutes and 4000 CPU minutes.
· Up to 2000 times during the step for a long analysis (over 4000 CPU minutes).
A degree-of-freedom variable can be monitored in the status file while the analysis is running by using
the *MONITOR option. The *DIAGNOSTICS option can also be used to write additional diagnostic
information to the status file (see ``Explicit dynamic analysis,'' Section 6.2.1, and ``Adjusting initial
surface positions and specifying initial clearances in contact pairs, '' Section 20.2.2, for details).
Errors that can be detected only while packaging the data for ABAQUS/Explicit or during analysis are
also written to the status file.
Monitoring a degree of freedom in the status file
Use the *MONITOR option within a step definition to write the current value of a node and degree of
freedom to the status file.
Use the NODE and DOF parameters on the *MONITOR option to specify the node and degree of
freedom to be monitored. The value of the node and degree of freedom being monitored will appear in
the status file for every increment written by ABAQUS/Explicit during the analysis.
The node and degree of freedom being monitored can be changed from step to step by repeating the
*MONITOR option. The node and degree of freedom specified in the last occurrence of this option in
a step will be used for that step.
Usage: *MONITOR, NODE=node_number, DOF=dof
Requesting kinetic energy output
Set the ALLKE parameter on the *PRINT option equal to YES to write the kinetic energy for the
model to the status file. This output is written periodically throughout the step. The kinetic energy
output is printed by default and can be included or excluded from step to step by repeating the *PRINT
option.
Usage: *PRINT, ALLKE=YES
or
NO
Requesting total energy output
Set the ETOTAL parameter on the *PRINT option equal to YES to write the energy balance for the
model to the status file. This output is written periodically throughout the step. The energy balance is
not printed by default and can be included or excluded from step to step by repeating the *PRINT
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Output
option.
Usage: *PRINT, ETOTAL=YES
or
NO
Requesting output of the critical element
Set the CRITICAL ELEMENT parameter on the *PRINT option equal to YES to output the number of
the element with the current minimum stable time increment and its value to the status file. This output
is written periodically throughout the step. The critical element output is printed by default and can be
included or excluded from step to step by repeating the *PRINT option.
Usage: *PRINT, CRITICAL ELEMENT=YES
or
NO
Requesting output of the change in the total mass
Set the DMASS parameter on the *PRINT option equal to YES to write the percent change in total
mass of the model due to mass scaling to the status file. This output is written periodically throughout
the step. The percent change in total mass is printed by default only if mass scaling is present in the
model and can be included or excluded from step to step by repeating the *PRINT option.
Usage: *PRINT, DMASS=YES
or
NO
Requesting output in multiple steps
Output requests apply to the step in which they are given and to all subsequent steps until they are
respecified.
Postprocessing with ABAQUS/Viewer
ABAQUS/Viewer provides interactive graphical postprocessing from the ABAQUS/Explicit output
database file. Capabilities include model and deformed shape plotting, contour plotting, vector
plotting, X-Y plotting, and animation.
ABAQUS/Viewer can produce hard-copy output in the standard ABAQUS neutral plot file format. See
the ABAQUS/Viewer User's Manual for further details.
4.1.2 Output to the results file
Output quantities from the elements, nodes, and whole model can be written to the results file.
References
· ``Output,'' Section 4.1.1
· *FILE OUTPUT
· *EL FILE
· *ENERGY FILE
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· *NODE FILE
Overview
Output variables are available for:
· element integration points, element section points, whole elements, and element sets;
· nodes; and
· the whole model.
All of the output variables are defined in ``Output variable identifiers,'' Section 4.2.1.
For ABAQUS models defined in terms of an assembly of part instances (see ``Defining an assembly,''
Section 2.5.1), output in the results file is given in terms of node, element, set, and surface labels
generated internally by ABAQUS. See ``Output,'' Section 4.1.1, for details on how to relate the
internally generated numbers and names to those specified by the user.
Requesting output in ABAQUS/Explicit
Analysis results are written to the selected results file by using the *FILE OUTPUT option, as
explained in ``Output,'' Section 4.1.1. The *FILE OUTPUT option can appear only once per step but
remains in effect in subsequent steps unless it is redefined.
File output
The *FILE OUTPUT option works in conjunction with the *EL FILE, *NODE FILE, and *ENERGY
FILE options, as explained below.
The frequency of file output is controlled by the NUMBER INTERVAL and TIME MARKS
parameters on the *FILE OUTPUT option. The data are always written at the start and end of each step
in which the *FILE OUTPUT option is active. In addition, NUMBER INTERVAL must be set equal to
the number of intervals during the step at which file output will be written. The times at which the
results are written are referred to as time marks.
If NUMBER INTERVAL=10, ABAQUS/Explicit will write results 11 times: the values at the
beginning of the step and at the end of 10 equal time intervals throughout the step. The value of the
NUMBER INTERVAL parameter must be a positive integer.
By default, results will be written at the increment ending immediately after each time mark (TIME
MARKS=NO). If TIME MARKS=YES, the time increment size will be adjusted so that an increment
will end exactly at each of the time marks calculated by dividing the step into N equal intervals.
Usage: *FILE OUTPUT, NUMBER INTERVAL=n, TIME MARKS=YES
or
NO
Element output
Use the *EL FILE option within a step to output element variables (stresses, strains, section forces,
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Output
element energies, etc.) to the selected results ( .sel) file. This option can be repeated as often as
necessary to define output for different types of element variables, different element sets, etc. The same
element (or element set) can appear in several *EL FILE options.
The *EL FILE output must be converted to the results ( .fil) file, as explained in ``Output,'' Section
4.1.1.
Element output requests remain in effect for subsequent steps unless they are redefined; the appearance
of a single *EL FILE option in a step removes all *EL FILE definitions from a previous step.
Selecting the element output variables
The following types of element variables are recognized for the purpose of defining output:
· "Element integration point" variables are associated with the integration points at which the
material calculations are performed (for example, components of stress and strain).
· "Element section point" variables are associated with the cross-section of a beam or a shell (for
example, bending moments and membrane forces on the section).
· "Whole element" variables are attributes of an entire element (for example, the total energy content
of the element).
The element variables that can be written to the results file are defined in ``Output variable identifiers,''
Section 4.2.1. ABAQUS/Explicit writes element variables only at the integration points where they are
calculated. The complete stress or strain tensors can be written, or individual scalar variables such as
equivalent plastic strain can be written.
Selecting the elements for which output is required
Use the ELSET parameter on the *EL FILE option to define the element set for which output is being
requested. If this parameter is omitted, the output will be printed for all elements and all rebars in the
model.
Usage: *EL FILE, ELSET=element_set_name
Specifying the section point in beams and shells
Output will be provided at all section points in beam and shell elements for requests made by the *EL
FILE option.
Requesting output for rebars in a reinforced model
Output for the rebars in the specified ELSET is always included for requests made by the *EL FILE
option.
Controlling the frequency of output
The frequency of *EL FILE output is controlled by the NUMBER INTERVAL and TIME MARKS
parameters on the *FILE OUTPUT option.
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Output
Specifying the directions for element output
For components of stress, strain, and similar material variables, 1, 2, and 3 refer to the directions in an
orthogonal coordinate system. If the *ORIENTATION option is not used with the element, the
stress/strain components are in the default directions defined by the convention given in
``Conventions,'' Section 1.2.2: global directions for solid elements, surface directions for shell and
membrane elements, and axial and transverse directions for beam elements.
If an *ORIENTATION option is associated with the element, the element output variable components
are in the local directions defined by the orientation (see ``Orientations,'' Section 2.2.3). The local
directions will always be written to the results file when the *EL FILE option is used and tensor output
is requested for any variable (see below). They are written automatically to the output database file.
The local directions defined in the reference configuration are rotated into the current configuration by
the average material rotation. See ``State storage,'' Section 1.5.5 of the ABAQUS Theory Manual, for
details.
Results file format
An element header record (the type 1 record described in ``Results file output format,'' Section 5.1.2) is
created for each integration point and section point in an element.
Output of local directions to the results file
In addition to the element header record, a direction record of type 85 is written when complete stress
or strain tensor output is requested.
The components are given in the local coordinate system, which may be inherent to the element (as is
the case in shells and membranes) or may have been defined with the *ORIENTATION option
(``Orientations,'' Section 2.2.3). For shells a direction record is written for every material point in the
section when tensor output is requested.
Direction output is not provided for trusses, two-dimensional beams, or axisymmetric shells.
Default element output
The *EL FILE option must be included for element results to be written to the selected results file; no
default output is provided.
Node output
Use the *NODE FILE option within a step to output nodal variables (displacements, reaction forces,
etc.) to the selected results ( .sel) file. This option can be repeated as often as necessary to define
output for different node sets. The same node (or node set) can appear in several *NODE FILE
options.
The *NODE FILE output must be converted to the results ( .fil) file, as explained in ``Output,''
Section 4.1.1.
Nodal output requests remain in effect for subsequent steps unless they are redefined; the appearance
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Output
of a single *NODE FILE option in a step removes all *NODE FILE definitions from a previous step.
Selecting the nodal output variables
The nodal variables that can be written to the results file are defined in the "Nodal variables" portion of
``Output variable identifiers,'' Section 4.2.1.
Selecting the nodes for which output is required
Use the NSET parameter on the *NODE FILE option to define the node set for which output is being
requested. If this parameter is omitted, the output will be printed for all nodes in the model.
Usage: *NODE FILE, NSET=node_set_name
Controlling the frequency of output
The frequency of *NODE FILE output is controlled by the NUMBER INTERVAL and TIME MARKS
parameters on the *FILE OUTPUT option.
Specifying the directions for nodal output
For nodal variables 1, 2, and 3 refer to the global directions X, Y, and Z, respectively. For axisymmetric
elements 1 and 2 refer to the global directions r and z. The data in the selected results file are always
output in the global directions, even if the *TRANSFORM option has been used to define local
directions at a node.
Results file format
There is no header or direction record for nodes, so it makes little difference whether items are
requested on a single line or multiple lines. If all results in a record are zero, the record is not written to
the results file.
Default nodal output
The *NODE FILE option must be included for nodal results to be written to the selected results file; no
default output is provided.
Total energy output
Use the *ENERGY FILE option within a step to output the total energy of the model or of a specific
element set to the selected results ( .sel) file. The *ENERGY FILE output must be converted to the
results (.fil) file as explained in ``Output,'' Section 4.1.1. Energy output requests remain in effect for
subsequent steps.
Selecting the energy output variables
When the *ENERGY FILE option is used, all of the total energy quantities listed in ``Output variable
identifiers,'' Section 4.2.1, are output; the variables cannot be selected individually.
Selecting the element set for which total energy output is
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Output
required
The *ENERGY FILE option does not provide output for selected element sets; when this option is
used, the total energies for the whole model will be output.
Usage: *ENERGY FILE
Controlling the frequency of output
The frequency of *ENERGY FILE output is controlled by the NUMBER INTERVAL and TIME
MARKS parameters on the *FILE OUTPUT option.
Default energy output
The *ENERGY FILE option must be included for total energy output to be written to the selected
results file; no default output is provided.
4.1.3 Output to the output database
This section describes how to write output to the output database. See the ABAQUS Command
Language Manual for a description of how to use the ABAQUS Command Language or C++ to access
an output database.
References
· ``Output,'' Section 4.1.1
· ``The postprocessing calculator,'' Section 4.3.1
· *OUTPUT
· *CONTACT OUTPUT
· *ELEMENT OUTPUT
· *ENERGY OUTPUT
· *INCREMENTATION OUTPUT
· *NODE OUTPUT
Overview
Output variables are available for:
· element integration points, element section points, whole elements, and element sets;
· nodes; and
· the whole model.
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Output
All the output variables are defined in ``Output variable identifiers,'' Section 4.2.1.
Model information and analysis results are stored in terms of an assembly of part instances (see
``Defining parts and an assembly,'' Section 2.5.1).
Requesting output to the output database
Analysis results are written to the output database by using the *OUTPUT option. Two types of output
are available:
· Field output is intended for infrequent requests for a large portion of the model and can be used to
generate contour plots, animations, symbol plots, and displaced shape plots in ABAQUS/Viewer.
Only complete sets of basic variables (for example, all the stress or strain components) can be
requested as field output.
· History output is intended for relatively frequent output requests for small portions of the model
and is displayed in X-Y data plots in ABAQUS/Viewer. Individual variables (such as a particular
stress component) can be requested.
The *OUTPUT option can be repeated as often as necessary within a step to produce both field and
history output at multiple frequencies.
Requesting field output
Include the FIELD parameter on the *OUTPUT option to request field output. The *CONTACT
OUTPUT, *ELEMENT OUTPUT, and/or *NODE OUTPUT options must be used in conjunction with
the *OUTPUT, FIELD option to request specific output variables.
Usage: *OUTPUT, FIELD
Requesting history output
Include the HISTORY parameter on the *OUTPUT option to request history output. The *CONTACT
OUTPUT, *ELEMENT OUTPUT, *ENERGY OUTPUT, *INCREMENTATION OUTPUT, and/or
*NODE OUTPUT options must be used in conjunction with the *OUTPUT, HISTORY option to
request specific output variables.
Usage: *OUTPUT, HISTORY
Controlling the output frequency
Control of the output frequency depends upon whether field or history output was selected.
Controlling the output frequency for field output
The data are always written at the start and end of each step in which the *OUTPUT, FIELD option is
active. In addition, use the NUMBER INTERVAL and TIME MARKS parameters to control the
output frequency.
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Set the NUMBER INTERVAL parameter equal to the number of intervals during the step at which
field output will be written. The value of this parameter must be a positive integer. For example, if
NUMBER INTERVAL=10 ABAQUS/Explicit will write field data 11 times: the values at the
beginning of the step and at the end of 10 equal time intervals throughout the step. If the NUMBER
INTERVAL parameter is omitted, output will be written at 20 intervals by default.
The times at which the results are written are referred to as time marks. By default, field data will be
written at the increment ending immediately after each time mark (TIME MARKS=NO). Set TIME
MARKS=YES to adjust the time increment size so that an increment will end exactly at each of the
time marks calculated by dividing the step into n equal intervals.
Usage: *OUTPUT, FIELD, NUMBER INTERVAL=n, TIME MARKS=YES or NO
Controlling the output frequency for history output
If history output is selected, the output frequency can be specified in terms of either increments or
regular intervals throughout the step.
Specifying history output in increments
Use the FREQUENCY parameter to specify the output frequency in increments. The data will be
written at this frequency as well as at the end of each step of the analysis.
Usage: *OUTPUT, HISTORY, FREQUENCY=n
Specifying history output at regular intervals
Use the TIME INTERVAL parameter to write the results at regular intervals throughout the step as
well as at the end of the step. The time increment size will not be adjusted to meet the time marks
defined by the TIME INTERVAL parameter; results will be written at the increment ending
immediately after each time mark, as defined by multiples of the time interval, t.
Usage: *OUTPUT, HISTORY, TIME INTERVAL=t
Default history output
If neither the FREQUENCY parameter nor the TIME INTERVAL parameter is specified, history
output will be written at 200 equally spaced intervals throughout the step.
Requesting output in multiple steps
Output requests apply to the step in which they are given and to all subsequent steps until they are
respecified.
Specifying additional output requests
Set OP=ADD to specify additional output requests. The output requests defined in previous steps will
remain in effect.
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Output
Usage: Use one of the following options:
*OUTPUT, FIELD, NUMBER INTERVAL=n, OP=ADD
*OUTPUT, HISTORY, FREQUENCY=n, OP=ADD
*OUTPUT, HISTORY, TIME INTERVAL=t, OP=ADD
Replacing or removing an output request of the same type and
frequency
Set OP=REPLACE to replace an output request of the same type (e.g., field or history) and frequency
with the new requests being defined with this *OUTPUT option. No other previously defined requests
will be affected.
To remove a previously defined request, use OP=REPLACE without specifying new output requests.
The OP=REPLACE option cannot be used to change the frequency of a previously defined output
request. If no matching request is found, the request specified will be added as if OP=ADD were used.
Usage: Use one of the following options:
*OUTPUT, FIELD, NUMBER INTERVAL=n, OP=REPLACE
*OUTPUT, HISTORY, FREQUENCY=n, OP=REPLACE
*OUTPUT, HISTORY, TIME INTERVAL=t, OP=REPLACE
Removing all previously defined output requests
Set OP=NEW to remove all output requests defined in previous steps and allow new requests to be
defined. This value is the default. The use of OP=NEW on either an *OUTPUT, FIELD or an
*OUTPUT, HISTORY option removes both field and history output defined in previous steps. This
parameter value only affects output defined in previous steps; using it multiple times in a single step
will not affect output defined earlier in the same step.
This option is the default; it generates the same behavior as the options used for requesting output to
the results file ( file_name.fil) and the selected results file ( file_name.sel).
Usage: Use one of the following options:
*OUTPUT, FIELD, NUMBER INTERVAL=n, OP=NEW
*OUTPUT, HISTORY, FREQUENCY=n, OP=NEW
*OUTPUT, HISTORY, TIME INTERVAL=t, OP=NEW
If OP=NEW is used on any output request within a step, the parameter values OP=ADD and
OP=REPLACE have no meaning if they are used within the same step. In this case the ADD and
REPLACE values will be ignored, and the requests will be treated as if OP=NEW were used.
Suppressing output defined in previous steps
To suppress completely all output that has been defined in previous steps, set the value of the
NUMBER INTERVAL parameter to 0 for field output or set the value of the FREQUENCY parameter
to 0 for history output.
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Preselected output requests
There are two ways to define output variables quickly and easily. Both of these options are available
for the *OUTPUT option and for the individual options used for requesting specific variable types
(e.g., nodal). The use of these options with specific variable types will be explained in detail later in
this section.
Requesting procedure-specific preselected output requests
Set VARIABLE=PRESELECT to activate a procedure-specific set of commonly requested output
variables. See Table 4.1.3-1 for a list of procedure types and their accompanying preselected variables.
All the energy variables listed in the table are written to the output database as history data. The
remaining variables listed in the table are written to the output database as field data. The variables
written to the output database may change if the procedure type changes between steps.
If VARIABLE=PRESELECT is used on the *OUTPUT option and additional output variables are
requested on the data lines of the various ouput request options, the variables requested will be
appended to the variables contained in the preselected list.
Usage: Use one of the following options:
*OUTPUT, FIELD, VARIABLE=PRESELECT
*OUTPUT, HISTORY, VARIABLE=PRESELECT
Table 4.1.3-1. List of preselected variables for various procedure types.
Preselected nodal Preselected energy
Procedure type
Preselected
variables (history)
and surface
element variables
variables (field)
(field)
*ANNEAL
none
none
none
*DYNAMIC, EXPLICIT S, LE, PE, PEEQ, U, V, A, RF,
ALLKE, ALLSE,
PEMAG
CSTRESS
ALLWK, ALLPD,
ALLCD, ALLVD,
ALLAE, ALLIE,
ALLFD, ETOTAL
ALLKE, ALLSE,
S, LE, PE, PEEQ, U, V, A, RF,
*DYNAMIC
ALLWK, ALLPD,
CSTRESS, NT,
TEMPERATURE-DISPL PEMAG
ALLCD, ALLVD,
RFL
ACEMENT, EXPLICIT
ALLAE, ALLIE,
ALLFD, ALLIHE,
ALLHF, ETOTAL
Requesting all variables applicable to the current procedure and
material type
Set VARIABLE=ALL to request all variables applicable to the current procedure and material type.
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Output
Any output request options listed below the *OUTPUT option will be ignored in this case.
Usage: Use one of the following options:
*OUTPUT, FIELD, VARIABLE=ALL
*OUTPUT, HISTORY, VARIABLE=ALL
Default output
If no options for requesting output to the output database are present in an input file, output variables
equivalent to the VARIABLE=PRESELECT option on both the *OUTPUT, FIELD and *OUTPUT,
HISTORY options will be written automatically at 20 intervals for field output and 200 intervals for
history output. These defaults can be turned off by setting the odb_output_by_default environment
file parameter to no. See ``Using the ABAQUS environment settings,'' Section 3.4.1, for details.
Furthermore, the use of the *OUTPUT option without the OP parameter overrides the default field and
history output requests for that step. For large models the default output to the output database may
increase the solution time and required disk space considerably. In such cases the user is encouraged to
review carefully the relevance of the default output variables for the proposed analysis.
Output as a result of analysis termination
When an analysis encounters a fatal error in an increment, all variables applicable to the current
procedure and material type will be written automatically to the output database as field data. The
analysis will go through an additional increment with a zero time increment size before writing these
data.
Element output
Use the *ELEMENT OUTPUT option in conjunction with the *OUTPUT option to request that
element variables (stresses, strains, section forces, element energies, etc.) be written to the output
database. This option can be repeated as often as necessary to define output for different types of
element variables, different element sets, etc. The same element (or element set) can appear in several
*ELEMENT OUTPUT options.
Selecting the element output variables
The following types of element variables are recognized for the purpose of defining output:
· ``Element integration point'' variables are associated with the integration points at which material
calculations are performed (for example, components of stress and strain).
· ``Element section point'' variables are associated with the cross-section of a beam or a shell (for
example, bending moments and membrane forces on the section).
· ``Whole element'' variables are attributes of an entire element (for example, the total energy
content of the element).
The element variables that can be written to the output database are defined in ``Output variable
identifiers,'' Section 4.2.1.
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Output
Selecting elements for which output is required
Use the ELSET parameter on the *ELEMENT OUTPUT option to define the element set for which
output is being requested. If the ELSET or TRACER SET parameters are omitted, the output will be
written for all the elements in the model.
Usage: *ELEMENT OUTPUT, ELSET=element_set_name
Specifying the section point in beam and shell elements for
history output
For history output of beams and shells output is provided at the default section points. Nondefault
output points can be specified on the first data line of the *ELEMENT OUTPUT option.
Selecting the position of element integration point and section
point output
Integration point variables and section variables can be written as field output to the output database in
three different positions (INTEGRATION POINTS, CENTROIDAL, or NODES), as chosen by the
POSITION parameter on the *ELEMENT OUTPUT option. By default, output is provided at the
integration points. ABAQUS writes only integration point data to the output database. Transferring of
results from the integration points to the user-specified position is done by the postprocessing
calculator. See ``The postprocessing calculator,'' Section 4.3.1, for details. Element history output to
the output database is always provided at the integration points.
Obtaining output at the integration points
Set POSITION=INTEGRATION POINTS to output the variables at the integration points where they
are calculated. (The position of the integration points can be obtained by using output variable
COORD--see ``Output variable identifiers,'' Section 4.2.1.)
Usage: *ELEMENT OUTPUT, POSITION=INTEGRATION POINTS
Obtaining output at the centroid of each element
Set POSITION=CENTROIDAL to output the variables at the centroid of each element (the midpoint
between the end nodes of a beam element). Centroidal values are obtained through the postprocessing
calculator by interpolation of the integration point values if the integration scheme for the element does
not include a centroidal integration point.
Usage: *ELEMENT OUTPUT, POSITION=CENTROIDAL
Obtaining element output extrapolated to the nodes
Set POSITION=NODES to extrapolate the element integration point variables to the nodes of each
element independently, without averaging the results from adjoining elements.
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Output
Usage: *ELEMENT OUTPUT, POSITION=NODES
Extrapolation and interpolation of element output variables
The shape functions of the element are used by the postprocessing calculator for purposes of
extrapolation and interpolation of output variables. Extrapolated values are generally not as accurate as
the values calculated at the integration points. Therefore, adequately detailed meshing is necessary
around nodes where accurate nodal values of such element results are needed.
For derived variables, such as Mises equivalent stress, the components are first extrapolated or
interpolated. The derived value is then calculated from the extrapolated or interpolated components.
Controlling the output frequency
Parameters on the *OUTPUT option (described earlier in this section) control the output frequency for
*ELEMENT OUTPUT.
Requesting preselected output
Set VARIABLE=PRESELECT to request the preselected, procedure-specific element output variables
described in Table 4.1.3-1. Additional variables can be defined on the data lines of the *ELEMENT
OUTPUT option.
Set VARIABLE=ALL to request all element variables applicable to the current procedure and material
type. Any variables defined on the data lines will be ignored.
Usage: *ELEMENT OUTPUT, VARIABLE=PRESELECT
or
ALL
Specifying the directions for element output
For components of stress, strain, and similar material variables 1, 2, and 3 refer to the directions for an
orthogonal coordinate system. If the *ORIENTATION option is not used with the element, the
stress/strain components are in the default directions defined by the convention given in
``Orientations,'' Section 2.2.3: global directions for solid elements, surface directions for shell and
membrane elements, and axial and transverse directions for beam elements. If the *ORIENTATION
option is used, results will be written to the output database in the default directions, and a quaternion
representing the user-defined orientation will also be written. The results displayed in
ABAQUS/Viewer will be in the directions defined by the *ORIENTATION option. The local
(material) directions (averaged at the nodes) can be visualized in ABAQUS/Viewer by selecting
Plot->Material Orientations.
Node output
Use the *NODE OUTPUT option in conjunction with the *OUTPUT option to output nodal variables
(displacements, reaction forces, etc.) to the output database. This option can be repeated as often as
necessary to define output for different node sets. The same node (or node set) can appear in several
different *NODE OUTPUT options.
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Output
Selecting the nodal output variables
The nodal variables that can be written to the output database are defined in the ``Nodal variables''
section of ``Output variable identifiers,'' Section 4.2.1.
Selecting the nodes for which output is required
Use the NSET parameter on the *NODE OUTPUT option to define the node set for which output is
being requested. If the NSET or TRACER SET parameters are omitted, the output request will be
printed for all nodes in the model.
Usage: *NODE OUTPUT, NSET=node_set_name
Controlling the output frequency
Parameters on the *OUTPUT option (described earlier in this section) control the output frequency for
*NODE OUTPUT.
Requesting preselected output
Set VARIABLE=PRESELECT to request the preselected, procedure-specific, nodal output variables
described in Table 4.1.3-1. Additional variables can be defined on the data lines of the *NODE
OUTPUT option.
Set VARIABLE=ALL to request all nodal variables applicable to the current procedure type. Any
variables defined on the data lines will be ignored.
Usage: *NODE OUTPUT, VARIABLE=PRESELECT
or
ALL
Specifying the directions for nodal output
For nodal variables 1, 2, and 3 refer to the global directions X, Y , and Z, respectively. For
axisymmetric elements 1 and 2 refer to the global directions r and z. Nodal results are always written
to the output database in the global directions.
Tracer particle output
Tracer particles can be used to obtain output at specific material points that may not correspond to a
fixed location in the mesh if adaptive meshing is used. Tracer particles follow the material motion
throughout an analysis regardless of the mesh motion, which makes them ideal for use with adaptive
meshing (see ``Defining adaptive mesh domains,'' Section 7.6.2). Both nodal and element output can
be obtained at tracer particles.
Defining tracer particles
The initial location of a tracer particle is defined to be coincident with a node, called the "parent node."
Use the *TRACER PARTICLE option to indicate the nodes whose current locations correspond to the
initial locations of tracer particles. These parent nodes will be grouped into a tracer set, whose name
must be defined by the TRACER SET parameter on the *TRACER PARTICLE option. List the parent
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Output
nodes directly on the data lines of the *TRACER PARTICLE option. Node sets, as well as individual
nodes, can be listed.
Usage: *TRACER PARTICLE, TRACER SET=tracer_set_name
Particle birth stages
Sets of tracer particles can be released from the current locations of the parent nodes at multiple times
during a step. Each release of tracer particles is referred to as a "particle birth." After particle birth the
tracer particles follow the motion of the associated material regardless of the motion of the mesh. Use
the PARTICLE BIRTH STAGES parameter on the *TRACER PARTICLE option to indicate the
number of particle birth stages in a step. One particle birth will occur at the beginning of the step, and
the rest of the stages will be evenly spaced throughout the time period of the step. If the PARTICLE
BIRTH STAGES parameter is omitted from the *TRACER PARTICLE option, a single particle birth
will occur at the beginning of the step.
Usage: *TRACER PARTICLE, TRACER SET=tracer_set_name, PARTICLE BIRTH STAGE
Tracer particles in the output database
Tracer sets will appear as both node and element sets in the output database. If a tracer set has multiple
birth stages, additional node and element sets will be created that group all the tracer particles
associated with a given birth stage. These subsets are named by appending the birth stage number to
the tracer set name. For example, if a tracer set with the name INLET is defined with two particle birth
stages, three node sets and three element sets will be created in the output database: INLET Stage
1, INLET Stage 2, and INLET (which contains all the nodes/elements from both INLET Stage
1 and INLET Stage 2).
Internal field output requests are generated automatically for the requested output variables for all the
elements or nodes in the domain that completely defines the space of possible tracer particle locations.
This region is determined by ABAQUS/Explicit and typically corresponds to the elements attached to
the parent nodes and any intersecting adaptive mesh domains. The postprocessing calculator (see ``The
postprocessing calculator,'' Section 4.3.1) will compute the value of any requested output quantity at a
tracer particle by interpolating the results from the element that encompasses the particle at the time of
output.
Requesting output at tracer particles
Use the TRACER SET parameter on the *NODE OUTPUT and *ELEMENT OUTPUT options to
indicate the name of the tracer set for which node or element output is being requested. Output will be
given for all tracer particles that are associated with the tracer set name.
Usage: *NODE OUTPUT, TRACER SET=tracer_set_name
*ELEMENT OUTPUT, TRACER SET=tracer_set_name
Field output at tracer particles
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Output
Displacement is the only valid field request for tracer particles. The positions of the tracer particles in a
specific tracer set can be obtained by requesting displacements with the *NODE OUTPUT option in
conjunction with the *OUTPUT, FIELD option. Tracer particle displacements are output automatically
if displacement output has been requested for the entire model. The node and element sets created for
tracer particles in the output database may be used to control the display of tracer particles in
ABAQUS/Viewer.
Usage: *OUTPUT, FIELD
*NODE OUTPUT, TRACER SET=tracer_set_name
U
History output at tracer particles
Requesting history output for tracer particles is similar to requesting history output for elements and
nodes. Any valid element integration point variable can be requested. U, V, A, and COORD are the
only valid nodal requests. Whole element variables and element section variables may not be
requested. History data will be available for a tracer particle only after its birth.
A tracer particle history output request will trigger an internal field output request for the desired
variables for all the elements or nodes in the domain that completely defines the space of possible
tracer particle locations.
To request history output for a set of tracer particles, use the *NODE OUTPUT and/or *ELEMENT
OUTPUT options in conjunction with the *OUTPUT, HISTORY option.
Usage: *OUTPUT, HISTORY
*NODE OUTPUT, TRACER SET=tracer_set_name
*ELEMENT OUTPUT, TRACER SET=tracer_set_name
Tracer particle propagation in multiple steps
Once defined, all tracer particles remain active in subsequent steps. However, no further particle births
will occur in the steps that follow the tracer set definition. New tracer particles can be defined in
subsequent steps by repeating the *TRACER PARTICLE option with a new tracer set name. The same
tracer set name cannot appear in more than one *TRACER PARTICLE option within an analysis.
Tracer particle deactivation
Individual tracer particles will be deactivated if they flow out of the mesh across an Eulerian boundary
or are currently tracking material points inside a failed element that has been deleted from the mesh.
History data for tracer particles will be zero at all times after deactivation.
Controlling the output frequency at tracer particles
Parameters on the *OUTPUT option (described earlier in this section) control the output frequency for
tracer particle output.
Warning: Requesting tracer set history output at a high frequency may cause the output database
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Output
(.odb) to become large. The disk space required to store the field data is directly proportional to
the size of the adaptive mesh domain and the number of tracer sets. The disk space usage is
independent of the number of tracer particles in a tracer set. The output database file size will be
reduced after the postanalysis calculation has been performed.
Total energy output
Use the *ENERGY OUTPUT option in conjunction with the *OUTPUT option to output the total
energy of the model or of a specific element set to the output database. This option is available only for
history-type output.
Selecting the energy output variables
The energy variables that can be written to the output database are defined in the ``Total energy output
quantities'' section of ``Output variable identifiers,'' Section 4.2.1. The desired variables should be
listed on the data lines of the *ENERGY OUTPUT option.
Selecting the element set for which total energy output is
required
Use the ELSET parameter on the *ENERGY OUTPUT option to define the element set for which total
energy output is being requested. If this parameter is used, the energies are summed for all of the
elements in the specified set.
If the ELSET parameter is omitted, the total energies for the whole model will be output. If total energy
output for both the whole model and for different element sets is desired, the *ENERGY OUTPUT
option must be included multiple times: once without the ELSET parameter to request energy output
for the whole model and once for each element set specified with the ELSET parameter.
Usage: *ENERGY OUTPUT, ELSET=element_set_name
Controlling the output frequency
Parameters on the *OUTPUT, HISTORY option (described earlier in this section) control the output
frequency for *ENERGY OUTPUT.
Requesting preselected output
Set VARIABLE=PRESELECT to request the preselected, procedure-specific energy output variables
described in Table 4.1.3-1. Additional variables can be defined on the data lines of the *ENERGY
OUTPUT option.
Set VARIABLE=ALL to request all energy output variables applicable to the current procedure and
material type. Any variables defined on data lines will be ignored.
Usage: *ENERGY OUTPUT, VARIABLE=PRESELECT
Surface output
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or
ALL
Output
Use the *CONTACT OUTPUT option in conjunction with the *OUTPUT option to write variables
associated with surfaces in contact problems to the output database. The *CONTACT OUTPUT option
can be repeated as often as necessary to define output for different contact pair sets and different types
of surface variables.
Selecting the surface output variables
The surface variables that can be written to the output database are listed in the ``Surface variables''
section of ``Output variable identifiers,'' Section 4.2.1. The calculation of the output variable
CSTRESS is done by the postprocessing calculator (see ``The postprocessing calculator,'' Section
4.3.1).
Selecting the contact pairs for which output is required
Use the CPSET parameter to select the contact pairs for which surface output is desired. Surface output
is contact pair-specific, so that contact output for a particular surface involved in a CPSET will include
only the contributions from the selected contact pair if the surface is involved in multiple contact pairs.
Surface output is available only for discrete (node-based or element-based) surfaces; it is not available
for any analytical surfaces within a contact pair. Use the NSET parameter to select the spot-welded
node sets for which output is desired.
If both of these parameters are omitted, surface variables will be written for all the contact pairs in the
model.
Usage: *CONTACT OUTPUT, CPSET=contact_pair_set_name, NSET=node_set_name
Controlling the output frequency
Parameters on the *OUTPUT option (described earlier in this section) control the output frequency for
*CONTACT OUTPUT.
Requesting preselected output
Set VARIABLE=PRESELECT to request the preselected, procedure-specific surface output variables
described in Table 4.1.3-1. Additional variables can be defined on the data lines of the *CONTACT
OUTPUT option.
Set VARIABLE=ALL to request all surface variables applicable to the current procedure. Any
variables defined on the data lines will be ignored.
Usage: *CONTACT OUTPUT, VARIABLE=PRESELECT
or
ALL
Time incrementation variables
Use the *INCREMENTATION OUTPUT option in conjunction with the *OUTPUT option to output
incrementation variables. Incrementation variables are available only as history output.
Selecting the incrementation output variables
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Output
The variables available with this option are the ABAQUS/Explicit time increment size, DT, and the
steady-state detection variables SSPEEQ, SSSPRD, SSFORC, and SSTORQ.
Controlling the output frequency
The output frequency for *INCREMENTATION OUTPUT output is controlled by either the TIME
INTERVAL or FREQUENCY parameter on the *OUTPUT option.
Example
The following listing is an example of requesting multiple types of output over a multi-step analysis.
*STEP
*DYNAMIC, EXPLICIT
,.1
.
.
*OUTPUT, FIELD, NUMBER INTERVAL=5, TIME MARKS=YES
*ELEMENT OUTPUT, VARIABLE=PRESELECT
PEQC,
*ELEMENT OUTPUT, ELSET=SMALL
PE,
*NODE OUTPUT, NSET=NSMALL
U, RF
*OUTPUT, HISTORY, TIME INTERVAL=0.005
*INCREMENTATION OUTPUT
DT
*ENERGY OUTPUT
ALLKE, ALLSE, ALLWK
*ENERGY OUTPUT, ELSET=SMALL
ALLPD
*END STEP
*STEP
*DYNAMIC, EXPLICIT
,.1
.
.
*OUTPUT, HISTORY, OP=REPLACE, TIME INTERVAL=0.005
*ENERGY OUTPUT, ELSET=SMALL
ALLKE, ALLPD, ALLSE
*OUTPUT, FIELD, OP=ADD, NUMBER INTERVAL=10
*ELEMENT OUTPUT
ELEN
*END STEP
The above input listing will produce both field and history output for Step 1. Field output will be
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Output
written at 5 equally spaced intervals, and the time marks will be hit exactly . This field output request
consists of preselected element variables for the whole model, as well as the variable PEEQ. In
addition, plastic strains will be written out for element set SMALL, and the nodal variables U and RF
will be written to the output database for node set NSMALL. History output will be written at a time
interval of 0.005. The ABAQUS/Explicit time step, DT, will be written, along with the
variablesALLKE, ALLSE, and ALLWK for the whole model. In addition, ALLPD will be written for
element set SMALL.
In Step 2 the history output defined in Step 1 is replaced by a request for the energy variables ALLKE,
ALLPD, and ALLSE for element set SMALL. The history output defined in Step 1 is removed. The
field output request defined in Step 1 is passed into Step 2 unchanged, but another field output request
for element energies at 10 equally spaced intervals is added.
4.2 Output variables
4.2.1 Output variable identifiers
This section describes the output variables that are available in ABAQUS/Explicit.
References
· ``Output,'' Section 4.1.1
· ``Output to the results file,'' Section 4.1.2
· ``Output to the output database, '' Section 4.1.3
Overview
Except for the information in the status file, results can be obtained from ABAQUS/Explicit only by
postprocessing.
The tables in this section list all of the output variables that are available in ABAQUS/Explicit. These
output variables can be requested for output to the results ( .fil) file using the *FILE OUTPUT
option (see ``Output to the results file,'' Section 4.1.2) or as either field- or history-type output to the
output database ( .odb) file (see ``Output to the output database, '' Section 4.1.3). All results are
available for postprocessing at the restart intervals except those results that are available only as output
to the output database, for example, CSTRESS.
Notation used in the output variable descriptions
The words .fil, .odb Field, and .odb History following the variable's description indicate the
availability of the output variable. .fil refers to output to the results file written using the *FILE
OUTPUT option. The output variable can be written to the respective file if the word ``yes'' appears
after the category name; ``no'' means that the variable is not available to that file.
If the word ``calculator'' appears after either of the .odb category names, the postprocessing calculator
must be used to extract the variable from the output database.
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Output
Direction definitions
The direction definitions depend on the variable type.
Direction definitions for element variables
For components of stress, strain, and similar material variables, 1, 2, and 3 refer to the directions in an
orthogonal coordinate system. These are global directions for solid elements, surface directions for
shell and membrane elements, and axial and transverse directions for beam elements. However, if an
*ORIENTATION (``Orientations,'' Section 2.2.3) is associated with the elements for which output is
being requested, 1, 2, and 3 are local directions.
Direction definitions for nodal variables
For nodal variables, 1, 2, and 3 refer to the global directions (1= X, 2=Y , 3=Z except for axisymmetric
elements, in which case 1=R, 2=Z). Even if the *TRANSFORM option (``Transformed coordinate
systems,'' Section 2.1.4) has been invoked at a node, the data in the results file and the selected results
file are still output in the global directions.
If the *NODE OUTPUT option is used to request field data for a node included in a *TRANSFORM
definition, a quaternion representing the rotation from the global directions is written to the output
database. ABAQUS/Viewer automatically uses this quaternion to transform the nodal results into the
local directions. Nodal history data written to the output database are always stored in the global
directions.
Principal value output
Output of the principal values can be requested for stresses, logarithmic strains, and nominal strains.
Either all principal values or the minimum, intermediate, or maximum values can be obtained. All
principal values of tensor ABC are obtained with the request ABCP, and the minimum, intermediate,
and maximum principal values are obtained with the requests ABCP1, ABCP2, and ABCP3,
respectively. For three-dimensional, plane strain, and axisymmetric elements all three principal values
are obtained. For plane stress, membrane, and shell elements only the in-plane principal values are
obtained, and only the minimum and maximum principal values can be requested. Principal values
cannot be obtained for beam and truss elements, and principal values of plastic strains cannot be
requested.
Tensor output to the output database
Tensor variables that are written to the output database as field-type output are written as principal
values and a quaternion that represents the rotation of the coordinate axes from the global system to
the principal direction system. ABAQUS/Viewer calculates all the components and invariants from
these principal values and the quaternion. Therefore, when a tensor variable is requested as field data,
it is unnecessary to ask for principal values or invariants since they are always available in
ABAQUS/Viewer. If, however, a principal value is desired as history-type output, it must be explicitly
requested since ABAQUS/Viewer does no calculations on history data.
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Output
Requesting output of components
Individual components of variables can be requested as history-type output in the output database for
X-Y plotting in ABAQUS/Viewer. Individual component requests are not available for field-type
output. If a particular component is desired for contouring in ABAQUS/Viewer, request field output of
the generic variable (e.g., S for stress). Output for individual components of this field output can be
requested in ABAQUS/Viewer.
Element integration point variables
Element integration point variables are output using the *EL FILE option (see ``Output to the results
file,'' Section 4.1.2) and the *ELEMENT OUTPUT option (see ``Output to the output database, ''
Section 4.1.3).
Tensors and invariants
S
All stress components.
.fil: yes .odb Field: yes .odb History: yes
Sij
ij-component of stress (i ∙ j ∙ 3).
.fil: no .odb Field: no .odb History: yes
SP
All principal stress components.
.fil: yes .odb Field: yes .odb History: yes
SPn
Minimum, intermediate, and maximum principal stress components ( SP1 ∙ SP2 ∙ SP3).
.fil: no .odb Field: no .odb History: yes
E
All infinitesimal strain components for geometrically linear analysis.
.fil: yes .odb Field: yes .odb History: yes
Eij
ij-component of infinitesimal strain (i ∙ j ∙ 3).
.fil: no .odb Field: no .odb History: yes
LE
All logarithmic strain components.
.fil: yes .odb Field: yes .odb History: yes
LEij
ij-component of logarithmic strain (i ∙ j ∙ 3).
.fil: no .odb Field: no .odb History: yes
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Output
LEP
All principal logarithmic strain components.
.fil: yes .odb Field: yes .odb History: yes
LEPn
Minimum, intermediate, and maximum principal logarithmic strain components ( LEP1 ∙ LEP2 ∙
LEP3).
.fil: no .odb Field: no .odb History: yes
NE
All nominal strain components.
.fil: yes .odb Field: yes .odb History: yes
NEij
ij-component of nominal strain (i ∙ j ∙ 3).
.fil: no .odb Field: no .odb History: yes
NEP
All principal nominal strain components.
.fil: yes .odb Field: yes .odb History: yes
NEPn
Minimum, intermediate, and maximum principal nominal strain components ( NEP1 ∙ NEP2 ∙
NEP3).
.fil: no .odb Field: no .odb History: yes
PE
All plastic strain components.
.fil: yes .odb Field: yes .odb History: yes
PEij
ij-component of plastic strain (i ∙ j ∙ 3).
.fil: no .odb Field: no .odb History: yes
PEP
All principal plastic strains.
.fil: no .odb Field: yes .odb History: yes
PEPn
Minimum, intermediate, and maximum principal plastic strains.
.fil: no .odb Field: no .odb History: yes
ERV
Volumetric strain rate.
.fil: yes .odb Field: yes .odb History: yes
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Output
MISES
q
Mises equivalent stress, defined as q = 32 S : S, where S is the deviatoric stress tensor, defined
as S = ¾ + pI, where ¾ is the stress and p = ¡ 13 trace(¾ ) is the equivalent pressure stress.
.fil: yes .odb Field: yes .odb History: yes
PRESS
Equivalent pressure stress, p =¡ 13 trace(¾ ).
.fil: yes .odb Field: yes .odb History: yes
PEEQ
Equivalent plastic strain.
For porous metal plasticity PEEQ is the equivalent plastic strain in the matrix material defined as
R ¾ :d"pl
.
(1¡f )¾y
For cap plasticity PEEQ gives pb (the cap position).
For foam plasticity PEEQ gives pc (the current position of the yield surface).
.fil: yes .odb Field: yes .odb History: yes
Additional element stresses
TSHR
All transverse shear stress components for shell elements S4R and S3R.
.fil: yes .odb Field: yes .odb History: yes
TSHR13
13-component of transverse shear stress.
.fil: no .odb Field: no .odb History: yes
TSHR23
23-component of transverse shear stress.
.fil: no .odb Field: no .odb History: yes
Energy densities
ENER
All energy densities.
.fil: yes .odb Field: yes .odb History: yes
SENER
Elastic strain energy density, per unit volume.
.fil: no .odb Field: no .odb History: yes
PENER
Energy dissipated by rate-independent and rate-dependent plasticity, per unit volume.
.fil: no .odb Field: no .odb History: yes
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Output
CENER
Energy dissipated by viscoelasticity, per unit volume (not supported for hyperelastic and
hyperfoam material models).
.fil: no .odb Field: no .odb History: yes
VENER
Energy dissipated by viscous effects, per unit volume.
.fil: no .odb Field: no .odb History: yes
State and field variables
SDV
Solution-dependent state variables.
.fil: yes .odb Field: yes .odb History: yes
SDVn
Solution-dependent state variable n.
.fil: no .odb Field: no .odb History: yes
TEMP
Temperature.
.fil: yes .odb Field: yes .odb History: yes
DENSITY
Material density.
.fil: no .odb Field: yes .odb History: yes
FV
Field variables.
.fil: no .odb Field: yes .odb History: yes
FVn
Field variable n.
.fil: no .odb Field: no .odb History: yes
Composite failure measures
CFAILURE
All failure measure components.
.fil: no .odb Field: yes .odb History: no
MSTRS
Maximum stress theory failure measure.
.fil: no .odb Field: no .odb History: no
TSAIH
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Output
Tsai-Hill theory failure measure.
.fil: no .odb Field: no .odb History: no
TSAIW
Tsai-Wu theory failure measure.
.fil: no .odb Field: no .odb History: no
AZZIT
Azzi-Tsai-Hill theory failure measure.
.fil: no .odb Field: no .odb History: no
MSTRN
Maximum strain theory failure measure.
.fil: no .odb Field: no .odb History: no
Additional plasticity quantities
PEQC
All equivalent plastic strains, when the model has more than one yield/failure surface.
.fil: yes .odb Field: yes .odb History: yes
PEQCn
nth equivalent plastic strain ( n = 1; 2; 3; 4 ).
For cap plasticity: PEQC provides equivalent plastic strains for all three possible yield/failure
surfaces (Drucker-Prager failure surface - PEQC1, cap surface - PEQC2, and transition surface PEQC3) and the total volumetric plastic strain ( PEQC4). The first three identifiers also provide a
yes/no flag, telling whether the yield surface is currently active or not (AC YIELD: "actively
yielding").
When PEQC is requested as output to the output database, the active yield flags for each
component are named AC YIELD1, AC YIELD2, etc.
.fil: no .odb Field: no .odb History: yes
VOIDR
Void ratio. Available only for points where the *CAP PLASTICITY material behavior is included.
.fil: no .odb Field: yes .odb History: yes
Porous metal plasticity quantities
VVF
Void volume fraction (porous metal plasticity).
.fil: yes .odb Field: yes .odb History: yes
VVFG
Void volume fraction due to growth (porous metal plasticity).
.fil: yes .odb Field: yes .odb History: yes
1-263
Output
VVFN
Void volume fraction due to nucleation (porous metal plasticity).
.fil: yes .odb Field: yes .odb History: yes
Cracking model quantities
CKE
All cracking strain components.
.fil: yes .odb Field: no .odb History: no
CKEij
ij-component of cracking strain.
.fil: no .odb Field: no .odb History: no
CKLE
All cracking strain components in local crack axes.
.fil: yes .odb Field: no .odb History: no
CKLEij
ij-component of cracking strain in local crack axes.
.fil: no .odb Field: no .odb History: no
CKEMAG
Cracking strain magnitude, defined as
q
¡ ck ¢2
2
2
(eck
+ (eck
nn ) + ett
ss ) .
.fil: yes .odb Field: no .odb History: no
CKLS
All stress components in local crack axes.
.fil: yes .odb Field: no .odb History: no
CKLSij
ij-component of stress in local crack axes.
.fil: no .odb Field: no .odb History: no
CRACK
Crack orientations.
.fil: yes .odb Field: no .odb History: no
CKSTAT
Crack status of each crack. CKSTAT can have the following values for each crack: 0.0=uncracked,
1.0=closed crack, 2.0=actively cracking, 3.0=crack closing/reopening.
.fil: yes .odb Field: no .odb History: no
Rebar quantities
RBFOR
1-264
Output
Force in rebar.
.fil: yes .odb Field: yes .odb History: yes
RBANG
Angle, in degrees, between rebar and isoparametric direction specified with the ISODIRECTION
parameter on the *REBAR option. Available only for shell and membrane elements.
.fil: yes .odb Field: no .odb History: no
RBROT
Change in angle, in degrees, between rebar and isoparametric direction specified with the
ISODIRECTION parameter on the *REBAR option. Available only for shell and membrane
elements.
.fil: yes .odb Field: no .odb History: no
Coupled thermal-stress elements
HFL
Current magnitude and components of the heat flux vector.
.fil: yes .odb Field: yes .odb History: yes
HFLM
Current magnitude of the heat flux vector.
.fil: no .odb Field: no .odb History: yes
HFLn
Component n of the heat flux vector (n = 1; 2; 3 ).
.fil: no .odb Field: no .odb History: yes
Element section variables
Element section variables are output using the *EL FILE option (see ``Output to the results file,''
Section 4.1.2) and the *ELEMENT OUTPUT option (see ``Output to the output database, '' Section
4.1.3). These variables are available only for beam and shell elements with the exception of STH,
which is also available for membrane elements. They are defined for particular elements in the element
descriptions in Part V, "Elements."
STH
Section thickness (shell and membrane elements only).
.fil: yes .odb Field: yes .odb History: yes
SF
All section resultant components, both translational (forces) and rotational (moments).
.fil: yes .odb Field: yes .odb History: yes
SFn
Section force component n, n = 1; 2; 3; 4; 5 for shells; n = 1; 2; 3 for beams.
1-265
Output
.fil: no .odb Field: no .odb History: yes
SMn
Section moment component n, n = 1; 2; 3 .
.fil: no .odb Field: no .odb History: yes
SE
All section nominal strains, both translational and rotational (e.g., midplane strain and curvature in
shells).
.fil: yes .odb Field: yes .odb History: yes
SEn
Section nominal strain component n, n = 1; 2; 3; 4; 5; 6 for shells; n = 1; 2; 3 for beams.
.fil: no .odb Field: no .odb History: yes
SKn
Section curvature change or twist n, n = 1; 2; 3 .
.fil: no .odb Field: no .odb History: yes
SSAVG
All average membrane and transverse shear stress components (shell elements only).
.fil: yes .odb Field: automatic .odb History: no
SSAVGn
Average membrane or transverse shear stress component n, n = 1; 2; 3; 4; 5 (shell elements only).
.fil: no .odb Field: no .odb History: no
Whole element variables
Whole element variables are output using the *EL FILE option (see ``Output to the results file,''
Section 4.1.2) and the *ELEMENT OUTPUT option (see ``Output to the output database, '' Section
4.1.3).
ELEN
All energy magnitudes in the element.
.fil: yes .odb Field: yes .odb History: yes
ELSE
Total elastic strain energy in the element (includes energy in transverse shear deformation in
shells).
.fil: no .odb Field: no .odb History: yes
ELCD
Total energy dissipated in the element by viscoelastic deformation. (Not supported for hyperelastic
and hyperfoam material models.)
.fil: no .odb Field: no .odb History: yes
1-266
Output
ELPD
Total energy dissipated in the element by rate-independent and rate-dependent plastic deformation.
.fil: no .odb Field: no .odb History: yes
ELVD
Total energy dissipated in the element by viscous effects. This includes bulk viscosity and material
damping.
.fil: no .odb Field: no .odb History: yes
ELASE
Total "artificial" strain energy in the element. This includes hourglass energy and drilling stiffness
energy in shells.
.fil: no .odb Field: no .odb History: yes
ELIHE
Internal heat energy in the element.
.fil: no .odb Field: no .odb History: yes
ELEDEN
All element energy density components.
.fil: no .odb Field: automatic .odb History: no
ESEDEN
Total elastic strain energy density in the element.
.fil: no .odb Field: no .odb History: no
EPDDEN
Total energy dissipated per unit volume in the element by rate-independent and rate-dependent
plastic deformation.
.fil: no .odb Field: no .odb History: no
ECDDEN
Total energy dissipated per unit volume in the element by viscoelasticity.
.fil: no .odb Field: no .odb History: no
EVDDEN
Total energy dissipated per unit volume in the element by viscous effects.
.fil: no .odb Field: no .odb History: no
EASEDEN
Total "artificial" strain energy density in the element (energy associated with constraints used to
remove singular modes, such as hourglass control).
.fil: no .odb Field: no .odb History: no
EIHEDEN
Internal heat energy density in the element.
1-267
Output
.fil: no .odb Field: no .odb History: no
EDT
Element stable time increment.
.fil: yes .odb Field: yes .odb History: yes
EMSF
Element mass scaling factor.
.fil: yes .odb Field: yes .odb History: yes
STATUS
Status of element (shear failure model, tensile failure model, porous failure criterion, brittle failure
model, Johnson-Cook plasticity model, and VUMAT). The status of an element is 1.0 if the element
is active, 0.0 if the element is not.
.fil: yes .odb Field: yes .odb History: yes
Connector elements
CTF
All components of connector total forces and moments.
.fil: yes .odb Field: no .odb History: yes
CTFn
Connector total force component n (n = 1; 2; 3 ).
.fil: no .odb Field: no .odb History: yes
CTMn
Connector total moment component n (n = 1; 2; 3 ).
.fil: no .odb Field: no .odb History: yes
CEF
All components of connector elastic forces and moments.
.fil: yes .odb Field: no .odb History: yes
CEFn
Connector elastic force component n (n = 1; 2; 3 ).
.fil: no .odb Field: no .odb History: yes
CEMn
Connector elastic moment component n (n = 1; 2; 3 ).
.fil: no .odb Field: no .odb History: yes
CVF
All components of connector viscous forces and moments.
.fil: yes .odb Field: no .odb History: yes
1-268
Output
CVFn
Connector viscous force component n (n = 1; 2; 3 ).
.fil: no .odb Field: no .odb History: yes
CVMn
Connector viscous moment component n (n = 1; 2; 3 ).
.fil: no .odb Field: no .odb History: yes
CSF
All components of connector friction forces and moments.
.fil: yes .odb Field: no .odb History: yes
CSFn
Connector friction force component n (n = 1; 2; 3 ).
.fil: no .odb Field: no .odb History: yes
CSMn
Connector friction moment component n (n = 1; 2; 3 ).
.fil: no .odb Field: no .odb History: yes
CRF
All components of connector reaction forces and moments.
.fil: yes .odb Field: no .odb History: yes
CRFn
Connector reaction force component n (n = 1; 2; 3 ).
.fil: no .odb Field: no .odb History: yes
CRMn
Connector reaction moment component n (n = 1; 2; 3 ).
.fil: no .odb Field: no .odb History: yes
CCF
All components of connector concentrated forces and moments.
.fil: yes .odb Field: no .odb History: yes
CCFn
Connector concentrated force component n (n = 1; 2; 3 ).
.fil: no .odb Field: no .odb History: yes
CCMn
Connector concentrated moment component n (n = 1; 2; 3 ).
.fil: no .odb Field: no .odb History: yes
CP
Relative positions in all directions.
1-269
Output
.fil: yes .odb Field: no .odb History: yes
CPn
Relative position in the n-direction (n = 1; 2; 3 ).
.fil: no .odb Field: no .odb History: yes
CPRn
Relative angular position in the n-direction (n = 1; 2; 3 ).
.fil: no .odb Field: no .odb History: yes
CU
Relative displacements and rotations in all directions.
.fil: yes .odb Field: no .odb History: yes
CUn
Relative displacement in the n-direction (n = 1; 2; 3 ).
.fil: no .odb Field: no .odb History: yes
CURn
Relative rotation in the n-direction (n = 1; 2; 3 ).
.fil: no .odb Field: no .odb History: yes
CCU
Constitutive displacements and rotations in all directions.
.fil: yes .odb Field: no .odb History: yes
CCUn
Constitutive displacement in the n-direction (n = 1; 2; 3 ).
.fil: no .odb Field: no .odb History: yes
CCURn
Constitutive rotation in the n-direction (n = 1; 2; 3 ).
.fil: no .odb Field: no .odb History: yes
CV
Relative velocities in all directions.
.fil: yes .odb Field: no .odb History: yes
CVn
Relative velocity in the n-direction (n = 1; 2; 3 ).
.fil: no .odb Field: no .odb History: yes
CVRn
Relative angular velocity in the n-direction (n = 1; 2; 3 ).
.fil: no .odb Field: no .odb History: yes
1-270
Output
CA
Relative accelerations in all directions.
.fil: yes .odb Field: no .odb History: yes
CAn
Relative acceleration in the n-direction (n = 1; 2; 3 ).
.fil: no .odb Field: no .odb History: yes
CARn
Relative angular acceleration in the n-direction (n = 1; 2; 3 ).
.fil: no .odb Field: no .odb History: yes
CSLST
All flags for connector stop and connector lock status.
.fil: yes .odb Field: no .odb History: yes
CSLSTi
Flag for connector stop and connector lock status in the i-direction (i = 1; :::; 6 ).
.fil: no .odb Field: no .odb History: yes
CFAILST
All flags for connector failure status.
.fil: yes .odb Field: no .odb History: yes
CFAILSTi
Flag for connector failure status in the i-direction (i = 1; :::; 6 ).
.fil: no .odb Field: no .odb History: yes
Nodal variables
Nodal variables are output using the *NODE FILE option (see ``Output to the results file,'' Section
4.1.2) and the *NODE OUTPUT option (see ``Output to the output database, '' Section 4.1.3).
COORD
Current spatial coordinates, both translational and rotational.
.fil: yes .odb Field: yes .odb History: yes
U
Displacement components.
*FILE OUTPUT and field-type output: both translation and rotation.
History-type output: translation only. Rotation results should be requested by components.
.fil: yes .odb Field: yes .odb History: yes
Un
un displacement component (n = 1; 2; 3 ).
.fil: no .odb Field: no .odb History: yes
1-271
Output
URn
Án rotation component (n = 1; 2; 3 ).
.fil: no .odb Field: no .odb History: yes
V
Velocity components (both translation and rotation).
*FILE OUTPUT and field-type output: both translation and rotation.
History-type output: translation only. Rotation results should be requested by components.
.fil: yes .odb Field: yes .odb History: yes
Vn
u_ n velocity component (n = 1; 2; 3 ).
.fil: no .odb Field: no .odb History: yes
VRn
Á_ n rotational velocity component (n = 1; 2; 3 ).
.fil: no .odb Field: no .odb History: yes
A
Acceleration components (both translation and rotation).
*FILE OUTPUT and field-type output: both translation and rotation.
History-type output: translation only. Rotation results should be requested by components.
.fil: yes .odb Field: yes .odb History: yes
An
u
Än acceleration component (n = 1; 2; 3 ).
.fil: no .odb Field: no .odb History: yes
ARn
ÁÄ1 rotational acceleration component (n = 1; 2; 3 ).
.fil: no .odb Field: no .odb History: yes
NT
All temperature values at a node. Available only for coupled thermal-stress analysis.
.fil: yes .odb Field: yes .odb History: yes
NTn
Temperature degree of freedom n at a node (n = 11). Available only for coupled thermal-stress
analysis.
.fil: no .odb Field: no .odb History: yes
RF
Reaction force and moment components.
*FILE OUTPUT and field-type output: both translation and rotation.
History-type output: translation only. Rotation results should be requested by components.
.fil: yes .odb Field: yes .odb History: yes
1-272
Output
RFn
Reaction force component n (n = 1; 2; 3 ).
.fil: no .odb Field: no .odb History: yes
RFL
All reaction flux values. Available only for coupled thermal-stress analysis.
.fil: yes .odb Field: yes .odb History: yes
RFLn
Reaction flux value n at a node (n = 11). Available only for coupled thermal-stress analysis.
.fil: no .odb Field: yes .odb History: yes
RMn
Án reaction moment component (n = 1; 2; 3 ).
.fil: no .odb Field: no .odb History: yes
PCAV
Hydrostatic fluid pressure.
.fil: yes .odb Field: yes .odb History: yes
CVOL
Hydrostatic fluid cavity volume.
.fil: yes .odb Field: yes .odb History: yes
BONDSTAT
Spot weld bond status.
.fil: no .odb Field: no .odb History: no
BONDLOAD
Spot weld bond load.
.fil: no .odb Field: no .odb History: no
Surface variables
Surface variables are output using the *CONTACT OUTPUT option (see ``Output to the output
database,'' Section 4.1.3).
Mechanical analysis-nodal quantities
CSTRESS
Contact pressure (CPRESS) and frictional shear (CSHEAR).
.fil: no .odb Field: automatic .odb History: no
FSLIP
Length of contact slip path at slave nodes during contact ( FSLIPEQ) and components of net
contact slip in local tangent directions ( FSLIP1 and FSLIP2). These variables remain constant
1-273
Output
while a slave node is not in contact.
.fil: no .odb Field: yes .odb History: no
FSLIPR
Magnitude of contact slip rate at slave nodes during contact ( FSLIPR) and components of contact
slip rate in local tangent directions ( FSLIPR1 and FSLIPR2). These variables are set to zero while
a slave node is not in contact.
.fil: no .odb Field: yes .odb History: no
BONDSTAT
Spot weld bond status.
.fil: no .odb Field: no .odb History: yes
BONDLOAD
Spot weld bond load.
.fil: no .odb Field: no .odb History: yes
Coupled temperature-displacement analysis
HFL
Heat flux per unit area leaving the surface.
.fil: no .odb Field: yes .odb History: no
HFLA
HFL multiplied by the area.
.fil: no .odb Field: yes .odb History: no
HTL
Time integrated HFL.
.fil: no .odb Field: yes .odb History: no
HTLA
HTL multiplied by the area.
.fil: no .odb Field: yes .odb History: no
SFDR
Heat flux per unit area due to frictional dissipation.
.fil: no .odb Field: yes .odb History: no
SFDRA
SFDR multiplied by the area.
.fil: no .odb Field: yes .odb History: no
SFDRT
Time integrated SFDR.
.fil: no .odb Field: yes .odb History: no
1-274
Output
SFDRTA
SFDRT multiplied by the area.
.fil: no .odb Field: yes .odb History: no
Total energy output
All of these variables are written to the results file when the *ENERGY FILE option is specified. See
``Output to the results file,'' Section 4.1.2, for details on the *ENERGY FILE option. Total energy
values can also be output to the output database using the *ENERGY OUTPUT option as history-type
data only (see ``Output to the output database, '' Section 4.1.3). Moreover, energy history totals can be
requested for part of the model as well as the whole model. Energy history totals for part of the model
are specified by including the ELSET parameter on the *ENERGY OUTPUT option.
ALLAE
"Artificial" strain energy associated with constraints used to remove singular modes (such as
hourglass control).
.fil: yes .odb Field: no .odb History: yes
ALLCD
Energy dissipated by viscoelasticity. (Not supported for hyperelastic and hyperfoam material
models.)
.fil: yes .odb Field: no .odb History: yes
ALLFD
Total energy dissipated through frictional effects. (Available only for the whole model.)
.fil: yes .odb Field: no .odb History: yes
ALLIE
Total strain energy. (ALLIE=ALLSE + ALLPD + ALLCD + ALLAE.)
.fil: yes .odb Field: no .odb History: yes
ALLKE
Kinetic energy.
.fil: yes .odb Field: no .odb History: yes
ALLPD
Energy dissipated by rate-independent and rate-dependent plastic deformation.
.fil: yes .odb Field: no .odb History: yes
ALLSE
Recoverable strain energy.
.fil: yes .odb Field: no .odb History: yes
ALLVD
Energy dissipated by viscous effects.
.fil: yes .odb Field: no .odb History: yes
1-275
Output
ALLWK
External work. (Available only for the whole model.)
.fil: yes .odb Field: no .odb History: yes
ALLIHE
Internal heat energy.
.fil: yes .odb Field: no .odb History: yes
ALLHF
External heat energy through external fluxes.
.fil: yes .odb Field: no .odb History: yes
ETOTAL
Energy balance defined as: ALLKE + ALLIE + ALLVD + ALLFD + ALLIHE - ALLWK ALLHF. (Available only for the whole model.)
.fil: yes .odb Field: no .odb History: yes
Time increment and mass output
The DT and DMASS variables are always written to the selected results file when the *FILE OUTPUT
option is specified. The time increment and the steady-state detection variables SSPEEQ, SSSPRD,
SSFORC, and SSTORQ can be written to the output database as history-type data only using the
*INCREMENTATION OUTPUT option (see ``Output to the output database, '' Section 4.1.3).
DT
Time increment.
.fil: yes .odb Field: no .odb History: yes
DMASS
Percent change in mass of the model due to mass scaling.
.fil: yes .odb Field: no .odb History: no
SSPEEQ
Steady-state equivalent plastic strain norms.
.fil: no .odb Field: no .odb History: yes
SSPEEQn
Steady-state equivalent plastic strain norm n.
.fil: no .odb Field: no .odb History: yes
SSSPRD
Steady-state spread strain norms.
.fil: no .odb Field: no .odb History: yes
SSSPRDn
Steady-state spread norm n.
1-276
Output
.fil: no .odb Field: no .odb History: yes
SSFORC
Steady-state force norms.
.fil: no .odb Field: no .odb History: yes
SSFORCn
Steady-state force norm n.
.fil: no .odb Field: no .odb History: yes
SSTORQ
Steady-state torque norms.
.fil: no .odb Field: no .odb History: yes
SSTORQn
Steady-state torque norm n.
.fil: no .odb Field: no .odb History: yes
4.3 The postprocessing calculator
4.3.1 The postprocessing calculator
The postprocessing calculator can perform operations on output quantities written to the output
database (job-name.odb). The postprocessing calculator is for use only with ABAQUS/Viewer.
References
· ``Output to the output database, '' Section 4.1.3
· ``Output variable identifiers,'' Section 4.2.1
· ``Execution procedure for ABAQUS/Standard and ABAQUS/Explicit,'' Section 3.2.1
Overview
The postprocessing calculator calculates output quantities from data written to the output database by
ABAQUS/Explicit. It then expands the output database by writing these new output quantities to the
output database. Once this expansion is done, it is not possible to convert the output database back to
its original form.
Functionality of the calculator
The postprocessing calculator performs the following calculations on data written to the output
database:
· Extrapolation of integration point quantities to the nodes or interpolation of integration point
quantities to the centroid of an element. This kind of output is requested using the POSITION
parameter on the *ELEMENT OUTPUT option. See ``Output to the output database, '' Section
1-277
Output
4.1.3, for details.
· Calculation of the output variables CPRESS and CSHEAR. See ``Output variable identifiers,''
Section 4.2.1.
· Calculation of the output variables SSAVG and ELEDEN. See ``Output variable identifiers,''
Section 4.2.1.
· Calculation of history output at tracer particles. See ``Output to the output database, '' Section
4.1.3.
Running the calculator
By default, the postprocessing calculator will run automatically upon the completion of an analysis.
During the execution of the analysis, ABAQUS will determine if there are keywords in the input file
that require the use of the calculator and will initiate the calculator upon completion if it is required.
The user can override this default behavior by using the environment variable auto_calculate in the
ABAQUS environment file. See ``Using the ABAQUS environment settings,'' Section 3.4.1, for
details.
The user can run the postprocessing calculator manually by using the convert=odb option on the
abaqus execution procedure.
The postprocessing calculator may not be available on all platforms. If the user tries to run the
calculator on a platform that does not support it, a warning message will be output to the screen. To
obtain the desired output, copy the output database file to a valid platform and run the calculator. Refer
to the ABAQUS Site Guide for a list of the platforms that support the postprocessing calculator.
To see the postprocessed results before an analysis is complete, the user can run the postprocessing
calculator manually while the analysis is still running, using the oldjob option in conjunction with the
convert=odb option on the abaqus execution procedure. The postprocessing calculator will write a
new output database using the value of the job parameter as the file name.
If the postprocessing calculator is run during an analysis without the oldjob option, ABAQUS will ask
the user to confirm that the existing output database can be overwritten. The user should make sure the
analysis is complete before running the postprocessing calculator manually without the oldjob option.
If the analysis is still running when the postprocessing calculator is run without using the oldjob
option, the output database will be corrupted.
For a detailed description of the procedure for running the postprocessing calculator manually, see
``Execution procedure for ABAQUS/Standard and ABAQUS/Explicit,'' Section 3.2.1.
If an analysis aborts because available CPU time has expired and the user restarts the analysis, the
postprocessing calculator will not automatically expand the output database from the original, aborted
run. The user must manually run the postprocessing calculator to expand the original output database
using the procedure outlined above.
1-278
File Output Format
5. File Output Format
5.1 Accessing the results file
5.1.1 Accessing the results file: overview
Writing information to the results file
The ABAQUS results file is the medium through which analysis results can be carried over into other
software, such as postprocessing programs. The results file is written by using the options described in
``Output to the results file,'' Section 4.1.2. ``Output,'' Section 4.1.1, describes how the file is written
when ASCII format is requested.
An ABAQUS model can be defined in terms of an assembly of part instances (see ``Defining an
assembly,'' Section 2.5.1). However, the results file is not organized by part; it contains internal node
and element numbers (see ``Output,'' Section 4.1.1). A map between the original numbers and part
instance names and the internal numbers is written to the data file.
Accessing information in the results file
This chapter contains technical descriptions of the results file and is intended to be read by users or
programmers who need to write programs that use the results file.
· ``Results file output format,'' Section 5.1.2, describes the format of the individual records in the
results file.
· ``Accessing the results file information,'' Section 5.1.3, describes the subroutine calls required to
read the file output, contains an example of a program written to use the ABAQUS results file, and
shows how the user can write (or modify) a results file using the ABAQUS file format.
· ``Utility routines for accessing the results file,'' Section 5.1.4, describes the utility subroutines that
can be used to access the results file.
5.1.2 Results file output format
This section describes the format of the ABAQUS results file.
References
· ``Accessing the results file: overview,'' Section 5.1.1
· ``Output variable identifiers,'' Section 4.2.1
Overview
This section describes the format of the individual records in the results file. Where applicable, the
output variable identifier used in writing a given value to the file is printed below the corresponding
2-279
File Output Format
record type description.
Record format
The results file is written as a sequential file. Each record has the following format:
Location
Length
Description
1
1
Record length(N W )
2
1
Record type key
3,4...
(N W ¡ 2)
Attributes
All words on the results file are of the same length, whether they contain integer, floating point
number, or character string data. The word length is 8 bytes.
The attributes in a given record may depend on the element type being considered. For example, the
stress components associated with three-dimensional shell elements are ¾11 , ¾22 , and ¾12 (in local
directions), while those associated with three-dimensional solids are ¾xx , ¾yy , ¾zz , ¾xy , ¾xz , and ¾yz
(in global directions if no *ORIENTATION is specified). Thus, care must be used in postprocessing
the file output to obtain appropriate results. Refer to Part V, "Elements," for a definition of the
ordering of element-dependent attributes.
In models that are defined in terms of an assembly of part instances, the results file contains internal
(global) node and element numbers, as explained in ``Output,'' Section 4.1.1. Part and assembly
records are not included in the results file.
Local coordinate system
If the components of an element quantity are in local directions, a record defining the current
directions is generated automatically for each point at which component output (record types 11, 89, or
90) is requested. The local coordinate system may be inherent to the element, as is the case in shells
and membranes, or may have been defined with the *ORIENTATION option (see ``Orientations,''
Section 2.2.3). For shells a direction record is written for every material point in the section when
tensor output is requested, and a separate direction record is written for section forces and section
strains. Direction output is not provided for trusses, two-dimensional beams, and axisymmetric shells
Label record
Some record types include labels, such as element and node set names, written in A8 format. If a label
exceeds 8 characters, an integer identifier will be written instead. This identifier can then be used to
cross-reference the actual label stored in 10A8 format on record type 1940.
Records written for any file output request
Record key: 1900
Record type: Element definitions
Attributes: 1 - Element number.
2 - Element type (characters, A8 format, left justified).
3 - First node on the element.
4 - Second node on the element.
5 - Etc.
2-280
File Output Format
Quadrilateral/brick elements that are degenerate (i.e., possessing identical nodes) are written out in
record 1900 as corresponding triangular/tetrahedral/wedge elements. For example, a CPE4R element
with two identical nodes is written as a CPE3 element, and a C3D8R element with identical third and
fourth nodes and identical seventh and eighth nodes is written as a C3D6 element.
Record key: 1901
Record type: Node definitions
Attributes: 1 - Node number.
2 - First coordinate.
3 - Second coordinate.
4 - Etc.
Record 1902 (below) defines the location of each active degree of freedom. For example, if the model
contains only two-dimensional beam elements, the only active degrees of freedom are 1, 2, and 6.
Therefore, this record would have the attributes (1, 2, 0, 0, 0, 3), meaning that degree of freedom 1
(ux ) is the first active variable at each node; degree of freedom 2 ( ux ) is the second active variable at
each node; degrees of freedom 3, 4, and 5 are not active in the model; and degree of freedom 6 is the
third active variable at each node.
Record key: 1902
Record type: Active degrees of freedom
Attributes: 1 - Location in nodal arrays of degree of freedom 1 (0 if dof 1 not active in the model).
2 - Location in nodal arrays of degree of freedom 2 (0 if dof 2 not active in the model).
3 - Etc.
Record key: 1911
Record type: Output request definition
Attributes: 1 - Flag for element-based output (0) or nodal output (1).
2 - Set name (node or element set) used in the request.
3 - Element type (only for element output).
Record key: 1921
Record type: ABAQUS Version, date, time
Attributes: 1 - ABAQUS Version number (A8 format).
2 - Date (2A8) format.
3 - Date cont'd.
4 - Time (A8 format).
5 - Number of elements in the model.
6 - Number of nodes in the model.
Record key: 1922
Record type: Heading
Attribute: 1 - Attributes 1-10. The heading entered as the first data line of the *HEADING option.
Record key: 1931
Record type: Node set.
Attributes: 1 - Node set name (A8 format). Only node sets defined as part of the model definition are
written.
2 - First node in the node set.
3 - Second node in the node set.
4 - Etc.
Record key: 1932
Record type: Node set continuation
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File Output Format
Attributes: 1 - Node number in the node set of the previous 1931 record.
2 - Etc.
Record key: 1933
Record type: Element set
Attributes: 1 - Element set name (A8 format). Only element sets defined as part of the model
definition are written.
2 - First element in the element set.
3 - Second element in the element set.
4 - Etc.
Record key: 1934
Record type: Element set continuation
Attributes: 1 - Element number in the element set of the previous 1933 record.
2 - Etc.
Record key: 1940
Record type: Label cross-reference
Attributes: 1 - Integer reference.
2 - Label (10A8 format).
Records written once per increment
Record key: 2000
Record type: Increment start record
Attributes: 1 - Total time.
2 - Step time.
3 - Currently not used.
4 - Currently not used.
5 - Procedure type: gives a key to the step type. See Table 5.1.2-1 at the end of this
section.
6 - Step number.
7 - Increment number.
8 - Currently not used.
9 - Currently not used.
10 - Currently not used.
11 - Time increment.
12 - Attributes 12-21. The step subheading entered as the first data line of the *STEP
option (A8 format).
The following record is written after all data records have been written for the increment.
Record key: 2001
Record type: Increment end record
Attribute: 1 - No attributes.
Records written when the *EL FILE option is used
These records contain data about element variables at integration points within the elements, at the
centroid of elements, or at the nodes of an element.
Record key: 1
Record type: Element header record
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File Output Format
Attributes: 1 - Element number.
2 - Integration point number if the subsequent records contain integration point data. 1 for
all element types in ABAQUS/Explicit.
3 - Section point number if this is a shell or beam element and the subsequent records
contain data at an integration point through the section. 0 for continuum elements and for
section values in beams and shell elements.
4 - Location identification. 0 if the subsequent records contain data at the element's
integration point; 3 if the subsequent records contain data associated with rebar within an
element.
5 - Rebar name if the subsequent records contain values associated with a named rebar.
6 - Number of direct stresses at a point ( NDI).
7 - Number of shear stresses at a point ( NSHR).
8 - Number of directions in which displacement or temperature gradients are computed in
the element (NDIR).
9 - Number of section force or section strain components ( NSFC).
Record key: 2
Output variable identifier: TEMP
Record type: Temperature
Attribute: 1 - Temperature.
Record key: 5
Output variable identifier: SDV
Record type: Solution-dependent state variables
Attributes: 1 - State variable 1.
2 - State variable 2.
3 - Etc.
Record key: 11
Output variable identifier: S
Record type: Stresses
Attributes: 1 - First stress component.
2 - Second stress component.
3 - Etc. (See the element description in Part V, "Elements," for a definition of the number
and type of the components for the element type.)
Record key: 13
Output variable identifier: SF
Record type: Section forces and moments
Attributes: 1 - First section force.
2 - Second section force.
3 - Etc. (See Part V, "Elements," for a description of which section forces are available for
each beam or shell element type.)
Record key: 14
Output variable identifier: ENER
Record type: Energy densities
Attributes: 1 - Elastic strain energy.
2 - Plastic dissipation.
3 - Viscoelastic dissipation (not supported for hyperelastic and hyperfoam material
2-283
File Output Format
models).
4 - Viscous dissipation.
5 - Currently not used.
Record key: 19
Output variable identifier: ELEN
Record type: Energy summed over element
Attributes: 1 - Currently not used.
2 - Strain energy.
3 - Plastic dissipation.
4 - Viscoelastic dissipation (not supported for hyperelastic and hyperfoam material
models).
5 - Viscous dissipation.
6 - Artificial strain energy.
7 - Currently not used.
8 - Currently not used.
9 - Internal heat energy.
Record key: 21
Output variable identifier: E
Record type: Infinitesimal strains
Attributes: 1 - First infinitesimal strain component.
2 - Second infinitesimal strain component.
3 - Etc. (See the element description in Part V, "Elements," for a definition of the number
and type of the components for the element type.)
Record key: 22
Output variable identifier: PE
Record type: Plastic strains
Attributes: 1 - First plastic strain component.
2 - Second plastic strain component.
3 - Etc.; followed by "0.0, UNUSED, 0.0" for consistency with the length of the
ABAQUS/Standard plastic strain record. (See Part V, "Elements," for a definition of the
number and the type of the components for the element type.)
Record key: 26
Output variable identifier: CRACK
Record type: 3-D concrete crack direction (3-D, plane strain, and axisymmetric). The crack direction
vectors are in the global axes.
Attributes: 1 - 11-component. This is the first component of the first crack.
2 - 12-component. This is the first component of the first crack.
3 - 13-component. This is the third component of the first crack.
4 - 21-component. This is the first component of the second crack.
5 - 22-component. This is the second component of the second crack.
6 - 23-component. This is the third component of the second crack.
7 - 31-component. This is the first component of the third crack.
8 - 32-component. This is the second component of the third crack.
9 - 33-component. This is the third component of the third crack.
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File Output Format
Record key: 26
Output variable identifier: CRACK
Record type: 2-D concrete crack direction (plane stress, shells, and membranes). The crack direction
vectors are in the global axes for the continuum elements and in the local element basis system axes
for the structural elements.
Attributes: 1 - 11-component. This is the first component of the first crack.
2 - 12-component. This is the first component of the first crack.
3 - 21-component. This is the first component of the second crack.
4 - 22-component. This is the second component of the second crack.
5 - Not used (=0)
6 - Not used (=0)
7 - Not used (=0)
8 - Not used (=0)
9 - Not used (=0)
Record key: 26
Output variable identifier: CRACK
Record type: 1-D concrete crack direction (beams and trusses). The crack direction vector is always
along the path of the element.
Attributes: 1 - 11-component. This is the first component of the first crack.
2 - Not used (=0)
3 - Not used (=0)
4 - Not used (=0)
5 - Not used (=0)
6 - Not used (=0)
7 - Not used (=0)
8 - Not used (=0)
9 - Not used (=0)
Record key: 27
Output variable identifier: STH
Record type: Shell thickness
Attribute: 1 - Current thickness.
Record key: 28
Output variable identifier: HFL
Record type: Heat flux vector
Attributes: 1 - Magnitude.
2 - First component.
3 - Second component.
4 - Etc.
Record key: 29
Output variable identifier: SE
Record type: Section strains
Attributes: 1 - First section strain.
2 - Second section strain.
3 - Etc. (See the element description in Part V, "Elements," for a definition of what section
strains are available for each beam or shell element type.)
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File Output Format
Record key: 45
Output variable identifier: PEQC
Record type: Equivalent plastic strain components for cap plasticity
Attributes: 1 - Equivalent plastic strain for Drucker-Prager failure surface.
2 - Actively yielding flag (yes or no, A8 format) for Drucker-Prager failure surface.
3 - Equivalent plastic strain for cap surface.
4 - Actively yielding flag (yes or no, A8 format) for cap surface.
5 - Equivalent plastic strain for transition surface.
6 - Actively yielding flag (yes or no, A8 format) for transition surface.
7 - Total volumetric plastic strain.
8 - Actively yielding flag (yes or no, A8 format).
Record key: 48
Output variable identifier: TSHR
Record type: Transverse shear stresses in 13 and 23 planes
Attributes: 1 - Component 13.
2 - Component 23.
Record key: 61
Output variable identifier: STATUS
Record type: Element status
Attribute: 1 - Status of element (shear failure model, tensile failure model, porous failure criterion,
brittle failure model, Johnson-Cook plasticity model, and VUMAT). The status of an element
is 1.0 if the element is active, 0.0 if the element is not.
Record key: 73
Output variable identifier: PEEQ
Record type: Equivalent plastic strain
Attribute: 1 - Equivalent plastic strain. For cap plasticity it is pb (the cap position).
Record key: 74
Output variable identifier: PRESS
Record type: Mean pressure stress
Attribute: 1 - Mean pressure stress.
Record key: 75
Output variable identifier: MISES
Record type: Mises equivalent stress
Attribute: 1 - Mises stress.
Record key: 79
Output variable identifier: ERV
Record type: Volumetric strain rate
Attribute: 1 - Volumetric strain rate.
Record key: 89
Output variable identifier: LE
Record type: Logarithmic strains
Attributes: 1 - First logarithmic strain component.
2 - Second logarithmic strain component.
3 - Etc. (See Part V, "Elements," for a definition of the number and the type of the
components for the element type.)
Record key: 90
Output variable identifier: NE
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File Output Format
Record type: Nominal strains
Attributes: 1 - First nominal strain component.
2 - Second nominal strain component.
3 - Etc. (See Part V, "Elements," for a definition of the number and the type of the
components for the element type.)
Record key: 476
Output variable identifier: EMSF
Record type: Scaling factor
Attribute: 1 - Element mass scaling factor.
Record key: 477
Output variable identifier: EDT
Record type: Element time increment
Attribute: 1 - Element stable time increment.
Principal value records
For all principal values, the number of components equals NDI unless NDI equals 1, in which case the
number of components equals NDI plus NSHR, where NDI and NSHR are given on the element header
record. In the cases where NDI equals 2, only the in-plane values are given.
Record key: 401
Output variable identifier: SP
Record type: Principal stresses
Attributes: 1 - Minimum principal stress.
2 - Etc.
Record key: 403
Output variable identifier: EP
Record type: Principal infinitesimal strains
Attributes: 1 - Minimum principal infinitesimal strain.
2 - Etc.
Record key: 404
Output variable identifier: NEP
Record type: Principal nominal strains
Attributes: 1 - Minimum principal nominal strain.
2 - Etc.
Record key: 405
Output variable identifier: LEP
Record type: Principal logarithmic strains
Attributes: 1 - Minimum principal logarithmic strain.
2 - Etc.
Records for porous metal plasticity
Record key: 413
Output variable identifier: VVF
Record type: Void volume fraction
Attribute: 1 - f .
Record key: 414
Output variable identifier: VVFG
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File Output Format
Record type: Void volume fraction (growth)
Attribute: 1 - fgr .
Record key: 415
Output variable identifier: VVFN
Record type: Void volume fraction (nucleation)
Attribute: 1 - fnucl .
Records for brittle cracking
Record key: 421
Output variable identifier: CKE
Record type: Cracking strains
Attributes: 1 - First cracking strain component.
2 - Second cracking strain component.
3 - Etc. (See Part V, "Elements," for a definition of the number and the type of the
components for the element type.)
Record key: 422
Output variable identifier: CKLE
Record type: Local cracking strains
Attributes: 1 - First strain component in local crack directions.
2 - Second strain component in local crack directions.
3 - Etc. (See Part V, "Elements," for a definition of the number and the type of the
components for the element type.)
Record key: 423
Output variable identifier: CKLS
Record type: Local cracking stresses
Attributes: 1 - First stress component in local crack directions.
2 - Second stress component in local crack directions.
3 - Etc. (See Part V, "Elements," for a definition of the number and the type of the
components for the element type.)
Record key: 424
Output variable identifier: CKSTAT
Record type: Status of cracks
Attributes: 1 - Status of first crack (if a 1-D, 2-D, or 3-D analysis). CKSTAT can have the following
values: 0.0=uncracked, 1.0=closed crack, 2.0=actively cracking, 3.0=crack
closing/reopening.
2 - Status of second crack (if a 2-D or 3-D analysis).
3 - Status of third crack (if a 3-D analysis).
Record key: 441
Output variable identifier: CKEMAG
Record type: Cracking strain magnitude
Attribute: 1 - Magnitude of cracking strain.
Records for connector elements
Record key: 495
Output variable identifier: CTF
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File Output Format
Record type: Connector total force
Attributes: 1 - First component of total force.
2 - Second component of total force.
3 - Etc.
Record key: 496
Output variable identifier: CEF
Record type: Connector elastic force
Attributes: 1 - First component of elastic force.
2 - Second component of elastic force.
3 - Etc.
Record key: 497
Output variable identifier: CVF
Record type: Connector viscous force
Attributes: 1 - First component of viscous force.
2 - Second component of viscous force.
3 - Etc.
Record key: 498
Output variable identifier: CSF
Record type: Connector friction force
Attributes: 1 - First component of friction force.
2 - Second component of friction force.
3 - Etc.
Record key: 499
Output variable identifier: CSLST
Record type: Connector lock and connector stop status flags
Attributes: 1 - Flag in the 1-direction.
2 - Flag in the 2-direction.
3 - Etc.
Record key: 500
Output variable identifier: CRF
Record type: Connector reaction force
Attributes: 1 - First component of reaction force.
2 - Second component of reaction force.
3 - Etc.
Record key: 501
Output variable identifier: CCF
Record type: Connector concentrated force
Attributes: 1 - First component of concentrated force.
2 - Second component of concentrated force.
3 - Etc.
Record key: 502
Output variable identifier: CP
Record type: Connector relative position
Attributes: 1 - First component of relative position.
2 - Second component of relative position.
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File Output Format
3 - Etc.
Record key: 503
Output variable identifier: CU
Record type: Connector relative displacement
Attributes: 1 - First component of relative displacement.
2 - Second component of relative displacement.
3 - Etc.
Record key: 504
Output variable identifier: CCU
Record type: Connector constitutive displacement
Attributes: 1 - First component of constitutive displacement.
2 - Second component of constitutive displacement.
3 - Etc.
Record key: 505
Output variable identifier: CV
Record type: Connector relative velocity
Attributes: 1 - First component of relative velocity.
2 - Second component of relative velocity.
3 - Etc.
Record key: 506
Output variable identifier: CA
Record type: Connector relative acceleration
Attributes: 1 - First component of relative acceleration.
2 - Second component of relative acceleration.
3 - Etc.
Record key: 507
Output variable identifier: CFAILST
Record type: Connector failure status flags
Attributes: 1 - Flag in the 1-direction.
2 - Flag in the 2-direction.
3 - Etc.
Records for rebar quantities
Record key: 442
Output variable identifier: RBFOR
Record type: Force in rebar
Attribute: 1 - Magnitude.
Record key: 443
Output variable identifier: RBANG
Record type: Rebar angle
Attribute: 1 - Angle, in degrees, between the isoparametric direction specified by the
ISODIRECTION parameter on the *REBAR option and the reinforcing. Available only for
shell and membrane elements.
Record key: 444
Output variable identifier: RBROT
Record type: Change in rebar angle
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File Output Format
Attribute: 1 - Change in angle, in degrees, between the isoparametric direction specified by the
ISODIRECTION parameter on the *REBAR option and the reinforcing. Available only for
shell and membrane elements.
Record for component output
The following record is generated automatically when component output is requested for a material or
a section point and the components are given in a local coordinate system. Only the first two directions
are given; if needed, the third direction can be obtained as the cross product of the first two. The
direction record is not generated for trusses, two-dimensional beams, and axisymmetric shells.
Record key: 85
Record type: Local coordinate directions
Attributes: 1 - First component of the first direction.
2 - Second component of the first direction.
3 - Third component of the first direction.
4 - First component of the second direction.
5 - Second component of the second direction.
6 - Third component of the second direction.
Records written when the *NODE FILE option is used
Record key: 101
Output variable identifier: U
Record type: Displacements
Attributes: 1 - Node number.
2 - First component of displacement.
3 - Second component of displacement.
4 - Etc.
Record key: 102
Output variable identifier: V
Record type: Velocities
Attributes: 1 - Node number.
2 - First component of velocity.
3 - Second component of velocity.
4 - Etc.
Record key: 103
Output variable identifier: A
Record type: Accelerations
Attributes: 1 - Node number.
2 - First component of acceleration.
3 - Second component of acceleration.
4 - Etc.
Record key: 104
Output variable identifier: RF
Record type: Reaction forces
Attributes: 1 - Node number.
2 - First component of reaction force.
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File Output Format
3 - Second component of reaction force.
4 - Etc.
Record key: 107
Output variable identifier: COORD
Record type: Coordinates
Attributes: 1 - Node number.
2 - First coordinate.
3 - Second coordinate.
4 - Etc.
Record key: 136
Output variable identifier: PCAV
Record type: Fluid cavity pressure
Attributes: 1 - Fluid cavity reference node number.
2 - Pressure.
Record key: 137
Output variable identifier: CVOL
Record type: Fluid cavity volume
Attributes: 1 - Fluid cavity reference node number.
2 - Volume.
Record key: 201
Output variable identifier: NT
Record type: Temperatures
Attributes: 1 - Node number.
2 - Temperature.
Record key: 204
Output variable identifier: RFL
Record type: Reaction fluxes
Attributes: 1 - Node number.
2 - First component of reaction flux.
3 - Second component of reaction flux.
4 - Etc.
The following record refers to the entire model:
Record key: 1999
Record type: Total energies record
Attributes: 1 - Total kinetic energy (ALLKE).
2 - Total recoverable (elastic) strain energy (ALLSE).
3 - Total external work (ALLWK).
4 - Total inelastic dissipation ( ALLPD).
5 - Total viscoelastic dissipation ( ALLCD).
6 - Total viscous dissipation (ALLVD) (not supported for hyperelastic and hyperfoam
material models).
7 - Currently not used.
8 - Total artificial strain energy (ALLAE).
9 - Currently not used.
10 - Currently not used.
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File Output Format
11 - Total strain energy (ALLIE).
12 - Total energy balance (ETOTAL).
13 - Total energy dissipated through frictional effects (ALLFD).
14 - Currently not used.
15 - Percent change in mass (DMASS).
16 - Internal heat energy (ALLIHE).
17 - External heat energy (ALLHF).
Procedure type keys
Table 5.1.2-1. Keys to produce type on step record (record key 2000) of the file output.
Key Description
17
*DYNAMIC, EXPLICIT
74
*DYNAMIC TEMPERATURE-DISPLACEMENT, EXPLICIT
98
*ANNEAL
5.1.3 Accessing the results file information
This section describes how to access the results file information.
References
· ``Accessing the results file: overview,'' Section 5.1.1
· ``Results file output format,'' Section 5.1.2
· ``Utility routines for accessing the results file,'' Section 5.1.4
Overview
The ABAQUS results ( .fil) file is written using internal data management routines to minimize I/O
cost. A postprocessing program must use these same ABAQUS data management routines to read the
results file. The following utility subroutines must be called to obtain data from the ABAQUS results
file:
· INITPF
· DBRNU
· DBFILE
· POSFIL
The user can also write a file in the format of the ABAQUS results file by using the following utility
subroutines:
· INITPF
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File Output Format
· DBFILW
The syntax of these utility subroutines is described in ``Utility routines for accessing the results file,''
Section 5.1.4.
Reading floating point and integer variables
To read both floating point and integer variables in the records, the following coding can be used in the
postprocessing program:
INCLUDE 'aba_param.inc'
DIMENSION ARRAY(513), JRRAY(NPRECD,513)
EQUIVALENCE (ARRAY(1),JRRAY(1,1))
With this technique, for example, the record key is available after each call to DBFILE with LOP=0 as
KEY =
JRRAY (1,2)
The use of aba_param.inc eliminates the need to have different versions of the code for single and
double precision. The file aba_param.inc defines an appropriate IMPLICIT REAL statement and
sets the value of NPRECD to 1 or 2, depending upon whether the machine uses single or double
precision. The file aba_param.inc is referenced from the site subdirectory of the ABAQUS
installation when the postprocessing program is compiled and linked using ABAQUS/Make (explained
below).
Linking the postprocessing program
The postprocessing program must be linked using the make parameter when running the ABAQUS
execution procedure (see ``Execution procedure for ABAQUS/Make,'' Section 3.2.10). To link
properly, the postprocessing program cannot contain a FORTRAN PROGRAM statement. Instead, the
program must begin with a FORTRAN SUBROUTINE with the name HKSMAIN.
Compiling, linking, and running a postprocessing program consists of two steps. For example, if the
name of the postprocessing program is postproc.f, use the following command to compile and link
postproc.f:
abaqus make job=postproc
The program must then be run using the command:
abaqus postproc
Calling the utility subroutines for reading the results file
Subroutine INITPF must be called before any results file is accessed. This subroutine contains
FORTRAN OPEN statements for all FORTRAN units assigned to results files through the call to
INITPF; therefore, the user's code must not contain any OPEN statements for these units. ABAQUS
constructs a file name for a given unit based on information supplied as LRUNIT(1,K1) and FNAME,
as discussed in ``Utility routines for accessing the results file,'' Section 5.1.4.
Subroutine DBRNU must also be called before reading the first results file and then again each time the
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File Output Format
user needs to change to reading another results file. This subroutine simply establishes the FORTRAN
unit number of the results file being read; no information is returned. DBRNU can be called before or
after INITPF but must be called before DBFILE.
Subroutine DBFILE is used to read each record from the results file. This subroutine will return one
record at a time in the format described in ``Results file output format,'' Section 5.1.2.
Example
The following program reads all the von Mises stresses in the results file and obtains the maximum
value. Then, it prints this value along with the element, section point, and integration point numbers
where it occurred.
In this example FORTRAN unit 8 is used to read the results file, and the name of the results file is
assumed to be TEST.fil. The results file is assumed to be a binary file, and only one results file will
be read. Thus, LRUNIT is dimensioned as LRUNIT(2,1); and in the call to the INITPF routine NRU
is set to 1, LRUNIT(1,1) is set to 8, and LRUNIT(2,1) is set to 2. A new results file will not be
written, so LOUTF is set to zero.
SUBROUTINE HKSMAIN
C
C
Calculate the maximum von Mises stress and its location
C
INCLUDE 'aba_param.inc'
CHARACTER*80 FNAME
DIMENSION ARRAY(513),JRRAY(NPRECD,513),LRUNIT(2,1)
EQUIVALENCE (ARRAY(1),JRRAY(1,1))
C
C
File initialization
C
FNAME='TEST'
NRU=1
LRUNIT(1,1)=8
LRUNIT(2,1)=2
LOUTF=0
CALL INITPF(FNAME,NRU,LRUNIT,LOUTF)
JUNIT=8
CALL DBRNU(JUNIT)
C
C
Loop on all records in results file
C
STRESS=0.
DO 100 K1=1,99999
C
CALL DBFILE(0,ARRAY,JRCD)
IF(JRCD.NE.0)GO TO 110
2-295
File Output Format
KEY=JRRAY(1,2)
C
IF(KEY.EQ.1) THEN
C
C
C
C
Element header record:
extract element, sec pt, int pt numbers
JEL=JRRAY(1,3)
JPNT=JRRAY(1,4)
JSPNT=JRRAY(1,5)
C
ELSE IF(KEY.EQ.75)THEN
C
C
C
Stress invariant record: extract von Mises stress
IF(ARRAY(3).GT.STRESS)THEN
STRESS=ARRAY(3)
KEL=JEL
KPNT=JPNT
KSPNT=JSPNT
END IF
C
END IF
C
100
110
CONTINUE
CONTINUE
C
WRITE(6,120) KEL,KPNT,KSPNT,STRESS
120 FORMAT(5X,'ELEMENT',I5,5X,'POINT',I4,5X,'SECTION POINT',
1 I4,5X,'STRESS',1PG12.3)
STOP
END
Writing a file in the results file format
Subroutine DBFILW can be used to write a file in the format of the ABAQUS results file to modify the
file information or to add additional information before postprocessing. Subroutine INITPF must be
called before DBFILW.
The file will be written to FORTRAN unit 9 with the extension .fin. Unit 9 is opened by ABAQUS
when DBFILW is first called; the user's coding must not open or redefine unit 9, but the user must
ensure that FORTRAN unit 9 is saved following the job.
The DBFILW subroutine can be used to convert the ABAQUS results file from binary to ASCII format
to transfer it from one computer system to another. Alternatively, this conversion can be done
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File Output Format
automatically by using the abaqus ascfil execution procedure, as described in ``Execution procedure
for ASCII translation of results (.fil) files,'' Section 3.2.6.
Example: Merging discontinuous files
A results file can be written during an analysis and then a new results file can be written on the restart
of that analysis without making the files continuous. For postprocessing purposes, the files must be
made continuous. The following user-defined postprocessing program illustrates the process of writing
a file in the results file format by joining two results files. (Alternatively, the ABAQUS/Append
execution procedure can be used to automatically make the two results files continuous ( ``Execution
procedure for joining results (.fil) files,'' Section 3.2.7).)
The original results file will be read on FORTRAN unit 8 and is assumed to be named TEST.fil.
The second results file will be read on FORTRAN unit 10, with a name of TEST.010. Both files are
assumed to have been written in ASCII format. The format of the new results file will also be ASCII
and will be placed in the file TEST.fin.
SUBROUTINE HKSMAIN
INCLUDE 'aba_param.inc'
CHARACTER*80 FNAME
DIMENSION ARRAY(513),JRRAY(NPRECD,513),LRUNIT(2,2)
EQUIVALENCE (ARRAY(1),JRRAY(1,1))
C
C PROGRAM TO MERGE TWO RESULTS FILES
C
FNAME='TEST'
NRU=2
LRUNIT(1,1)=8
LRUNIT(2,1)=1
LRUNIT(1,2)=10
LRUNIT(2,2)=1
LOUTF=1
CALL INITPF(FNAME,NRU,LRUNIT,LOUTF)
JUNIT=8
CALL DBRNU(JUNIT)
100 CONTINUE
CALL DBFILE(0,ARRAY,JRCD)
IF (JRCD .NE. 0) GO TO 110
LOP=1
CALL DBFILW(LOP,ARRAY,JRCD)
GO TO 100
110 CONTINUE
JUNIT=10
CALL DBRNU(JUNIT)
I2001=0
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File Output Format
C
C
C
C
200 CONTINUE
CALL DBFILE(0,ARRAY,JRCD)
IF (JRCD .NE. 0) GO TO 210
SKIP THE HEADER RECORDS BUT LEAVE THE OUTPUT REQUEST
DEFINITION RECORDS
IF(JRRAY(1,2).GE.1900.AND.JRRAY(1,2).LE.1910) GO TO 200
IF(JRRAY(1,2).GE.1912.AND.JRRAY(1,2).LE.1922) GO TO 200
SKIP THE FIRST 2001 RECORD WHICH INDICATES THE END OF
THE HEADER RECORDS
IF(I2001.EQ.0.AND.JRRAY(1,2).EQ.2001) THEN
I2001=1
GO TO 200
ENDIF
LOP=1
CALL DBFILW(LOP,ARRAY,JRCD)
GO TO 200
210 CONTINUE
STOP
END
5.1.4 Utility routines for accessing the results file
The ABAQUS results ( .fil) file can be accessed with the utility routines described in this section.
Access is subsequent to an analysis by a user-written postprocessing program.
Reference
· ``Accessing the results file information,'' Section 5.1.3
Overview
The following utility subroutines are available:
· DBFILE (read from a file)
· DBFILW (write to a file)
· DBRNU (set a unit number for a file)
· INITPF (initialize a file)
These utility subroutines are described below in alphabetical order.
DBFILE (read from a file)
Interface
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File Output Format
CALL DBFILE(LOP,ARRAY,JRCD)
Variable to be provided to the utility routine
LOP
A flag, which must be set by the user before calling DBFILE, indicating the operation. Set
LOP=0 to read the next record in the file; set LOP=2 to rewind the file currently being read (for
example, if it is necessary to read the file more than once, it must be rewound since it is a
sequential file). If LOP=2 is used, the file must first be read to the end, and it should be
rewound only when the end-of-file is reached.
Variables returned from the utility routine
ARRAY
The array containing one record from the file, in the format described in ``Results file output
format,'' Section 5.1.2. When LOP=0, this array will be filled by the data management routines
with the contents of the next record in the file as each call to DBFILE is executed. ARRAY must
be dimensioned adequately in the user's routines to contain the largest record in the file. For
almost all cases 500 words is sufficient. The exceptions arise if the problem definition includes
user materials that use more than this many state variables. When the results file has been
written on a system on which ABAQUS runs in double precision, ARRAY must be declared
double precision in the user's routine.
JRCD
Returned as nonzero if an end-of-file marker is read when DBFILE is called with LOP=0.
DBFILW (write to a file)
Interface
CALL DBFILW(LOP,ARRAY,JRCD)
Variables to be provided to the utility routine
ARRAY
The array containing one record to be written to the file, in the format described in ``Results file
output format,'' Section 5.1.2.
JRCD
Not currently used.
LOP
Not currently used.
DBRNU (set a unit number for a file)
Interface
CALL DBRNU(JUNIT)
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File Output Format
Variable to be provided to the utility routine
JUNIT
The FORTRAN unit number of the results file to be read.
INITPF (initialize a file)
Interface
CALL INITPF(FNAME,NRU,LRUNIT,LOUTF)
Variables to be provided to the utility routine
FNAME
A character string defining the root file name (that is, the name without an extension) of the
files being read or written. FNAME must be declared as CHARACTER*80 and can include the
directory specification as well as the root file name. The extension of each individual file is
defined by the LRUNIT array below. See the discussion below for file naming conventions.
NRU
An integer giving the number of results files that the postprocessing program will read.
Normally only one results file is read, but sometimes it is necessary to read several results
files--for example, to merge them into a single file.
LRUNIT
An integer array that must be dimensioned LRUNIT(2,NRU) in the postprocessing program
and must contain the following data before INITPF is called: LRUNIT(1,K1) is the
FORTRAN unit number on which the K1th results file will be read. Valid unit numbers are 1
through 4, 8, and 14 through 30. All other units are reserved by ABAQUS. See below for
naming conventions based on the unit numbers. LRUNIT(2,K1) is an integer that must be set
to 2 if the K1th results file was written as a binary file or set to 1 if the K1th results file was
written in ASCII format.
LOUTF
Needs to be defined only if the program that is making the call to INITPF will also write an
output file in the ABAQUS results file format (for example, if results files are being merged
into a single results file or if a results file is being converted from binary to ASCII format). In
that case LOUTF should be set to 2 if the output file is to be written as a binary file or set to 1 if
the output file is to be written as an ASCII file. This results file will be written with the file
name extension .fin. See ``Accessing the results file information,'' Section 5.1.3, for a
discussion of writing results files; see below for information on the naming of this file.
File naming conventions
The file extension is derived from the value of LRUNIT(1,K1). If LRUNIT(1,K1) is 8, the file
name will be constructed with the extension fil. Any other unit number will result in a file extension
of 0nn, where nn is the number assigned to LRUNIT(1,K1). For example, if LRUNIT(1,K1) is 3,
the file extension is .003; if LRUNIT(1,K1) is 15, the file extension is .015. If an output file has
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File Output Format
been indicated by a nonzero value of LOUTF, its extension will be .fin.
For example, to read a file xxxx.fil, set LRUNIT(1,K1) to 8 and the character variable FNAME to
xxxx using assignment or data statements. If desired, FNAME can include a directory specification,
device name, or path. Operating system environment and shell variables will not be translated properly
and, therefore, should not be used.
All error messages generated by ABAQUS are written to FORTRAN unit 6. On most machines error
messages will be printed by default directly to the screen if the program is run interactively. The user
can include an open statement for unit 6 in the main program to redirect messages to a file. If the user
wishes to read or write to units other than those units specified in LRUNIT, OPEN statements for those
units may have to be included in the program (depending upon the computer being used). Unit
numbers of such auxiliary files should be greater than 50 to avoid any conflict with ABAQUS internal
files.
Additional examples
· ``Joining data from multiple results files and converting file format: FJOIN,'' Section 11.1.2 of the
ABAQUS Example Problems Manual
· ``Calculation of principal stresses and strains and their directions: FPRIN,'' Section 11.1.3 of the
ABAQUS Example Problems Manual
· ``Creation of a perturbed mesh from original coordinate data and eigenvectors: FPERT,'' Section
11.1.4 of the ABAQUS Example Problems Manual
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Analysis
Part III: Analysis
0-302
Analysis Types
6. Analysis Types
6.1 Introduction
6.1.1 Procedures: overview
Overview
An analysis history is defined in ABAQUS/Explicit by:
· dividing the problem history into steps;
· specifying an analysis procedure for each step; and
· prescribing loads, boundary conditions, and output requests for each step.
Steps
A basic concept in ABAQUS is the division of the problem history into steps. A step is any convenient
phase of the history.
A step starts with the *STEP option and ends with the *END STEP option. The *STEP option includes
optional data lines that can be used to specify a subheading; this subheading is for convenience only.
The first data line given appears in the data ( .dat) file.
Usage: Use the first option to begin a step and the second option to end a step:
*STEP
*END STEP
Defining the analysis procedure
For each step the user chooses an analysis procedure. This choice defines the type of analysis to be
performed during the step. In ABAQUS/Explicit only two procedures are available: the dynamic
procedure (which can include adiabatic thermal analysis) and the anneal procedure. The procedure
definition option must immediately follow the *STEP option. The available analysis procedures are
described in the sections that follow. Any combination of procedures can be used from step to step, but
only one procedure is allowed per step.
The rest of the step definition consists of load, boundary, and output request specifications (see
``Applying loads: overview,'' Section 18.4.1; ``Boundary conditions,'' Section 18.3.1; and ``Output,''
Section 4.1.1).
Geometrically linear and nonlinear analysis
It is possible in ABAQUS/Explicit to define a problem as a "small-displacement" analysis by setting
NLGEOM=NO on the *STEP option. A "small-displacement" analysis means that geometric
nonlinearity is ignored in the element calculations--the kinematic relationships are linearized. By
default, large displacements and rotations are accounted for in the contact constraints even if
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Analysis Types
NLGEOM=NO is specified (see ``Contact analysis: overview,'' Section 20.1.1, and ``Relative surface
motions,'' Section 20.3.4). The elements in a small-displacement analysis are formulated in the
reference (original) configuration, using original nodal coordinates. This can provide more accurate
(less noisy) results in most cases where the strains and rotations are small. The errors in such an
approximation are of the order of the strains and rotations compared to unity. The approximation also
eliminates any possibility of modeling bifurcation buckling, which is sometimes a critical aspect of a
structure's response. The user must consider these issues when interpreting the results of such an
analysis. For "small-displacement" analysis the infinitesimal strain measure is used, which is output
with the strain output variable E; strain output specified with output variables LE and NE is the same
as with E.
The alternative to a "small-displacement" analysis is to include large-displacement effects by setting
NLGEOM=YES on the *STEP option. Most elements are then formulated in the current configuration
using current nodal positions. Elements therefore distort from their original shapes as the deformation
increases. With sufficiently large deformations, the elements may become so distorted that they are no
longer suitable for use; for example, the volume of the element at an integration point may become
negative. In this situation ABAQUS/Explicit will issue a warning message indicating the problem.
Geometric nonlinearities are accounted for in stress analysis if the NLGEOM parameter on the *STEP
option has been set equal to YES. The default value for the NLGEOM parameter in an
ABAQUS/Explicit analysis is YES unless the ABAQUS/Explicit analysis is an import analysis, in
which case the default value of NLGEOM parameter is the same as the value of the parameter at the
time of import.
Usage: *STEP, NLGEOM=YES
For geometrically linear analyses the NLGEOM parameter must be set equal to NO in the first step and
continue to be set equal to NO in each successive step. Once the NLGEOM parameter has been
omitted or set equal to YES, a large-displacement formulation will be used in all following steps in the
analysis: there is no way to turn it off.
Usage: *STEP, NLGEOM=NO
Multiple steps
The analysis procedure can be changed from step to step in any meaningful way, so the user has great
flexibility in performing analyses. Since the state of the model (stresses, strains, temperatures, etc.) is
updated throughout all analysis steps, the effects of previous history are always included in the
response in each new analysis step.
The most obvious reason for using several steps in an analysis is to change analysis procedure type.
However, several steps can also be used as a matter of convenience--for example, to change output
requests, contact pairs, boundary conditions, or loading. Sometimes an analysis may have progressed
to a point where the present step definition needs to be modified. ABAQUS provides for this
contingency with the restart option, whereby a step can be terminated prematurely and a new step can
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Analysis Types
be defined for the problem continuation (see ``Restarting an analysis,'' Section 7.1.1).
Optional history data (see ``Defining a model in ABAQUS,'' Section 1.3.1) prescribing the loading,
boundary conditions, and output controls will remain in effect for all subsequent analysis steps,
including those that are defined in a restart analysis, until they are modified or reset.
Analysis procedures in ABAQUS/Explicit
The following analysis procedures are available:
· ``Explicit dynamic analysis,'' Section 6.2.1
· ``Fully coupled thermal-stress analysis,'' Section 6.3.1
· ``Annealing procedure,'' Section 6.2.2
· ``Adiabatic analysis,'' Section 6.3.2
In addition, the following analysis techniques are provided:
· ``Restarting an analysis,'' Section 7.1.1
· ``Introducing a geometric imperfection into a model,'' Section 7.2.1
· ``Transferring results between ABAQUS/Explicit and ABAQUS/Standard,'' Section 7.3.1
· ``Modeling fluid-filled cavities,'' Section 7.4.1
· ``Mass scaling,'' Section 7.5.1
Prescribed conditions
By default, the explicit dynamics procedure in ABAQUS/Explicit applies loads and boundary
conditions instantaneously (as a step function).
Prescribing nondefault amplitude variations
Complicated time variations of loadings and boundary conditions can be prescribed by using the
*AMPLITUDE option (see ``Amplitude curves,'' Section 18.1.2). A user subroutine is also provided
for coding general loadings (see ``User subroutines: overview,'' Section 21.1.1).
6.2 Dynamic stress/displacement analysis
6.2.1 Explicit dynamic analysis
The *DYNAMIC, EXPLICIT option is used to perform a dynamic analysis with ABAQUS/Explicit.
References
· *DYNAMIC
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Analysis Types
· ``Procedures: overview,'' Section 6.1.1
Overview
An explicit dynamic analysis:
· is computationally efficient for the analysis of large models with relatively short dynamic response
times and for the analysis of extremely discontinuous events or processes;
· allows for the definition of very general contact conditions ( ``Contact analysis: overview,'' Section
20.1.1);
· uses a consistent, large-deformation theory--models can undergo large rotations and large
deformation;
· can use a geometrically linear deformation theory--strains and rotations are assumed to be small
(see ``Procedures: overview,'' Section 6.1.1);
· can be used to perform an adiabatic stress analysis if inelastic dissipation is expected to generate
heat in the material (see ``Adiabatic analysis,'' Section 6.3.2);
· can be used to perform quasi-static analyses with complicated contact conditions; and
· allows for either automatic or fixed time incrementation to be used--by default, ABAQUS/Explicit
uses automatic time incrementation with the global time estimator.
Explicit dynamic analysis
The explicit dynamics procedure performs a large number of small time increments efficiently. An
explicit central difference time integration rule is used; each increment is relatively inexpensive
(compared to the direct-integration dynamic analysis procedure available in ABAQUS/Standard)
because there is no solution for a set of simultaneous equations. The explicit central difference
operator satisfies the dynamic equilibrium equations at the beginning of the increment, t; the
accelerations calculated at time t are used to advance the velocity solution to time t + ¢t=2 and the
displacement solution to time t + ¢t.
Usage: *DYNAMIC, EXPLICIT
Numerical implementation
The explicit dynamics analysis procedure is based upon the implementation of an explicit integration
rule together with the use of diagonal ("lumped") element mass matrices. The equations of motion for
the body are integrated using the explicit central difference integration rule
u_ N
_N
(i+ 1 ) = u
(i¡ 1 ) +
2
2
¢t(i+1) + ¢t(i) N
Ä(i) ;
u
2
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Analysis Types
N
uN
_N
(i+1) = u(i) + ¢t(i+1) u
(i+ 1 ) ;
2
where uN is a degree of freedom (a displacement or rotation component) and the subscript i refers to
the increment number in an explicit dynamics step. The central difference integration operator is
explicit in the sense that the kinematic state is advanced using known values of u_ N
ÄN
(i¡1=2) and u
(i) from
the previous increment.
The explicit integration rule is quite simple but by itself does not provide the computational efficiency
associated with the explicit dynamics procedure. The key to the computational efficiency of the
explicit procedure is the use of diagonal element mass matrices because the accelerations at the
beginning of the increment are computed by
NJ
u
ÄN
)
(i) = (M
¡1
J
J
(P(i)
¡ I(i)
);
where M N J is the mass matrix, P J is the applied load vector, and I J is the internal force vector. A
lumped mass matrix is used because its inverse is simple to compute and because the vector
multiplication of the mass inverse by the inertial force requires only n operations, where n is the
number of degrees of freedom in the model. The explicit procedure requires no iterations and no
tangent stiffness matrix.
Nodal mass and inertia
The explicit integration scheme in ABAQUS/Explicit requires nodal mass or inertia to exist at all
activated degrees of freedom (see ``Conventions,'' Section 1.2.2) unless constraints are applied using
boundary conditions. More precisely, a nonzero nodal mass must exist unless all activated translational
degrees of freedom are constrained and nonzero rotary inertia must exist unless all activated rotational
degrees of freedom are constrained. Nodes that are part of a rigid body do not require mass, but the
entire rigid body must possess mass and inertia unless constraints are used.
When degrees of freedom at a node are activated by elements with a nonzero mass density (e.g., solid,
shell, beam) or mass and inertia elements, a nonzero nodal mass or inertia occurs naturally from the
assemblage of lumped mass contributions.
When degrees of freedom at a node are activated by elements with no mass (e.g., spring, dashpot, or
connector elements), care must be taken either to constrain the node or to add mass and inertia as
appropriate.
Stability
The explicit procedure integrates through time by using many small time increments. The central
difference operator is conditionally stable, and the stability limit for the operator (with no damping) is
given in terms of the highest frequency of the system as
¢t ∙
2
!max
:
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Analysis Types
With damping, the stable time increment is given by
¢t ∙
2
!max
p
2
( 1 + »max
¡ »max );
where »max is the fraction of critical damping in the mode with the highest frequency. In
ABAQUS/Explicit a small amount of damping is introduced in the form of bulk viscosity (discussed
below) to control high frequency oscillations. Physical forms of damping, such as dashpots or material
damping, can also be introduced. Contrary to our usual engineering intuition, introducing damping to
the solution reduces the stable time increment.
Estimating the stable time increment size
An approximation to the stability limit is often written as the smallest transit time of a dilatational
wave across any of the elements in the mesh
¢t ¼
Lmin
;
cd
where Lmin is the smallest element dimension in the mesh and cd is the dilatational wave speed in
terms of ¸0 and ¹0 , defined below.
In general, for beams, shells, and membranes the element thickness or cross-sectional dimensions are
not the smallest element dimension; the stability limit is based upon the midplane or membrane
dimensions only. When the transverse shear stiffness is defined for shell elements using the
*TRANSVERSE SHEAR STIFFNESS option, the stable time increment will also be based on the
transverse shear behavior.
This estimate for ¢t is only approximate and in most cases is not a conservative (safe) estimate. In
general, the actual stable time increment chosen by ABAQUS/Explicit will be less than this estimate
p
p
by a factor between 1= 2 and 1 in a two-dimensional model and between 1= 3 and 1 in a
three-dimensional model. The time increment chosen by ABAQUS/Explicit also accounts for any
stiffness behavior in a model associated with penalty contact. For further discussion see the section on
computational cost below.
Stable time increment report
ABAQUS/Explicit writes a report to the status ( .sta) file during the datacheck phase of the analysis
that contains an estimate of the minimum stable time increment and a listing of the elements with the
smallest stable time increments and their values. The initial stable time increments listed do not
include damping (bulk viscosity), mass scaling, or penalty contact effects.
This listing is provided because often a few elements have much smaller stability limits than the rest of
the elements in the mesh. The stable time increment can be increased by modifying the mesh to
increase the size of the controlling element or by using an appropriate mass scaling option.
Dilatational wave speed
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Analysis Types
The current dilatational wave speed, cd , is determined in ABAQUS/Explicit by calculating the
effective hypoelastic material moduli from the material's constitutive response. Effective Lamé's
^ and G
^ = 2^
¹, are determined in the following manner. Define ¢p as the increment in the
constants, ¸
mean stress, ¢S as the increment in the deviatoric stress, ¢²vol as the increment of volumetric strain,
and ¢e as the deviatoric strain increment. We assume a hypoelastic stress-strain rule of the form
^ + 2^
¢p = (3¸
¹)¢²vol ;
¢S = 2^
¹¢e :
The effective moduli can then be computed as
¢p
^ + 2^
^ = 3¸
3K
¹=
;
¢²vol
2^
¹=
¢S : ¢e
;
¢e : ¢e
1 ^
^ + 2^
¸
¹ = (3K
+ 4^
¹) :
3
For shell elements defined by the *SHELL SECTION option, the effective moduli for the section are
computed by integrating the effective moduli at the section points through the thickness. These
effective moduli represent the element stiffness and determine the current dilatational wave speed in
the element as
cd =
s
^ + 2^
¸
¹
;
½
where ½ is the density of the material.
In an isotropic, elastic material the effective Lamé's constants can be defined in terms of Young's
modulus, E, and Poisson's ratio, º, by
^ = ¸0 =
¸
Eº
(1 + º )(1 ¡ 2º )
and
¹
^ = ¹0 =
E
:
2(1 + º )
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Analysis Types
Time incrementation
The time increment used in an analysis must be smaller than the stability limit of the central difference
operator. Failure to use a small enough time increment will result in an unstable solution. When the
solution becomes unstable, the time history response of solution variables such as displacements will
usually oscillate with increasing amplitudes. The total energy balance will also change significantly.
If the model contains only one material type, the initial time increment is directly proportional to the
size of the smallest element in the mesh. If the mesh contains uniform size elements but contains
multiple material descriptions, the element with the highest wave speed will determine the initial time
increment.
In nonlinear problems--those with large deformations and/or nonlinear material response--the highest
frequency of the model will continually change, which consequently changes the stability limit.
ABAQUS/Explicit has two strategies for time incrementation control: fully automatic time
incrementation (where the code accounts for changes in the stability limit) and fixed time
incrementation.
Automatic time incrementation
The default time incrementation scheme in ABAQUS/Explicit is fully automatic and requires no user
intervention. Two types of estimates are used to determine the stability limit: element by element and
global. An analysis always starts by using the element-by-element estimation method and may switch
to the global estimation method under certain circumstances, as explained below.
Element-by-element estimation
In an analysis ABAQUS/Explicit initially uses a stability limit based on the highest element frequency
in the whole model. This element-by-element estimate is determined using the current dilatational
wave speed in each element.
The element-by-element estimate is conservative; it will give a smaller stable time increment than the
true stability limit that is based upon the maximum frequency of the entire model. In general,
constraints such as boundary conditions and kinematic contact have the effect of compressing the
eigenvalue spectrum, and the element-by-element estimates do not take this into account.
The concept of the stable time increment as the time required to propagate a dilatational wave across
the smallest element dimension is useful for interpreting how the explicit procedure chooses the time
increment when element-by-element stability estimation controls the time increment. As the step
proceeds, the global stability estimate, if used, will make the time increment less sensitive to element
size.
To use the element-by-element estimation throughout a step, include the ELEMENT BY ELEMENT
parameter on the *DYNAMIC option.
Usage: *DYNAMIC, EXPLICIT, ELEMENT BY ELEMENT
Global estimation
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Analysis Types
The stability limit will be determined by the global estimator as the step proceeds unless the
ELEMENT BY ELEMENT parameter is used, fixed time incrementation is specified, or one of the
conditions explained below prevents the use of global estimation. The switch to the global estimation
method occurs once the algorithm determines that the accuracy of the global estimation method is
acceptable.
The adaptive, global estimation algorithm determines the maximum frequency of the entire model
using the current dilatational wave speed. This algorithm continuously updates the estimate for the
maximum frequency. The global estimator will usually allow time increments that exceed the
element-by-element values.
ABAQUS/Explicit monitors the effectiveness of the global estimation algorithm. If the cost for
computing the global time estimate is more than its benefit, the code will turn off the global estimation
algorithm and simply use the element-by-element estimates to save computation time.
Conditions that will prevent the use of the global time estimator
The global estimation algorithm will not be used when any of the following capabilities are included in
the model:
· Fluid elements
· Infinite elements
· Dashpots
· Thick shells (thickness to characteristic length ratio larger than 0.92)
· Thick beams (thickness to length ratio larger than 1.0)
· The JWL equation of state
· Material damping
· Nonisotropic elastic materials with temperature and field variable dependency
Fixed time incrementation
A fixed time incrementation scheme is also available in ABAQUS/Explicit. The fixed time increment
size is determined either by the initial element-by-element stability estimate for the step or by a time
increment specified directly by the user.
Fixed time incrementation may be useful when a more accurate representation of the higher mode
response of a problem is required. In this case, a time increment size smaller than the
element-by-element estimates may be used. The element-by-element estimate can be obtained simply
by running a datacheck analysis (see ``Execution procedure for ABAQUS/Standard and
ABAQUS/Explicit,'' Section 3.2.1).
When fixed time incrementation is used, ABAQUS/Explicit will not check that the computed response
is stable during the step. The user should ensure that a valid response has been obtained by carefully
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Analysis Types
checking the energy history and other response variables.
Basing the fixed time increment size on the element-by-element
stability limit
Include the FIXED TIME INCREMENTATION parameter on the *DYNAMIC option to use time
increments the size of the initial element-by-element stability limit throughout a step. The dilatational
wave speed in each element at the beginning of the step is used to compute the fixed time increment
size.
Usage: *DYNAMIC, EXPLICIT, FIXED TIME INCREMENTATION
Ensuring stability when fixed time incrementation is used
To reduce the chance of a solution going unstable, the initial stable time increment that
ABAQUS/Explicit computes can be adjusted by a constant scaling factor defined by the SCALE
FACTOR parameter on the *DYNAMIC option.
Usage: *DYNAMIC, EXPLICIT, FIXED TIME INCREMENTATION, SCALE FACTOR=f
Specifying the fixed time increment size directly
Include the DIRECT USER CONTROL parameter on the *DYNAMIC option to specify a time
increment size directly on the data line of the *DYNAMIC option.
Usage: *DYNAMIC, EXPLICIT, DIRECT USER CONTROL
Advantages of the explicit method
The use of small increments (dictated by the stability limit) is advantageous because it allows the
solution to proceed without iterations and without requiring tangent stiffness matrices to be formed. It
also simplifies the treatment of contact.
The explicit dynamics procedure is ideally suited for analyzing high-speed dynamic events, but many
of the advantages of the explicit procedure also apply to the analysis of slower (quasi-static) processes.
A good example is sheet metal forming, where contact dominates the solution and local instabilities
may form due to wrinkling of the sheet.
The results in an explicit dynamics analysis are not automatically checked for accuracy as they are in
ABAQUS/Standard (ABAQUS/Standard uses the half-step residual). In most cases this is not of
concern because the dominant response of a model is usually in a mode associated with the structural
response of the model as a whole. As a result, the solution changes only slightly in any one time
increment. While the analysis may take an extremely large number of increments, each increment is
relatively inexpensive, often resulting in an economical solution. It is not uncommon for
ABAQUS/Explicit to take over 105 increments for an analysis. The method is, therefore,
computationally attractive for problems where the total dynamic response time that must be modeled is
only a few orders of magnitude longer than the stability limit; for example, wave propagation studies
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Analysis Types
or some "event and response" applications, especially when the software is highly tuned to process
many increments very quickly.
The software tuning requirement imposes some practical restrictions on modeling capabilities with
explicit integration. For example, only first-order, displacement method elements (4-node
quadrilaterals, 8-node bricks, etc.) are used, and each degree of freedom in the model must have mass
or rotary inertia associated with it.
Computational cost
The computer time involved in running a simulation using explicit time integration with a given mesh
is proportional to the time period of the event. The time increment based on the element-by-element
stability estimate can be rewritten (ignoring damping) in the form
µ
¢t ∙ min Le
r
½
^ + 2^
¸
¹
¶
;
where the minimum is taken over all elements in the mesh, Le is a characteristic length associated with
an element (see ``Explicit dynamic analysis,'' Section 2.4.5 of the ABAQUS Theory Manual), ½ is the
^ and ¹
^ are the effective Lamé's constants for the material in
density of the material in the element, and ¸
the element (defined above).
The time increment from the global stability estimate may be somewhat larger, but for this discussion
we will assume that the above inequality always holds (when the inequality does not hold, the solution
time will be somewhat faster).
For linear, nonisotropic elastic materials this stability limit is further scaled down by the square root of
the ratio of the effective material stiffness to the maximum material stiffness in one particular
direction. Since this effectively means that the time increment can be no larger than the time required
to propagate a stress wave across an element, the computer time involved in running a quasi-static
analysis can be very large: the cost of the simulation is directly proportional to the number of time
increments required.
The number of increments, n, required is n = T =¢t if ¢t remains constant, where T is the time
period of the event being simulated. (Even the element-by-element approximation of ¢t will not
remain constant in general, since element distortion will change Le and nonlinear material response
will change the effective Lamé constants. But the assumption is sufficiently accurate for the purposes
of this discussion.) Thus,
0
n ¼ T max @
1
Le
s
1
^ + 2^
¸
¹ A
:
½
In a two-dimensional analysis refining the mesh by a factor of two in each direction will increase the
run time in the explicit procedure by a factor of eight--four times as many elements and half the
original time increment size. Similarly, in a three-dimensional analysis, refining the mesh by a factor of
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Analysis Types
two in each direction will increase the run time by a factor of sixteen.
In a quasi-static analysis it is expedient to reduce the computational cost by either speeding up the
simulation or by scaling the mass. In either case the kinetic energy should be monitored to ensure that
the ratio of kinetic energy to internal energy does not get too large--typically less than 10%.
Reducing the computational cost by speeding up the simulation
To reduce the number of increments required, n, we can speed up the simulation compared to the time
of the actual process--that is, we can artificially reduce the time period of the event, T . This will
introduce two possible errors. If the simulation speed is increased too much, the increased inertia
forces will change the predicted response (in an extreme case the problem will exhibit wave
propagation response). The only way to avoid this error is to choose a speed-up that is not too large.
The other error is that some aspects of the problem other than inertia forces--for example, material
behavior--may also be rate dependent. In this case the actual time period of the event being modeled
cannot be changed.
Reducing the computational cost by using mass scaling
Artificially increasing the material density, ½, by a factor f 2 reduces n to n=f , just like decreasing T to
T =f . This concept, called "mass scaling," reduces the ratio of the event time to the time for wave
propagation across an element while leaving the event time fixed, which allows rate-dependent
behavior to be included in the analysis. Mass scaling has exactly the same effect on inertia forces as
speeding up the time of simulation.
Mass scaling is attractive because it can be used in rate-dependent problems, but it must be used with
care to ensure that the inertia forces do not dominate and change the solution. Mass scaling can be
invoked by using the *FIXED MASS SCALING and *VARIABLE MASS SCALING options (see
``Mass scaling,'' Section 7.5.1).
Mass scaling can also be accomplished by altering the density specified on the *DENSITY option;
however, the *FIXED MASS SCALING and *VARIABLE MASS SCALING options provide more
versatile methods of scaling the mass of the entire model or specific element sets in the model.
Bulk viscosity
Bulk viscosity introduces damping associated with volumetric straining. Its purpose is to improve the
modeling of high-speed dynamic events. ABAQUS/Explicit contains two forms of bulk viscosity:
linear and quadratic. Linear bulk viscosity is always included in an ABAQUS/Explicit analysis.
The bulk viscosity parameters b1 and b2 defined below can be redefined by using the *BULK
VISCOSITY option. The *BULK VISCOSITY option is history data and can be changed from step to
step. If the default values are changed in a step, the new values will be used in subsequent steps until
they are redefined.
Usage: *BULK VISCOSITY
Linear bulk viscosity
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Analysis Types
Linear bulk viscosity is found in all elements and is introduced to damp "ringing" in the highest
element frequency. This damping is sometimes referred to as truncation frequency damping. It
generates a bulk viscosity pressure that is linear in the volumetric strain rate
pbv1 = b1 ½cd Le ²_vol ;
where b1 is a damping coefficient (default=.06), ½ is the current material density, cd is the current
dilatational wave speed, Le is an element characteristic length, and ²_vol is the volumetric strain rate.
Quadratic bulk viscosity
The second form of bulk viscosity pressure is found only in solid continuum elements (except the
plane stress element CPS4R). This form is quadratic in the volumetric strain rate
pbv2 = ½(b2 Le ²_vol )2 ;
where b2 is a damping coefficient (default=1.2) and all other quantities are as defined for the linear
bulk viscosity. Quadratic bulk viscosity is applied only if the volumetric strain rate is compressive.
The quadratic bulk viscosity pressure will smear a shock front across several elements and is
introduced to prevent elements from collapsing under extremely high velocity gradients. Consider a
simple one-element problem in which the nodes on one side of the element are fixed and the nodes on
the other side have an initial velocity in the direction of the fixed nodes. If the initial velocity is equal
to the dilatational wave speed of the material, without the quadratic bulk viscosity, the element would
collapse to zero volume in one time increment (because the stable time increment size is precisely the
transit time of a dilatational wave across the element). The quadratic bulk viscosity pressure will
introduce a resisting pressure that will prevent the element from collapsing.
Fraction of critical damping due to bulk viscosity
The bulk viscosity pressure is not included in the material point stresses because it is intended as a
numerical effect only--it is not considered part of the material's constitutive response. The bulk
viscosity pressures are based upon the dilatational mode of each element. The fraction of critical
damping in the dilatational mode of each element is given by
» = b1 ¡ b22
Le
min(0; ²_vol ) :
cd
Rotational bulk viscosity for shell elements
For the displacement degrees of freedom, bulk viscosity introduces damping associated with
volumetric straining. Linear bulk viscosity or truncation frequency damping is used to damp the high
frequency ringing that leads to unwanted noise in the solution or spurious overshoot in the response
amplitude. For the same reason, in shells the high frequency ringing in the rotational degrees of
freedom is damped with linear bulk viscosity acting on the mean curvature strain rate. This damping
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Analysis Types
generates a bulk viscosity "pressure moment," m, which is linear in the mean curvature strain rate
m = b1
h20
½cd L∙_ ;
12
where b1 is a damping coefficient (default = 0.06), h0 is the original thickness, ½ is the mass density,
cd is the current dilatational wave speed, L is the characteristic length used for rotary inertia and
transverse shear stiffness scaling (see ``Finite-strain shell element formulation,'' Section 3.6.5 of the
ABAQUS Theory Manual), and ∙_ = ∙_ 11 + ∙_ 22 is twice the mean curvature strain rate. The resultant
pressure moment mh, where h is the current thickness, is added to the direct components of the
moment resultant.
Material damping
Defining inelastic material behavior, dashpots, etc. will introduce energy dissipation into a model. In
addition to these mechanisms, general ("Rayleigh") material damping can be introduced by using the
*DAMPING option (see ``Material damping,'' Section 11.1.1). Adding damping to a model, especially
stiffness proportional damping, ¯R , may significantly reduce the stable time increment.
Usage: *DAMPING, ALPHA=®R , BETA=¯R
Obtaining diagnostic information about the deformation speed
The deformation speed in an element is defined as the largest absolute value of all the deformation rate
components of an element times the element characteristic length, Le . The *DIAGNOSTICS option
can be included within a step definition to request diagnostic information about the deformation speed.
In a multistep analysis the values of the *DIAGNOSTICS parameters remain in effect until they are
explicitly redefined.
Deformation speed warnings
By default, ABAQUS/Explicit will check for a relatively large deformation speed in all the elements
since too high a value may cause the element to deform or collapse unrealistically. A warning message
is issued if the ratio of deformation speed versus dilatational wave speed in an element reaches the
value specified for the "warning ratio." By default, the warning ratio is 0.3. This limit can be redefined
by using the WARNING RATIO parameter on the *DIAGNOSTICS option.
The first occurrence of the warning message is written to the status ( .sta) file; subsequent
occurrences are written to the message ( .msg) file. See ``Output,'' Section 4.1.1, for a description of
these output files.
Generally when the ratio of deformation speed to dilatational wave speed is greater than 0.3, it is an
indication that the purely mechanical material constitutive relationship is no longer valid and that a
thermo-mechanical equation of state material is required.
Usage: *DIAGNOSTICS, WARNING RATIO=ratio
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Analysis Types
Deformation speed errors
An error message is issued and the analysis is terminated when the maximum ratio of deformation
speed versus current dilatational wave speed for any element is greater than the "cutoff ratio." By
default, the cutoff ratio is 1.0. This limit can be redefined by using the CUTOFF RATIO parameter on
the *DIAGNOSTICS option.
The check for this cutoff ratio is not applied to any model that has an equation of state material (see
``Equation of state,'' Section 9.5.1) or a user-defined material (see ``User-defined material behavior,''
Section 11.4.1).
Usage: *DIAGNOSTICS, CUTOFF RATIO=ratio
Obtaining a summary of the deformation speed information
Set the DEFORMATION SPEED CHECK parameter on the *DIAGNOSTICS option equal to
SUMMARY to obtain warning and error messages for only the element with the largest ratio of
deformation speed to dilatational wave speed.
Usage: *DIAGNOSTICS, DEFORMATION SPEED CHECK=SUMMARY
Obtaining detailed deformation speed information
Set the DEFORMATION SPEED CHECK parameter on the *DIAGNOSTICS option equal to
DETAIL to obtain warning and error messages for all elements with large deformation speed to
dilatational wave speed ratios.
Usage: *DIAGNOSTICS, DEFORMATION SPEED CHECK=DETAIL
Disabling deformation speed checks
Set the DEFORMATION SPEED CHECK parameter on the *DIAGNOSTICS option equal to OFF to
bypass the checks for large deformation speed.
Usage: *DIAGNOSTICS, DEFORMATION SPEED CHECK=OFF
Monitoring output variables for extreme values
There are some analyses in which it is useful to monitor the value of a variable at every increment. For
example, in a force-driven analysis such as hydro-forming, the simulation time that is sufficient to
model the completion of the physical process may depend on the magnitude of the displacement of a
node or a group of nodes in the model. Another example is a drop test simulation where the postfailure
response is not of interest. Monitoring the values of critical variables and halting the analysis when
those variables exceed a given criterion can reduce computational expense and turnaround time.
For such problems ABAQUS/Explicit allows output variables to be monitored during an analysis to
verify whether or not their values have exceeded or fallen below user-specified values in specified
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Analysis Types
element or node sets. Comparisons of specified element integration point variables, element section
variables, or nodal variables with user-specified values are performed at every increment. At the first
occurrence of a variable exceeding the user-specified bounds, the variable name, the associated
element or node number, and the increment number are written to the status ( .sta) file. In addition,
the user can request that the analysis be stopped and/or the output state be written in the increment
following the one in which the variable has exceeded the user-specified bound. At the end of each step
in which variables are monitored, the maximum, minimum, or absolute maximum value that each
variable attains during the course of the analysis, along with the number of the element or node where
the extreme value occurred, will be written to the status file.
Defining the element and nodal variables to be monitored
To define the variables to be monitored and their associated bounds, use the *EXTREME VALUE
option in conjunction with the *EXTREME ELEMENT VALUE and/or *EXTREME NODE VALUE
options in the history portion of the input file. The *EXTREME VALUE option can be repeated in the
same step, and the *EXTREME ELEMENT VALUE and *EXTREME NODE VALUE options can be
repeated as many times as necessary.
The element output variables that can be monitored include all the element integration point variables
and element section point variables that are available for history-type output to the output database.
Similarly, the nodal output variables that can be monitored include all the nodal variables that are
available for history output to the output database. The keys identifying the output variables are
defined in ``Output variable identifiers,'' Section 4.2.1. Only scalar quantities can be monitored.
Tensors and vectors cannot be monitored unless indicated individually by components.
Use the ELSET or NSET parameter to define the element or node set, respectively, whose members are
to be monitored for peak values.
Usage: Use the following options:
*EXTREME VALUE
*EXTREME ELEMENT VALUE, ELSET=element_set_name
*EXTREME NODE VALUE, NSET=nset_set_name
Halting the analysis when the extreme value criterion is met
Set the HALT parameter on the *EXTREME VALUE option equal to YES to halt the analysis when
the extreme value criterion is met. The analysis will stop at the end of the increment following the one
in which any of the element or nodal variables defined under the *EXTREME ELEMENT VALUE and
*EXTREME NODE VALUE options exceeded the prescribed bounds.
Usage: Use the following options:
*EXTREME VALUE, HALT=YES
*EXTREME ELEMENT VALUE and/or *EXTREME NODE VALUE
Obtaining output when the extreme value criterion is met
Set the OUTPUT parameter on the *EXTREME ELEMENT VALUE option or the *EXTREME
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Analysis Types
NODE VALUE option equal to YES to obtain field-type output to the output database and an
additional restart state when any of the selected variables fall outside the specified bounds for the first
time during the analysis. The output will be written in the increment following the one in which such
an occurrence took place. Since output is automatically written when the analysis terminates, this
parameter has an effect only if the HALT parameter is set to NO (the default value).
Usage: Use either or both of the following options in conjunction with the *EXTREME VALUE
option:
*EXTREME ELEMENT VALUE, ELSET=element_set_name, OUTPUT=YES
*EXTREME NODE VALUE, NSET=node_set_name, OUTPUT=YES
Monitoring variables in a multistep analysis
In a multistep analysis the definitions specified with the *EXTREME ELEMENT VALUE and
*EXTREME NODE VALUE options remain in effect until they are redefined. The user must redefine
all options to add or change any variables, element or node sets, or maxima or minima.
Stopping the monitoring of variables in a new step
Use the *EXTREME VALUE option without the *EXTREME ELEMENT VALUE and *EXTREME
NODE VALUE options to stop monitoring variables in a new step.
Usage: *EXTREME VALUE
Initial conditions
``Initial conditions,'' Section 18.2.1, describes all of the initial conditions that are available for an
explicit dynamic analysis.
Boundary conditions
The *BOUNDARY option is used to apply boundary conditions to degrees of freedom in both the
model definition and history definition sections of the input file (see ``Boundary conditions,'' Section
18.3.1).
Boundary conditions applied during a *DYNAMIC response step should use appropriate
*AMPLITUDE references (``Amplitude curves,'' Section 18.1.2). If boundary conditions are specified
for the step without *AMPLITUDE references, they are applied instantaneously at the beginning of the
step. Since ABAQUS/Explicit does not admit jumps in displacement, the value of a nonzero
displacement boundary condition that is specified without an *AMPLITUDE reference will be ignored,
and a zero displacement boundary condition will be enforced.
Loads
The loading options available for an explicit dynamic analysis are explained in ``Applying loads:
overview,'' Section 18.4.1. Concentrated nodal forces or moments can be applied to the displacement
or rotation degrees of freedom (1-6). Distributed pressure forces or body forces can also be applied; the
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Analysis Types
distributed load types available with particular elements are described in Part V, "Elements."
As with boundary conditions, loads applied during a *DYNAMIC response step should use
appropriate *AMPLITUDE references (``Amplitude curves,'' Section 18.1.2). If loads are specified for
the step without *AMPLITUDE references, they are applied instantaneously at the beginning of the
step.
Predefined fields
The following predefined fields can be specified, as described in ``Predefined fields,'' Section 18.5.1:
· Although temperature is not a degree of freedom in explicit dynamic analysis, nodal temperatures
can be specified by using the *TEMPERATURE option. Any difference between the applied and
initial temperatures will cause thermal strain if a thermal expansion coefficient is given for the
material (``Thermal expansion,'' Section 11.1.2). The specified temperature also affects
temperature-dependent material properties, if any.
· The values of user-defined field variables can be specified using the *FIELD option. These values
only affect field-variable-dependent material properties, if any.
Material options
Any of the material models in ABAQUS/Explicit can be used in a general explicit dynamic analysis
(see ``Combining material properties,'' Section 8.1.3).
Elements
All of the elements available in ABAQUS/Explicit can be used in an explicit dynamic analysis. The
elements are listed in Part V, "Elements."
If coupled temperature-displacement elements are used in an explicit dynamic analysis, the
temperature degrees of freedom will be ignored.
Output
The element output available for a dynamic analysis includes stress; strain; energies; and the values of
state, field, and user-defined variables. The nodal output available includes displacements, velocities,
accelerations, reaction forces, and coordinates. All of the output variable identifiers are outlined in
``Output variable identifiers,'' Section 4.2.1. The types of output available are described in ``Output,''
Section 4.1.1.
Energy output is particularly important in checking the accuracy of the solution in an explicit dynamics
analysis. The following energy values are summed over the entire model and are available by using the
*ENERGY FILE and/or *ENERGY OUTPUT options (see ``Output to the results file,'' Section 4.1.2,
and ``Output to the output database, '' Section 4.1.3):
ETOTAL
Energy balance. ETOTAL=ALLIE + ALLKE + ALLVD + ALLFD ¡ ALLWK.
ALLIE
Total strain energy. ALLIE=ALLSE + ALLPD + ALLCD + ALLAE, where
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Analysis Types
ALLSE=recoverable strain energy, ALLPD=energy dissipated by plastic dissipation,
ALLCD=energy dissipated by viscoelasticity (not available for hyperelastic and
hyperfoam materials), and ALLAE="artificial" strain energy.
ALLKE
Kinetic energy.
ALLVD
Energy dissipated by viscous effects.
ALLFD
Energy dissipated by frictional effects.
ALLWK
External work.
The "artificial" strain energy associated with constraints used to remove singular modes (such as
hourglass control) should be negligible compared to "real" energies such as ALLKE and ALLSE.
In a quasi-static analysis the value of the kinetic energy, ALLKE, should not exceed a small fraction of
the value of the strain energy, ALLIE.
Template
*HEADING
...
*MATERIAL, NAME=name
*ELASTIC
...
*DENSITY
Data lines to define density
*DAMPING, ALPHA =®, BETA=¯
Data lines to define Rayleigh damping
...
*BOUNDARY
Data lines to specify zero-valued boundary conditions
*INITIAL CONDITIONS, TYPE=type
Data lines to specify initial conditions
*AMPLITUDE, NAME=name
Data lines to define amplitude variations
*************************
*STEP
*DYNAMIC, EXPLICIT
Data line to specify the time period of the step
*DIAGNOSTICS, DEFORMATION SPEED CHECK=SUMMARY
*BOUNDARY, AMPLITUDE=name
Data lines to describe zero-valued or nonzero boundary conditions
*CLOAD and/or *DLOAD
Data lines to specify loading
*TEMPERATURE and/or *FIELD
Data lines to specify predefined fields
*FILE OUTPUT, NUMBER INTERVAL=n
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Analysis Types
*EL FILE
Data line specifying element output variables
*NODE FILE
Data line specifying node output variables
*ENERGY FILE
*OUTPUT, FIELD, NUMBER INTERVAL=n
*ELEMENT OUTPUT
Data line specifying element output variables
*NODE OUTPUT
Data line specifying node output variables
*OUTPUT, HISTORY, TIME INTERVAL=t
*ELEMENT OUTPUT, ELSET=element set name
Data line specifying element output variables
*NODE OUTPUT, NSET=node set name
Data line specifying node output variables
*ENERGY OUTPUT
Data line specifying energy output variables
*END STEP
*************************
*STEP
*DYNAMIC, EXPLICIT, ELEMENT BY ELEMENT
...
*BULK VISCOSITY
Data line to define linear and/or quadratic bulk viscosity in this step
...
*END STEP
6.2.2 Annealing procedure
The *ANNEAL procedure is used to set state variables and velocities to zero.
Reference
· *ANNEAL
Overview
The anneal procedure:
· is used to anneal a structure by setting all appropriate state variables and velocities to zero;
and
· is intended only for metal plasticity models and user-defined material models.
The annealing process
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Analysis Types
During the *ANNEAL procedure ABAQUS/Explicit sets all appropriate state variables to zero. These
variables include stresses, strains, plastic strains, and velocities. The thinning strain ( LE33, NE33) in
shells, membranes, and plane stress continuum elements is not annealed to zero; only the in-plane
strains are annealed.
There is no time scale in an annealing step; therefore, time does not advance. The annealing process
occurs instantaneously. No data are required for the *ANNEAL option.
Usage: *ANNEAL
Temperatures
Thermal strains are set to zero, and the temperature at all nodes in the model will be set to a uniform
temperature or will be maintained at the current temperature during the anneal procedure. By default,
the temperature at all nodes is maintained at the current temperature. The TEMPERATURE parameter
on the *ANNEAL option can be used to specify a different final temperature by setting
TEMPERATURE=µ.
Usage: *ANNEAL, TEMPERATURE=µ
Initial conditions
The initial state for the *ANNEAL step is the state of the model at the end of the last explicit dynamics
analysis step.
Boundary conditions
It is not appropriate to specify new boundary conditions or to modify boundary conditions in an
*ANNEAL procedure; all boundary conditions in effect prior to this procedure will remain fixed.
Loads
It is not meaningful to specify loads in an *ANNEAL procedure.
Predefined fields
It is not meaningful to specify predefined fields in an *ANNEAL procedure.
Material options
The annealing procedure is intended only for metal plasticity models and user-defined materials
modeled with user subroutine VUMAT (``VUMAT,'' Section 21.2.3).
Elements
All of the elements that are available in ABAQUS/Explicit can be used in an *ANNEAL procedure.
The elements are listed in Part V, "Elements."
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Analysis Types
Output
There is no output associated with an anneal step.
Template
*HEADING
...
**
*STEP
*DYNAMIC, EXPLICIT (,ADIABATIC) or
*DYNAMIC TEMPERATURE-DISPLACEMENT, EXPLICIT
Data line to specify the time period of the step
*BOUNDARY, AMPLITUDE=name
Data lines to describe zero-valued or nonzero boundary conditions
*CLOAD and/or *DLOAD
Data lines to specify loads
*TEMPERATURE and/or *FIELD
Data lines to specify values of predefined fields
*END STEP
**
*STEP
*ANNEAL (,TEMPERATURE=µ )
*END STEP
**
*STEP
*DYNAMIC, EXPLICIT (,ADIABATIC)
Data line to specify the time period of the step
*BOUNDARY, AMPLITUDE=name
Data lines to describe zero-valued or nonzero boundary conditions
*CLOAD and/or *DLOAD
Data lines to specify loads
*TEMPERATURE and/or *FIELD
Data lines to specify values of predefined fields
*END STEP
6.3 Heat transfer and thermal-stress analysis
6.3.1 Fully coupled thermal-stress analysis
A dynamic fully coupled thermal-stress analysis is performed by using the *DYNAMIC
TEMPERATURE-DISPLACEMENT option.
References
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Analysis Types
· *DYNAMIC TEMPERATURE-DISPLACEMENT
· ``Procedures: overview,'' Section 6.1.1
Overview
A dynamic fully coupled thermal-stress analysis:
· is performed when the mechanical and thermal solutions affect each other strongly and, therefore,
must be obtained simultaneously;
· includes inertia effects;
· models transient thermal response; and
· requires the use of elements with both temperature and displacement degrees of freedom .
Fully coupled thermal-stress analysis
Fully coupled thermal-stress analysis is needed when the stress analysis is dependent on the
temperature distribution and the temperature distribution depends on the stress solution. For example,
metalworking problems may include significant heating due to inelastic deformation of the material
which, in turn, changes the material properties. Also, contact conditions exist in some problems where
the heat conducted between surfaces may depend strongly on the separation of the surfaces or the
pressure transmitted across the surfaces (see ``Thermal surface interactions,'' Section 20.4.1). For such
cases the thermal and mechanical solutions must be obtained simultaneously rather than sequentially.
Coupled temperature-displacement elements are provided for this purpose.
The heat transfer equations are integrated using the explicit forward difference time integration rule
N
N
N
µ(i+1)
= µ(i)
+ ¢t(i+1) µ_(i)
;
where µN is the temperature at node N and the subscript i refers to the increment number in an explicit
dynamic step. The forward difference integration is explicit in the sense that no equations need to be
solved when a lumped capacitance matrix is used. The current temperatures are obtained using known
N
N
values of µ_(i)
from the previous increment. The values of µ_(i)
are computed at the beginning of the
increment by
¡1
N
J
J
µ_(i)
= (C N J ) (P(i)
¡ F(i)
);
where C N J is the lumped capacitance matrix, P J is the applied nodal source vector, and F J is the
internal flux vector.
The mechanical solution response is obtained using the explicit central difference integration rule with
a lumped mass matrix as described in ``Explicit dynamic analysis,'' Section 6.2.1. Since both the
forward difference and central difference integrations are explicit, the heat transfer and mechanical
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Analysis Types
solutions are obtained simultaneously by an explicit coupling. Therefore, no iterations or tangent
stiffness matrices are required.
Explicit integration can be less expensive computationally and simplifies the treatment of contact. For
more information about the advantages of the explicit method and computational cost, see ``Explicit
dynamic analysis,'' Section 6.2.1.
Stability
The explicit procedure integrates through time by using many small time increments. The central
difference and forward difference operators are conditionally stable. The stability limit for both
operators (with no damping in the mechanical solution response) is obtained by choosing
¢t ∙ min(
2
;
2
!max ¸max
);
where !max is the highest frequency in the system of equations of the mechanical solution response
and ¸max is the largest eigenvalue in the system of equations of the thermal solution response.
Estimating the time increment size
An approximation to the stability limit for the forward difference operator in the thermal solution
response is given by
¢t ¼
L2min
;
2®
where L2min is the smallest element dimension in the mesh and ® =
k
½c
is the thermal diffusivity of
the material. The parameters k, ½, and c represent the material's thermal conductivity, density, and
specific heat, respectively.
In most applications of explicit analysis the mechanical response will govern the stability limit. The
thermal response may govern the stability limit when material parameter values are non-physical or a
very large amount of mass scaling is used. The calculation of the time increment size for the
mechanical solution response is discussed in ``Explicit dynamic analysis,'' Section 6.2.1.
Stable time increment report
ABAQUS/Explicit writes a report to the status ( .sta) file during the datacheck phase of the analysis
that contains an estimate of the minimum stable time increment and a listing of the elements with the
smallest stable time increments and their values. The initial minimum stable time increment accounts
for the stability requirements of both the thermal and mechanical solution responses. The initial stable
time increments listed do not include damping (bulk viscosity), mass scaling, or penalty contact effects
in the mechanical solution response.
This listing is provided because often a few elements have much smaller stability limits than the rest of
the elements in the mesh. The stable time increment can be increased by modifying the mesh to
increase the size of the controlling element or by using an appropriate mass scaling option.
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Analysis Types
Time incrementation
The time increment used in an analysis must be smaller than the stability limits of the central and
forward difference operators. Failure to use such a time increment will result in an unstable solution.
When the solution becomes unstable, the time history response of solution variables, such as
displacements, will usually oscillate with increasing amplitudes. The total energy balance will also
change significantly.
ABAQUS/Explicit has two strategies for time incrementation control: fully automatic time
incrementation (where the code accounts for changes in the stability limit) and fixed time
incrementation.
Automatic time incrementation
The default time incrementation scheme in ABAQUS/Explicit is fully automatic and requires no user
intervention. Two types of estimates are used to determine the stability limit: element-by-element for
both the thermal and mechanical solution responses and global for the mechanical solution response.
An analysis always starts by using the element-by-element estimation method and may switch to the
global estimation method under certain circumstances, as explained in ``Explicit dynamic analysis,''
Section 6.2.1.
Element-by-element estimation
In an analysis ABAQUS/Explicit initially uses a stability limit based on the thermal and mechanical
solution responses in the whole model. This element-by-element estimate is determined using the
smallest time increment size due to the thermal and mechanical solution responses in each element.
The element-by-element estimate is conservative; it will give a smaller stable time increment than the
true stability limit, which is based upon the maximum frequency of the entire model. In general,
constraints such as boundary conditions and kinematic contact have the effect of compressing the
eigenvalue spectrum, and the element-by-element estimates do not take this into account (see ``Explicit
dynamic analysis,'' Section 6.2.1)
To use the element-by-element estimation throughout a step, include the ELEMENT BY ELEMENT
parameter on the *DYNAMIC TEMPERATURE-DISPLACEMENT option.
Usage: *DYNAMIC TEMPERATURE-DISPLACEMENT, EXPLICIT, ELEMENT BY ELEMENT
Global estimation
The stable time increment size due to the mechanical solution response will be determined by the
global estimator as the step proceeds unless the ELEMENT BY ELEMENT parameter is used, fixed
time incrementation is specified, or one of the conditions explained in ``Explicit dynamic analysis,''
Section 6.2.1, prevents the use of global estimation. The stable time increment size due to the thermal
solution response will always be determined by using an element-by-element estimation method. The
switch to the global estimation method in mechanical solution response occurs once the algorithm
determines that the accuracy of the global estimation method is acceptable. For details, see ``Explicit
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dynamic analysis,'' Section 6.2.1.
Fixed time incrementation
A fixed time incrementation scheme is also available in ABAQUS/Explicit. The fixed time increment
size is determined either by the initial element-by-element stability estimate for the step or by a time
increment specified directly by the user.
Fixed time incrementation may be useful when a more accurate representation of the higher mode
response of a problem is required. In this case a time increment size smaller than the
element-by-element estimates may be used. The element-by-element estimate can be obtained simply
by running a datacheck analysis (see ``Execution procedure for ABAQUS/Standard and
ABAQUS/Explicit,'' Section 3.2.1).
When fixed time incrementation is used, ABAQUS/Explicit will not check that the computed response
is stable during the step. The user should ensure that a valid response has been obtained by carefully
checking the energy history and other response variables.
Basing the fixed time increment size on the element-by-element
stability limit
Include the FIXED TIME INCREMENTATION parameter on the *DYNAMIC
TEMPERATURE-DISPLACEMENT option to use time increments the size of the initial
element-by-element stability limit throughout a step. The dilatational wave speed and the thermal
diffusivity in each element at the beginning of the step are used to compute the fixed time increment
size.
Usage: *DYNAMIC TEMPERATURE-DISPLACEMENT, EXPLICIT,
FIXED TIME INCREMENTATION
Ensuring stability when fixed time incrementation is used
To reduce the chance of a solution going unstable, the initial stable time increment that
ABAQUS/Explicit computes can be adjusted by a constant scaling factor defined by the SCALE
FACTOR parameter on the *DYNAMIC TEMPERATURE-DISPLACEMENT option.
Usage: *DYNAMIC TEMPERATURE-DISPLACEMENT, EXPLICIT,
FIXED TIME INCREMENTATION, SCALE FACTOR=f
Specifying the fixed time increment size directly
Include the DIRECT USER CONTROL parameter on the *DYNAMIC
TEMPERATURE-DISPLACEMENT option to specify a time increment size directly on the data line
of the *DYNAMIC TEMPERATURE-DISPLACEMENT option.
Usage: *DYNAMIC TEMPERATURE-DISPLACEMENT, EXPLICIT, DIRECT USER CONTROL
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Monitoring output variables for extreme values
The extreme values defined as the element and nodal variables in a coupled thermal-stress analysis can
be monitored exactly as described in ``Explicit dynamic analysis,'' Section 6.2.1, for a pure mechanical
analysis.
Initial conditions
By default, the initial temperature of all nodes is zero. Use the TYPE=TEMPERATURE parameter on
the *INITIAL CONDITIONS option to specify nonzero initial temperatures. See ``Initial conditions,''
Section 18.2.1.
Boundary conditions
The *BOUNDARY option can be used to prescribe both temperatures (degree of freedom 11) and
displacements/rotations (degrees of freedom 1-6) at nodes in fully coupled thermal-stress analysis (see
``Boundary conditions,'' Section 18.3.1). Boundary conditions can be specified as functions of time by
referring to *AMPLITUDE options (``Amplitude curves,'' Section 18.1.2).
Loads
The following types of thermal loads can be prescribed in a fully coupled thermal-stress analysis, as
described in ``Thermal loads,'' Section 18.4.3:
· Concentrated heat fluxes can be prescribed by using the *CFLUX option.
· Body fluxes and distributed surface fluxes can be prescribed by using the *DFLUX and *DSFLUX
options.
· Node-based film conditions and radiation conditions can be defined by using the *CFILM and
*CRADIATE options, respectively.
· Convective film conditions and radiation conditions can be defined by using the *FILM, *SFILM,
*RADIATE, and *SRADIATE options, respectively.
The following types of mechanical loads can be prescribed, as described in ``Concentrated and
distributed loads,'' Section 18.4.2:
· Concentrated nodal forces can be applied to the displacement degrees of freedom (1-6) by using
the *CLOAD option.
· Distributed pressure forces or body forces can be applied by using the *DLOAD and *DSLOAD
options; the distributed load types available with particular elements are described in Part V,
"Elements."
Predefined fields
The *TEMPERATURE option cannot be used in a fully coupled thermal-stress analysis to prescribe
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temperatures; the *BOUNDARY option should be used instead to prescribe temperature degree of
freedom 11.
The *FIELD option can be used in a fully coupled thermal-stress analysis to specify values of
user-defined field variables during the analysis. These values affect only field-variable-dependent
material properties, if any. See ``Predefined fields,'' Section 18.5.1.
Material options
The materials used for the coupled temperature-displacement elements must have both thermal
properties, such as conductivity, and mechanical properties, such as elasticity, defined. See Part IV,
"Materials," for details on the material models available in ABAQUS.
Thermal strain will arise if the *EXPANSION option is used in the material property definition--see
``Thermal expansion,'' Section 11.1.2.
Inelastic energy dissipation as a heat source
The *INELASTIC HEAT FRACTION option can be used in a fully coupled thermal-stress analysis to
provide for inelastic energy dissipation as a heat source. Plastic straining gives rise to a heat flux per
unit volume of
¾ : "_ pl ;
r pl = ´¾
where r pl is the heat flux that is added into the thermal energy balance, ´ is the factor defined by the
*INELASTIC HEAT FRACTION option (assumed constant), ¾ is the stress, and "_ pl is the rate of
plastic straining.
This option is typically used in the simulation of high-speed manufacturing processes involving large
amounts of inelastic strain, where the heating of the material caused by its deformation significantly
influences temperature-dependent material properties. The generated heat is treated as a volumetric
heat flux source term in the heat balance equation.
The *INELASTIC HEAT FRACTION option is available only for materials whose inelastic behavior
is defined by the *PLASTIC option (``Inelastic behavior,'' Section 10.1.1). It cannot be used with the
combined isotropic/kinematic hardening model.
Usage: *INELASTIC HEAT FRACTION
Elements
All of the elements available in ABAQUS/Explicit can be used in the *DYNAMIC
TEMPERATURE-DISPLACEMENT, EXPLICIT procedure. The elements are listed in Part V,
"Elements."
Output
All of the output variable identifiers are outlined in ``Output variable identifiers,'' Section 4.2.1. The
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types of output available are described in ``Output,'' Section 4.1.1.
Template
*HEADING
...
** Specify the coupled temperature-displacement element type
*ELEMENT, TYPE=CPS4RT
...
**
*STEP
*DYNAMIC TEMPERATURE-DISPLACEMENT, EXPLICIT
Data line to define incrementation
*BOUNDARY
Data lines to define nonzero boundary conditions on displacement or
temperature degrees of freedom
*CFLUX and/or *CFILM and/or
*CRADIATE and/or *DFLUX and/or
*DSFLUX and/or *FILM and/or
*SFILM and/or *RADIATE and/or
*SRADIATE
Data lines to define thermal loads
*CLOAD and/or *DLOAD and/or *DSLOAD
Data lines to define mechanical loads
*FIELD
Data lines to define field variable values
*END STEP
6.3.2 Adiabatic analysis
An adiabatic stress analysis can be performed using the *DYNAMIC procedure.
References
· *DYNAMIC
· *DENSITY
· *INELASTIC HEAT FRACTION
· *SPECIFIC HEAT
· ``Procedures: overview,'' Section 6.1.1
Overview
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An adiabatic stress analysis:
· is used in cases where mechanical deformation causes heating but the event is so rapid that this
heat has no time to diffuse through the material--for example, a very high-speed forming process;
and
· requires that a material's density, specific heat, and inelastic heat fraction (fraction of inelastic
dissipation rate that appears as heat flux) be specified.
Adiabatic analysis
Use the ADIABATIC parameter on the *DYNAMIC option to perform adiabatic thermal-stress
analysis with metal plasticity material models. No allowance is made for conduction of heat in an
adiabatic analysis. For problems where both inelastic heating and conduction of the heat are important,
a coupled temperature-displacement analysis must be performed (``Fully coupled thermal-stress
analysis,'' Section 6.3.1).
Adiabatic analysis is typically used to simulate high-speed manufacturing processes involving large
amounts of inelastic strain, where the heating of the material caused by its deformation is an important
effect because of temperature-dependent material properties. The temperature increase is calculated
directly at the material integration points according to the adiabatic thermal energy increases caused by
inelastic deformation; temperature is not a degree of freedom in the problem.
In an adiabatic analysis plastic straining gives rise to a heat flux per unit volume of
¾ : "_ pl ;
r pl = ´¾
where r pl is the heat flux that is added into the thermal energy balance, ´ is the factor defined by the
*INELASTIC HEAT FRACTION option (assumed constant), ¾ is the stress, and "_ pl is the rate of
plastic straining. The heat equation solved at each integration point is
½c(µ)µ_ = rpl ;
where ½ is the material density and c(µ) is the specific heat (see ``Density,'' Section 8.2.1, and
``Specific heat,'' Section 11.2.3).
Usage: *DYNAMIC, EXPLICIT, ADIABATIC
Initial conditions
Initial temperatures can be prescribed at nodes using the *INITIAL CONDITIONS,
TYPE=TEMPERATURE option. Initial values of stresses, field variables, solution-dependent state
variables, etc. can also be specified (see ``Initial conditions,'' Section 18.2.1).
Boundary conditions
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Boundary conditions can be applied to displacement degrees of freedom in an adiabatic analysis in the
same way that they are applied in nonadiabatic explicit dynamic steps (see ``Boundary conditions,''
Section 18.3.1). Temperature is not a degree of freedom in an adiabatic analysis.
Loads
The loading options available for an adiabatic analysis are the same as those available for nonadiabatic
explicit dynamic steps (see ``Applying loads: overview,'' Section 18.4.1).
The following types of mechanical loads can be prescribed, as described in ``Concentrated and
distributed loads,'' Section 18.4.2:
· Concentrated nodal forces can be applied to the displacement degrees of freedom (1-6) by using
the *CLOAD option.
· Distributed pressure forces or body forces can be applied by using the *DLOAD option; the
distributed load types available with particular elements are described in Part V, "Elements."
Predefined fields
The *TEMPERATURE option cannot be used during an adiabatic analysis step.
The values of user-defined field variables can be specified by using the *FIELD option; these values
affect only field-variable-dependent material properties, if any. See ``Predefined fields,'' Section
18.5.1.
Material options
Only Mises plasticity with isotropic hardening is allowed in adiabatic stress analysis. The material
definition must include the *PLASTIC option (``Inelastic behavior,'' Section 10.1.1). Rate effects can
be included.
The *DENSITY, the *INELASTIC HEAT FRACTION, and the *SPECIFIC HEAT options must be
included in the material data block defining the material in which heat will be generated by plastic
dissipation.
The *INELASTIC HEAT FRACTION option specifies the amount of inelastic dissipation used to
calculate the increase in temperature. The default value of the inelastic heat fraction is 0.9. If the
*INELASTIC HEAT FRACTION option is not included in the material definition, the heat generated
by inelastic deformation is not included in the analysis.
Usage: All of the following options must be included in the material definition:
*DENSITY
*INELASTIC HEAT FRACTION
*SPECIFIC HEAT
Temperature-dependent material properties
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Material properties can be temperature dependent. Since the only source of temperature change in
adiabatic analysis is inelastic deformation, the temperature can only rise. This temperature rise may
cause thermal expansion (usually a small effect) and localization of the deformation if the flow stress is
reduced by the temperature rise. Since the adiabatic assumption applies only in rapid events and
inelastic deformation usually causes significant temperature rises only if the deformation is substantial,
the strain rates are often large in adiabatic analysis. The softening of the material caused by the
temperature rise may, thus, be offset somewhat by strengthening associated with rate dependence if the
material is rate sensitive.
Elements
All of the elements available in ABAQUS/Explicit can be used in an adiabatic analysis. Mass or spring
elements will not contribute to the heating of the material since they cannot generate plastic strains.
The elements are listed in Part V, "Elements."
If coupled temperature-displacement elements are used in an adiabatic analysis, the temperature
degrees of freedom will be ignored.
Output
Since temperatures are updated at the material calculation points, output of temperature is available
with output variable TEMP, not with output variable NT.
The element output available for an adiabatic analysis includes stress; strain; energies; the values of
state, field, and user-defined variables; and composite failure measures. The nodal output available
includes displacements, reaction forces, and coordinates. All of the output variable identifiers are
outlined in ``Output variable identifiers,'' Section 4.2.1.
Template
*HEADING
...
*MATERIAL, NAME=name
*ELASTIC, TYPE=ISOTROPIC
Data lines to define isotropic linear elasticity
*PLASTIC
Data lines to define metal plasticity
*DENSITY
Data lines to define density
*INELASTIC HEAT FRACTION
Data line to define inelastic heat fraction
*SPECIFIC HEAT
Data lines to define specific heat
...
*BOUNDARY
Data lines to specify zero-valued boundary conditions
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*INITIAL CONDITIONS, TYPE=type
Data lines to specify initial conditions
*AMPLITUDE, NAME=name
Data lines to define amplitude variations
**
*STEP
*DYNAMIC, EXPLICIT, ADIABATIC
Data line to specify the time period of the step
*BOUNDARY, AMPLITUDE=name
Data lines to describe nonzero or zero-valued boundary conditions
*CLOAD and/or *DLOAD
Data lines to specify loads
*FIELD
Data lines to define field variable values
*END STEP
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7. Analysis Techniques
7.1 Restarting an analysis
7.1.1 Restarting an analysis
An analysis can be restarted by using the *RESTART, WRITE and *RESTART, READ options.
References
· *RESTART
· ``Output,'' Section 4.1.1
Overview
The *RESTART, WRITE option is used to write the model definition and state to the state
(job-name.abq) and part (. prt) files. These files, which will for convenience be referred to as the
"restart file," allow an analysis to be completed up to a certain point in a particular run and restarted
and continued in a subsequent run with the *RESTART, READ option.
Writing a state file
Include the WRITE parameter on the *RESTART option to request output to the state file. If the
*RESTART, WRITE option is not used, a state file will be created with results at only the beginning
and end of each step.
The *RESTART, WRITE option can be used as either model data or history data. The amount of data
written to the state file is controlled by using the NUMBER INTERVAL, TIME MARKS, and
OVERLAY parameters, as described below.
Controlling the frequency of output to the state file
Use the NUMBER INTERVAL and TIME MARKS parameters to specify the number of increments
and the times at which results will be written to the state file. The variables to be written cannot be
specified; a complete set of data is written each time. Therefore, the state file can be quite large. The
user should rely on output to the selected results and results files (see below) if higher resolution in
time is desired for a selected subset of results.
If NUMBER INTERVAL=n, ABAQUS/Explicit will divide the step into n time intervals and write the
results at the beginning of the step and the end of each interval, for a total of n+1 points for the step.
By default, the results will be written to the state file at the increment ending immediately after the
time dictated by the NUMBER INTERVAL parameter (TIME MARKS=NO). Set TIME
MARKS=YES to write results at the exact times calculated by dividing the step into n equal intervals.
Results are always written at the end of the step, so the TIME MARKS parameter is not necessary if
results are required only at the end of a step.
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If a problem precludes the analysis from continuing to completion, such as if an element becomes
excessively distorted, ABAQUS/Explicit will attempt to save the last completed increment in the state
file.
Usage: *RESTART, WRITE, NUMBER INTERVAL=n, TIME MARKS=YES
or
NO
Overlaying results on the state file
The OVERLAY parameter on the *RESTART option can be used to specify that only one increment
should be retained on the state file per step, thus minimizing the size of the file. As the data for an
increment are written, they overlay the data from the previous increment, if any, written for the same
step. The OVERLAY parameter can be used as a step-dependent option.
The advantage of this option is that it minimizes the space required to store the state file. The
disadvantage is that if an analysis terminates due to a system error, all data in the current step may be
lost.
Usage: *RESTART, WRITE, OVERLAY
Restarting an analysis
An analysis is restarted (continued) by including the *RESTART, READ option in an input file. This
option will read the state, analysis database, and part files created by the original analysis. The restart
(.res) file, the package (.pac) file, the state ( .abq) file, and the selected results ( .sel) file are all
used by ABAQUS/Explicit for restarting an analysis and must be saved upon completion of the first
job. Since restart files can be very large, sufficient disk space must be provided.
When the READ parameter is included, the *RESTART option must appear as model data. It is
normally the first option in the input file after the *HEADING option. The new run continues the
analysis from the step specified by the STEP parameter on the *RESTART, READ option. If the END
STEP and INTERVAL parameters are omitted, the analysis is restarted from the last interval available
in the state file for the specified STEP. (The use of the END STEP and INTERVAL parameters to
terminate a step is discussed below.)
Usage: *RESTART, READ, STEP=step,
Supplying additional model and history data in the restart
analysis
It is possible to define steps subsequent to the step at which restart is being made. It is also possible to
supply new amplitude definitions, new node sets, and new element sets during the restart analysis.
Existing sets cannot be modified.
Continuation of optional history data in restart analyses
The rules governing the continuation of optional history data--loading, boundary conditions, and
output controls (see ``Defining a model in ABAQUS,'' Section 1.3.1)--are the same for the steps
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defined in the restart analysis and the original analysis. For a discussion of the rules governing the
continuation of optional history data, see ``Procedures: overview,'' Section 6.1.1.
Identifying the analysis to be restarted
In a restart analysis the user must specify the name of the state file that contains the specified STEP
and INTERVAL. This file name is given either as the value of the oldjob parameter in the command
for running ABAQUS/Explicit or by answering a request made by the command procedure (see
``Execution procedure for ABAQUS/Standard and ABAQUS/Explicit,'' Section 3.2.1).
ABAQUS/Explicit will issue an error message if the step and interval at which restart is requested do
not exist in the specified state file.
Continuing an analysis without changes
In cases where restart is being performed simply to continue a long step (which might have been
terminated because the time limit for the job was exceeded, for example), use the recover option on
the ABAQUS execution procedure (see ``Execution procedure for ABAQUS/Standard and
ABAQUS/Explicit,'' Section 3.2.1). Do not use *RESTART, READ for this purpose.
Simultaneously reading and writing a restart file
The READ and WRITE parameters can be defined on the same *RESTART option to indicate a
continuation of the previous analysis and the writing of results to a new state file. The option
*RESTART, READ, STEP=p, WRITE, NUMBER INTERVAL=n
will restart the analysis from the last saved interval of Step p and will cause ABAQUS/Explicit to write
restart states in subsequent steps based on the new value of n.
Terminating a step
Use the END STEP parameter to terminate an analysis step prior to its completion. The option
*RESTART, READ, STEP=p
will restart from the last saved interval of step p and continue the step to completion. The option
*RESTART, READ, STEP=p, INTERVAL=n, END STEP
will restart from interval n of Step p, end Step p at that point, and continue with newly defined steps.
The END STEP parameter tells ABAQUS that the step from which the analysis is being restarted
should be terminated at the time of restart, regardless of the step end time that had been given in the
previous analysis. Thus, the step is considered to be completed even though all of the loading may not
have been applied. Continuation of the analysis will be defined by history data provided in the restart
run.
It may be necessary to use the END STEP parameter when an unforeseen event occurs (for example,
contact surface definitions may require modification due to unforeseen displacements) or when the
output requests are producing too much or too little information.
Usage: *RESTART, READ, STEP=p, INTERVAL=n, END STEP
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Amplitude references
Care should be taken if loads and boundary conditions refer to amplitude curves ( ``Amplitude curves,''
Section 18.1.2). If the TIME parameter of the *AMPLITUDE option is set to TOTAL TIME, the loads
and boundary conditions will continue to be applied according to the amplitude definition. However, if
the TIME parameter is set to STEP TIME (default), the loads and boundary conditions will be held
constant at their values at the time the step is terminated.
Temperatures and field variables applied in the old step will remain in the new step if they are not
redefined using the *TEMPERATURE or *FIELD options. If an amplitude curve was not specified,
these quantities will continue to be applied according to the default amplitude for the procedure.
Continuation of selected results file output upon restart
The ABAQUS/Explicit selected results file (job-name.sel) contains user-specified results (see
``Output,'' Section 4.1.1). The selected results file from the old job must be available upon restart.
ABAQUS/Explicit will copy the information from the old file into the selected results file for the new
job up to the restart point, and then begin writing the new results following that point.
Restarting with user subroutines
User subroutines are not written to the state file. Therefore, if the original analysis was run with any
user subroutines, these subroutines must be included again in the restart run. These subroutines can be
modified on restart; however, modifications should be made with caution because they may invalidate
the solution from which the restart is being made.
Examples
Suppose a job was stopped by the user because too much output was being generated. The last
information on the state file is from Step 2, Interval 4 at a time of .004. Step 2 has a time period of .010
and NUMBER INTERVAL=10. The following input file could be used to restart this job and redefine
the remainder of the step with reduced output requests:
*HEADING
*RESTART, READ, END STEP, STEP=2, INTERVAL=4
*STEP
*DYNAMIC, EXPLICIT
, .006
*RESTART, WRITE, NUMBER INTERVAL=2
*END STEP
Next, suppose a job stopped prior to completion because a CPU time limit was exceeded. If no
additional steps are desired, use the recover parameter on the ABAQUS execution procedure (see
``Execution procedure for ABAQUS/Standard and ABAQUS/Explicit,'' Section 3.2.1). The command
line would have the following syntax:
abaqus job=jobname recover
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In this case no data file is needed (unless user subroutines are being used).
Finally, suppose a one step job stopped prior to completion because a CPU time limit was exceeded
and the user has decided that a second step should be added with new boundary condition definitions.
The following input file could be used to restart this job, complete the remaining part of Step 1, and
complete Step 2:
*HEADING
*RESTART, READ, STEP=1
**
** This defines Step 2
**
*STEP
*DYNAMIC, EXPLICIT
, .003
*BOUNDARY, OP=NEW
...
*END STEP
7.2 Geometric imperfections
7.2.1 Introducing a geometric imperfection into a model
The *IMPERFECTION option is used to introduce a geometric imperfection pattern into a model for a
postbuckling load-displacement analysis.
Reference
· *IMPERFECTION
Overview
A geometric imperfection pattern:
· is generally introduced in a model for a postbuckling load-displacement analysis;
· can be defined as a linear superposition of buckling eigenmodes obtained from a previous
*BUCKLE or *FREQUENCYanalysis performed with ABAQUS/Standard;
· can be based on the solution obtained from a previous *STATIC analysis performed with
ABAQUS/Standard; or
· can be specified directly on the data lines.
Introducing geometric imperfections
Imperfections are usually introduced by perturbations in the geometry. ABAQUS offers three ways to
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define an imperfection: as a linear superposition of buckling eigenmodes, from the displacements of a
*STATIC analysis, or by specifying the node number and imperfection values directly on the data
lines. Only the translational degrees of freedom are modified. ABAQUS will then calculate the
normals using the standard algorithm based on the perturbed coordinates. Unless the precise shape of
an imperfection is known, an imperfection consisting of multiple superimposed buckling modes can be
introduced.
The usual approach involves two analysis runs with the same model definition, using
ABAQUS/Standard to establish the probable collapse modes and ABAQUS/Explicit to perform the
postbuckling analysis:
1. In the first analysis run perform an eigenvalue buckling analysis with ABAQUS/Standard on the
"perfect" structure to establish probable collapse modes and to verify that the mesh discretizes
those modes accurately. Write the eigenmodes in the default global system to the results file using
the *NODE FILE option with the (default) GLOBAL=YES parameter.
2. In the second analysis run use ABAQUS/Explicit to introduce an imperfection in the geometry by
adding these buckling modes to the "perfect" geometry by using the *IMPERFECTION option.
The lowest buckling modes are assumed to provide the most critical imperfections, so usually
these are scaled and added to the perfect geometry to create the perturbed mesh. The imperfection
thus has the form
¢xi =
M
X
wi Á i ;
i=1
where Ái is the ith mode shape and wi is the associated scale factor.
The scale factors of the various modes must be chosen by the user; usually the lowest buckling
mode should have the largest factor. The magnitudes of the perturbations used are typically a few
percent of a relative structural dimension such as a beam cross-section or shell thickness.
3. Perform a postbuckling analysis with ABAQUS/Explicit on the perturbed structure.
ABAQUS imports imperfection data through the user node labels. ABAQUS does not check model
compatibility between both analysis runs. Node set definitions in the original model and the model
with the imperfection may be different. Eigenmodes cannot be read from the results file in models that
include part and assembly definitions.
Defining an imperfection based on eigenmode data
To define an imperfection based on the superposition of weighted mode shapes, specify the results file
and step from a previous *FREQUENCY or *BUCKLE analysis. The optional NSET parameter can be
used to import eigenmode data for the specified node set.
Usage: *IMPERFECTION, FILE=results_file, STEP=step, NSET=name
Defining an imperfection based on static analysis data
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To define an imperfection based on the deformed geometry of a previous static analysis (``Unstable
collapse and postbuckling analysis,'' Section 6.2.4), specify the results file and step from a previous
*STATIC analysis. The optional INC parameter defines the increment number from which
displacement data are read. (If this parameter is omitted, ABAQUS will read data from the last
increment available for the specified step on the results file.) The optional NSET parameter can be
used to import modal data for the specified node set.
Usage: *IMPERFECTION, FILE=results_file, STEP=step, INC=inc, NSET=name
Defining an imperfection directly in the input file
Use the INPUT parameter to specify the imperfection as a table of node numbers and coordinate
perturbations in the global coordinate system from an input file. If no input file is specified, ABAQUS
assumes that the data follow the option. The optional SYSTEM parameter can be used to specify the
imperfection as perturbation values in cylindrical or spherical coordinates.
Usage: *IMPERFECTION, SYSTEM=name, INPUT=input file
Imperfection sensitivity
The response of some structures depends strongly on the imperfections in the original geometry,
particularly if the buckling modes interact after buckling occurs. Hence, imperfections based on a
single buckling mode tend to yield nonconservative results. By adjusting the magnitude of the scaling
factors of the various buckling modes, the imperfection sensitivity of the structure can be assessed.
Normally, a number of analyses should be conducted to investigate the sensitivity of a structure to
imperfections.
The imperfect structure will be easier to analyze if the imperfection is large. If the imperfection is
small, the deformation will be quite small (relative to the imperfection) below the critical load. The
response will grow quickly near the critical load, introducing a rapid change in behavior.
On the other hand, if the imperfection is large, the postbuckling response will grow steadily before the
critical load is reached. In this case the transition into postbuckled behavior will be smooth and
relatively easy to analyze.
Template
The following example illustrates a postbuckling analysis of a structure with an imperfection defined
by a linear superposition of the buckling eigenmodes and involves two analysis runs with the same
model definition.
The initial analysis run performs an eigenvalue buckling analysis with ABAQUS/Standard to establish
the probable collapse modes and writes them to the results file.
*HEADING
Initial analysis run to write the buckling modes to the results file
*NODE
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Data lines to define initial "perfect" geometry
...
**
*STEP
*BUCKLE
Data lines to define the number of buckling eigenmodes
*CLOAD and/or *DLOAD and/or *TEMPERATURE
Data lines to specify the reference load, Pref
*NODE FILE, GLOBAL=YES, LAST MODE=n
U
*END STEP
The second analysis run introduces the imperfection and performs a postbuckling analysis with
ABAQUS/Explicit.
*HEADING
Second analysis run to define the imperfection and perform the postbuckling analysis
*NODE
Data lines to define initial "perfect" geometry
...
*IMPERFECTION, FILE=results_file, STEP=step
Data lines specifying the mode number and its associated scale factor
...
**
*STEP
*DYNAMIC, EXPLICIT
Data line to define the time period of the step.
*CLOAD and/or *DLOAD and/or *TEMPERATURE
*END STEP
7.3 Importing and transferring results
7.3.1 Transferring results between ABAQUS/Explicit and
ABAQUS/Standard
Results can be transferred between ABAQUS/Explicit and ABAQUS/Standard by using the *IMPORT
option.
References
· *IMPORT
· *IMPORT ELSET
· *IMPORT NSET
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· *IMPORT CONTROLS
Overview
ABAQUS provides the capability to import a deformed mesh and its associated material state from
ABAQUS/Standard into ABAQUS/Explicit and vice versa. This capability is particularly useful in
manufacturing problems; for example, the entire sheet metal forming process (which requires an initial
preloading, forming, and subsequent springback) can be analyzed. In this case the initial preloading
can be simulated with ABAQUS/Standard using a static procedure and the subsequent forming process
can be simulated with ABAQUS/Explicit. Finally, the springback analysis can be performed with
ABAQUS/Standard.
For this capability to work the same version of ABAQUS/Explicit and ABAQUS/Standard must be run
on computers that are binary compatible.
Saving the analysis results
The *RESTART, WRITE option is used to save the analysis results when transferring results from
ABAQUS/Explicit to ABAQUS/Standard or vice versa. The specific use of the option in each case is
described below. The *RESTART, WRITE option is described in more detail in ``Restarting an
analysis,'' Section 7.1.1.
Saving results from ABAQUS/Explicit
If the results are to be imported from an ABAQUS/Explicit analysis, the *RESTART, WRITE option
must be used with the original ABAQUS/Explicit job to write the results to the state ( .abq) file at the
time when transfer of the state of the deformed body is required. The state ( .abq), package (.pac),
and part (.prt) files will be used for importing the results from ABAQUS/Explicit.
If the results are to be imported at an exact time during a step of an ABAQUS/Explicit analysis, set
TIME MARKS=YES on the *RESTART option. Results are always written at the end of a step, so the
TIME MARKS parameter is not necessary if results will be read only from the end of a step.
Usage: *RESTART, WRITE, NUMBER INTERVAL=n, TIME MARKS=YES
or
NO
Saving results from ABAQUS/Standard
If the results are to be imported from an ABAQUS/Standard analysis, the *RESTART, WRITE option
must be used with the original ABAQUS/Standard job to write results to the restart ( .res), analysis
database (.mdl and .stt), and part ( .prt) files. The FREQUENCY parameter can be used to
specify the increments at which restart information will be written. Restart information is always
written at the end of a step in addition to the requested increments whenever the *RESTART, WRITE
option is used with ABAQUS/Standard.
Usage: *RESTART, WRITE, FREQUENCY=n
Specifying the transfer of model data and results
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Specify the name of the job from which results data will be obtained by using the oldjob parameter in
the command for running ABAQUS. If this parameter is omitted, ABAQUS will prompt for the job
name (see ``Execution procedure for ABAQUS/Standard and ABAQUS/Explicit,'' Section 3.2.1).
Use the *IMPORT option in the model definition portion of the input file to import the results.
If the results are imported from an ABAQUS/Explicit analysis, use the STEP and INTERVAL
parameters to specify the step and interval on the state file for which the results are to be imported. If
the STEP and INTERVAL parameters are omitted, the results written at the end of the analysis are
imported.
Usage: *IMPORT, STEP=step, INTERVAL=interval
If the results are imported from an ABAQUS/Standard analysis, use the STEP and INCREMENT
parameters to specify the step and increment on the restart file for which the results are to be imported.
If the STEP and INCREMENT parameters are omitted, the results written at the end of the analysis are
imported.
Usage: *IMPORT, STEP=step, INCREMENT=increment
Specify the element sets that are to be imported on the data line of the *IMPORT option. Each element
set can contain only elements with element types common to ABAQUS/Explicit and
ABAQUS/Standard. In addition, each element set can contain only elements that were defined in the
original analysis using the same element property definition (e.g., *SOLID SECTION). To ensure that
this requirement is satisfied in the import analysis, use the same element set names utilized to define
the properties in the original analysis.
Element property definitions of imported elements can be redefined only if UPDATE=YES and
STATE=NO on the *IMPORT option. In this case the material orientation definitions
(*ORIENTATION), hourglass stiffness or hourglass control definitions, and transverse shear stiffness
definitions (in case of shell elements) of the imported elements can also be redefined.
For other combinations of the UPDATE and STATE parameters on the *IMPORT option, the
information required to define the section for each imported element will be imported from the original
analysis. Material orientations for the imported elements cannot be redefined; the values will be
transferred from the original analysis. Hourglass stiffness or hourglass control definitions for the
imported elements cannot be redefined; the default values will be used in the import analysis.
Transverse shear stiffness for imported shell elements cannot be redefined; the values will be
transferred from the original analysis.
Only nodes associated with the imported elements are imported. New nodes can be defined. To prevent
any ambiguity regarding element and node definitions, the *IMPORT option must be specified before
any options that define the rest of the model in the input file. In addition, it can be specified only
once.
Nodes or elements that use the same numbers as nodes or elements being imported can be defined
provided that UPDATE=YES and STATE=NO on the *IMPORT option. The new definitions will
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overwrite the imported definitions. However, if UPDATE=NO or STATE=YES, new nodes or
elements cannot use the imported node and element numbers.
``Springback of two-dimensional draw bending,'' Section 1.5.1 of the ABAQUS Example Problems
Manual, and ``Axisymmetric forming of a circular cup,'' Section 1.3.8 of the ABAQUS Example
Problems Manual, illustrate the importing capability.
Updating the imported configuration
Once the current model configuration of ABAQUS/Standard is imported into ABAQUS/Explicit (or
ABAQUS/Explicit into ABAQUS/Standard), the analysis can be continued with or without updating
the reference configuration to be the imported configuration. If the reference configuration is not
updated to be the imported configuration, the displacements and strains are reported as total values
relative to the original reference configuration and will, hence, be continuous. If the reference
configuration is updated to be the imported configuration, displacements and strains reported in the
import analysis are the total values relative to the updated reference configuration. This option is
useful if results need to be displayed relative to the imported configuration, such as may be desirable in
springback analysis. The reference configuration cannot be updated if the imported analysis is
geometrically linear.
Use the UPDATE parameter to specify whether the reference configuration is to be updated or not. Set
UPDATE=YES to specify that the reference configuration is to be updated to the imported
configuration for the import analysis. Set UPDATE=NO otherwise.
Usage: *IMPORT, STEP=step, UPDATE=YES
or
NO
Importing the material state
Use the STATE parameter on the *IMPORT option to specify whether or not the associated material
state should be imported.
Usage: *IMPORT, STATE=YES
or
NO
The only material state quantities that are imported with the stresses are the equivalent plastic strains
and user-defined state variables. Thus, only the material state for the linear elastic, hyperelastic,
hyperfoam, and Mises plasticity models or materials defined in user subroutine UMAT and VUMAT are
imported correctly for further analysis. If the original analysis uses the viscoelastic material model, the
import analysis will not be allowed to continue. For all other material models only stresses will be
imported if STATE=YES is specified on *IMPORT option. No state variables will be imported.
If material behavior is defined in a user subroutine, the user must ensure that the UMAT and VUMAT are
consistent.
Importing element set and node set definitions
All element set and node set definitions are imported by default. They can also be selectively imported
by using the *IMPORT ELSET and *IMPORT NSET options. If element set names or node set names
are specified on the data lines of these options, only these element sets or node sets will be
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imported.
The *IMPORT ELSET and *IMPORT NSET options provide a convenient way of selectively reusing
the element or node sets defined in the original analysis. However, any members of such sets that do
not belong to the imported elements specified on the data lines of the *IMPORT option (or all the
elements imported if the default is used) are removed from the sets specified by the *IMPORT ELSET
and *IMPORT NSET options.
For example, suppose three element sets-- SHELL3D, MEMB, and ALL--were defined in the original
analysis. Element set ALL contains all of the elements in element sets SHELL3D and MEMB, as well as
other elements. Element sets SHELL3D and MEMB are listed on the data line of the *IMPORT option,
and element set ALL is listed on the data line of the *IMPORT ELSET option. If element 100 belongs
to element set ALL but not to either element set SHELL3D or element set MEMB, it will not be imported
and will be removed from the list of elements belonging to element set ALL. The *IMPORT,
*IMPORT ELSET, and *IMPORT NSET options are processed before any node or element definitions
in the import input file; therefore, even if element 100 is subsequently redefined in the import analysis,
it will not belong to element set ALL (unless it is explicitly assigned to element set ALL in the import
analysis).
The *IMPORT ELSET and *IMPORT NSET options must appear, singly or together, immediately
after the *IMPORT option in the input file.
Only node and element sets defined in the original or previous import analysis are available for
importing. New sets defined during a restart run cannot be imported.
Usage: Use either or both of the following options immediately following the *IMPORT option:
*IMPORT ELSET
*IMPORT NSET
Specifying NLGEOM in an import analysis
By default, ABAQUS/Standard uses a small-strain formulation. This default can be changed by
specifying NLGEOM=YES on the *STEP option. By default, ABAQUS/Explicit uses a
large-deformation formulation; i.e., NLGEOM=YES by default. The small-strain formulation can be
invoked by setting NLGEOM=NO in the first step of the ABAQUS/Explicit analysis. In a subsequent
step the large-deformation formulation can be invoked by setting NLGEOM=YES.
The default value for the NLGEOM parameter in an import analysis is the same as the value of the
parameter at the time of import. Once NLGEOM=YES is defined in a given step in any analysis, it will
remain active in all the subsequent steps, whether or not the analysis is imported. See ``Procedures:
overview,'' Section 6.1.1, for details regarding the use of the NLGEOM parameter.
If NLGEOM=NO at the time of import, the reference configuration cannot be updated: *IMPORT,
UPDATE=YES is not allowed.
Specifying initial conditions for imported elements and nodes
Initial conditions can be specified on the imported elements or nodes only under certain conditions.
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Table 7.3.1-1 lists the initial conditions that can be allowed depending on the STATE parameter on the
*IMPORT option. The UPDATE parameter on the *IMPORT option can be set to either YES or NO as
desired.
Table 7.3.1-1. Valid initial conditions.
TYPE=
STATE=
HARDENING
NO
RATIO
NO
RELATIVE DENSITY
NO
ROTATING
YES or NO
VELOCITY
SOLUTION
NO
STRESS
NO
VELOCITY
YES or NO
Nodal transformation
Nodal transformations defined with the *TRANSFORM option are not imported; transformations can
be defined independently in the import analysis. Continuous displacements, velocities, etc. are
obtained only if the nodal transformations in the import analysis are the same as those in the original
analysis. Use of the same transformations is also recommended for nodes with boundary conditions or
point loads defined in a local system.
New model definitions
New nodes, elements, and material properties can be added to the model in an import analysis once the
import options are specified. Nodal coordinates must be defined in the updated configuration,
regardless of the value of the UPDATE parameter on the *IMPORT option. The usual ABAQUS
options can be used. Imported material definitions can be used with the new elements (which will need
new section property definitions).
Specifying a tolerance for shell normals in the updated
configuration
When the imported configuration is updated (*IMPORT, UPDATE=YES), the mesh discretization may
not satisfy the mesh geometry checks imposed in ABAQUS/Explicit or ABAQUS/Standard to evaluate
whether or not a mesh is reasonable. In the case of highly warped shell elements it is possible that the
normal at the center of the element that is calculated from the midsurface interpolation may differ from
the normal that is interpolated from the rotated normals at the nodes. If the difference exceeds the
tolerance specified, the analysis will terminate. This suggests that a fine mesh may be required to
model areas of high curvature change to achieve a successful analysis.
The unit normal computed from the midsurface interpolation, n1 , and that predicted by the
interpolation of the rotated normals at the nodes, n2 , must satisfy the condition:
1 ¡ ftol ∙ jn1 ¢ n2 j ;
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where the tolerance, ftol , can be specified by using the parameter NORMAL TOL on the *IMPORT
CONTROLS option. If this option is not used, a default value of ftol = 0:1 is used.
Usage: *IMPORT CONTROLS, NORMAL TOL=tolerance
Contact
Contact definitions specified in the original analysis and contact state are not imported. Contact can be
defined again in the import analysis by specifying the surfaces and contact pairs; however, the user
may not be able to use the exact contact definitions that were used in the original analysis because of
differences in the contact capabilities between ABAQUS/Standard and ABAQUS/Explicit.
The contact constraint enforcement may be different in ABAQUS/Standard and ABAQUS/Explicit.
For instance, ABAQUS/Standard always uses a "master-slave" approach, whereas ABAQUS/Explicit
can use a "balanced master-slave" approach. ABAQUS/Standard does not account for the thickness
and midsurface offset for shell and membrane elements in the contact formulation, whereas
ABAQUS/Explicit does. Thus, when the contact conditions are defined in the import analysis, the
contact state that existed in the previous analysis may not be reproduced at the beginning of the import
analysis. This could lead to a redistribution of stresses and an analysis that differs from what is desired
by the user.
For a detailed description of the contact capabilities in ABAQUS and the differences in the contact
capabilities between ABAQUS/Standard and ABAQUS/Explicit, refer to ``Contact analysis:
overview,'' Section 20.1.1.
Procedures
Results can be imported into ABAQUS/Explicit only from a general analysis step involving static
stress analysis, dynamic stress analysis, or steady-state transport analysis in ABAQUS/Standard.
Results transfer from linear perturbation procedures ( ``Linear and nonlinear procedures,'' Section
6.1.2) is not allowed.
ABAQUS/Standard offers several analysis procedures that can be used in an import analysis. These
procedures can be used to perform an eigenvalue analysis, static or dynamic stress analysis, buckling
analysis, etc. See ``Procedures: overview,'' Section 6.1.1, for a discussion of the available procedures.
For springback analysis of a formed component the first step in the ABAQUS/Standard analysis
usually consists of a *STATIC analysis procedure so that the initial out-of-balance forces can be
removed gradually from the system. The removal of these forces is performed automatically by
ABAQUS/Standard during the first static analysis step, as described below. If the first step in the
ABAQUS/Standard analysis is not a *STATIC step (such as a *DYNAMIC step), the analysis
proceeds directly from the state imported from the ABAQUS/Explicit analysis.
Achieving static equilibrium when importing into
ABAQUS/Standard
When the current state of a deformed body in an explicit dynamic analysis is imported into a static
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analysis, the model will not initially be in static equilibrium. Initial out-of-balance forces must be
applied to the deformed body in dynamic equilibrium to achieve static equilibrium. Both dynamic
forces (inertia and damping) and boundary interaction forces contribute to the initial out-of-balance
forces. The boundary forces are the result of interactions from fixed boundary and contact conditions.
Any changes in the boundary and contact conditions from the ABAQUS/Explicit analysis to the
ABAQUS/Standard analysis will contribute to the initial out-of-balance forces.
In general the instantaneous removal of the initial out-of-balance forces in a static analysis will lead to
convergence problems. Hence, these forces need to be removed gradually until complete static
equilibrium is achieved. During this process of removing the out-of-balance forces, the body will
deform further and a redistribution of internal forces will occur, resulting in a new stress state. (This is
essentially what occurs during "springback," when a formed product is removed from the worktools.)
When the first step in the ABAQUS/Standard analysis is a *STATIC procedure, the following
algorithm is used to remove the initial out-of-balance forces automatically:
1. The imported stresses are defined at the start of the analysis as the initial stresses in the
material.
2. An additional set of artificial stresses is defined at each material point. These stresses are equal in
magnitude to the imported stresses but are of opposite sign. The sum of the material point stresses
and these artificial stresses, thus, creates zero internal forces at the beginning of the step.
3. The internal artificial stresses are ramped off linearly in time during the first step. Thus, at the end
of the step the artificial stresses have been removed completely and the remaining stresses in the
material will be the residual stress state associated with static equilibrium.
Once static equilibrium has been obtained, subsequent steps can be defined using any analysis
procedure that would normally follow a static analysis in ABAQUS.
When the first step is not a static analysis, no artificial stress state is applied and the imported stresses
are used in the internal force computations for the element.
Boundary conditions
Boundary conditions and multi-point constraints specified in the original analysis are not imported.
They must be defined again in the import analysis. In some cases nonzero boundary conditions
imposed in the original analysis need to be maintained at the same values in the import analysis when
the imported configuration is not updated. In such cases, the AMPLITUDE parameter on the *STEP
option can be set to STEP so that the newly applied boundary conditions are applied instantaneously
and held at that value for the duration of the step. Alternatively, the AMPLITUDE parameter on the
*BOUNDARY option can be used and the appropriate amplitude curve can be defined using the
*AMPLITUDE option (``Amplitude curves,'' Section 18.1.2). If boundary conditions in the original
analysis are applied in a local system defined with the *TRANSFORM option, the same
*TRANSFORM option should be used in the import analysis.
For discussions on applying boundary conditions and multi-point constraints, see ``Boundary
conditions,'' Section 18.3.1, and ``Kinematic constraints: overview,'' Section 19.1.1.
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Loads
Loads defined in the original analysis are not imported. Loads may, therefore, need to be redefined in
the import analysis. There are no restrictions on the loads that can be applied when results are
imported from one analysis to the other. In cases when the loads need to be maintained at the same
values as in the original analysis, the AMPLITUDE parameter on the *STEP option can be set to STEP
to apply the loads instantaneously at the start of the step and hold them for the duration of the step. See
``Procedures: overview,'' Section 6.1.1, for further details. Alternatively, the *AMPLITUDE parameter
on the loading options can be used and the amplitude curve can be defined using the *AMPLITUDE
option (``Amplitude curves,'' Section 18.1.2). If point loads in the original analysis are applied in a
local system defined with the *TRANSFORM option and the loads must be maintained in the import
analysis, the load application is simplified if the same *TRANSFORM option is used in the import
analysis.
See ``Applying loads: overview,'' Section 18.4.1, for an overview of the loading options available in
ABAQUS.
Predefined fields
Temperatures and field variables at nodes are not imported. If the temperature is a state variable (as in
an adiabatic analysis where temperature is an integration point quantity), it will be imported when
STATE=YES on the *IMPORT option. If the original analysis uses the *TEMPERATURE or *FIELD
option to vary the temperatures or the field variables at nodes, the import analysis will not be allowed
to continue.
If the original analysis uses the *INITIAL CONDITIONS, TYPE=TEMPERATURE or FIELD option,
the import analysis will not be allowed to continue. In addition, specification of initial conditions for
temperatures and field variables is not allowed in an import analysis. Initial temperatures can be
specified in the import analysis only if it is an adiabatic analysis.
Material options
All material property definitions and orientations associated with imported elements are imported by
default. Material properties can be changed by respecifying the material property definitions with the
same material name in the import input file. All relevant material properties must be redefined since
the old definitions that were imported by default will be overwritten. Material orientations associated
with imported elements can be changed only if UPDATE=YES and STATE=NO on the *IMPORT
option; the material orientations associated with imported elements cannot be redefined for other
combinations of the UPDATE and STATE parameter values.
If mass scaling (``Mass scaling,'' Section 7.5.1) is used in ABAQUS/Explicit, the scaled masses will
not be transferred to the subsequent import analysis in ABAQUS/Standard. The mass of the model for
the ABAQUS/Standard analysis will be based on either the imported or the redefined density
definitions.
The material model must be redefined in the import analysis if changes to material damping are
required.
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When material definitions are changed, care must be taken to ensure that a consistent material state is
maintained. It may sometimes be possible to simplify the material definition. For example, if a Mises
plasticity model was used in the ABAQUS/Explicit analysis and no further plastic yielding is expected
in the ABAQUS/Standard analysis (as is generally the case for springback simulations), a linear elastic
material can be used for the ABAQUS/Standard analysis. However, if further nonlinear material
behavior is expected, no changes to the existing material definitions should be made. The history of the
state variables will not be maintained if the material models are not the same in both the original
analysis and the import analysis.
Elements
The import capability is available for first-order continuum, shell, membrane, truss, and rigid elements
that are common to both ABAQUS/Explicit and ABAQUS/Standard, as defined in Table 7.3.1-2.
Beam elements, infinite elements, and fluid elements cannot be imported. Rebars and associated forces
cannot be imported. Only rigid elements defined as part of a rigid body in the original analysis will be
imported. Rigid elements for which the thickness is interpolated from the nodes in an
ABAQUS/Explicit analysis will not be imported into ABAQUS/Standard. Deformable elements
defined as part of a rigid body in the original analysis cannot be imported. Nodes that are part of a rigid
body (defined using the parameters TIE NSET and PIN NSET on the *RIGID BODY option) cannot be
imported. Failed elements in ABAQUS/Explicit will not be imported into ABAQUS/Standard.
Elements that are being removed or are inactive (due to *MODEL CHANGE) in ABAQUS/Standard
will not be imported into ABAQUS/Explicit.
Rigid surfaces will not be imported.
Table 7.3.1-2. Common element types that can be transferred between ABAQUS/Explicit and
ABAQUS/Standard or vice versa.
Common element
types
CPS4R, CPS3
CPE4R, CPE3
CAX4R, CAX3
C3D8R, C3D4, C3D6
M3D4R, M3D3
R2D2
R3D3, R3D4
RAX2
S4R, S3R
SAX1
T2D2
T3D2
When the S3R shell elements are imported from ABAQUS/Explicit into ABAQUS/Standard, they are
converted into degenerated S4R elements automatically. However, when the S3R shell elements are
imported from ABAQUS/Standard into ABAQUS/Explicit, they remain S3R elements.
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Using *SECTION CONTROLS in an import analysis
The *SECTION CONTROLS option cannot be used in ABAQUS/Standard and is not imported from
ABAQUS/Explicit into ABAQUS/Standard. When importing results from ABAQUS/Standard into
ABAQUS/Explicit, the default kinematic formulation, order of accuracy in the element formulation,
and hourglass control approach in ABAQUS/Explicit will be used in the ABAQUS/Explicit analysis.
When importing results from ABAQUS/Explicit into ABAQUS/Standard, the default hourglass
stiffness in ABAQUS/Standard will be used in the ABAQUS/Standard analysis.
If the KINEMATIC SPLIT parameter is set to a nondefault value for solid elements in the
ABAQUS/Explicit analysis, the differences in the kinematic formulations may lead to errors in
ABAQUS/Standard if the elements are distorted or the rotations are large.
The existing differences in hourglass control formulations between ABAQUS/Explicit and
ABAQUS/Standard may also cause errors when the hourglass forces contribute significantly to the
solution.
Using the first-order accurate element formulation (default in ABAQUS/Explicit) in
ABAQUS/Explicit and the second-order accurate element formulation (default and the only option) in
ABAQUS/Standard is not expected to cause significant errors since the time increment size in
ABAQUS/Explicit is inherently small.
Membrane and shell element thickness computation
The computations for membrane and shell element thicknesses are described below.
Shell elements defined using *SHELL GENERAL SECTION
For shells defined using *SHELL GENERAL SECTION the current thickness is computed based on
the effective Poisson's ratio, which is 0.5 by default, in both ABAQUS/Explicit and
ABAQUS/Standard.
Usage: Use the following option:
*SHELL GENERAL SECTION, POISSON=
Shell elements defined using *SHELL SECTION and membrane
elements
For shells defined using *SHELL SECTION and for membranes in ABAQUS/Standard, the current
thickness is computed based on the effective Poisson's ratio, which is 0.5 by default. In
ABAQUS/Explicit, on the other hand, the computation of the thickness could be based either on the
effective Poisson's ratio or the through-thickness strains, with the computation based on the
through-thickness strains used by default.
If the POISSON parameter on *SHELL SECTION or *MEMBRANE SECTION is not specified in an
original ABAQUS/Explicit or ABAQUS/Standard analysis or is set equal to MATERIAL in an original
ABAQUS/Explicit analysis, the thickness computations in the original and all subsequent import
analyses are carried out using the default methods. In other words, the thicknesses in all
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ABAQUS/Standard analyses are computed using the default effective Poisson's ratio of 0.5, while the
thicknesses in all ABAQUS/Explicit analyses are computed using the through-thickness strains.
When the POISSON parameter is assigned a numerical value in an original ABAQUS/Standard or
ABAQUS/Explicit analysis, the thickness computations in the original analysis and all subsequent
import analyses are performed using the specified value for the effective Poisson's ratio.
Usage: Use one of the following options:
*SHELL SECTION, POISSON=
*SHELL SECTION, POISSON=MATERIAL
*MEMBRANE SECTION, POISSON=
*MEMBRANE SECTION, POISSON=MATERIAL
Output
Output can be requested for an import analysis in the same way as for an analysis in which the results
are not imported. The output variables available in ABAQUS/Standard are listed in ``Output variable
identifiers,'' Section 4.2.1. The output variables available in ABAQUS/Explicit are listed in ``Output
variable identifiers,'' Section 4.2.1.
The values of the following material point output variables will be continuous in an import analysis
when STATE=YES on the *IMPORT option: stress, equivalent plastic strain ( PEEQ), and
solution-dependent state variables ( SDV) for UMAT and VUMAT.
If the reference configuration is not updated (*IMPORT, UPDATE=NO), the displacements, strains,
whole element variables, section variables, and energy quantities will be reported relative to the
original configuration. Accelerations are recomputed at the start of an import analysis in
ABAQUS/Explicit and may be different from those obtained at the end of an ABAQUS/Standard
analysis. The differences in accelerations arise from the recalculation of the internal forces created by
the imported stresses using the ABAQUS/Explicit element formulation algorithms.
If the reference configuration is updated (*IMPORT, UPDATE=YES), displacements, strains, whole
element variables, section variables, and energy quantities will not be continuous in an import analysis
and will be reported relative to the updated reference configuration.
Time and step number will not be continuous between the original and the import analyses if
UPDATE=YES on the *IMPORT option. Time and step number will be continuous only if
UPDATE=NO.
Limitations
The import option has the following known limitations. Where applicable, details are given in the
relevant sections.
· The same version of ABAQUS/Explicit and ABAQUS/Standard must be run on computers that are
binary compatible.
· The capability is not available for beam elements; fluid elements; infinite elements; and spring,
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mass, dashpot, rotary inertia, and connector elements. Rebar are not imported. See the discussion
on elements for further details.
· Surface definitions and contact pair definitions are not imported. Analytical rigid surfaces will not
be imported.
· The viscoelastic material model cannot be imported. If STATE=YES on the *IMPORT option,
only stresses will be imported for material models other than those defined by linear elasticity,
hyperelasticity, hyperfoam, and Mises plasticity. See the discussion on importing the material state
for details.
· Temperatures and field variables at nodes are not imported. If the temperature is a state variable
(as in an adiabatic analysis where temperature is an integration point quantity), it will be imported
when STATE=YES on the *IMPORT option. See the discussion on temperatures and field
variables for details.
· Loads, boundary conditions, multi-point constraints, and equations are not imported.
· The *MODEL CHANGE option cannot be used in the first step of an import analysis in
ABAQUS/Standard. It can be used in the subsequent steps.
· The *SECTION CONTROLS option is not imported from ABAQUS/Explicit into
ABAQUS/Standard.
· The *SYMMETRIC MODEL GENERATION option cannot be used in an import analysis in
ABAQUS/Standard.
· The results file, restart file, or output database file generated during the import analysis is not
appended to the results file, restart file, or output database file of the original analysis.
· The *IMPORT options cannot be used in a model that contains an assembly of part instances.
Template
Transferring results between ABAQUS/Explicit and
ABAQUS/Standard:
ABAQUS/Explicit analysis:
*HEADING
...
*MATERIAL, NAME=mat1
*ELASTIC
Data lines to define linear elasticity
*PLASTIC
Data lines to define Mises plasticity
*DENSITY
Data line to define the density of the material
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...
*BOUNDARY
Data lines to define boundary conditions
*STEP
*DYNAMIC, EXPLICIT
...
*RESTART, WRITE, NUMBER INTERVAL=n
*END STEP
ABAQUS/Standard analysis:
*HEADING
*IMPORT, STEP=step, INTERVAL=interval, STATE=YES, UPDATE=NO
Data lines to specify element sets to be imported
*IMPORT ELSET
Data lines to specify element set definitions to be imported
*IMPORT NSET
Data lines to specify node set definitions to be imported
**
*** Optionally redefine the material block
**
*MATERIAL, NAME=mat1
*ELASTIC
Data lines to redefine linear elasticity
*PLASTIC
Data lines to redefine Mises plasticity
...
*BOUNDARY
Data lines to redefine boundary conditions
*STEP, NLGEOM=YES
*STATIC
...
*END STEP
Transferring results between ABAQUS/Standard and
ABAQUS/Explicit:
ABAQUS/Standard analysis:
*HEADING
...
*MATERIAL, NAME=mat1
*ELASTIC
Data lines to define linear elasticity
*PLASTIC
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Data lines to define Mises plasticity
*DENSITY
Data line to define the density of the material
...
*BOUNDARY
Data lines to define boundary conditions
*STEP
*STATIC
...
*RESTART, WRITE, FREQUENCY=n
*END STEP
ABAQUS/Explicit analysis:
*HEADING
*IMPORT, STEP=step, INCREMENT=increment, STATE=YES, UPDATE=NO
Data lines to specify element sets to be imported
*IMPORT ELSET
Data lines to specify element set definitions to be imported
*IMPORT NSET
Data lines to specify node set definitions to be imported
**
*** Optionally redefine the material block
**
*MATERIAL, NAME=mat1
*ELASTIC
Data lines to redefine linear elasticity
*PLASTIC
Data lines to redefine Mises plasticity
...
*BOUNDARY
Data lines to redefine boundary conditions
*STEP
*DYNAMIC, EXPLICIT
...
*END STEP
7.4 Hydrostatic fluid modeling
7.4.1 Modeling fluid-filled cavities
Fluid-filled cavities are modeled using hydrostatic fluid elements.
References
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· ``Hydrostatic fluid elements,'' Section 17.1.1
· ``Fluid link elements,'' Section 17.1.3
· ``Hydrostatic fluid model,'' Section 11.3.1
Overview
Fluid-filled cavities are modeled by:
· using standard finite elements to model the fluid-filled structure;
· using hydrostatic fluid elements to provide the coupling between the deformation of the fluid-filled
structure and the pressure exerted by the contained fluid on the cavity boundary of the structure;
· defining the hydrostatic fluid properties; and
· using fluid link elements to model the transfer of fluid between multiple fluid cavities or between a
cavity and the environment, if necessary.
Introduction
In certain applications it may be necessary to predict the mechanical response of a fluid-filled or a
gas-filled structure. A primary difficulty in addressing such applications is the coupling between the
deformation of the structure and the pressure exerted by the contained fluid or gas on the structure.
Figure 7.4.1-1 illustrates a simple example of a fluid-filled structure subjected to a system of external
loads. The response of the structure depends not only on the external loads but also on the pressure
exerted by the fluid, which, in turn, is affected by the deformation of the structure. The hydrostatic
fluid elements provide the coupling needed to analyze such situations. The cavity is assumed to be
completely filled with fluid; that is, effects such as sloshing cannot be modeled.
Discretizing the fluid cavity
Hydrostatic fluid elements are surface elements that cover the boundary of the fluid cavity. In regions
where standard finite elements are used to model the boundary of the cavity, the hydrostatic fluid
elements share the nodes at the cavity boundary with the standard elements.
Consider the example presented in Figure 7.4.1-1. Hydrostatic fluid elements are defined around the
cavity boundary as indicated in Figure 7.4.1-2. A hydrostatic fluid element is also defined along the
bottom rigid boundary of the cavity, even though no standard elements exist along this boundary.
Figure 7.4.1-1 Fluid-filled structure.
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Figure 7.4.1-2 Axisymmetric model of fluid-filled structure.
This fluid element is needed to define the cavity completely and to ensure proper calculation of its
volume.
Defining the location of the cavity reference node
All hydrostatic fluid elements associated with a given cavity share a common node known as the cavity
reference node. This cavity reference node has a single degree of freedom representing the pressure
inside the fluid cavity. The cavity reference node is also used in calculating the cavity volume.
If the cavity is not bounded by symmetry planes, it must be completely enclosed with hydrostatic fluid
elements. In this case the location of the cavity reference node is arbitrary and does not have to lie
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inside the cavity.
If as a result of symmetry only a portion of the cavity boundary is modeled with standard elements, the
cavity reference node must be located on the symmetry plane or axis (Figure 7.4.1-2). If multiple
symmetry planes exist, the cavity reference node must be located on the intersection of the symmetry
planes (Figure 7.4.1-3). For an axisymmetric analysis the cavity reference node must be located on the
axis of symmetry. These requirements are a consequence of the fluid cavity not being fully enclosed
with hydrostatic fluid elements.
Figure 7.4.1-3 Axisymmetric model with additional symmetry plane.
Defining hydrostatic fluid elements at nodes that are not attached
to standard elements
If hydrostatic fluid elements are defined with nodes that are not attached to standard elements, proper
displacement boundary conditions must be applied to these nodes. Thus, in the example shown in
Figure 7.4.1-2, the node located at the intersection of the axis of symmetry and the lower rigid
boundary of the cavity must be restrained in the r- and z-directions.
Modeling contact involving the cavity boundary
If a large amount of fluid is removed from a cavity or the material surrounding the cavity is very
flexible, the cavity may partially collapse, causing contact of the cavity wall. Either single or multiple
surface contact can be used to avoid unrealistic overclosure of the cavity (see Figure 7.4.1-4).
Figure 7.4.1-4 Partial collapse of fluid-filled structure.
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Modeling multiple fluid cavities
It is possible that a particular application may involve multiple fluid cavities with potential transfer of
fluid between the cavities due to a pressure differential. This situation can be analyzed by defining one
or more fluid link elements between the cavity reference nodes. The mass flow rate through the link
can be defined as a function of pressure differential, average pressure, average temperature, and
external field variables. Fluid transfer between a cavity and the environment can be modeled if one
side of the link is unconnected and the pressure at that end is prescribed with a boundary condition.
Defining the fluid inertia
The inertia of the fluid is not taken into account. To add the effect of inertia, use MASS elements on
the boundary of the cavity. The user should make sure that the total added mass corresponds to the
mass of the fluid in the cavity and that the distribution of the masses is a reasonable representation of
the distributed fluid mass for the type of loading to which the structure is subjected. Only the overall
effect of the fluid inertia can be modeled; the constant pressure assumption in the cavity makes it
impossible to model any pressure gradient-driven fluid motions. Thus, the approach assumes that the
time scale of the excitation is very long compared to typical response times for the fluid.
Procedures
Hydrostatic fluid elements can be used in all procedures.
Initial conditions
The initial fluid pressure can be specified by using the *INITIAL CONDITIONS option (``Initial
conditions,'' Section 18.2.1).
Boundary conditions
The pressure degree of freedom at the cavity reference node (degree of freedom number 8) is a primary
variable in the problem. Thus, it can be prescribed by using the *BOUNDARY option (``Boundary
conditions,'' Section 18.3.1), similar to the way displacements can be prescribed. Prescribing the
pressure at the cavity reference node is equivalent to applying a uniform pressure to the cavity
boundary using the *DLOAD option.
If the pressure is prescribed with a boundary condition, the fluid volume is automatically adjusted to
fill the cavity (that is, fluid is assumed to enter and leave the cavity as needed to maintain the
prescribed pressure). This behavior is useful in situations where a cavity is deformed prior to the
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introduction of a fluid. In a subsequent step *BOUNDARY, OP=NEW can be used to remove the
boundary condition on the pressure degree of freedom, thus "sealing" the cavity with the current fluid
volume.
Loads
Distributed pressures and body forces, as well as concentrated nodal forces, can be applied to the
fluid-filled structure, as described in ``Concentrated and distributed loads, '' Section 18.4.2.
Adding fluid to or removing fluid from a cavity
A prescribed quantity of fluid can be added to or removed from a cavity during the analysis by using
the *FLUID FLUX option to specify a mass flow rate, q. A positive value for q adds fluid to the cavity,
while a negative value removes fluid from the cavity.
Usage: *FLUID FLUX
The amount of fluid in the cavity will also change if the cavity pressure is prescribed with the
*BOUNDARY option as described above. If the boundary condition is subsequently removed (with
*BOUNDARY, OP=NEW), the amount of fluid in the cavity will change only if fluid link elements are
connected to, or a *FLUID FLUX is applied to, the cavity reference node.
Varying the mass flow rate throughout the step
By default, the mass flow rate will be applied instantaneously at the beginning of the step and left
unchanged for the duration of the step, regardless of the procedure being used in the step.
Alternatively, the variation of the rate throughout the step can be specified using the *AMPLITUDE
option (``Amplitude curves,'' Section 18.1.2).
Usage: *FLUID FLUX, AMPLITUDE=name
Predefined fields
Predefined temperature fields and user-defined field variables can be defined for both fluid-filled
structures and the enclosed fluids, as described in ``Predefined fields,'' Section 18.5.1.
Temperatures
Nodal temperatures can be specified by using the *TEMPERATURE option. When specifying the
temperature of an enclosed fluid, the cavity reference node must be used to define the uniform
temperature of the fluid.
A defined temperature field can also affect temperature-dependent material properties, if any exist, for
both fluid-filled structures and enclosed fluids.
Field variables
The values of user-defined field variables can be specified using the *FIELD option. These values will
affect field-variable-dependent material properties for both the fluid-filled structure and the enclosed
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fluid, if any exist.
Material options
The fluid within a fluid-filled cavity must be modeled by using one of the hydrostatic fluid models
(``Hydrostatic fluid model,'' Section 11.3.1). The following properties can be defined for a fluid: bulk
modulus and density. The structure itself can be modeled using any elastic or inelastic material
model.
Elements
Fluid-filled cavities are modeled using hydrostatic fluid elements ( ``Hydrostatic fluid elements,''
Section 17.1.1) and, if necessary, fluid link elements (``Fluid link elements,'' Section 17.1.3).
Output
The fluid pressure and cavity volume can be obtained at the nodes of the hydrostatic fluid elements
(output variables PCAV and CVOL, respectively).
Template
The following is an example of a hydrostatic fluid analysis.
*HEADING
...
*ELEMENT, TYPE=hydrostatic fluid element, ELSET=name_1
...
*ELEMENT, TYPE=fluid link element, ELSET=name_2
...
Define the hydrostatic fluid behavior
*PHYSICAL CONSTANTS, ABSOLUTE ZERO=
*FLUID PROPERTY, ELSET=name_1, REF NODE=number
...
*FLUID DENSITY
...
Define the fluid link properties
*FLUID LINK, ELSET=name_2
...
Specify the initial conditions
*INITIAL CONDITIONS, TYPE=TEMPERATURE
...
*INITIAL CONDITIONS, TYPE=FLUID PRESSURE
...
**
*STEP
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...
Change the temperature of the fluid
*TEMPERATURE
...
Change the amount of fluid in a cavity
*FLUID FLUX
...
*END STEP
7.5 Mass scaling
7.5.1 Mass scaling
Mass scaling is often used for computational efficiency in quasi-static analyses and in some dynamic
analyses that contain a few very small elements that control the stable time increment.
References
· *FIXED MASS SCALING
· *VARIABLE MASS SCALING
· ``Explicit dynamic analysis,'' Section 6.2.1
· ``Output,'' Section 4.1.1
Overview
Mass scaling can be used to:
· scale the mass of the entire model or scale the masses of individual elements and/or element sets;
· scale the mass on a per step basis in a multistep analysis;
· scale the mass at the beginning of the step and/or throughout the step;
Mass scaling can be performed by:
· scaling the masses of all specified elements by a user-supplied constant factor;
· scaling the masses of all specified elements by the same value so that the minimum stable time
increment for any element in the element set is equal to a user-supplied time increment;
· scaling the masses of only the elements in the element set whose element stable time increments
are less than a user-supplied time increment so that the element stable time increment for these
elements becomes equal to the user-supplied time increment;
· scaling the masses of all specified elements so that their element stable time increments each
become equal to the user-supplied time increment.
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Introduction
The explicit dynamics procedure is typically used to solve two classes of problems: transient dynamic
response calculations and quasi-static simulations involving complex nonlinear effects (most
commonly problems involving complex contact conditions). Because the explicit central difference
method is used to integrate the equations in time (see ``Explicit dynamic analysis,'' Section 6.2.1), the
discrete mass matrix used in the equilibrium equations plays a crucial role in both computational
efficiency and accuracy for both classes of problems. When used appropriately, mass scaling can often
improve the computational efficiency while retaining the necessary degree of accuracy required for a
particular problem class. However, the mass scaling techniques most appropriate for quasi-static
simulations may be very different from those that should be used for dynamic analyses.
Quasi-static analysis
For quasi-static simulations incorporating rate-independent material behavior, the natural time scale is
generally not important. To achieve an economical solution, it is often useful to reduce the time period
of the analysis or to increase the mass of the model artificially ("mass scaling"). Both alternatives yield
similar results for rate-independent materials, although mass scaling is the preferred means of reducing
the solution time if rate dependencies are included in the model because the natural time scale is
preserved.
Mass scaling for quasi-static analysis is usually performed on the entire model. However, when
different parts of a model have different stiffness and mass properties, it may be useful to scale only
selected parts of the model or to scale each of the parts independently. In any case, it is never necessary
to reduce the mass of the model from its physical value, and it is generally not possible to increase the
mass arbitrarily without degrading accuracy. A limited amount of mass scaling is usually possible for
most quasi-static cases and will result in a corresponding increase in the time increment used by
ABAQUS/Explicit and a corresponding reduction in computational time. However, the user must
ensure that changes in the mass and consequent increases in the inertial forces do not alter the solution
significantly.
Although mass scaling can be achieved by modifying the densities of the materials in the model, the
options described in this section offer much more flexibility, especially in multi-step analyses.
See ``Rolling of thick plates,'' Section 1.3.7 of the ABAQUS Example Problems Manual, for a
discussion of using mass scaling in a quasi-static analysis.
Dynamic analysis
The natural time scale is always important in dynamic analysis and an accurate representation of the
physical mass and inertia in the model is required to capture the transient response. However, many
complex dynamic models contain a few very small elements, which will force ABAQUS/Explicit to
use a small time increment to integrate the entire model in time. These small elements are often the
result of a difficult mesh generation task. By scaling the masses of these controlling elements at the
beginning of the step, the stable time increment can be increased significantly, yet the effect on the
overall dynamic behavior of the model may be negligible.
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During an impact analysis, elements near the impact zone typically experience large amounts of
deformation. The reduced characteristic lengths of these elements results in a smaller global time
increment. Scaling the mass of these elements as required throughout the simulation can significantly
decrease the computation time. For cases in which the compressed elements are impacting a stationary
rigid body, increases in mass for these small elements during the simulation will have very little effect
on the overall dynamic response.
Mass scaling for truly dynamic events should almost always occur only for a limited number of
elements and should never significantly increase the overall mass properties of the model, which
would degrade the accuracy of the dynamic solution.
See ``Impact of a copper rod,'' Section 1.3.10 of the ABAQUS Benchmarks Manual, for a discussion of
using mass scaling in a dynamic analysis.
Stable time increments
Throughout this section the term "element stable time increment" refers to the stable time increment of
a single element. The term "element-by-element stable time increment" refers to the minimum element
stable time increment within a specific element set. The term "stable time increment" refers to the
stable time increment of the entire model, regardless of whether the global estimator or the
element-by-element estimator is used.
Introducing mass scaling into a model
Two options are available in ABAQUS/Explicit to perform mass scaling: *FIXED MASS SCALING
and *VARIABLE MASS SCALING. These options can be applied separately, or they can be applied
together to define an overall mass scaling strategy. The options can also apply globally to the entire
model or, alternatively, on an element set by element set basis.
Fixed mass scaling
The *FIXED MASS SCALING option is used to scale the originally defined element masses that are
assembled into the global nodal mass matrix. Fixed mass scaling is performed at the beginning of the
step for which the option is specified. The resulting scaled mass matrix is then used for each increment
within the step unless a *VARIABLE MASS SCALING option is also used. The scaled mass matrix is
also carried over to a subsequent step unless a *FIXED MASS SCALING option is used in that
subsequent step.
Two basic approaches are available for fixed mass scaling: the user can define a mass scaling factor
directly, or the user can define a desired minimum stable time increment for which the mass scaling
factors are determined by ABAQUS/Explicit.
Fixed mass scaling provides a simple means to modify the mass properties of a quasi-static model at
the beginning of an analysis or to modify the masses of a few small elements in a dynamic model so
that they do not control the stable time increment size. Since the scaling operation is performed only
once at the beginning of the step for which the option is used, fixed mass scaling is computationally
efficient.
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Variable mass scaling
The *VARIABLE MASS SCALING option is used to scale the mass of elements periodically during a
step. Variable mass scaling may scale the masses in addition to any fixed mass scaling that is specified.
When using this option, the user defines a desired minimum stable time increment: mass scaling
factors will be calculated automatically and applied, as required, throughout the step.
Variable mass scaling is most useful when the stiffness properties that control the stable time
increment change drastically during a step. This situation can occur in both quasi-static bulk forming
and dynamic simulations in which elements are highly compressed or crushed.
Defining a scale factor directly
Defining a scale factor directly is useful for quasi-static analyses in which the kinetic energy in the
model should remain small. Use the FACTOR parameter with the *FIXED MASS SCALING option to
define a mass scaling factor that is applied to all elements in an element set. The masses of the
elements will be scaled at the beginning of the step and held fixed throughout the step unless further
modified by a *VARIABLE MASS SCALING option.
Usage: *FIXED MASS SCALING, FACTOR=scale_factor
For example, the option below scales the masses of elements contained in element set elset by a factor
of 10.
*FIXED MASS SCALING, FACTOR=10., ELSET=elset
Defining a desired element-by-element stable time increment
Use the DT parameter with either the *FIXED MASS SCALING or the *VARIABLE MASS
SCALING option to define a desired element-by-element stable time increment for an element set.
ABAQUS/Explicit will then determine the necessary mass scaling factors. There are three mutually
exclusive methods available to scale the mass of the model when a desired element-by-element stable
time increment is defined. Each method is described in detail later in this section.
To determine the stable time increment used during an increment, ABAQUS/Explicit first determines
the smallest stable time increment on an element-by-element basis. Then, a global estimation algorithm
determines a stable time increment based on the highest frequency of the model. The larger of the two
estimates determines the stable time increment used. In general, the stable time increment determined
by the global estimator will be greater than the stable time increment determined by the
element-by-element estimator. When the *FIXED MASS SCALING or the *VARIABLE MASS
SCALING option is used with the DT parameter to scale the mass of a set of elements, the
element-by-element stable time increment estimate is being affected directly. If all of the elements in
the model are being scaled by a single mass scaling definition, the element-by-element estimate will
equal the value assigned to the DT parameter unless the penalty method is being used to enforce
contact constraints. Penalty contact can cause the element-by-element estimate to be slightly below the
value assigned to the DT parameter (see ``Contact surface interactions: overview,'' Section 20.3.1). The
actual stable time increment used may be greater than the value assigned to the DT parameter because
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of the use of the global estimator. If mass scaling is performed on only a portion of the model, the
elements that are not scaled may have element stable time increments that are less than the value
assigned to DT and in that case will control the element-by-element stable time increment estimate. As
a result, if only portions of the model are being scaled, the time increment used will generally not equal
the value assigned to the DT parameter.
If the DIRECT USER CONTROL parameter or the FIXED TIME INCREMENTATION parameter is
included on the *DYNAMIC option, the time increment used will be calculated according to the rules
described in ``Explicit dynamic analysis,'' Section 6.2.1.
Scaling the mass uniformly
Scaling the mass uniformly is useful for quasi-static analyses in which the kinetic energy in the model
should remain small. This approach is similar to defining a scale factor directly. In both cases the
masses of all the elements specified are scaled uniformly by a single factor. However, with this method
the mass scaling factor is determined by ABAQUS/Explicit instead of being specified by the user.
Set the TYPE parameter equal to UNIFORM to scale the masses of the elements in a given element set
by determining a single mass scaling factor to be applied uniformly to all of these elements so that the
minimum stable time increment within these elements is equal to the value assigned to DT.
Usage: Use either of the following options:
*FIXED MASS SCALING, TYPE=UNIFORM, DT=dt, ELSET=elset or
*VARIABLE MASS SCALING, TYPE=UNIFORM, DT=dt, ELSET=elset
Scaling only elements with element stable time increments below
DT
Scaling elements with element stable time increments below a user-specified value is appropriate for
both quasi-static and dynamic analyses. It is useful for increasing the element stable time increment of
the most critical elements. When the mesh at the beginning of an analysis or a step contains a few very
small elements that control the stable time increment size, use the *FIXED MASS SCALING option
with TYPE=BELOW MIN to scale the masses of those elements and start the step with a desired time
increment value.
Usage: *FIXED MASS SCALING, TYPE=BELOW MIN, DT=dt
Increasing the mass of only these controlling elements means that the stable time increment can be
increased significantly, yet the effect on the overall behavior of the model may be negligible.
For analyses in which evolving deformation creates a limited number of small elements, use the
*VARIABLE MASS SCALING option with TYPE=BELOW MIN to scale the masses of those
elements, thereby limiting the reduction in the stable time increment.
Usage: *VARIABLE MASS SCALING, TYPE=BELOW MIN, DT=dt
Scaling all elements to have equal element stable time
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increments
Scaling all elements such that they have the same stable time increment effectively contracts the
eigenspectrum of the model; that is, it reduces the range between the lowest and highest natural
frequency of the model. Because of the drastic change in mass properties, this approach is appropriate
only for quasi-static analyses. It implies that some elements may have mass scaling factors that are less
than one.
Set the TYPE parameter equal to SET EQUAL DT to scale the masses of the elements in a given
element set so that they each have an element stable time increment equal to a user-supplied time
increment.
Usage: Use either of the following options:
*FIXED MASS SCALING, TYPE=SET EQUAL DT, DT=dt, ELSET=elset or
*VARIABLE MASS SCALING, TYPE=SET EQUAL DT, DT=dt, ELSET=elset
Global and local mass scaling
Including the ELSET parameter on either the *FIXED MASS SCALING or *VARIABLE MASS
SCALING option scales the mass of a localized region of the model. Omitting the ELSET parameter
implies that mass scaling will be performed for all elements. A global definition can be overwritten by
a local definition for a given element set by repeating the option with the ELSET parameter included.
Example 1
Different mass scaling factors may be useful when materials with vastly different wave speeds or mesh
refinements are present in an analysis. In this example a scale factor of 50 may be desirable for the
masses of all elements in a quasi-static analysis, except for a few elements for which a mass scaling
factor of 500 is used.
*FIXED MASS SCALING, FACTOR=50.0
*FIXED MASS SCALING, FACTOR=500.0, ELSET=elset1
The first *FIXED MASS SCALING option scales the masses of all elements in the model by a factor
of 50. The second *FIXED MASS SCALING option overrides the first definition for the elements
contained in element set elset1 by scaling their masses by a factor of 500.
Example 2
An alternative method of scaling the masses of elements in elset1 is to assign a stable time increment
to them and allow ABAQUS/Explicit to determine the mass scaling factors.
*FIXED MASS SCALING, FACTOR=50.0
*FIXED MASS SCALING, DT=.5E-6, TYPE=BELOW MIN, ELSET=elset1
The first *FIXED MASS SCALING option scales the masses in the entire model by a factor of 50. The
second *FIXED MASS SCALING option overrides the first option by scaling the masses of any
elements in elset1 whose stable time increments are less than :5 £ 10¡6 .
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Mass scaling at the beginning of the step
The *FIXED MASS SCALING option is used to prescribe mass scaling only at the beginning of a step.
The *FIXED MASS SCALING option always scales the original element masses. When the FACTOR
parameter is included, the mass is scaled by the value assigned to the parameter. If the DT parameter is
used, the mass scaling is based on a user-specified element-by-element stable time increment. If both
the FACTOR and the DT parameters are included, the mass is first scaled by the value assigned to the
FACTOR parameter and then possibly scaled again, depending on the values assigned to the DT and
TYPE parameters.
The optional ELSET parameter is used to define local mass scaling for a specific element set. If the
ELSET parameter is omitted, the *FIXED MASS SCALING definition will apply to all elements in the
model. Only one *FIXED MASS SCALING option is permitted per element set. Multiple *FIXED
MASS SCALING options cannot contain overlapping element sets. Local mass scaling definitions will
overwrite global definitions for the specified element sets.
Usage: *FIXED MASS SCALING, FACTOR=factor, DT=dt, TYPE=type, ELSET=elset
Example
Assume that for a quasi-static analysis a mass scaling factor of 50 is applied to all the elements in the
model. Furthermore, assume that even after being scaled by a factor of 50, a few extremely small or
poorly shaped elements are causing the stable time increment to be less than a desired minimum. To
increase the stable time increment, the following option is used:
*FIXED MASS SCALING, FACTOR=50., TYPE=BELOW MIN, DT=.5E-6
The FACTOR parameter causes the masses of all the elements in the model to be scaled by a factor of
50. If any element's stable time increment is still below 0:5 £ 10¡6 after being scaled by a factor of
50.0, its mass will be scaled such that its stable time increment is equal to 0:5 £ 10¡6 .
Mass scaling throughout the step
The *VARIABLE MASS SCALING option with the DT parameter is used to define mass scaling that
is to be performed at the beginning and throughout the step. Either the FREQUENCY or the NUMBER
INTERVAL parameter must be used to define how frequently mass scaling is to be performed.
The optional ELSET parameter is used to define local mass scaling for a specific element set. If the
ELSET parameter is omitted, the *VARIABLE MASS SCALING definition will apply to all elements
in the model. Only one *VARIABLE MASS SCALING option is permitted per element set. Multiple
*VARIABLE MASS SCALING options cannot contain overlapping element sets. Local mass scaling
definitions will overwrite global definitions for the specified element sets.
Usage: *VARIABLE MASS SCALING, DT=dt, TYPE=type, ELSET=elset
Calculating the mass scaling at equally spaced increments
Use the FREQUENCY parameter to specify the number of increments between mass scaling
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calculations. Care should be taken when choosing the value of the FREQUENCY parameter, since
performing mass scaling every few increments during an analysis may result in noticeable additional
computational cost per increment.
Usage: *VARIABLE MASS SCALING, TYPE=type, DT=dt, FREQUENCY=n
For example, setting FREQUENCY=5 will cause mass scaling to be performed at the beginning of the
step and at increments 5, 10, 15, etc.
Calculating the mass scaling at equally spaced time intervals
Use the NUMBER INTERVAL parameter to specify the number of equally spaced time intervals at
which the mass scaling calculations are to be performed.
Usage: *VARIABLE MASS SCALING, TYPE=type, DT=dt, NUMBER INTERVAL=n
For example, setting NUMBER INTERVAL=5 in a step with a duration of one second will cause mass
scaling to be performed at the beginning of the step and at times of .2 , .4, .6, .8, and 1.0 seconds.
Different mass scaling at the beginning and during the step
There are cases where it is desirable to include mass scaling at the beginning of a step that may be
modified further throughout the step.
Usage: Use both of the following options:
*FIXED MASS SCALING, FACTOR=factor, TYPE=type, DT=dt_init
*VARIABLE MASS SCALING, TYPE=type, DT=dt_min, FREQUENCY=n
NUMBER INTERVAL=n
or
Example
Assume that in a dynamic impact analysis, a few extremely small or poorly shaped elements exist in
the mesh and consequently control the stable time increment. To prevent these elements from
controlling the stable time increment, it is desirable to scale their masses at the beginning of the step.
In addition, elements in a region of the mesh will develop severe distortions as a result of impact with
a fixed rigid surface. Consequently, elements in the impact zone may eventually control the stable time
increment.
Since the elements in the impact zone are essentially stationary against the rigid surface, selectively
scaling their masses will guarantee that the overall dynamic response is not adversely affected. Mass
scaling these elements by prescribing a time increment to limit the reduction in the element-by-element
stable time increment may decrease run time substantially.
*FIXED MASS SCALING, TYPE=BELOW MIN, DT=1.0E-6
*VARIABLE MASS SCALING, TYPE=BELOW MIN, DT=.5E-6, FREQUENCY=10,
ELSET=elset1
In this case all elements in the model are checked at the beginning of the step. If any elements have
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element stable time increments less than 1:0 £ 10¡6 , their masses are scaled (independently) such that
the element-by-element stable time increment equals 1:0 £ 10¡6 . This scaling remains in effect
throughout the step and is not further modified, except for those elements in elset1. The *VARIABLE
MASS SCALING definition causes the elements contained in elset1 to be scaled throughout the step
so that their stable time increments do not become less than 0:5 £ 10¡6 . Because only elements in
elset1 are scaled during the step, it is possible that a stable time increment less than 0:5 £ 10¡6 may
result.
Mass scaling in a multiple step analysis
Mass scaling definitions can be retained or removed from step to step. In addition, the scaled element
masses can be carried forward or reinitialized from step to step. The following rules apply for mass
scaling across steps:
· All *VARIABLE MASS SCALING definitions are retained automatically from a previous step
unless a *VARIABLE MASS SCALING option is included in the new step, in which case all
definitions from previous steps are ignored.
· The element masses at the end of a previous step, whether they are scaled or unscaled, are
automatically carried forward to the new step unless a *FIXED MASS SCALING option is used in
the new step to reinitialize the element masses to their original or new scaled values.
Removing mass scaling definitions
Any *VARIABLE MASS SCALING definition in the current step causes all *VARIABLE MASS
SCALING definitions from previous steps to be removed.
Usage: *VARIABLE MASS SCALING
Any previously applied *VARIABLE MASS SCALING definitions must be respecified in the current
step to be retained.
Example
Assume that during the first step of a quasi-static analysis, elements will experience distortions that
will cause the stable time increment to decrease dramatically. Furthermore, assume that the
deformation during the second step will not be large enough to have any further effect on the stable
time increment.
*HEADING
...
*STEP
...
*VARIABLE MASS SCALING, TYPE=BELOW MIN, DT=1.E-5, FREQUENCY=10
...
*END STEP
*STEP
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...
*VARIABLE MASS SCALING
...
*END STEP
During the first step the *VARIABLE MASS SCALING option scales the mass of the entire model at
the beginning of the step and every tenth increment such that the element-by-element stable time
increment equals 1 £ 10¡5 . The *VARIABLE MASS SCALING option without any parameters in the
second step prevents any further mass scaling. The scaled mass matrix from the first step is carried
over to be used during the second step.
Reinitializing the mass
Use of the *FIXED MASS SCALING option without any parameters in steps other than the first step
reinitializes the masses of elements to their original values. Thus, the *FIXED MASS SCALING
option can be used to prevent the scaled mass from a previous step from being used in a new step,
which is particularly useful when transitioning from a quasi-static simulation step where mass scaling
is appropriate to a dynamic step in which no scaling is desired. To reinitialize the mass of the entire
model to its original value for a new step, use the *FIXED MASS SCALING option with no
parameters.
Usage: *FIXED MASS SCALING
To scale the original mass for a new step, include the applicable FACTOR parameter or the applicable
DT and TYPE parameters. To use the original mass or scaled original mass for only a portion of the
model for a new step, use the *FIXED MASS SCALING option with the ELSET parameter.
Example
Assume that an analysis contains a quasi-static step followed by a dynamic step. Mass scaling can be
performed during the quasi-static step but turned off during the dynamic step.
*HEADING
...
*STEP
...
*FIXED MASS SCALING, TYPE=BELOW MIN, DT=1.E-5
...
*END STEP
*STEP
...
*FIXED MASS SCALING
...
*END STEP
During the first step the *FIXED MASS SCALING option scales the mass of the entire model at the
beginning of the step such that the element-by-element stable time increment at the beginning of the
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first step equals 1:0 £ 10¡5 . The *FIXED MASS SCALING option in the second step then
reinitializes the mass matrix for the entire model.
When mass scaling is or is not used
The following entities are not affected by mass scaling. Densities associated with any of the relevant
items in this list will remain unscaled.
· Gravity loads, viscous pressure loads
· Adiabatic heat calculations
· *EOS material
· Fluid and fluid link elements
· Spring and dashpot elements
Mass, rotary inertia, infinite, and rigid elements can be scaled. However, because none of the elements
has an associated stable time increment, they can be scaled only using either the FACTOR parameter
or the DT parameter with TYPE=UNIFORM. If the DT parameter is used, at least one element with a
stable time increment must be included in the mass scaling definition. Rotary inertia in shell and beam
elements is based on the scaled mass.
The mass of infinite elements can be scaled; however, the infinite elements will not act as quiet
boundaries unless the densities of each adjacent deformable element are scaled by the same factor. The
mass of both elements will be scaled by the same factor if they are both included in the same *FIXED
MASS SCALING or *VARIABLE MASS SCALING definition.
Output
Output variable EMSF provides the element mass scaling factor. ABAQUS/Viewer can be used to
obtain contour and history plots of EMSF. Output variable DMASS provides the total percent change
in mass of the model as a result of mass scaling and is available for history plotting in
ABAQUS/Viewer. Output variable DMASS is not available on an element set basis.
Output variable EDT provides the element stable time increment. The element stable time increment
includes the effect of mass scaling. ABAQUS/Viewer can be used to obtain history plots of EDT.
7.6 Adaptive meshing
7.6.1 Adaptive meshing: overview
Adaptive meshing is a tool that makes it possible to maintain a high-quality mesh throughout an
analysis, even when large deformations occur, by allowing the mesh to move independently of the
material. Adaptive meshing in ABAQUS/Explicit does not alter the topology (elements and
connectivity) of the mesh.
The adaptive meshing technique in ABAQUS/Explicit combines the features of pure Lagrangian
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analysis (in which the mesh follows the material, as is usually the case in ABAQUS) and Eulerian
analysis (in which the mesh is fixed spatially and the material flows through the mesh, as is used in the
convective heat transfer capability in ABAQUS/Standard). This type of adaptive meshing is often
referred to as Arbitrary Lagrangian-Eulerian (ALE) analysis.
Adaptive meshing in ABAQUS/Explicit is intended for use in modeling large-deformation problems. It
does not attempt to minimize discretization errors in small-deformation analyses.
Features of adaptive meshing
Adaptive meshing:
· can often maintain a high-quality mesh under severe material deformation by allowing the mesh to
move independently of the underlying material;
· maintains a topologically similar mesh throughout the analysis (i.e., elements are not created or
destroyed);
· can be used to analyze Lagrangian problems (in which no material leaves the mesh) and Eulerian
problems (in which material flows through the mesh);
· can be used as a continuous adaptive meshing tool for transient analysis problems undergoing
large deformations (such as dynamic impact, penetration, and forging problems);
· can be used as a solution technique to model steady-state processes (such as extrusion or rolling);
· can be used as a tool to analyze the transient phase in a steady-state process; and
· can be used with dynamic, adiabatic, or coupled thermal-stress procedures.
Activating adaptive meshing
Adaptive meshing can be applied to an entire model or to individual parts of a model. Adaptive
meshing domains are defined by using the *ADAPTIVE MESH option. This option is the only one
required to activate adaptive meshing. A Lagrangian adaptive mesh domain will be created, so that the
domain as a whole will follow the material originally inside it, which is the proper physical
interpretation for most structural analyses. Additional options are provided for controlling the mesh
and for introducing Eulerian boundaries to allow material to flow into or out of the domain modeled.
The subsequent sections of ``Adaptive meshing,'' Section 7.6," describe the various options that can be
used with adaptive meshing. Although these options give the user the ability to exercise detailed
control over adaptive meshing, they are not necessary for many Lagrangian problems.
· To take full advantage of all the adaptive mesh features in ABAQUS/Explicit, it is important to
understand the concepts of adaptive mesh domains, boundary regions, boundary edges, geometric
features, and mesh constraints. These concepts are explained in ``Defining adaptive mesh
domains,'' Section 7.6.2. Instructions for applying boundary conditions, loads, and surfaces to
adaptive mesh boundaries are also provided in that section.
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· ``Adaptive meshing and remapping,'' Section 7.6.3, outlines the methods used to move the mesh
and to remap solution variables to the new mesh. The section also presents options for controlling
these algorithms. Although the default methods have been chosen to work well for a wide variety
of problems, the user may wish to override the defaults to balance the robustness and efficiency of
adaptive meshing or to extend the use of adaptive meshing to relatively difficult or unusual
applications.
· Various output and diagnostic options are available for verifying the formation of adaptive mesh
domains and for interpreting the results of an analysis. These options are explained in ``Output and
diagnostics for adaptive meshing,'' Section 7.6.4.
· ``Modeling techniques for Eulerian adaptive mesh domains, '' Section 7.6.5, gives advice, in the
form of examples and modeling hints, on setting up and interpreting Eulerian problems using
adaptive meshing.
Uses for adaptive meshing
Adaptive meshing is of great value in any problem where large deformation is anticipated because
improved mesh quality can prevent the analysis from terminating as a result of severe mesh distortion.
Adaptive meshing often provides faster, more accurate, and more robust solutions than pure
Lagrangian analyses.
Adaptive meshing is particularly effective for simulations of metal-forming processes such as forging,
extrusion, and rolling because these types of problems usually involve large amounts of
nonrecoverable deformation. Because the final shape of the product can be drastically different from
the original shape, a mesh that is optimal for the original product geometry can become unsuitable in
later stages of the process, when large material deformation leads to severe element distortion and
entanglement. Element aspect ratios can also degrade in zones with high strain concentrations. Both of
these factors can lead to a loss of accuracy, a reduction in the size of the stable time increment, or even
termination of the problem.
Illustrative examples
To illustrate the value of adaptive meshing, simple examples of transient and steady-state forming
applications follow. For simplicity, two-dimensional cases are shown.
Axisymmetric forging
In this example a well-lubricated rigid die of sinusoidal shape moves down to deform a blank of
rectangular cross-section (see Figure 7.6.1-1).
Figure 7.6.1-1 A blank and a sinusoidal die.
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The indentation depth is 80% of the original blank thickness. Material extrudes upward and outward
(radially) as the blank is indented. The die is modeled with an analytical rigid surface, and the blank is
modeled with axisymmetric continuum elements in a regular mesh configuration. The blank is assumed
to have elastic-plastic material properties.
A pure Lagrangian analysis of this problem does not run to completion because of excessive distortion
in several elements, as shown in Figure 7.6.1-2. The contact surface cannot be treated correctly
because of the gross distortion of the elements at the troughs of the sinusoidal rigid surface.
Figure 7.6.1-2 Eventually, the purely Lagrangian analysis will terminate because of excessive element
distortion.
Adaptive meshing allows the problem to run to completion. A Lagrangian adaptive mesh domain is
created for the entire blank with the *ADAPTIVE MESH option. ABAQUS automatically chooses
suitable defaults for adaptive meshing; hence, the adaptive mesh approach requires only two additional
input lines:
*HEADING
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...
*ELSET, ELSET=BLANK
***************************
*STEP
*DYNAMIC, EXPLICIT
...
*ADAPTIVE MESH, ELSET=BLANK
...
*END STEP
Figure 7.6.1-3 and Figure 7.6.1-4 show the deformed mesh at various stages of the forming analysis.
Because the mesh refinement is maintained on the portions of the slave surface that contact the die
troughs as the material flows radially, the contact conditions are resolved correctly throughout the
analysis.
Figure 7.6.1-3 Deformed configuration at an intermediate stage of the analysis.
Figure 7.6.1-4 Deformed configuration upon completion of the analysis.
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Steady-state rolling example
This example shows how adaptive meshing can be used in a steady-state simulation to allow the flow
of material through Eulerian boundaries on the problem domain. A steel plate is passed through a
symmetric roll stand to reduce its height by 50%. This simulation is run until it reaches steady-state
conditions.
Figure 7.6.1-5 and Figure 7.6.1-6 show the initial and final (steady-state) configurations in a purely
Lagrangian model of this problem.
Figure 7.6.1-5 The initial configuration of the roller and the undeformed blank in the pure Lagrangian
model.
Figure 7.6.1-6 The final steady-state configuration in the pure Lagrangian model.
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Figure 7.6.1-7 shows this problem modeled using an Eulerian adaptive mesh domain, where material
flows through the mesh. Only the region near the roller is modeled. The exact location of the free
surface does not need to be known to set up the problem: it is created in a likely location, and the final
steady-state position is found as part of the solution. Although not shown, a focused mesh can be used
to capture steep strain gradients directly beneath the roller. The Eulerian domain reaches the same
steady-state solution as obtained with the Lagrangian approach.
Figure 7.6.1-7 The initial Eulerian adaptive mesh domain.
The Eulerian adaptive mesh domain is created by defining an inflow and an outflow boundary on the
adaptive mesh domain. Adaptive mesh constraints are applied normal to these boundaries so that
material will flow through the mesh (see ``Defining adaptive mesh domains,'' Section 7.6.2). Frictional
contact between the roller and the blank pulls material through the adaptive mesh domain.
The problem is set up by making the following modifications to the input file for the pure Lagrangian
analysis:
*HEADING
...
*ELSET, ELSET=BILLET
...
*ELSET, ELSET=INFLOW
...
*ELSET, ELSET=OUTFLOW
...
*NSET, NSET=INFLOW
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...
*NSET, NSET=OUTFLOW
...
*SURFACE, NAME=INFLOW, REGION TYPE=EULERIAN
INFLOW, S1
*SURFACE, NAME=OUTFLOW, REGION TYPE=EULERIAN
OUTFLOW, S2
***************************
*STEP
*DYNAMIC, EXPLICIT
Data line to specify the time period of the step
...
*ADAPTIVE MESH, ELSET=BILLET, CONTROLS=ADAPT
*ADAPTIVE MESH CONTROLS, NAME=ADAPT, FREE BOUNDARY UPWINDING=0.5
*ADAPTIVE MESH CONSTRAINT, TYPE=DISPLACEMENT
INFLOW, 1, 1, 0.0
100, 2, 2, 0.0
OUTFLOW, 1, 1, 0.0
...
*END STEP
The *ADAPTIVE MESH CONTROLS option is not necessary in this problem, but it is shown as an
example of its use. See ``Adaptive meshing and remapping,'' Section 7.6.3, for details on this option.
7.6.2 Defining adaptive mesh domains
The *ADAPTIVE MESH option is used to apply continuous adaptive meshing to certain areas of a
mesh during an analysis.
References
· ``Adaptive meshing: overview,'' Section 7.6.1
· ``Adaptive meshing and remapping,'' Section 7.6.3
· *ADAPTIVE MESH
Overview
Adaptive mesh domains:
· define the portions of a finite element model where mesh movement is independent of material
deformation;
· can be used to analyze Lagrangian or Eulerian problems;
· can contain only first-order, reduced-integration, solid elements (4-node quadrilaterals, 3-node
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triangles, 8-node hexahedra, and 4-node tetrahedra);
· are created from element sets;
· can be used in planar, axisymmetric, and three-dimensional geometries; and
· have boundary regions where loads, boundary conditions, and surfaces can be defined.
Defining an adaptive mesh domain
Adaptive meshing is performed in adaptive mesh domains, which can be either Lagrangian or Eulerian.
Within either type of adaptive mesh domain the mesh will move independently of the material.
Lagrangian adaptive mesh domains are usually used to analyze transient problems with large
deformations. On the boundary of a Lagrangian domain the mesh will follow the material in the
direction normal to the boundary, so that the mesh covers the same material domain at all times.
Eulerian adaptive mesh domains are usually used to analyze steady-state processes involving material
flow. On certain user-defined boundaries of an Eulerian domain, material can flow into or out of the
mesh. By default, the mesh is not fixed spatially on these boundaries; mesh constraints must be applied
to prevent the mesh from moving with the material, as described in the subsection "Mesh constraints,"
presented later in this section. There can never be any "empty" elements; all elements in the domain
must be filled completely with material at all times.
An element set is used to define the portion of the original mesh that will be subject to adaptive
meshing. Use the ELSET parameter on the *ADAPTIVE MESH option to specify the element set that
will be adaptively meshed. Multiple adaptive mesh domains can be defined by reusing the
*ADAPTIVE MESH option (for example, to prevent material from flowing from one domain to
another or to apply adaptive meshing to unconnected domains). The element sets used to create
adaptive mesh domains cannot overlap.
Usage: *ADAPTIVE MESH, ELSET=name
Modifying an adaptive mesh domain
Use either the *ADAPTIVE MESH option or the *ADAPTIVE MESH, OP=MOD option to make
changes to existing adaptive mesh domains. When these options are used, all existing adaptive mesh
domains remain defined.
Usage: The following options are equivalent:
*ADAPTIVE MESH, ELSET=name
*ADAPTIVE MESH, ELSET=name, OP=MOD
Removing an adaptive mesh domain
Use the *ADAPTIVE MESH, OP=NEW option to remove all previously defined adaptive mesh
domains. Any adaptive mesh domains that are to be retained must be respecified.
If the OP=NEW parameter is used on any *ADAPTIVE MESH option within a step, it must be used on
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all *ADAPTIVE MESH options in the step.
Usage: *ADAPTIVE MESH, ELSET=name, OP=NEW
Adding an adaptive mesh domain
Use the *ADAPTIVE MESH; *ADAPTIVE MESH, OP=MOD; or *ADAPTIVE MESH, OP=NEW
options to specify additional adaptive mesh domains.
Splitting adaptive mesh domains
User-defined adaptive mesh domains are examined by ABAQUS. The user-defined domain will be
modeled using a single adaptive mesh if the domain:
· consists of a single element type;
· consists of a single connected region;
· consists of a single material;
· is subject to a uniform body force (including zero body force); and
· has identical section controls.
The user-defined domain will be split into multiple adaptive mesh domains, separated by boundary
regions, if the domain:
· consists of multiple element types;
· spans part instances;
· consists of multiple regions (including regions that are connected by less than a single element
face, only by contact conditions, or only by connectors such as MPCs);
· consists of multiple materials;
· is subject to multiple body force definitions; or
· is subject to multiple section control definitions.
In this documentation the term "adaptive mesh domain" refers to a single domain after splitting by
ABAQUS. On the rare occasion that a reference is made to an adaptive mesh domain prior to the
automatic splitting, it is referred to as a "user-defined adaptive mesh domain." Since adaptive mesh
domains are split across element types, degenerate elements should be used for mixed domains that
include both triangles and quadrilaterals (or tetrahedron and bricks). For example, when defining a
mixed plane strain domain with quadrilateral and triangular elements, the CPE4R element type should
be used to define both quadrilaterals and degenerated quadrilaterals. Using the CPE3 element will
result in split domains, which is generally not desirable.
Adaptive mesh boundary regions
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Each adaptive mesh domain has a boundary, which can consist of one or more regions. (Regions, in
this context, are surfaces in three-dimensional models or lines in two-dimensional or axisymmetric
models.) A boundary region can be either Lagrangian, sliding, or Eulerian. Some boundary regions are
created automatically by ABAQUS; others can be created by defining boundary conditions, loads, and
surfaces. Adaptive mesh boundary regions are separated by edges in three dimensions and by corners
in two dimensions. Both edges and corners are referred to as "boundary region edges" throughout this
documentation.
Boundary region edges
Two types of boundary region edges can exist: Lagrangian and sliding. Lagrangian edges are always
associated with a material line. Material can never flow past a Lagrangian edge, and nodes can move
only along a Lagrangian edge (like beads on a string). Sliding edges are associated only with the mesh.
Material can flow past a sliding edge (that is, sliding edges are free to slide over the underlying
material).
Lagrangian edges can be viewed with ABAQUS/Viewer; see ``Output and diagnostics for adaptive
meshing,'' Section 7.6.4.
Lagrangian boundary regions
Lagrangian boundary regions are the most common boundary regions in structural finite element
analysis; therefore, with the exception of contact surfaces, they are always the default in
ABAQUS/Explicit. A Lagrangian boundary region has the most constraints of all the boundary region
types. The mesh is constrained to move with the material in the direction normal to the surface of the
boundary region and in the directions perpendicular to the boundary region edges.
Lagrangian boundary regions have Lagrangian edges: the edges follow the material. On the interior of
a Lagrangian boundary region, the mesh can move independently of the material in the surface of the
boundary region. Thus, a Lagrangian boundary region can be thought of as a "mesh patch" that follows
the material. Nodes are free to move within and along the edges of the patch but cannot leave the
patch.
Lagrangian corners
A Lagrangian corner is formed where two Lagrangian edges meet. The node at a Lagrangian corner is
constrained to move with the material in all directions; it is nonadaptive.
Sliding boundary regions
A sliding boundary region is the same as a Lagrangian boundary region except that it has a sliding
edge. Sliding boundary regions are created by default when the *SURFACE option is used to define a
surface on the boundary of an adaptive mesh domain.
The mesh is constrained to move with the material in the direction normal to the boundary region, but
it is completely unconstrained in the directions tangential to the boundary region. Thus, a sliding
boundary region can be thought of as a "mesh patch" that moves independently of the underlying
material.
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Sliding boundary regions can be created by defining a surface, boundary condition, or load on the
boundary of an adaptive mesh domain (as explained later in this section). Since the mesh is totally
unconstrained in the directions tangential to a sliding boundary region, the location of an applied
boundary condition or load may not be physically meaningful as the mesh moves over the material.
Therefore, to retain the spatial meaning of an applied boundary condition or load, spatial mesh
constraints (described in the subsection "Mesh constraints," presented later in this section) are usually
applied tangential to sliding boundary regions.
Eulerian boundary regions
Eulerian boundary regions can be defined on the exterior of a model where it makes physical sense to
let material flow across the boundary (for example, at the inlet and outlet of a steady-state extrusion or
rolling problem). This flow across the boundary distinguishes Eulerian boundary regions from
Lagrangian or sliding boundary regions.
Eulerian boundary regions have sliding edges and must lie completely on an exterior surface of a
model. It makes no physical sense to allow material flow to originate on an interior surface. Eulerian
boundary regions must be defined explicitly by the user since, by default, ABAQUS assumes that no
material flows into or out of an adaptive mesh domain.
Eulerian boundary regions are created by defining a surface, a boundary condition, or a load on the
boundary of an adaptive mesh domain. On Eulerian boundary regions the mesh motion usually should
be constrained in the direction normal to the material motion; therefore, the surface mesh should be
fixed in space using spatial mesh constraints (described in the subsection "Mesh constraints,"
presented later in this section). Applying these constraints normal to an Eulerian boundary region
allows material to flow into or out of the mesh, as in a fluid flow problem, while allowing adaptive
meshing to occur on the surface of the boundary region to maximize mesh quality.
The material flowing into an Eulerian boundary region is assumed to have the same properties as the
material that is inside the adaptive mesh domain.
Techniques for modeling Eulerian domains are presented in ``Modeling techniques for Eulerian
adaptive mesh domains,'' Section 7.6.5.
Creation of boundary regions
ABAQUS will create adaptive mesh boundary regions automatically on
· the exterior of a model,
· the boundary between different adaptive mesh domains, or
· the boundary between an adaptive mesh domain and a nonadaptive domain.
By default, a boundary region on the exterior of a model will be Lagrangian, so that the boundary
region follows the material, and loads, boundary conditions, etc. will retain their Lagrangian
interpretation. A boundary region between different adaptive mesh domains is always Lagrangian: no
material can flow through such a boundary region. A boundary region between an adaptive mesh
domain and a nonadaptive domain is always nonadaptive: the nodes on this boundary are constrained
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to move exactly with the underlying material in all directions.
The boundary between two different materials can never "flow" through the mesh; such a physical
boundary is always associated with a Lagrangian boundary region or a nonadaptive mesh boundary.
Figure 7.6.2-1 shows some boundary regions that will be created automatically by ABAQUS. In the
model shown in this figure ABAQUS splits the user-defined adaptive mesh domain into two adaptive
mesh domains because the original domain is composed of two different materials.
Figure 7.6.2-1 Automatic splitting of mesh domains and creation of boundary regions.
In addition to the boundary regions created automatically by ABAQUS, Lagrangian, sliding, and
Eulerian boundary regions can be created by the definition of surfaces, boundary conditions, and loads,
as described later in this section.
Geometric features
Many models include distinct geometric kinks that take the form of geometric edges or corners. It is
usually not desirable to perform adaptive meshing across such geometric features unless they flatten.
Once a geometric feature does flatten, it is usually best if the feature is deactivated so that adaptive
meshing will occur across it. This is especially true when adaptive mesh domains are subject to large
deformation.
The adaptive meshing algorithm in ABAQUS/Explicit will respect geometric features on Lagrangian
and sliding boundaries. In three dimensions geometric features consist of edges and corners (see Figure
7.6.2-2), while in two dimensions they consist of only corners. If a geometric edge coincides with the
edge of a Lagrangian boundary region, the presence of the geometric feature has no effect on the
treatment of the edge: material cannot flow perpendicular to a Lagrangian edge.
Geometric features are not detected or tracked on Eulerian boundary regions because they generally are
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not physically meaningful.
Output options are available for viewing the formation of geometric edges and corners--see ``Output
and diagnostics for adaptive meshing,'' Section 7.6.4.
Figure 7.6.2-2 Geometric features formed on a solid block with a crack.
Controlling the detection of geometric edges and corners
Geometric features are identified initially as edges on boundary regions where the angle between the
normals on adjacent element faces is greater than the initial geometric feature angle, µI
(0± ∙ µI ∙ 180± ). See Figure 7.6.2-3. The default value for the initial geometric feature angle is
µI = 30± .
Figure 7.6.2-3 Detection and deactivation of geometric features.
Setting µI = 180± will ensure that no geometric edges or corners are formed on the boundary of the
adaptive mesh domain. Use the INITIAL FEATURE ANGLE parameter on the *ADAPTIVE MESH
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CONTROLS option to change the value of the angle that will be used to recognize geometric
features.
Usage: *ADAPTIVE MESH CONTROLS, NAME=name, INITIAL FEATURE ANGLE=µI
Controlling the deactivation of geometric edges and corners
Geometric features affect only Lagrangian and sliding boundary regions, where they act as temporary
Lagrangian edges. During each mesh sweep in an adaptive mesh increment, nodes along a geometric
edge are positioned by applying the basic smoothing methods (see ``Adaptive meshing and
remapping,'' Section 7.6.3). The nodes are constrained to lie along the discrete geometric edge unless
the angle forming the geometric edge becomes less than the transition geometric feature angle, µT
(0± ∙ µT ∙ 180± ). The default value for the transition feature angle is µT = 30± . If the angle across
the geometric edge becomes less than µT , the boundary surface is considered to be flattened
sufficiently for the feature to be deactivated, and the mesh is allowed to slide freely over the material
(unconstrained by the deactivated geometric edge). Geometric corners are allowed to flatten in a
similar fashion. This logic allows great flexibility in mesh adaptation while preserving geometric
features in the model.
Setting µT = 0± will ensure that no geometric edges or corners are ever deactivated. Use the
TRANSITION FEATURE ANGLE parameter on the *ADAPTIVE MESH CONTROLS option to
change the transition feature angle.
Usage: *ADAPTIVE MESH CONTROLS, NAME=name, TRANSITION FEATURE ANGLE=µT
Mesh constraints
In most adaptive mesh problems the motion of nodes in the mesh is determined by the meshing
algorithm, with constraints imposed by the domain boundary and the boundary region edges. However,
there are cases when the motion of the nodes must be defined explicitly by the user. As explained
earlier, Eulerian and sliding boundary regions generally require mesh constraints for the regions to be
physically meaningful. In some problems the user may wish to keep certain nodes fixed, to move nodes
in a particular direction, or to force certain nodes to move with the material. In other problems the user
may desire a node or particular set of nodes to follow the material motion. The *ADAPTIVE MESH
CONSTRAINT option allows full control over the mesh movement and acts independently of any
boundary conditions or loads applied to the underlying material.
Applying spatial mesh constraints
Set the CONSTRAINT TYPE parameter on the *ADAPTIVE MESH CONSTRAINT option equal to
SPATIAL (the default) to prescribe spatial mesh motion that is independent of the material motion.
The nodes to which the constraint is applied, the directions of the prescribed motion, and the amplitude
of the prescribed motion are given on the data line of the *ADAPTIVE MESH CONSTRAINT option.
Usage: The following options are equivalent:
*ADAPTIVE MESH CONSTRAINT
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*ADAPTIVE MESH CONSTRAINT, CONSTRAINT TYPE=SPATIAL
Rules for applying spatial mesh constraints
Spatial mesh constraints can be applied without restriction to nodes on an Eulerian boundary region or
in the interior of an adaptive mesh domain.
In both two and three dimensions nodes at Lagrangian and active geometric corners are fully
constrained to move with the underlying material. Therefore, no mesh constraints can be applied at
such corners.
Mesh constraints applied using the *ADAPTIVE MESH CONSTRAINT option must not conflict with
other mesh constraints inherent to Lagrangian and sliding boundary regions; therefore, mesh
constraints can be applied only tangentially to a Lagrangian or sliding boundary region. This restriction
implies that mesh constraints can be applied only in two directions in a three-dimensional boundary
region, in one direction in a two-dimensional boundary region, or in one direction on a Lagrangian or
active geometric edge. It may not always be feasible to adhere to this rule, particularly if the boundary
experiences finite rotation. Therefore, if the normal to a boundary region is not perpendicular to a
prescribed mesh constraint at a node, it is always moved along the current surface of the boundary
region so that the projection of the mesh motion in the direction of the prescribed constraint is correct
(see Figure 7.6.2-4).
Figure 7.6.2-4 Enforcing a spatial mesh constraint.
If the normal to the boundary region approaches the direction of the applied mesh constraint, large
mesh motions will be required to satisfy the constraint. By default, an analysis is terminated if the
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angle between the normal to the boundary region and the direction of the prescribed constraint
becomes less than µC . This cut-off angle is referred to as the mesh constraint angle, and its default
value is 60°.
The mesh constraint angle, µC , is also used when adaptive mesh constraints are applied to nodes along
a Lagrangian or active geometric edge. Since independent mesh motion cannot be prescribed
perpendicular to these edges, an analysis is terminated if the angle between the prescribed constraint
and the plane perpendicular to the edge falls below the specified mesh constraint angle.
Use the MESH CONSTRAINT ANGLE parameter on the *ADAPTIVE MESH CONTROLS option to
change the value of the mesh constraint angle ( 5± ∙ µC ∙ 85± ). Setting µC < 45± is not recommended
because it may cause errors in determining the free surface geometry, especially for curved surfaces.
Usage: *ADAPTIVE MESH CONTROLS, MESH CONSTRAINT ANGLE=µC
Prescribing mesh displacement
Set the TYPE parameter on the *ADAPTIVE MESH CONSTRAINT option equal to
DISPLACEMENT (the default) to prescribe a displacement for the mesh motion.
Usage: The following options are equivalent:
*ADAPTIVE MESH CONSTRAINT
*ADAPTIVE MESH CONSTRAINT, TYPE=DISPLACEMENT
Prescribing mesh velocity
Set the TYPE parameter on the *ADAPTIVE MESH CONSTRAINT option equal to VELOCITY to
prescribe a velocity for the mesh motion.
Usage: *ADAPTIVE MESH CONSTRAINT, TYPE=VELOCITY
Defining mesh constraints that vary with time
The prescribed magnitude of a nonzero mesh constraint can vary with time during a step according to
an amplitude definition (see ``Amplitude curves,'' Section 18.1.2).
Usage: Use both of the following options:
*AMPLITUDE, NAME=name
*ADAPTIVE MESH CONSTRAINT, AMPLITUDE=name
Applying spatial mesh constraints in local directions
Spatial mesh constraints are applied in local directions if the *TRANSFORM option is used at a node;
otherwise, they are applied in global directions.
Applying Lagrangian mesh constraints
Set the CONSTRAINT TYPE parameter on the *ADAPTIVE MESH CONSTRAINT option equal to
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LAGRANGIAN to force certain nodes in the mesh to follow the material motion (i.e., to make these
nodes nonadaptive). The nodes to which the constraint will be applied are specified on the data line of
the *ADAPTIVE MESH CONSTRAINT option.
Usage: *ADAPTIVE MESH CONSTRAINT, CONSTRAINT TYPE=LAGRANGIAN
Modifying adaptive mesh constraints
Use either the *ADAPTIVE MESH CONSTRAINT option or the *ADAPTIVE MESH
CONSTRAINT, OP=MOD option to make changes to existing adaptive mesh constraints. When these
options are used, all existing adaptive mesh constraints remain active.
Usage: The following options are equivalent:
*ADAPTIVE MESH CONSTRAINT,
*ADAPTIVE MESH CONSTRAINT, OP=MOD
Removing adaptive mesh constraints
Use the *ADAPTIVE MESH CONSTRAINT, OP=NEW option to remove all previously defined
adaptive mesh constraints. Any adaptive mesh constraints that are to be retained must be respecified.
If the OP=NEW parameter is used on any *ADAPTIVE MESH CONSTRAINT option within a step, it
must be used on all *ADAPTIVE MESH CONSTRAINT options in the step.
Usage: *ADAPTIVE MESH CONSTRAINT, OP=NEW
Adding adaptive mesh constraints
Use the *ADAPTIVE MESH CONSTRAINT; *ADAPTIVE MESH CONSTRAINT, OP=MOD; or
*ADAPTIVE MESH CONSTRAINT, OP=NEW options to specify additional adaptive mesh
constraints.
Initial conditions
There are no initial conditions specific to adaptive meshing; initial conditions can be defined in the
same way as in nonadaptive problems. If initial mesh sweeps are performed to smooth the mesh at the
beginning of a step (see ``Adaptive meshing and remapping,'' Section 7.6.3), all initial conditions
(except temperatures and field variables, which are discussed in the subsection "Predefined fields,"
presented later in this section) are remapped to the new mesh. Initial temperatures are remapped during
adaptive meshing in an adiabatic analysis.
Initial conditions prescribed near an inflow Eulerian boundary region will affect the state of the
material flowing into the domain throughout the analysis. See ``Modeling techniques for Eulerian
adaptive mesh domains,'' Section 7.6.5, for a discussion of the proper treatment of inflow boundaries.
Defining surfaces on adaptive mesh boundaries
When the *SURFACE option is used to define a surface on the boundary of an adaptive mesh domain,
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ABAQUS creates a boundary region coinciding with the surface. By default, a sliding boundary region
is created. The REGION TYPE parameter on the *SURFACE option can be used to create a
Lagrangian or Eulerian boundary region instead.
A surface defined in the interior of an adaptive mesh domain will move independently of the material
(unless constrained by mesh constraints).
Defining a sliding boundary region using a surface
By default, the boundary region created by a surface definition will be sliding (the surface edge will
slide freely over the material). The REGION TYPE parameter on the *SURFACE option can be used
to specify the sliding boundary region type.
Usage: The following options are equivalent:
*SURFACE
*SURFACE, REGION TYPE=SLIDING
Defining a Lagrangian boundary region using a surface
To force the surface edge to follow the material, set the REGION TYPE parameter on the *SURFACE
option equal to LAGRANGIAN.
Usage: *SURFACE, REGION TYPE=LAGRANGIAN
Defining an Eulerian boundary region using a surface
To decouple the surface from the material motion, set the REGION TYPE parameter on the
*SURFACE option equal to EULERIAN and apply spatial mesh constraints normal to the surface. If
no mesh constraints are applied, the surface will behave like a sliding boundary region (no material
will flow through the surface).
As an example, it is often assumed that there is no normal or shear stress in the material at the outflow
boundary of an Eulerian domain. This condition can be modeled by defining an Eulerian boundary
region using the *SURFACE option and applying spatial mesh constraints perpendicular to the surface,
as shown in Figure 7.6.2-5.
Usage: *SURFACE, REGION TYPE=EULERIAN
Figure 7.6.2-5 Modeling the outflow boundary of an Eulerian adaptive mesh domain.
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Contact
Lagrangian and sliding boundary regions created using the *SURFACE option can be used in contact
pairs; they have the same meaning as surfaces defined on nonadaptive regions. Since contact generally
involves relative sliding between bodies, sliding boundary regions are typically appropriate for contact
surfaces.
Surfaces defined on Eulerian boundary regions cannot be used in contact pairs.
If the TIED, SMALL SLIDING, or NO SEPARATION parameters are used to define a contact pair, all
the nodes on both surfaces are nonadaptive (see ``Defining tied contact,'' Section 20.2.4; ``Defining
contact pairs,'' Section 20.2.1; and ``Interaction normal to the surface,'' Section 20.3.2). Similarly, the
nodes at which spot welds are defined are nonadaptive (see ``Spot welds,'' Section 20.3.5.)
Distributed loads
When the *DLOAD option is used to apply a distributed pressure load to the boundary of an adaptive
mesh domain, ABAQUS creates a boundary region that coincides with the area of the load application.
The characteristics of boundary regions created in this way are identical to those of boundary regions
created by defining surfaces. If a pressure load is applied to a surface in the interior of an adaptive
mesh domain, the nodes on the surface will move with the material in all directions (i.e., they will be
nonadaptive).
Boundary regions created by different pressure loads may overlap. If pressure loads with the same
magnitude and amplitude definition are applied to adjacent regions, the regions will be merged into a
single boundary region to minimize the number of Lagrangian edges and corners formed (see Figure
7.6.2-6).
Figure 7.6.2-6 Applying distributed pressure loads to an adaptive mesh domain.
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If a nonuniform pressure is applied (for example, a pressure that varies linearly over a surface) or if a
pressure load is defined in user subroutine VDLOAD, each element face or edge becomes a separate
Lagrangian boundary region. Since Lagrangian corners are formed where Lagrangian edges meet, all
nodes will follow the material in every direction, and each region becomes nonadaptive. Likewise, if a
nonuniform body force is applied to an adaptive mesh domain, the domain is split into multiple
domains, each with a uniform body force. If this splitting results in one-element domains, the region
becomes nonadaptive.
Defining a Lagrangian boundary region with a pressure load
By default, the boundary region created to coincide with a pressure load will be Lagrangian. Pressure
loads applied to Lagrangian regions are identical to pressure loads applied to nonadaptive regions,
except that the mesh can move inside the boundary region. The REGION TYPE parameter on the
*DLOAD option can be used to specify the Lagrangian boundary region type.
Usage: The following options are equivalent:
*DLOAD
*DLOAD, REGION TYPE=LAGRANGIAN
Defining a sliding boundary region with a pressure load
A pressure load can be applied to a sliding boundary region to simulate a load that is fixed in space
while material moves past it (see Figure 7.6.2-7). A sliding edge is unconstrained in the direction
tangential to the boundary region; therefore, unless the mesh is constrained with the *ADAPTIVE
MESH CONSTRAINT option, the area of the load application will move according to the adaptive
meshing algorithm, which is probably not physically meaningful.
To allow a pressure load to slide over the material, set the REGION TYPE parameter on the *DLOAD
option equal to SLIDING.
Usage: *DLOAD, REGION TYPE=SLIDING
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Figure 7.6.2-7 Applying a sliding distributed pressure load to an adaptive mesh domain.
Defining an Eulerian boundary region with a pressure load
To decouple the area of pressure application from the material motion, set the REGION TYPE
parameter on the *DLOAD option equal to EULERIAN and apply spatial mesh constraints normal to
the surface. If no mesh constraints are applied, the mesh will behave like a sliding boundary region (no
material will flow through the surface).
As an example, it is often assumed that a uniform ambient pressure exists at the outflow boundary of
an Eulerian domain. This condition can be modeled by defining the pressure at an Eulerian boundary
region using the *DLOAD option and applying spatial mesh constraints perpendicular to the surface,
as shown in Figure 7.6.2-8.
Usage: *DLOAD, REGION TYPE=EULERIAN
Figure 7.6.2-8 Modeling an ambient pressure at the outflow boundary of an Eulerian adaptive mesh
domain.
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Distributed surface fluxes and thermal conditions
In coupled thermal-stress analysis ABAQUS also creates boundary regions for distributed surface
fluxes, convective film conditions, and radiation conditions when using the *DFLUX, *FILM, and
*RADIATE options, respectively. The rules governing boundary regions with these options are
identical to those discussed for distributed loads. The ability to specify boundary region type and the
usage of the REGION TYPE parameter on these options is also the same.
Concentrated loads
When the *CLOAD option is used to apply a concentrated load to the boundary of an adaptive mesh
domain, ABAQUS creates a boundary region to coincide with the load. Every node to which a
concentrated load is applied will be considered its own boundary region because it is not possible to
identify a surface area associated with a concentrated load. However, the REGION TYPE parameter on
the *CLOAD option can be used to control the behavior of each one-node region.
If concentrated loads are applied to nodes in the interior of an adaptive mesh domain, those nodes will
move with the material in all directions (i.e., they will be nonadaptive).
Defining a Lagrangian boundary region with a concentrated load
By default, the boundary region created by a concentrated load will be Lagrangian. Each one-node
Lagrangian boundary region will follow the material in every direction (the nodes will be
nonadaptive). The REGION TYPE parameter on the *CLOAD option can be used to specify the
Lagrangian boundary region type.
Usage: The following options are equivalent:
*CLOAD
*CLOAD, REGION TYPE=LAGRANGIAN
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Defining a sliding boundary region with a concentrated load
A concentrated load can be applied to a sliding boundary region to simulate a load that is fixed in
space while material moves past it (see Figure 7.6.2-9). A sliding node is unconstrained in the
direction tangential to the boundary region; therefore, unless the mesh is constrained with the
*ADAPTIVE MESH CONSTRAINT option, the point of load application will move according to the
adaptive meshing algorithm, which is probably not physically meaningful.
Figure 7.6.2-9 Applying a concentrated sliding load to an adaptive mesh domain.
To allow the concentrated load to slide freely over the material, set the REGION TYPE parameter on
the *CLOAD option equal to SLIDING.
Usage: *CLOAD, REGION TYPE=SLIDING
Defining an Eulerian boundary region with a concentrated load
To decouple the concentrated load from the material motion, set the REGION TYPE parameter on the
*CLOAD option equal to EULERIAN and apply spatial mesh constraints normal to the surface. If no
mesh constraints are applied, each one-node boundary region will behave like a sliding boundary
region.
Usage: *CLOAD, REGION TYPE=EULERIAN
Concentrated fluxes and thermal conditions
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In coupled thermal-stress analysis ABAQUS also creates boundary regions for concentrated heat
fluxes, film conditions, and radiation conditions when using the *CFLUX, *CFILM, and *CRADIATE
options, respectively. The rules governing boundary regions with these options are identical to those
discussed for concentrated loads. The ability to specify boundary region type and the usage of the
REGION TYPE parameter on these options is also the same.
Boundary conditions
Lagrangian, sliding, and Eulerian boundary regions can be created by applying kinematic constraints to
the boundary of an adaptive mesh domain. If kinematic boundary conditions are applied to nodes in the
interior of an adaptive mesh domain, those nodes will move with the material in all directions (i.e.,
they will be nonadaptive), regardless of the value of the REGION TYPE parameter on the
*BOUNDARY option.
Defining a Lagrangian boundary region using a boundary
condition
By default, the boundary region created by a kinematic boundary condition will be Lagrangian.
ABAQUS will recognize surface-type and point or edge constraints automatically and will create an
appropriate Lagrangian boundary region for each type, as explained in the following subsections.
The REGION TYPE parameter on the *BOUNDARY option can be used to specify a Lagrangian
boundary region.
Usage: The following options are equivalent:
*BOUNDARY
*BOUNDARY, REGION TYPE=LAGRANGIAN
Surface-type constraints applied using boundary conditions
Although boundary conditions are always applied to individual nodes in ABAQUS, they often
represent physical constraints on surfaces. For example, symmetry conditions, where nodes are
constrained to move in a plane, are actually surface constraints. A fully clamped ( ENCASTRE)
condition along a boundary can also be considered a surface constraint. (During adaptive meshing it is
meaningful to allow nodes to move along a fully clamped edge.)
ABAQUS will examine an adaptive mesh boundary and try to create regions that are coincident with
the applied boundary conditions. Currently, ABAQUS can create boundary regions for surface-based
constraints on:
· symmetry planes,
· fully clamped planes, and
· planes on which a uniform motion is prescribed.
Figure 7.6.2-2 shows an example in which boundary regions are created by applying surface-type
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boundary conditions. This figure shows a block of material with a crack and three symmetry planes
(therefore, three Lagrangian boundary regions). Material will not flow across any symmetry plane, yet
adaptive meshing can be performed within each Lagrangian boundary region. This flexibility is often
helpful in problems that have significant deformation.
Point or edge constraints applied using boundary conditions
Some boundary conditions represent point or edge constraints. For example, a displacement can be
prescribed at a node. The boundary regions associated with such nodes are exactly the same as those
created by concentrated loads.
Defining a sliding boundary region using a boundary condition
A sliding boundary region associated with a boundary condition can move according to the adaptive
meshing algorithm. Since this behavior is probably not physically meaningful, the edges of a sliding
boundary region are usually fixed in the direction tangential to the surface using adaptive mesh
constraints. This approach can be used, for example, to simulate frictionless contact between a rigid
punch and a deformable body, as shown in Figure 7.6.2-10. In this example the punch is replaced by a
sliding boundary region with a constant velocity boundary condition applied in the area of "contact." A
tangential mesh constraint is applied to the edge of the boundary region at node N (the other edge is
constrained by the Lagrangian boundary region created automatically on the symmetry plane). This
problem definition allows material to flow radially underneath the "punch" while retaining the original
size and location of the "contact" area.
Figure 7.6.2-10 Contact simulation using a sliding boundary region.
ABAQUS makes no distinction between surface-type constraints and point or edge constraints for
sliding boundary regions.
To allow the boundary condition to slide freely over the material, set the REGION TYPE parameter on
the *BOUNDARY option equal to SLIDING.
Usage: *BOUNDARY, REGION TYPE=SLIDING
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Defining an Eulerian boundary region using a boundary
condition
To decouple the boundary region from the material motion, set the REGION TYPE parameter on the
*BOUNDARY option equal to EULERIAN and apply spatial mesh constraints normal to the surface.
If no mesh constraints are applied, the mesh will behave like a sliding boundary region (no material
will flow through the surface).
As an example, the mass flow rate at an Eulerian inflow boundary can be prescribed by defining an
Eulerian boundary region using a boundary condition.
ABAQUS makes no distinction between surface-type constraints and point or edge constraints for
Eulerian boundary regions.
Usage: *BOUNDARY, REGION TYPE=EULERIAN
Overlapping boundary regions
A Lagrangian boundary region can overlap any number of other Lagrangian or sliding boundary
regions (see Figure 7.6.2-11). If two boundary regions partially overlap, three regions are formed: the
overlapping region and the two initial regions minus the overlapping region. A sliding boundary region
is formed when a Lagrangian and a sliding boundary region overlap.
Figure 7.6.2-11 Overlapping boundary regions.
An Eulerian boundary region can never overlap a Lagrangian or sliding boundary region. Furthermore,
an Eulerian boundary region can never share a boundary with or overlap a nonadaptive region.
Because infinite elements are nonadaptive, this latter restriction implies that infinite elements cannot
be used to simulate ambient conditions at an outflow boundary.
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Coincident edges
Edges shared by different types of boundary regions are subject to the following rules:
· An edge shared between a Lagrangian and a sliding boundary region will be Lagrangian.
· An edge shared between a Lagrangian and an Eulerian boundary region will be sliding.
· An edge shared between a Lagrangian and a nonadaptive boundary region will be nonadaptive.
· An edge shared between a sliding and a nonadaptive boundary region will be nonadaptive.
· An edge of an Eulerian boundary region can never be coincident with an edge of a nonadaptive
region.
Predefined fields
There are no restrictions on applying prescribed temperatures or field variables in an adaptive mesh
domain, but these nodal values are not remapped when adaptive meshing is performed. Therefore,
predefined fields that are not spatially uniform may not be meaningful within an adaptive mesh
domain. (Time-varying, spatially uniform predefined fields are acceptable, since adaptive meshing is
applied at discrete instances in time.) However, if temperature or field variable data are collected from
a spatial frame of reference, it may make physical sense to apply a spatially varying field for an
Eulerian domain in which the mesh does not move. ABAQUS does not perform any checks or
calculations on predefined fields for adaptive meshing; the user must ensure that the predefined fields
are meaningful.
Material options
All material models and options, except for brittle cracking ( ``Cracking model for concrete,'' Section
10.4.1), can be used in an adaptive mesh domain.
If the *POROUS FAILURE CRITERIA, *SHEAR FAILURE, or *TENSILE FAILURE options are
used within an adaptive mesh domain, ABAQUS will continuously monitor the status of elements
while performing adaptive meshing. When elements within the domain fail, the nodes along the
interface between the failed and unfailed elements will become nonadaptive. This has the effect of
creating a material boundary between the failed and unfailed zones.
When failure occurs in elements that use the *SHEAR FAILURE or *TENSILE FAILURE options
with ELEMENT DELETION=NO, elements in the failure zone will not be deleted; they can carry
some states of stress. Adaptive meshing will occur within the failure zone but not along the interface
with the unfailed material.
Elements
An adaptive mesh domain can contain only first-order, reduced-integration, solid elements. All
elements within an adaptive mesh domain must have the same geometry (all two-dimensional,
three-dimensional, axisymmetric, or plane strain, etc.). Since adaptive mesh domains are split across
element types, degenerate elements should be used for mixed domains that include both triangles and
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quadrilaterals (or tetrahedron and bricks). All elements other than first-order, reduced-integration,
solid elements, including mass, rotary inertia, and infinite elements, are nonadaptive. These elements
can be connected to an adaptive mesh domain, but their nodes are nonadaptive. All nodes and elements
on a rigid body are nonadaptive. Rebar are not supported within an adaptive mesh domain.
Multi-point constraints and equations
As with boundary conditions, multi-point constraints ( ``General multi-point constraints,'' Section
19.2.2) and equations (``Linear constraint equations,'' Section 19.2.1) are always applied to nodes but
sometimes represent constraints on surfaces. ABAQUS will recognize surface-type constraints when
the following conditions are satisfied:
· an equation, PIN MPC, or TIE MPC ties a node set to a single node; and
· all the nodes involved in the MPC or equation are coplanar and lie within the boundary region.
If these conditions are satisfied, a boundary region will be associated with the node set in the MPC or
equation. If the MPC is applied within a Lagrangian or sliding boundary region, a Lagrangian edge will
be created. If the MPC is applied within an Eulerian boundary region, no edge will be created. If the
above conditions are not satisfied, all nodes connected to the MPC or equation will be nonadaptive.
As an example, a constraint can be applied to force a plane section to remain plane in a Lagrangian
adaptive mesh domain, as shown in Figure 7.6.2-12(a). In this case all nodes are constrained by an
equation to lie in the same plane throughout the analysis, but adaptive meshing is allowed within the
plane.
As another example, consider the outflow boundary of an Eulerian domain, as shown in Figure
7.6.2-12(b). The outflow boundary of an Eulerian domain is often assumed to be far enough
downstream that the velocity is uniform but unknown. To model this condition, an Eulerian boundary
region is created at the outflow boundary using the *SURFACE, REGION TYPE=EULERIAN option.
The *ADAPTIVE MESH CONSTRAINT option is used to fix the mesh perpendicular to the boundary,
and all nodes on the plane are constrained by an equation to have the same velocity orthogonal to the
plane.
Figure 7.6.2-12 Using equations with adaptive meshing.
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Procedures
During an adiabatic analysis temperatures will be remapped properly in adaptive mesh domains.
Adaptive meshing is not used during annealing procedures or during geometrically linear analyses
(performed when the NLGEOM parameter on the *STEP option is set equal to NO).
The definitions of adaptive mesh domains, boundary regions, mesh constraints, and controls (as
explained in ``Adaptive meshing and remapping,'' Section 7.6.3) will propagate from step to step.
User subroutines
Solution-dependent state variables defined in user subroutine VUMAT will be remapped to the new
mesh when adaptive meshing is performed.
Solution-dependent state variables that are defined on a slave surface in user subroutine VFRIC will
not be remapped to the new mesh when adaptive meshing is performed. Therefore, to ensure physically
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meaningful results, the CONSTRAINT TYPE parameter on the *ADAPTIVE MESH CONSTRAINT
option should be set to LAGRANGIAN for nodes on the slave surface of a contact pair modeled using
VFRIC with solution-dependent state variables.
Output
Since the mesh is no longer constrained to the material when adaptive meshing is performed, output at
elements and nodes must be interpreted differently than in a pure Lagrangian problem. See ``Output
and diagnostics for adaptive meshing,'' Section 7.6.4, for details.
Template
To create a Lagrangian adaptive mesh domain:
*HEADING
...
*ELSET, ELSET=ADAPT
*************************
*STEP
*DYNAMIC, EXPLICIT
Data line to specify the time period of the step
*ADAPTIVE MESH, ELSET=ADAPT
...
*END STEP
To create an Eulerian adaptive mesh domain with a prescribed velocity inflow condition and a
prescribed pressure outflow condition (both in the global x-direction):
*HEADING...
*ELSET, ELSET=ADAPT
...
*ELSET, ELSET=OUT
...
*NSET, NSET=INFLOW
...
*NSET, NSET=OUTFLOW
...
*SURFACE, NAME=INSURF, REGION TYPE=EULERIAN
Data lines to define the surface
*SURFACE, NAME=OUTSURF, REGION TYPE=EULERIAN
Data lines to define the surface
...
*EQUATION
Data lines specifying uniform velocity at the inflow
*************************
*STEP
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*DYNAMIC, EXPLICIT
Data line to specify the time period of the step
*ADAPTIVE MESH, ELSET=ADAPT
*ADAPTIVE MESH CONSTRAINT
INFLOW, 1, 1, 0
OUTFLOW, 1, 1, 0
*BOUNDARY, TYPE=VELOCITY, REGION TYPE=EULERIAN
INFLOW, 1, 1, 10.0
*DLOAD, REGION TYPE=EULERIAN
OUT, P2, 15.0
...
*END STEP
7.6.3 Adaptive meshing and remapping
The *ADAPTIVE MESH, *ADAPTIVE MESH CONSTRAINT, and *ADAPTIVE MESH
CONTROLS options can be used to customize the adaptive meshing capability in ABAQUS/Explicit.
References
· ``Adaptive meshing: overview,'' Section 7.6.1
· ``Defining adaptive mesh domains,'' Section 7.6.2
· ``Output and diagnostics for adaptive meshing,'' Section 7.6.4
· *ADAPTIVE MESH
· *ADAPTIVE MESH CONSTRAINT
· *ADAPTIVE MESH CONTROLS
Overview
Adaptive meshing consists of two fundamental tasks:
· creating a new mesh, and
· remapping solution variables from the old mesh to the new mesh with a process called advection.
The success of the adaptive meshing technique depends on the choice of the methods used for each of
these tasks. The default methods for creating a new mesh and for remapping solution variables have
been chosen carefully to work for a wide variety of problems. However, the user may wish to override
the default choices to balance the robustness and efficiency of adaptive meshing or to extend the use of
adaptive meshing to more difficult or unusual applications.
Meshing
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A new mesh:
· is created at a specified frequency for each adaptive domain;
· is found by sweeping iteratively over the adaptive mesh domain and moving nodes to smooth the
mesh; and
· can retain the initial gradation of the original mesh.
Remapping
The methods used for advecting solution variables to the new mesh:
· are consistent, monotonic, and (by default) accurate to the second order; and
· conserve mass, momentum, and energy.
Controlling the frequency of adaptive meshing
In most cases the frequency of adaptive meshing is the parameter that most affects the mesh quality
and the computational efficiency of adaptive meshing. A typical adaptive mesh application without
Eulerian boundaries will require adaptive meshing every 5-100 increments. In contrast, adaptive
meshing should generally be performed much more frequently in a steady-state process simulation
using Eulerian boundaries. Thus, if a spatial adaptive mesh constraint or an Eulerian boundary region
is defined on an adaptive mesh domain, the default frequency is 1; otherwise, the default frequency is
10.
Use the FREQUENCY parameter on the *ADAPTIVE MESH option to change the frequency of
adaptive meshing.
Usage: *ADAPTIVE MESH, FREQUENCY=number of increments
Controlling the intensity of adaptive meshing
During each adaptive meshing increment, the new mesh is created by performing one or more mesh
sweeps and then advecting the solution variables to the new mesh.
Mesh sweeps
In an adaptive meshing increment, a new, smoother mesh is created by sweeping iteratively over the
adaptive mesh domain. During each mesh sweep, nodes in the domain are relocated--based on the
current positions of neighboring nodes and elements--to reduce element distortion. In a typical sweep a
node is moved a fraction of the characteristic length of any element surrounding the node. Increasing
the number of sweeps increases the intensity of adaptive meshing in each adaptive meshing increment.
The default number of mesh sweeps is one.
Use the MESH SWEEPS parameter on the *ADAPTIVE MESH option to change the number of mesh
sweeps to be performed in each adaptive mesh increment.
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Usage: *ADAPTIVE MESH, MESH SWEEPS=number of sweeps
Advection sweeps
The process of mapping solution variables from an old mesh to a new mesh is referred to as an
advection sweep. At least one advection sweep is performed in every adaptive mesh increment. Ideally,
an advection sweep will be performed only once, after all mesh sweeps for the increment are complete.
However, numerical stability of the advection sweep is maintained only if the difference between the
old mesh and the new mesh is small. Therefore, if after a mesh sweep the total accumulated movement
of any node in the domain is greater than 50% of the characteristic length of any adjacent element, an
advection sweep is performed to remap the solution variables from the old mesh to the intermediate
mesh. Mesh sweeps will continue until the number specified with the MESH SWEEPS parameter is
reached or until the movement of any node again exceeds the 50% threshold. At this time an advection
sweep is performed again to map variables from the last intermediate mesh to the new intermediate
mesh. The cycle will continue until the number of mesh sweeps reaches the number specified with the
MESH SWEEPS parameter.
The number of advection sweeps per adaptive mesh increment required for each adaptive mesh domain
is determined automatically by ABAQUS/Explicit; the user cannot override this automatic calculation.
The number of advection sweeps is printed by default to the message ( .msg) file (see ``Output and
diagnostics for adaptive meshing,'' Section 7.6.4).
The computational cost of adaptive meshing
The cost of adaptive meshing depends on the frequency of remeshing, the number of mesh and
advection sweeps performed, and the size of the adaptive mesh domains. When compared to a purely
Lagrangian analysis, additional computational cost is incurred only within adaptive mesh increments.
Generally, the cost of one advection sweep is several times greater than the cost of one mesh sweep.
Multiple advection sweeps are triggered when adaptive meshing is performed too infrequently and/or a
high number of mesh sweeps is specified. Performing adaptive meshing more frequently and doing 1-5
mesh sweeps in each adaptive mesh increment will usually generate only one advection sweep,
minimizing the computational cost.
The relatively smooth mesh and improved element aspect ratios that result from adaptive meshing may
increase the stable time increment compared to a similar pure Lagrangian analysis. In some cases this
increase can offset the cost of adaptive meshing completely.
Although computational cost can vary greatly with the type of application, performing adaptive
meshing on the entire problem domain in every increment will typically increase the cost of the
analysis by 3-5 times that of a similar Lagrangian analysis. Defining adaptive mesh domains that cover
only a fraction of the entire problem domain will reduce the cost proportionally. Changing the
frequency to every 10-25 increments will result in CPU times that are only moderately higher than
those for a pure Lagrangian analysis.
Guidelines for controlling adaptive meshing frequency and
intensity
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Although the default values work well for many problems, difficult analyses may require a more
frequent adaptive meshing frequency or meshing with a higher intensity.
Guidelines for transient analysis
For problems without spatial adaptive mesh constraints or Eulerian boundary regions, the default
frequency for adaptive meshing is 10, and the default number of mesh sweeps is 1. The default values
are usually adequate for low- to moderate-rate dynamic problems and for quasi-static process
simulations undergoing moderate deformation. If the frequency or number of mesh sweeps is too low,
excess element distortion may cause the analysis to terminate before the mesh is adapted; or, if a
solution can be obtained, it may not be as accurate as the solution that could be obtained with a higher
quality mesh. In virtually all cases, however, performing adaptive meshing at any frequency will
reduce the distortion of elements (and, thus, improve the quality of the solution) compared to a pure
Lagrangian analysis.
For high-rate impact problems undergoing large amounts of deformation, it may be necessary to
increase the frequency of adaptive meshing or the number of mesh sweeps. It is generally less
expensive to increase the number of mesh sweeps slightly before increasing the frequency, as long as
the number of advection sweeps remains small.
For problems involving explosions taking place over just a few hundred increments, adaptive meshing
is usually required at every increment. It may also be necessary to increase the frequency of adaptive
meshing for quasi-static process simulations that involve large amounts of flow per increment.
For problems in which the deformation per increment is small, a high-quality mesh can be maintained
by performing adaptive meshing only every 25-100 increments. For these problems the additional cost
of adaptive meshing is negligible.
Guidelines for steady-state analysis
When an adaptive mesh domain contains Eulerian boundary regions or has spatial adaptive mesh
constraints, the default frequency of adaptive meshing is 1. This default frequency is conservative and
is chosen primarily because spatial mesh constraints are applied only during adaptive mesh increments.
Thus, between adaptive mesh increments the mesh may drift from its prescribed location, which may
affect the solution. However, drift from adaptive mesh constraints will always be eliminated in the next
adaptive mesh increment: it will not accumulate.
For problems in which the speed of deformation or the speed of material flow from element to element
is much less than the material wave speed, the frequency typically can be increased to 5 or higher. This
class of problems includes most steady-state process simulations, where the drift of the mesh from the
prescribed location is negligible over a few increments. By performing adaptive meshing less often,
steady-state simulations become competitive with their corresponding transient simulations. For
Eulerian domains in which the speed of the deformation or material flow is high, such as in dynamic
shock problems, the default frequency of 1 should be used.
Mesh smoothing methods
The determination of the new mesh in ABAQUS/Explicit is based on four aspects. Each of these
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aspects can be controlled with the *ADAPTIVE MESH CONTROLS option. Defaults have been
chosen so that the overall algorithm works well for most problems.
First, the calculation of the new mesh in ABAQUS/Explicit is based on some combination of three
basic smoothing methods: volume smoothing, Laplacian smoothing, and equipotential smoothing. The
smoothing methods are applied at each node in the adaptive mesh domain to determine the new
location of the node based on the locations of surrounding nodes or elements. Although all the
smoothing methods tend to smooth the mesh and reduce element distortion, the resulting meshes will
differ depending on the methods used.
Second, initial element gradation can be maintained at the expense of element distortion if desired.
Third, optimal positioning of the nodes before the basic smoothing methods are applied can improve
mesh quality and minimize the frequency of adaptive meshing required.
Finally, solution-dependent meshing is used to concentrate mesh refinement near areas of evolving
boundary curvature. This counteracts the tendency of the basic smoothing methods to reduce the mesh
refinement near concave boundaries where solution accuracy is important.
Volume smoothing
Volume smoothing relocates a node by computing a volume weighted average of the element centers in
the elements surrounding the node. In Figure 7.6.3-1 the new position of node M is determined by a
volume weighted average of the positions of the element centers, C, of the four surrounding elements.
The volume weighting will tend to push the node away from element center C1 and toward element
center C3, thus reducing element distortion.
Volume smoothing is very robust and is the default method in ABAQUS/Explicit. It works well for
both structured and highly unstructured domains. (A structured domain is one that contains no
degenerate elements and where every node is surrounded by four elements in two dimensions or eight
elements in three dimensions.)
Figure 7.6.3-1 Relocation of a node during a mesh sweep.
Laplacian smoothing
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Laplacian smoothing relocates a node by calculating the average of the positions of each of the
adjacent nodes connected by an element edge to the node in question. In Figure 7.6.3-1 the new
position of node M is determined by averaging the positions of the four nodes, L, connected to M by
element edges. The locations of nodes L2 and L3 will pull node M up and to the right to reduce
element distortion.
Laplacian smoothing is the least expensive smoothing algorithm and is commonly used in mesh
preprocessors. For low to moderately distorted mesh domains, the results of Laplacian smoothing are
similar to volume smoothing. For domains with boundaries of complex curvature, volume smoothing
generally results in a more balanced mesh.
Equipotential smoothing
Equipotential smoothing is a higher-order method that relocates a node by calculating a higher-order,
weighted average of the positions of the node's eight nearest neighbor nodes in two dimensions (or its
eighteen nearest neighbor nodes in three dimensions). In Figure 7.6.3-1 the new position of node M is
based on the position of all the surrounding nodes, L and E.
The weighted averaging for the equipotential smoothing method is fairly complex and is based on the
solution of the Laplace equation. Equipotential smoothing tends to minimize the local curvature of
lines running across a mesh over several elements. Although this tendency can be desirable for gently
curving domains, it can inhibit the ability of equipotential smoothing to reduce element distortion in
highly deformed and locally curved domains.
Equipotential smoothing can be performed only for nodes that are surrounded by a locally structured
mesh. Nodes that are surrounded by an unstructured mesh are moved with an equivalent amount of
volume smoothing when equipotential smoothing is chosen.
Combining smoothing methods
The default smoothing method in ABAQUS/Explicit is volume smoothing. To choose an alternate
smoothing method or to combine smoothing methods, specify the weighting factor for each method on
the data line of the *ADAPTIVE MESH CONTROLS option. When more than one smoothing method
is used, a node is relocated by computing a weighted average of the locations predicted by each chosen
method. All weights must be positive, and their sum should typically be 1.0. If the sum of the chosen
weights is less than 1.0, the mesh smoothing algorithm will be less aggressive at each adaptive mesh
increment. If the sum of the chosen weights is greater than 1.0, their values are normalized so that their
sum is 1.0.
For example, the following option could be used to define an equal blend of volume and equipotential
smoothing, with no Laplacian smoothing:
*ADAPTIVE MESH CONTROLS, NAME=name
0.5, 0.0, 0.5
Geometric enhancements to the basic smoothing methods
The conventional forms of the basic smoothing methods do not perform well in highly distorted
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domains. To ensure the robustness of adaptive meshing, ABAQUS/Explicit uses geometrically
enhanced forms of the basic smoothing algorithms by default. The enhanced forms are recommended
for all adaptive mesh applications. However, since the basic smoothing algorithms are used by many
finite element preprocessors, their conventional forms are provided as an option. Set the GEOMETRIC
ENHANCEMENT parameter on the *ADAPTIVE MESH CONTROLS option equal to NO to use the
conventional forms of the volume, Laplacian, or equipotential smoothing algorithms.
Usage: *ADAPTIVE MESH CONTROLS, NAME=name, GEOMETRIC ENHANCEMENT=NO
Specifying a uniform mesh smoothing objective
For adaptive mesh domains without any Eulerian boundary regions, the default objective of the mesh
smoothing methods is to minimize mesh distortion while improving element aspect ratios, at the
expense of diffusing initial mesh gradation. The uniform mesh smoothing objective is recommended
for problems with moderate to large overall deformation.
The SMOOTHING OBJECTIVE parameter on the *ADAPTIVE MESH CONTROLS option can be
set equal to UNIFORM to specify the uniform mesh smoothing objective.
Usage: *ADAPTIVE MESH CONTROLS, NAME=name, SMOOTHING OBJECTIVE=UNIFORM
Specifying a graded mesh smoothing objective
Alternatively, the smoothing methods can attempt to preserve initial mesh gradation while reducing
element distortion as the analysis evolves. This objective is the default for adaptive mesh domains with
one or more Eulerian boundary regions. The graded mesh smoothing objective is recommended only
for adaptive mesh domains with reasonably structured graded meshes undergoing low to moderate
overall deformation. Element distortion will be minimized, but the aspect ratios of adjacent elements
will be maintained approximately. Mesh gradation is particularly useful in steady-state problems where
overall deformations are small and a focused mesh is used in a specific area to capture high solution
gradients.
Set the SMOOTHING OBJECTIVE parameter on the *ADAPTIVE MESH CONTROLS option equal
to GRADED to specify the graded mesh smoothing objective.
Usage: *ADAPTIVE MESH CONTROLS, NAME=name, SMOOTHING OBJECTIVE=GRADED
Positioning nodes in Lagrangian domains
If an adaptive mesh domain has no Eulerian boundary regions, then, by default, the mesh sweeps are
based on current nodal locations, which account for material motion accumulated since the last
adaptive mesh increment. This approach is generally the best for Lagrangian problems that undergo
large overall deformation.
The MESHING PREDICTOR parameter on the *ADAPTIVE MESH CONTROLS option can be set
equal to CURRENT to request that the current deformed positions of nodes be used as the starting
locations for mesh smoothing.
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Usage: *ADAPTIVE MESH CONTROLS, NAME=name, MESHING PREDICTOR=CURRENT
Positioning nodes in Eulerian domains
Mesh sweeps can be based on the locations of nodes at the end of the previous adaptive mesh
increment. This technique is recommended for problems that are Eulerian in nature, where material
flow is significant compared to overall deformation. Therefore, it is the default for adaptive mesh
domains with one or more Eulerian boundary regions. This approach will result in a virtually stationary
mesh.
Set the MESHING PREDICTOR parameter on the *ADAPTIVE MESH CONTROLS option equal to
PREVIOUS to use the position of the nodes at the end of the previous adaptive mesh increment as a
starting location for mesh smoothing.
Usage: *ADAPTIVE MESH CONTROLS, NAME=name, MESHING PREDICTOR=PREVIOUS
Solution-dependent meshing based on concave boundary
curvature
Mesh smoothing algorithms based only on minimizing element distortion tend to reduce the mesh
refinement in areas of concave curvature, especially as the curvature evolves. Having sufficient mesh
refinement near highly curved boundaries is often important to model both the shape and volume of
the domain. To prevent the natural reduction in mesh refinement of areas near evolving concave
curvature, ABAQUS/Explicit uses solution-dependent meshing to focus mesh gradation toward these
areas automatically.
Although solution-dependent meshing may "pull" more elements into areas of high curvature, its
primary purpose is to retain the nominal refinement in these zones. Therefore, a fine mesh should
always be used when and where highly curved boundaries are expected and solution-dependent
meshing should generally not be used as a direct substitute for more elements.
The aggressiveness of the solution-dependent meshing is governed by the curvature refinement weight
®C . By default, ®C = 1, which correponds to an aggressivity level that has been chosen to work well
on a wide variety of problems. Use the CURVATURE REFINEMENT parameter on the *ADAPTIVE
MESH CONTROLS option to change the curvature refinement weight. A value of zero indicates no
solution dependence due to evolving boundary curvature, and a value greater than one increases the
aggressivity from the default.
Usage: *ADAPTIVE MESH CONTROLS, NAME=name, CURVATURE REFINEMENT=®C
Smoothing a distorted mesh at the beginning of a step
When an adaptive mesh domain contains a structured mesh of uniform density, the mesh will move
independently from the material only when the domain deforms. If the mesh is initially nonuniform,
the meshing algorithms in ABAQUS/Explicit will smooth the mesh even in the absence of deformation
or material transport.
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When the initial mesh contains highly distorted elements, it is often useful to smooth the mesh before
the step begins so that the best possible mesh is used throughout the step. When a uniform smoothing
objective is used, five mesh sweeps are performed by default at the beginning of the step in which the
adaptive mesh domain is defined. For a graded smoothing objective, two mesh sweeps are performed
by default at the beginning of the step without acccounting for gradation. The aspect ratios used for
gradation in all subsequent mesh sweeps are based on this locally smoothed mesh.
Use the INITIAL MESH SWEEPS parameter on the *ADAPTIVE MESH option to change the number
of mesh sweeps that will be performed at the beginning of the first step in which the adaptive mesh
definition is active.
Usage: *ADAPTIVE MESH, INITIAL MESH SWEEPS=number of initial sweeps
For example, the following option would smooth a badly distorted mesh with 15 mesh sweeps at the
beginning of the step, before performing adaptive meshing with three mesh sweeps every 20
increments throughout the step.
*ADAPTIVE MESH,FREQUENCY=20,MESH SWEEPS=3,INITIAL MESH SWEEPS=15
Initial conditions are advected to the new mesh when initial mesh sweeps are performed.
Meshing on boundary regions
Adaptive meshing on Lagrangian and sliding boundary regions is subject to the constraint that the
mesh and material must move together in the direction normal to the boundary. Nodes on the interior
of such a boundary are allowed to slide freely over the material within the boundary region, which
maximizes the amount of mesh smoothing that can be performed. Nodes are positioned in each mesh
sweep by applying the basic smoothing methods while constraining the nodes to lie on the boundary
region. In three dimensions some nodes on Lagrangian boundary regions will be on a Lagrangian edge.
In each mesh sweep these nodes are positioned by applying the basic smoothing methods while
constraining the node to lie along the discrete Lagrangian edge.
For problems in which the flow of material from element to element along the boundary is significant
compared to the deformation, oscillations in the boundary mesh can result if these constraints are
applied symmetrically with respect to the upstream and downstream directions of material flow.
ABAQUS/Explicit uses a Petrov-Galerkin weighting of the free boundary constraint to suppress any
oscillations. The algorithm is volume preserving, and the degree of upwinding is chosen automatically.
Advecting solution variables to the new mesh
The framework for adaptive meshing in ABAQUS/Explicit is the Arbitrary Lagrangian-Eulerian
method, which introduces advective terms into the momentum balance and mass conservation
equations to account for independent mesh and material motion. There are two basic ways to solve
these modified equations: solve the nonsymmetric system of equations directly, or decouple the
Lagrangian (material) motion from the additional mesh motion using an operator split. The operator
split method is used in ABAQUS/Explicit because of its computational efficiency. Furthermore, this
technique is appropriate in an explicit setting because small time increments limit the amount of
motion within a single increment.
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In an adaptive meshing increment the element formulations, boundary conditions, external loads,
contact conditions, etc. are handled first in a manner consistent with a pure Lagrangian analysis. Once
the Lagrangian motion is updated and mesh sweeps have been performed to find the new mesh, the
solution variables are remapped by performing an advection sweep. The advection sweep accounts for
the advective terms in the momentum balance and continuity equations.
Advection methods for element variables
Element and material state variables must be transferred from the old mesh to the new mesh in each
advection sweep. The number of variables to be advected depends on the material model and element
formulation; however, stress, history variables, density, and internal energy are always solution
variables. Two methods are available for the advection of element variables: the default second-order
method based on the work of Van Leer (Van Leer, 1977) and a first-order method based on donor cell
differencing.
Both advection methods incorporate the concept of upwinding. They also conserve the element
variables in an integral sense when mapping from the old mesh to the new mesh (that is, the value of
any solution variable integrated over the domain is unchanged by adaptive meshing). Using a
conservative algorithm to advect the element density and the internal energy automatically ensures
conservation of mass and energy for an adaptive mesh domain without Eulerian boundary regions.
Both advection methods are also monotonic and consistent. A method is monotonic if an element
quantity with a monotonic, increasing spatial distribution over a portion of the old mesh remains as
such in the new mesh. A method is consistent if, when solution variables are advected to a new mesh
that is identical to the old mesh, all element quantities remain unchanged.
Second-order advection
Second-order advection is used by default for all adaptive mesh domains. It is recommended for all
problems, ranging from quasi-static to transient dynamic shock. An element variable, Á, is remapped
from the old mesh to the new mesh by first determining a linear distribution of the variable in each old
element, as illustrated in Figure 7.6.3-2 for a simple one-dimensional mesh.
Figure 7.6.3-2 Second-order advection.
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The linear distribution of Á in the middle element depends on the values of Á in the two adjacent
elements. To construct the linear distribution:
1. A quadratic interpolation is constructed from the constant values of Á at the integration points of
the middle element and in its adjacent elements.
2. A trial linear distribution, Átrial , is found by differentiating the quadratic function to find the slope
at the integration point of the middle element.
3. The trial linear distribution in the middle element is limited by reducing its slope until its
minimum and maximum values are within the range of the original constant values in the adjacent
elements. This process is referred to as flux-limiting and is essential to ensure that the advection is
monotonic.
Once the flux-limited linear distributions are determined for all elements in the old mesh, these
distributions are integrated over each new element. The new value of the variable is found by dividing
the value of each integral by the new element volume. (See Figure 7.6.3-3 for a first-order example of
this calculation.)
Set the ADVECTION parameter on the *ADAPTIVE MESH CONTROLS option equal to SECOND
ORDER to specify explicitly that the second-order advection method should be used to remap element
variables.
Usage: *ADAPTIVE MESH CONTROLS, NAME=name, ADVECTION=SECOND ORDER
First-order advection
First-order advection is simple and computationally efficient; however, it tends to diffuse sharp
gradients over time, especially in transient dynamic analyses or other problems that require fairly
frequent adaptive meshing. Therefore, this technique should be used only as a computationally
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efficient alternative for quasi-static simulations that do not require frequent adaptive meshing.
Figure 7.6.3-3 illustrates the first-order method for a portion of a one-dimensional mesh. An element
variable, Á, is remapped from the old mesh to the new mesh by first assuming a constant value of the
variable for each old element. These values are then integrated over each new element. The new value
of the variable is found by dividing the value of each integral by the new element volume.
Figure 7.6.3-3 First-order advection.
Set the ADVECTION parameter on the *ADAPTIVE MESH CONTROLS option equal to FIRST
ORDER to specify that the first-order advection method should be used to remap element variables.
Usage: *ADAPTIVE MESH CONTROLS, NAME=name, ADVECTION=FIRST ORDER
Momentum advection
Nodal velocities are computed on a new mesh by first advecting momentum, then using the mass
distribution on the new mesh to calculate the velocity field. Advecting momentum directly ensures that
momentum is conserved properly in the adaptive mesh domain during remapping. Two methods are
available for advecting momentum: the default element center projection method and the half-index
shift method (Benson, 1992). Both methods are applicable for all adaptive mesh applications.
Element center projection method
The element center projection method is the default method used to advect momentum and requires the
fewest numerical operations. The element momentum is calculated first for the old mesh based on the
mass and velocity of the element nodes. The element momentum is then advected from the old mesh to
the new mesh by the same first- or second-order algorithms used for advecting element variables.
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Finally, the element momentum on the new mesh is assembled at the nodes using a projection. The
element center projection method requires the advection of only two or three extra variables in two
dimensions or three dimensions, respectively.
The MOMENTUM ADVECTION parameter on the *ADAPTIVE MESH CONTROLS option can be
set equal to ELEMENT CENTER PROJECTION to request explicitly the most computationally
efficient momentum advection method.
Usage: *ADAPTIVE MESH CONTROLS, NAME=name,
MOMENTUM ADVECTION=ELEMENT CENTER PROJECTION
Half-index shift method
The half-index shift method is computationally more intensive than the element center projection
method, but it may result in less wave dispersion for some problems. This method first shifts each of
the nodal momentum variables from the nodes surrounding an element to the element center. The
shifted momentum variables are then advected from the old mesh to the new mesh by the same first- or
second-order algorithms used for advecting element variables, providing momentum variables at the
center of the new elements. Finally, the momentum variables at the element centers in the new mesh
are shifted back to the nodes. The half-index shift method requires the advection of 8 or 24 extra
variables in two or three dimensions, respectively, which can increase the cost of each advection
sweep significantly.
Set the MOMENTUM ADVECTION parameter on the *ADAPTIVE MESH CONTROLS option equal
to HALF INDEX SHIFT to specify that the half-index shift method should be used for momentum
advection.
Usage: *ADAPTIVE MESH CONTROLS, NAME=name,
MOMENTUM ADVECTION=HALF INDEX SHIFT
Additional references
· Benson, D. J., "Momentum Advection on a Staggered Mesh," Journal of Computational Physics,
vol. 100, pp. 143-162, 1992.
· Van Leer, Bram, "Towards the Ultimate Conservative Difference Scheme III. Upstream-centered
Finite-Difference Schemes for Ideal Compressible Flow," Journal of Computational Physics, vol.
23, pp. 263-275, 1977.
· Van Leer, Bram, "Towards the Ultimate Conservative Difference Scheme IV. A New Approach
to Numerical Convection," Journal of Computational Physics, vol. 23, pp. 276-299, 1977.
7.6.4 Output and diagnostics for adaptive meshing
This section explains the output and diagnostic messages that are available for adaptive meshing
simulations.
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References
· ``Output to the output database, '' Section 4.1.3
· ``Adaptive meshing: overview,'' Section 7.6.1
· ``Defining adaptive mesh domains,'' Section 7.6.2
· *ADAPTIVE MESH
· *ADAPTIVE MESH CONTROLS
· *DIAGNOSTICS
· *TRACER PARTICLE
Overview
Output for adaptive meshing:
· can be used to verify the automatic splitting of user-defined domains, the formation of Lagrangian
edges and corners, the formation of geometric edges and corners, and the determination of
nonadaptive nodes;
· must be interpreted carefully, since the values of output variables at specific locations in the mesh
are no longer linked to values at particular material points;
· can include the definition of tracer particles, which follow material points and allow the user to
examine the trajectory of those points and plot material time histories of all element and nodal
variables at those points; and
· can include diagnostic information on the efficiency of adaptive meshing and the accuracy of
advection.
Verifying the model
Output that can be used to verify adaptive meshing models is available in the data ( .dat) file and in
the output database ( .odb) (see ``Output,'' Section 4.1.1, for details on these files).
Element sets
When user-defined adaptive mesh domains are split by ABAQUS/Explicit, the elements that compose
the new subdivided domains are printed to the data ( .dat) file.
New element sets are created and written to the output database ( .odb) for all adaptive mesh domains.
The name of the element set created for each domain is the user-defined name, plus the number of the
subdivision (1 if no subdivisions were created), plus the step number. For example, if the user-defined
adaptive mesh domain specified with ELSET=domain_name spanned three disjoint parts,
ABAQUS/Explicit would subdivide the user-defined domain into three domains and create three
element sets in the output database ( .odb) for the first step: domain_name -1-1, domain_name -2-1,
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and domain_name -3-1.
ABAQUS/Viewer can be used to verify the creation of the subdivided domains.
Edges and nonadaptive nodes
ABAQUS/Explicit automatically forms Lagrangian edges and corners and identifies nonadaptive nodes
based on the topology of the adaptive mesh domains, connections to nonadaptive domains, and
boundary regions specified by the user. Furthermore, geometric edges and corners are formed
automatically based on the initial geometry and the value of the initial feature angle. See ``Defining
adaptive mesh domains,'' Section 7.6.2. Lagrangian edges, geometric edges and corners, and
nonadaptive nodes (including Lagrangian corners) are output to the data ( .dat) file for each adaptive
mesh domain.
In addition, up to three node sets will be created in the output database ( .odb) for each adaptive mesh
domain in each step. The names of the node sets are created by concatenating the following
information:
· the domain element set name;
· the number of the subdivision (1 if no subdivisions were created);
· the letters LE for Lagrangian edge, GE for geometric edge or corner, or NA for nonadaptive nodes
(including Lagrangian corners); and
· the step number.
For example, if a user-defined three-dimensional adaptive mesh domain specified with
ELSET=domain_name is subdivided automatically into two adaptive mesh domains,
ABAQUS/Explicit will generate up to six node sets in the output database for the first step:
domain_name -1-LE-1, domain_name -1-GE-1, domain_name -1-NA-1, domain_name -2-LE-1,
domain_name -2-GE-1, and domain_name -2-NA-1.
Since boundary regions are separated by corners, not edges, in two dimensions, node sets will not be
created for Lagrangian edges in two-dimensional adaptive mesh domains. The Lagrangian corners are
included in the nonadaptive ( NA) node set, as for three-dimensional domains.
ABAQUS/Viewer can be used to verify the creation of Lagrangian edges and corners, geometric edges
and corners, and nonadaptive nodes.
Interpreting results
When adaptive meshing is not performed, the finite element mesh follows the material, which enables
a straightforward interpretation of analysis results. The user can visualize deformation and material
motion by studying the motion of the mesh. Each nodal and element output variable corresponds to a
specific material location, because the mesh is fixed to the same material point throughout time.
Once adaptive meshing takes place, the locations of mesh and material points deviate, and analysis
results must be interpreted accordingly. The motion of the mesh on the interior of an adaptive mesh
domain represents the composite effects of the material motion and adaptive meshing. The motion of
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the mesh and the motion of the material on Lagrangian and sliding boundary regions is identical in the
direction normal to the boundary but not in the direction tangential to it.
Nodal variables
When adaptive meshing is performed, a material point that is coincident with a node at the beginning
of the step may not remain coincident with that node throughout the step. Values of displacement and
current coordinates represent the motion of the node, not necessarily the motion of the material. All
other nodal variables--including velocity, acceleration, and reaction forces--represent the value of the
variable for the material particle at the current location of the node. Contour or vector plots of these
variables will show their correct spatial distribution and are, therefore, meaningful. However, time
histories of nodal variables for nodes that undergo adaptive meshing are generally not meaningful. In
steady-state problems, though, a velocity or acceleration time history based at a fixed spatial location
rather than at a specific material point may be useful.
Element variables
Similarly, when adaptive meshing is performed, a material particle that is coincident with an element
integration point at the beginning of a step may not remain so throughout the step. Therefore, element
integration point variables do not necessarily represent values at the same material point throughout
the step. Contour or vector plots of element integration point variables are meaningful for the same
reasons described for nodal variables. However, time histories are based at the spatial location of the
element integration point and not at a specific material point.
Whole element variables have a similar interpretation.
Tracking nodal or element variables at material points
Tracer particles can be defined to track material points in an adaptive mesh domain. These particles
can also be used to obtain time histories of nodal or element integration point variables that correspond
to the time variation of the variable at a specific material point. Tracer particles are defined by using
the *TRACER PARTICLE option (see ``Output to the output database, '' Section 4.1.3). Node and
element variable output can be requested for tracer particle sets to examine the trajectory of material
particles or to obtain material time histories. Output for tracer particles can be written only to the
output database ( .odb).
Using tracer particles in Lagrangian domains
In most adaptive meshing simulations using Lagrangian domains, the nodes and elements in the
domain correspond neither to a specific spatial location nor to a specific material point or volume.
Thus, time histories of variables at nodes and at element integration points are often physically
meaningless in a Lagrangian adaptive mesh domain. Tracer particles should be defined to view time
history information. Tracer particles can also be used to visualize the motion of the material.
The initial location of a tracer particle is defined to be coincident with a node, termed the parent node.
Tracer particles are defined in sets by defining multiple parent nodes or node sets. Use the *TRACER
PARTICLE option to indicate the nodes whose current locations correspond to the initial location of
the tracer particles; use the TRACER SET parameter to identify this set for use in output requests.
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Tracer particles are released from their parent nodes repeatedly at specified intervals during the step in
which they are defined. The particles follow material points for the remainder of that step and in all
subsequent steps.
Tracer particles are typically defined only on adaptive mesh domains, although they can be defined on
nodes connected to any low-order solid element in the model. For analyses in which adaptive meshing
is not performed until later steps, tracer particles can be defined in nonadaptive domains at the
beginning of an analysis and will be tracked continuously as the domain becomes adaptive. Similarly,
tracer particles will be tracked from domain to domain if adaptive mesh domain topologies change
from step to step.
Usage: *TRACER PARTICLE, TRACER SET=tracer_set_name
Using tracer particles in Eulerian domains
Time histories at nodes and element integration points in an Eulerian domain may have physical
meaning at points where spatial adaptive mesh constraints are applied. For example, the time variation
of equivalent plastic strain in elements along an outflow Eulerian boundary acts as a spatial time
history of that variable and can be used to evaluate whether the process has reached a steady-state
solution.
Tracer particles can be defined to evaluate the material time history of variables at a material point as it
flows through the Eulerian domain. Tracer particles can also be used to evaluate the trajectory and path
of material points as they pass through the domain.
Tracer particles can be assigned to any parent node in an Eulerian adaptive mesh domain. If a tracer
particle reaches an outflow boundary and material continues to flow out, the tracer particle will no
longer be tracked and all output history variables associated with the tracer particle will be zero after
deactivation.
When material flow through the mesh domain is significant, sets of tracer particles can be released
from the current locations of the parent nodes at multiple times during the step. Each release of tracer
particles is referred to as particle birth. After particle birth the tracer particles follow the motion of the
material regardless of the motion of the mesh. Use the PARTICLE BIRTH STAGES parameter on the
*TRACER PARTICLE option to indicate the number of particle birth stages in a step. These stages
will be evenly spaced throughout the time period of the step.
For example, a tracer particle set can be defined such that all nodes along an inflow Eulerian boundary
are parent nodes. Multiple birth stages can be specified so that a set of tracer particles is released from
the mesh at the inflow boundary periodically during the step. If enough birth stages are defined, the
domain will eventually be spanned with tracer particles as material flows from the inflow boundary to
the outflow boundary.
Usage: *TRACER PARTICLE, TRACER SET=tracer_set_name, PARTICLE BIRTH STAGE
Monitoring the progress of adaptive meshing
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Diagnostic information can be written to the message ( .msg) file to track the efficiency and accuracy
of adaptive meshing. The level of diagnostic output can be selected using the *DIAGNOSTICS option.
Obtaining a summary at the end of a step
By default, a summary of adaptive meshing information for each adaptive mesh domain will be written
to the message (.msg) file at the end of each step. This summary information includes:
· the average percentage of nodes moved,
· the maximum percentage of nodes moved,
· the minimum percentage of nodes moved, and
· the average number of advection sweeps.
Each value is calculated for a single adaptive mesh domain over all adaptive mesh increments. The
cost of advection is approximately proportional to the percentage of nodes moved, since variables are
not advected for elements that have not been relocated during adaptive meshing.
The ADAPTIVE MESH parameter on the *DIAGNOSTICS option can be set equal to STEP
SUMMARY to request a summary for each adaptive mesh domain at the end of each step.
Usage: *DIAGNOSTICS, ADAPTIVE MESH=STEP SUMMARY
Obtaining a summary for every adaptive mesh increment
In addition to the step summary information, the following diagnostics can be obtained for each
adaptive mesh domain at every adaptive mesh increment:
· the percentage of nodes moved, and
· the number of advection sweeps.
To obtain summary information at the end of the step and at every adaptive mesh increment, set the
ADAPTIVE MESH parameter on the *DIAGNOSTICS option equal to SUMMARY.
Usage: *DIAGNOSTICS, ADAPTIVE MESH=SUMMARY
Obtaining details of advection accuracy for every adaptive mesh
increment
The following detailed diagnostic information can also be written to the message ( .msg) file to track
the accuracy of the advection:
· mass and momentum before and after advection, and
· percentage volume change.
Set the ADAPTIVE MESH parameter on the *DIAGNOSTICS option equal to DETAIL to request the
most detailed diagnostics, which include advection accuracy measures and summary information for
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each adaptive mesh domain, reported at every adaptive mesh increment.
Usage: *DIAGNOSTICS, ADAPTIVE MESH=DETAIL
Suppressing adaptive mesh diagnostics
To suppress output of all adaptive mesh diagnostic information, set the ADAPTIVE MESH parameter
on the *DIAGNOSTICS option equal to OFF.
Usage: *DIAGNOSTICS, ADAPTIVE MESH=OFF
7.6.5 Modeling techniques for Eulerian adaptive mesh domains
This section presents techniques for modeling Eulerian domains using adaptive meshing in
ABAQUS/Explicit.
References
· ``Adaptive meshing: overview,'' Section 7.6.1
· ``Defining adaptive mesh domains,'' Section 7.6.2
· *ADAPTIVE MESH CONSTRAINT
Overview
An Eulerian adaptive mesh domain:
· is used to model material flowing through the mesh; and
· typically has two Eulerian boundary regions, one inflow and one outflow, connected by
Lagrangian and/or sliding boundary regions.
The correct combination of mesh constraints and material boundary conditions applied to an Eulerian
boundary region depends on whether the region acts as an inflow or an outflow boundary. The region
types and mesh constraints assigned to the boundary regions that are connected to the Eulerian
boundary regions must be chosen to simulate the correct physical behavior as well.
The adaptive meshing technique in ABAQUS/Explicit is robust if the mesh is underconstrained: the
modeling techniques presented in this section are intended to provide guidance in properly defining
Eulerian models.
Adaptive mesh constraints on Eulerian boundaries
Adaptive mesh constraints should be applied normal to an Eulerian boundary region; otherwise, the
motion of the mesh on the boundary is ambiguous. If no mesh constraints are applied normal to the
boundary, ABAQUS/Explicit will treat the region as if it were sliding, and the mesh will follow the
material normal to the boundary.
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Although there are no restrictions on specifying adaptive mesh constraints at nodes on an Eulerian
boundary region, the following guidelines should be followed in most cases:
· Mesh constraints should be applied to every node on the Eulerian boundary region, including the
corners and edges.
· Mesh constraints should be applied either only normal to the Eulerian boundary region or in every
direction. Mesh constraints should not be specified in only the direction tangential to an Eulerian
boundary region; such constraints are ambiguous and may result in undesirable motion of the mesh
at the boundary.
Loads and boundary conditions on Eulerian boundaries act on the material that instantaneously
coincides with the mesh at the surface. When used in combination with spatial adaptive mesh
constraints, physically meaningful Eulerian flow conditions can be defined.
Defining inflow Eulerian boundaries
The material flowing into an adaptive mesh domain through an Eulerian boundary will have the same
stress and material state as the material in the elements immediately adjacent to the boundary.
Therefore, it is important to maintain the stress and material state in those elements at the desired
values (which in many cases will be zero, to simulate stress-free material entering the Eulerian
domain). To accomplish this goal:
· position the inflow boundary far enough upstream from high solution gradients to ensure that the
response at the inflow boundary is smooth, and
· apply sufficient mesh and material constraints at the boundary (as described later in this
section).
To be physically meaningful, the size and shape of the inflow boundary region must be maintained. For
example, applying sufficient constraints is crucial for steady-state process simulations where the
cross-section of the workpiece entering the adaptive mesh domain is known and affects the response
downstream. The types of constraints appropriate for an inflow boundary depend on whether the
precise location of the inflow boundary region is known or whether it is part of the solution.
Known inflow boundary location
In many problems the area, shape, and position of the inflow boundary are known a priori. For
example, in the steady-state analysis of a forward extrusion process, an inflow Eulerian boundary can
be used to model the flow of material into the adaptive mesh domain. The size of the inflow boundary
is based on the known billet cross-section, and the location of the inflow boundary is fixed because of
the confined conditions on the material.
When the area, shape, and location of the inflow boundary are known, both material and mesh
constraints should be applied. Figure 7.6.5-1 shows a typical model setup for a two-dimensional
forward extrusion problem where either a prescribed mass flow rate or a prescribed uniform pressure is
applied to a known inflow boundary. Use the *BOUNDARY option at all nodes on the inflow
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boundary region to prescribe material constraints in the directions tangential to the boundary surface.
Preventing motion of the material tangential to the inflow boundary helps to maintain the stress and
material state of the elements adjacent to the Eulerian boundary.
Figure 7.6.5-1 Known inflow boundary.
Use the *ADAPTIVE MESH CONSTRAINT option at all nodes on the inflow boundary to apply mesh
constraints in the normal direction. In addition, apply mesh constraints in all tangential directions at
the edges and corners surrounding the Eulerian boundary region. These constraints fix the location and
size of the cross-sectional area at the inflow boundary.
If a nonuniform boundary condition or load is applied to the material at the inflow boundary or if the
initial material state in the elements adjacent to the boundary is nonuniform in the tangential direction,
apply tangential mesh constraints to the nodes strictly in the interior of the Eulerian boundary
region.
Although the application of mesh and material constraints tangential to and along the edges and
corners of an inflow Eulerian boundary may appear to be redundant, they are actually independent. For
example, consider a long billet with a variable cross-section, as shown in Figure 7.6.5-2.
Figure 7.6.5-2 Modeling a billet with a variable cross-section.
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The adaptive mesh domain, with its inflow and outflow Eulerian boundary regions, is assumed to
represent a portion of the billet along its length. The entire billet moves with a rigid body velocity
along its length (x-direction) so that material flows into one Eulerian boundary and out the other.
Boundary conditions are applied to the material at the inflow boundary to maintain this velocity. Mesh
constraints are applied normal to the inflow and outflow boundary regions. The mesh constraint
applied in the y-direction at node N is used to prescribe the known variable incoming cross-section of
the material. The motion of this node does not affect the velocity field of the material entering the
domain.
Unknown inflow boundary location
Sometimes, the location of the inflow boundary region is known only approximately; its precise
location will be determined from the solution. For these problems, apply adaptive mesh constraints
only in the direction normal to the Eulerian boundary region. In the absence of tangential mesh
constraints at the edges and corners of the Eulerian boundary region, ABAQUS/Explicit will move
these edges and corners with the material in the tangential direction but with the mesh constraints in
the normal direction. Therefore, material constraints should be applied using the *MPC or
*EQUATION options to preserve the cross-sectional area of the inflow boundary.
For example, consider a steady-state rolling simulation with multiple rollers in an asymmetric
configuration, as shown in Figure 7.6.5-3.
Figure 7.6.5-3 Unknown inflow boundary location.
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It may be impractical to extend the analysis domain as far as the guides on the upstream side, but
spatially fixing the inflow boundary at an arbitrary position in the y- and z-directions may cause
unrealistic stress on the workpiece as it finds an equilibrium position between the rollers. Mesh
constraints are applied normal to the Eulerian boundary region to fix the position of the inflow
boundary relative to the rollers in the x-direction. Material constraints (applied with the PIN MPC
option) are used to ensure that material enters the domain at a uniform velocity and that the
cross-section does not rotate. The material constraints will maintain the cross-sectional shape of the
section while allowing it to move laterally to the correct equilibrium position. Since tangential mesh
constraints are not used, the mesh will follow the material in the directions tangential to the Eulerian
boundary region.
Defining outflow Eulerian boundaries
Typically, adaptive mesh constraints should be applied only in the direction normal to the surface on
an Eulerian boundary region that acts as an outflow boundary. No tangential mesh constraints should
be applied to the edges or corners of an outflow boundary adjacent to a Lagrangian (or sliding)
boundary region acting as a free surface. In contrast to inflow boundaries, the cross-section of an
outflow boundary adjacent to a free surface is determined by the solution in the domain. At the edge or
corner where an Eulerian boundary region meets a Lagrangian or sliding boundary region, ABAQUS
will satisfy the applied mesh constraint normal to the Eulerian boundary region and the inherent mesh
constraint normal to the Lagrangian or sliding boundary region simultaneously, thus correctly handling
the evolution of the free surface adjacent to the outflow boundary. Figure 7.6.5-4 shows the evolution
of an outflow boundary from t0 to t1 , where material continues to flow through the outflow boundary.
Figure 7.6.5-4 ABAQUS will respect the free surface at an Eulerian outflow boundary.
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The mesh constraint normal to the Eulerian outflow boundary is applied by moving node N along the
free surface of the material, so that the outflow boundary "expands" with the material arriving from
upstream. Although not shown in the figure, mesh smoothing causes all other nodes on the outflow
boundary, with the exception of the node on the symmetry plane, to move up toward node N as the
boundary expands.
No special material boundary conditions are required at outflow Eulerian boundaries. Boundary
conditions tangential to the outflow boundary are recommended only if they are the same as those
defined upstream (e.g., a symmetry plane running along the length of an Eulerian domain). However,
to improve convergence to the steady-state solution in steady-state process simulations, it is often
useful to constrain the material velocity to be uniform normal to the outflow boundary using the *MPC
or *EQUATION options.
Defining Eulerian boundary regions that act as both inflow and
outflow boundaries
Although it is rarely appropriate, an Eulerian boundary region can act as both an inflow and an outflow
boundary at different times during the same analysis step. Adaptive mesh constraints and material
boundary conditions at such a boundary should be chosen to be physically meaningful for both inflow
and outflow situations.
For each node on the edges and corners of an Eulerian boundary region that does not have mesh
constraints tangential to the boundary surface, ABAQUS/Explicit will determine in each adaptive
mesh increment whether the boundary at the node is acting as an inflow or an outflow boundary. If an
inflow condition is detected, the node will move with the material in the tangential direction but with
the mesh constraints in the normal direction. If an outflow condition is detected, the movement of the
node will both follow the adjacent Lagrangian boundary region and satisfy the mesh constraint normal
to the Eulerian boundary region.
Lagrangian versus sliding boundary regions on Eulerian
domains
Many applications using Eulerian adaptive mesh domains, including the simulation of steady-state
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processes, have a primary direction of material flow and use a control volume approach to model the
process zone. These problems usually include two Eulerian boundary regions, representing an inflow
boundary and outflow boundary. The remaining surfaces between the Eulerian boundaries can be
either Lagrangian or sliding boundary regions. Determining which type of boundary region to use
between the two Eulerian boundary regions depends on the type of load or boundary condition that is
required:
· Use REGION TYPE=SLIDING to define boundary conditions or loads that act at a spatial location
on a portion of the surface along the length of the control volume. Apply adaptive mesh constraints
to fix the mesh spatially in the flow direction (and possibly in the direction transverse to the flow).
For example, a distributed pressure can be applied around the circumference of the control
volume, as shown in Figure 7.6.5-5.
Figure 7.6.5-5 Applying a spatial pressure load to a portion of the surface along the length of an
Eulerian control volume.
The distributed pressure load is defined using a sliding boundary region. Mesh constraints are
applied to fix the boundary region spatially in the flow direction. Similarly, a concentrated load
could be applied to a specific spatial location to model the effect of a very sharp body pressing into
the workpiece at a known location with a known force.
· Use REGION TYPE=SLIDING to define boundary conditions or loads that act along the entire
length of the Eulerian control volume between the inflow and outflow boundaries and act in a
spatial manner transversely to the flow. If the load acts on only a portion of the surface in the
transverse direction, it may be necessary to apply mesh constraints in the direction transverse to
the flow. For example, a boundary condition that acts as a knife edge along the length of the
domain is shown in Figure 7.6.5-6. Mesh constraints are applied in the transverse direction (and, if
the line of application is curved, along the line) to keep the boundary condition fixed spatially.
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Figure 7.6.5-6 Applying a boundary condition along the entire length of the Eulerian control
volume.
· Use REGION TYPE=LAGRANGIAN (default) to define boundary conditions or loads that act
along the entire length of the surface of the Eulerian control volume between the inflow and
outflow boundary and act in a Lagrangian manner transversely to the flow. In three dimensions,
symmetry conditions should typically act in a Lagrangian manner transverse to the flow direction.
In many cases geometric edges will prevent material from flowing off the symmetry plane and onto
the free surface. However, since geometric edges can be deactivated as surfaces flatten, Lagrangian
boundary regions should be used to define the symmetry planes for these types of problems. In
Figure 7.6.5-5 quarter-symmetry is assumed, and the symmetry planes are defined using
Lagrangian boundary regions. The resulting Lagrangian edges that run from one Eulerian boundary
to the other separate the symmetry planes from the free surface.
· Boundary conditions or loads that act on only a specific portion of the material between the inflow
and outflow boundaries cannot usually be modeled for problems utilizing Eulerian control
volumes. Since the mesh underneath the load or boundary condition must follow the material, it
will eventually be restricted by the Eulerian boundary. This treatment of loads and boundary
conditions is not usually consistent with a steady-state model and should not arise in practical
simulations using Eulerian adaptive mesh domains.
7.7 Steady-state detection
7.7.1 Steady-state detection
The *STEADY STATE DETECTION option is used in conjunction with the *STEADY STATE
CRITERIA option to define criteria for halting a uni-directional simulation when a steady-state
condition has been reached.
References
· *STEADY STATE DETECTION
· *STEADY STATE CRITERIA
· ``Output,'' Section 4.1.1
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Overview
Steady-state detection can be used to:
· detect the time in a quasi-static uni-directional simulation when a steady-state condition has been
reached and then terminate the simulation; and
· output quantities that are useful in tracking the progress of a uni-directional simulation.
Introduction
Many types of uni-directional processes are used to transform preformed shapes into forms more
suitable for further processing. The most common examples are rolling, wire drawing, and extrusion
processes. Since the processes are usually carried out at low speeds, explicit dynamic procedures such
as those in ABAQUS/Explicit are often used to model the processes as quasi-static. The analyses
usually consist of a workpiece that is formed into a desired shape by any number of rollers or other
forming surfaces along a primary direction. The forming surfaces are usually modeled as rigid bodies.
For rolling simulations the rigid body reference node is usually defined at the center of the roller. The
mesh of the workpiece is often extruded and may be constructed of multiple layers of material. As the
workpiece progresses through the forming surfaces, the shape eventually reaches a constant state. The
position where the workpiece exits the final forming surface is referred to as the exit plane and is
usually aligned with the rigid body reference node of the final forming surface. As soon as this
constant shape is reached, the analysis is considered to have reached steady state. The force and torque
on the final forming surfaces at this steady-state condition have also reached constant values or
oscillate about constant values. A significant computational savings can be achieved by detecting the
steady-state condition and halting the analysis either immediately or as soon as the steady-state
cross-section progresses beyond the exit plane to a position referred to as the cutting plane.
Mesh requirements
The workpiece mesh is required to meet certain conditions for use with the steady-state detection
capability. First, the mesh must be topologically regular in the primary direction. In other words, the
mesh should consist of multiple planes of elements with each plane being similar to its adjacent
leading and trailing planes in that it contains the same number of elements and the same element
topology in the cross-section. Furthermore, each element in a plane is connected to elements in leading
and trailing planes that reference the same material and section properties. Therefore, meshes with
multiple materials and section properties are permitted, but any row of elements in the primary
direction must be of the same type and must reference the same material and section properties (see
Figure 7.7.1-1).
Figure 7.7.1-1 Acceptable multiple-material extruded mesh for a rolling analysis.
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Steady-state detection criteria sampling
To determine if steady state has been reached, steady-state detection ``norms" are calculated, which
represent an averaged value of a variable of interest over the cross-section of the workpiece as material
passes through a given position along the primary direction. This position is referred to as the exit
plane and usually coincides with the position of the last rigid forming tool (e.g., roller) that the
workpiece passes through. The normal of the exit plane is by definition coincident with the primary
direction. The time intervals at which the norms are sampled vary depending on whether the rolling
analysis is modeled in an Eulerian or Lagrangian manner.
Sampling in a Lagrangian analysis
In a Lagrangian based analysis (which may include adaptive meshing employed on a Lagrangian
domain) the steady-state norms are calculated as the trailing control node of each plane of elements
passes the exit plane. Figure 7.7.1-2 illustrates the control node definitions.
Figure 7.7.1-2 Control node positioning.
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The time period of norm sampling is, therefore, based on the frequency at which the planes of elements
cross the exit plane. For output purposes the values of the norms are assumed to remain constant
between the times at which successive control nodes pass the exit plane.
Sampling in an Eulerian analysis
An Eulerian analysis employs a control volume approach in which material is drawn from an inflow
Eulerian boundary and is pushed or pulled out through an outflow boundary. Adaptive mesh domains
are defined on the workpiece, and sliding boundary regions are defined to model contact between the
workpiece and forming tools such as rollers. See ``Adaptive meshing: overview,'' Section 7.6.1, for
details of adaptive meshing techniques. The mesh remains relatively stationary while the material
moves through the exit plane. The time period between sampling is, therefore, based on the progress of
the material moving through the exit plane. To determine a time period in a manner consistent with the
Lagrangian case, the sampling period is determined by dividing the characteristic element length of the
workpiece by the speed of the material flow. This period is roughly the time it takes for material to
pass through an element of typical size.
Steady-state detection norm definitions
An individual norm is considered to have achieved steady state if its relative change in value over
three consecutive planes does not exceed a tolerance. The norm tolerances can be provided by the user;
or by leaving the entry blank, default values of tolerances will be chosen by ABAQUS/Explicit. The
norms can be output by requesting their identifiers listed in the definitions below.
Equivalent plastic strain norm
The plastic strain norm of a plane of elements is defined by summing the product of the equivalent
plastic strain and the element volume of each element on the plane, then dividing by the total volume
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of the elements on the plane. This norm provides a weighted average of the equivalent plastic strain for
the plane. The identifier for the equivalent plastic strain norm is SSPEEQ.
Spread norm
The spread norm of a plane of elements is computed as the largest of the area moments of inertia of the
cross-section of the plane. In determining the spread norm, the cross-section of the plane of elements is
determined by projecting the element faces whose normals originally coincided with the primary
direction onto the exit plane. The area moments of inertia are then determined about the centroid of the
section in the directions of the original principal axes of the cross-section. The identifier for the spread
norm is SSSPRD.
Force norm
The force norm is computed by averaging the magnitude of the force at the rigid body reference node
of a forming tool, such as the exit roller, over the time period between sampling points. The rigid body
reference node and force direction are provided by the user. The identifier for the force norm is
SSFORC.
Torque norm
The torque norm is computed by averaging the magnitude of the torque at the rigid body reference
node of a forming tool, such as the exit roller, over the time period between sampling points. The rigid
body reference node and torque direction are provided by the user. The identifier for the torque norm is
SSTORQ.
Requesting steady-state detection during an analysis
The *STEADY STATE DETECTION and *STEADY STATE CRITERIA options must be applied
together to define criteria that are used to determine if steady state has been reached.
ABAQUS/Explicit will halt the analysis based on the achievement of steady state.
Steady-state detection
The *STEADY STATE DETECTION option is used to define the elements in the workpiece, the
primary direction of the workpiece, the cutting position, and the type of sampling used. An element set
containing the elements of the workpiece is assigned to the ELSET parameter. The primary direction is
defined by entering the direction cosines with respect to the global Cartesian coordinate system. The
cutting position is defined by entering the global coordinates of a point lying in the cutting plane. The
normal to the cutting plane is assumed to coincide with the primary direction. Once steady state has
been detected, the analysis is terminated when the plane of the workpiece that was first detected to
have reached steady state has progressed to the cutting plane. The sampling method used is based on
the value assigned to the SAMPLING parameter.
Requesting sampling as elements pass the exit plane for a
Lagrangian analysis
To request that all steady-state norms be calculated as each plane of elements crosses the exit plane, set
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the SAMPLING parameter equal to PLANE BY PLANE.
Usage: *STEADY STATE DETECTION, ELSET=elset, SAMPLING=PLANE BY PLANE
Requesting sampling at uniform intervals for an Eulerian analysis
To request that all steady-state norms be calculated at an interval based on the time required for
material to progress the length of an average element, set the SAMPLING parameter equal to
UNIFORM.
Usage: *STEADY STATE DETECTION, ELSET=elset, SAMPLING=UNIFORM
Steady-state criteria
The *STEADY STATE CRITERIA option is used to define the criteria that must be met for steady
state to be achieved. The *STEADY STATE CRITERIA option can be entered any number of times.
Only when all of the criteria defined under any one *STEADY STATE CRITERIA option have been
satisfied will the analysis be considered to have reached steady state.
On the data line of the *STEADY STATE CRITERIA option, specify the norm type identifier, norm
tolerance, and the global coordinates of a point on the exit plane. For force and torque norms, also
enter the rigid body reference node of the forming tool at the exit plane and the direction cosines of the
force or torque. Exit planes can be defined separately for each norm definition.
Usage: Use the following options:
*STEADY STATE DETECTION, ELSET=elset,
SAMPLING=PLANE BY PLANE or UNIFORM
*STEADY STATE CRITERIA
*STEADY STATE CRITERIA
...
For example, assume that two sets of criteria are of interest and that the analysis can be terminated as
soon as either is satisfied. The input might be as follows:
*STEADY STATE DETECTION, ELSET=sheet, SAMPLING=PLANE BY PLANE
1.0, 0.0, 0.0,
6.0, 0.0, 0.0
*STEADY STATE CRITERIA
SSPEEQ,.002, 5.0, 0.0, 0.0
SSSPRD,.002, 5.0, 0.0, 0.0
SSFORC,.005, 5.0, 0.0, 0.0, 1000, 1.0, 0.0, 0.0
SSFORC,.005, 5.0, 0.0, 0.0, 1000, 0.0, 1.0, 0.0
SSTORQ,.005, 5.0, 0.0, 0.0, 1000, 0.0, 0.0, 1.0
*STEADY STATE CRITERIA
SSPEEQ,.001, 5.0, 0.0, 0.0
SSSPRD,.001, 5.0, 0.0, 0.0
SSFORC,.010, 5.0, 0.0, 0.0, 1000, 0.0, 1.0, 0.0
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Material options
The *STEADY STATE DETECTION option is intended to be used with plasticity-based materials
since the equivalent plastic strain norm would be zero for nonplasticity-based material models.
Procedures
One steady-state detection definition is allowed per analysis. The definition can be entered in any step
and is continued through subsequent steps in an analysis. A steady-state detection definition cannot be
entered in an annealing step or continued through an annealing step.
Elements
The current steady-state detection capabilities support the use of C3D8R and C3D8RT elements only.
Output
The output variables SSPEEQn, SSSPRDn, SSFORCn, and SSTORQn are used to output the
equivalent plastic strain, spread, force, and torque norms, respectively. ABAQUS/Viewer can be used
to obtain history plots of each of the steady-state detection norm variables. Individual norms can be
output by requesting the norm number listed as n, which is based on the order in which the norms are
entered. Referring to the previous example, if the force norm of the second *STEADY STATE
CRITERIA option were to be requested, the output identifier would be SSFORC3. If a steady-state
detection norm is requested that does not include a norm number, SSFORC for example, all norms of
that type are output.
Once steady state has been detected, an element set is created automatically by ABAQUS/Explicit and
written to the output database consisting of the plane of elements that first satisfied the steady-state
criteria. The element set created is named SteadyStatePlane and can be viewed with ABAQUS/Viewer.
If no output requests are made to the output database, the element set SteadyStatePlane will not be
created.
Template
*HEADING
...
*ELSET, ELSET=WORKPIECE
*************************
*STEP
*DYNAMIC, EXPLICIT
Data line to specify the time period of the step
...
*STEADY STATE DETECTION, ELSET=WORKPIECE, SAMPLING=PLANE BY PLANE
Data line specifying rolling direction and cutting plane position
*STEADY STATE CRITERIA
Data lines specifying steady-state detection norm criteria
...
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*OUTPUT, HISTORY, TIME INTERVAL=1.E-6
*INCREMENTATION OUTPUT
SSPEEQ, SSSPRD, SSFORC, SSTORQ
...
*END STEP
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Part IV: Materials
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Materials: Introduction
8. Materials: Introduction
8.1 Introduction
8.1.1 Material library: overview
This chapter describes how to define material properties in ABAQUS/Explicit and contains brief
descriptions of each of the material definitions provided. Further details of the more advanced options
are provided in the Theory Manual.
Defining material properties
Material properties are defined by:
· selecting material options and defining them in a "material data block" ( ``Material data definition,''
Section 8.1.2); and
· combining complementary material models such as elasticity and plasticity (``Combining material
properties,'' Section 8.1.3).
A local coordinate system can be used for material calculations ( ``Orientations,'' Section 2.2.3). Any
anisotropic properties must be given in this local system.
Available material models
The material library in ABAQUS is intended to provide comprehensive coverage of both linear and
nonlinear, isotropic and anisotropic material models. ABAQUS/Explicit uses a subset of the material
models from the general ABAQUS library. The use of numerical integration in the elements, including
numerical integration across the cross-sections of shells and beams, provides the flexibility to analyze
the most complex composite structures.
Material behaviors fall into the following general categories:
· general properties (material damping, density, thermal expansion);
· elastic mechanical properties;
· inelastic mechanical properties;
· thermal properties;
· equations of state; and
· hydrostatic fluid properties.
Some of the mechanical response options offered are mutually exclusive: such options cannot appear
together in a single material model. Some options require the presence of other options; for example,
the plasticity option requires the linear elasticity option. Such requirements are discussed at the end of
each material model description, as well as in ``Combining material properties,'' Section 8.1.3.
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Materials: Introduction
Using material models with various element types
There are no general restrictions on the use of particular material definitions with solid, shell, and
beam elements. Any combination that makes sense is acceptable. The few restrictions that do exist are
mentioned when that particular property is described in the pages that follow. A section on the
elements available for use with a material model appears at the end of each material description.
Using complete material definitions
A material definition can include properties that are not meaningful for the elements or analysis in
which the material is being used. Such properties will be ignored. For example, a material definition
can include heat transfer properties (conductivity, specific heat) as well as stress-strain properties
(elastic moduli, yield stress, etc). When this material definition is used with stress/displacement
elements, the heat transfer properties are ignored by ABAQUS. This capability allows the user to
develop complete material definitions and to use them in any analysis.
8.1.2 Material data definition
A material definition begins with the *MATERIAL option.
References
· *MATERIAL
· ``Material library: overview,'' Section 8.1.1
· ``Combining material properties,'' Section 8.1.3
· ``Orientations,'' Section 2.2.3
· ``Input syntax rules,'' Section 1.2.1
Overview
A material definition in ABAQUS/Explicit:
· is specified in a "material data block," which can contain multiple material options;
· is assigned a name, which is used to refer to those parts of the model that are made of that
material;
· can have temperature and/or field variable dependence; and
· can be specified in a local coordinate system through the use of the *ORIENTATION option,
which is required if the material is not isotropic.
Material data blocks
Any number of materials can be defined in an analysis. Each material definition is specified in a data
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Materials: Introduction
block, which is initiated by a *MATERIAL option. The material definition continues until an option
that does not define material properties (such as another *MATERIAL option) is introduced, at which
point the material definition is assumed to be complete.
The *MATERIAL option is followed by any number of material property definition options, as
required, to specify the actual material behavior. For example, in a linear static stress analysis only one
material property option, *ELASTIC, may be needed, while in a more complicated analysis several
material properties may be required. The order of the material options is not important. All material
options within the data block are assumed to define the same material.
When giving material properties, "stress" means "true" (Cauchy) stress (force per current area) and
"strain" means logarithmic strain,
"=
Z
dl
= ln
l
µ
l
l0
¶
;
unless otherwise indicated.
Assigning a name to a material definition
A name must be assigned to each material definition by using the NAME parameter on the
*MATERIAL option. This name allows the material to be referenced from the element property
definition options, which assigns this material behavior to elements in the model.
Usage: *MATERIAL, NAME=name
Specifying material data as functions of temperature and
independent field variables
Material data are often specified as functions of independent variables such as temperature. Material
properties are made temperature dependent by specifying them at several different temperatures.
In some cases a material property can be defined as a function of variables calculated by ABAQUS; for
example, to define a work-hardening curve, stress must be given as a function of equivalent plastic
strain.
Material properties can also be dependent on "field variables" (variables that can represent any
independent quantity and are defined at the nodes, as functions of time, by the user). For example,
material moduli can be functions of weave density in a composite or of phase fraction in an alloy.
Material properties are specified as functions of field variables by using the DEPENDENCIES
parameter on the material definition options, as described below. The initial values of field variables
are given as initial conditions (see ``Initial conditions,'' Section 18.2.1) and can be modified as
functions of time during an analysis (see ``Predefined fields,'' Section 18.5.1). This capability is useful
if, for example, material properties change with time because of irradiation or some other precalculated
environmental effect.
Interpolation of material data
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Materials: Introduction
In the simplest case of a constant property, only this value is entered. When the material data are
functions of only one variable, the data must be given in order of increasing values of the independent
variable. ABAQUS then interpolates linearly for values between those given. The property is assumed
to be constant outside the range of independent variables given. Thus, the user can give as many or as
few input values as are necessary for the material model.
When material properties depend on several variables, the variation of the properties with respect to
the first variable must be given at fixed values of the other variables, in ascending values of the second
variable, then of the third variable, and so on. The data lines must always be ordered so that the
independent variables are given increasing values. This process ensures that the value of the material
property is completely and uniquely defined at any values of the independent variables upon which the
property depends. See ``Input syntax rules,'' Section 1.2.1, for further explanation and an example.
Example: Temperature-dependent linear isotropic elasticity
Figure 8.1.2-1 shows a simple, isotropic, linear elastic material, giving the Young's modulus and the
Poisson's ratio as functions of temperature.
Figure 8.1.2-1 Example of material definition.
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Materials: Introduction
In this case six sets of values are used to specify the material description. For temperatures that are
outside the range defined by µ1 and µ6 , ABAQUS assumes constant values for E and º. The dotted
lines on the graph represent the straight-line approximations that will be used for this model.
Example: Elastic-plastic material
Figure 8.1.2-2 shows an elastic-plastic material for which the yield stress is dependent on the
equivalent plastic strain and temperature.
Figure 8.1.2-2 Example of material definition with two independent variables.
In this case the second independent variable (temperature) must be held constant, while the yield stress
is described as a function of the first independent variable (equivalent plastic strain). Then, a higher
value of temperature is chosen and the dependence on equivalent plastic strain is given at this
temperature. This process is repeated as often as necessary to describe the property variations in as
much detail as required.
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Materials: Introduction
Using the DEPENDENCIES parameter to define field variable
dependence
The DEPENDENCIES parameter is used with many material definition options to specify the number
of user-defined field variable dependencies required (see ``Predefined fields,'' Section 18.5.1). If the
parameter is omitted from a material option with which it is available, the material data are assumed
not to depend on field variables.
If more field variable dependencies are required than fit on a single data line, more data lines can be
added. Each data line can hold up to eight data items. For example, a linear, isotropic elastic material
can be defined as a function of temperature and seven field variables ( f v) as follows:
*ELASTIC, ISOTROPIC, DEPENDENCIES=7
E , º , µ , f v1 , f v2 , f v3 , f v4 , f v5
f v6 , f v7
This pair of data lines would be repeated as often as necessary to define the material as a function of
the temperature and field variables.
Usage: *MATERIAL OPTION, DEPENDENCIES=n
Regularizing user-defined data
Specifying material data as functions of independent variables requires a table lookup of the material
data values during the analysis. The table lookups occur frequently and are most economical if the
user's input data are regular. When there is only one independent variable, the concept of regular data
is simply that the data are defined on uniformly spaced intervals of the independent variable. If there
are multiple independent variables, there are two criteria which must be met to have regular data. First,
the data must be defined on uniformly spaced intervals of each of the independent variables. Second,
for each independent variable, the minimum and maximum values (the range) should be constant while
specifying the other independent variables. The material definition in Figure 8.1.2-2 illustrates a case
where the user's material data are not regular since ²11 6= ²12 and ²21 6= ²22 and ²31 6= ²32 .
The user is not required to specify regular material data. ABAQUS/Explicit will automatically
regularize the data defined by the user. For example, the temperature values in Figure 8.1.2-1may be
defined at 10°, 20°, 25°, 28°, 30°, and 35° C. In this case ABAQUS/Explicit can regularize the data by
defining the data over 25 increments of 1° C and the user's piecewise linear data data will be
reproduced exactly. This regularization requires the expansion of the user's data from values at 6
temperature points to values at 26 temperature points. This example is a case where a simple
regularization can reproduce the user's data exactly.
It is not always possible to regularize the input data so that they are reproduced exactly in a piecewise
linear manner. Suppose the yield stress is defined as a function of plastic strain as:
*PLASTIC
50000, .0
75000, .001
80000, .003
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Materials: Introduction
85000, .010
86000, 1.0
It is possible to regularize the data exactly but it is not very economical, since it requires the
subdivision of the data into 1000 regular intervals. Regularization is more difficult if the smallest
interval defined by the user is small compared to the range of the independent variable.
Error tolerance used in regularizing user-defined data
ABAQUS/Explicit uses an error tolerance to regularize the input data. The number of intervals in the
range of each independent variable is chosen such that the error between the piecewise linear
regularized data and each of the user's defined points is less than the tolerance times the range of the
dependent variable. In some cases, the number of intervals becomes excessive and ABAQUS/Explicit
cannot regularize the data using a reasonable number of intervals. The number of intervals considered
reasonable depends on the number of intervals defined by the user. If the user defined 50 or less
intervals, the maximum number of intervals used by ABAQUS/Explicit for regularization is equal to
100 times the number of user-defined intervals. If the user defined more than 50 intervals, the
maximum number of intervals used for regularization is equal to 5000 plus 10 times the number of
user-defined intervals above 50. If the number of intervals becomes excessive, the program stops
during the data checking phase and issues an error message. The user can either redefine the material
data or change the tolerance value. The default tolerance is 0.03. This value can be changed by using
the RTOL parameter on the *MATERIAL option.
The yield stress data in the example above is a typical case where such an error message may be
issued. In this case, the user can simply remove the last data point since it only produces a small
difference in the ultimate yield value.
Usage: *MATERIAL, RTOL=tolerance
8.1.3 Combining material properties
ABAQUS/Explicit provides a broad range of possible material behaviors. A material is defined by
choosing options that describe its behavior for the purpose of an analysis. This section describes the
general rules for combining material options. Specific information for each material model is also
summarized at the end of each material description section in this chapter.
References
· ``Material library: overview,'' Section 8.1.1
· ``Material data definition,'' Section 8.1.2
Overview
Some material options require the presence of other material options, and some exclude the use of
other material options. For example, the *PLASTIC option, used to define the yield stress for metal
plasticity, requires the *ELASTICor *EOS option and excludes all other rate-independent plasticity
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Materials: Introduction
options.
The *DENSITY option (``Density,'' Section 8.2.1) is required for all material models in
ABAQUS/Explicit except hydrostatic fluids.
Understanding the material model combination tables
The material model combination tables explain which options must be used together. The tables also
show the material options that cannot be combined. The options are assigned to categories because
exclusions are best described in terms of those categories. Some of the categories require explanation:
· "Complete mechanical definition options" are those options that, individually, completely define a
material's mechanical (stress-strain) behavior. An option in this category, therefore, excludes any
other such option and also excludes any option that defines part of a material's mechanical
behavior: those options that belong to the "Elasticity" and "Plasticity" categories.
· "Elasticity options" contains all of the basic elasticity models. If an option from the "Complete
mechanical definitions" category is not used and mechanical behavior is required, an option must
be selected from this category. This selection then excludes any other "Elasticity" option.
· "Enhancements for elasticity options" contains options that extend the modeling provided by the
elasticity options.
· "Plasticity options" contains all of the plasticity models.
If elastic-plastic behavior must be modeled, an appropriate plasticity model should be selected from
the "Plasticity options" category; an option from the "Elasticity options" category is then also
required.
Complete material definitions
ABAQUS requires that the material be sufficiently defined to provide suitable properties for those
elements with which the material is associated. Thus, a material associated with displacement or
structural elements must include either a "Complete mechanical definition" category option or an
"Elasticity" category option. It is not possible to modify or add to material property definitions once an
analysis is started.
All aspects of a material's behavior need not be fully defined; any behavior that is omitted is assumed
not to exist in that part of the model. For example, if a metal is defined using *ELASTIC but not
*PLASTIC, it is assumed not to have a yield stress. The user must ensure that the material is
adequately defined for the purpose of the analysis. The material can include definitions that are not
relevant for the analysis, as described in ``Material library: overview,'' Section 8.1.1. Thus, general
material behavior libraries can be included, without the user having to delete those options that are not
needed for a particular application. This generality offers great flexibility in material modeling.
Material model combination tables relevant to ABAQUS/Explicit
The material models can be combined as shown in the following tables.
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Materials: Introduction
Required option, except for hydrostatic fluid elements:
Option
*DENSITY
Requires
General options:
These options are unrestricted.
Option
Requires
*DAMPING
*ELASTIC or *HYPERELASTIC or
*HYPERFOAM
*DEPVAR
*EXPANSION
Complete mechanical definition option:
Option
*USER
MATERIAL
Requires
Thermal properties:
These options are unrestricted.
Option
Requires
*CONDUCTIVIT
Y
*SPECIFIC
HEAT
Elasticity and equation of state options:
These options are mutually exclusive.
Option
Requires
*ELASTIC
*EOS
*HYPERELASTIC
*HYPERFOAM
Enhancements for elasticity options:
Option
*EOS SHEAR
*FAIL STRAIN
*FAIL STRESS
*VISCOELASTI
C
Requires
*EOS
*ELASTIC
*ELASTIC
*ELASTIC or *HYPERELASTIC or *HYPERFOAM
(excludes all plasticity options and associated
enhancements)
Plasticity options:
These options are mutually exclusive.
Option
Requires
*BRITTLE
*ELASTIC, TYPE=ISO and *BRITTLE SHEAR
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Materials: Introduction
CRACKING
*CAP PLASTICITY
*DRUCKER
PRAGER
*FOAM
*PLASTIC
*CAP HARDENING and *ELASTIC
*DRUCKER PRAGER HARDENING and
*ELASTIC
*FOAM HARDENING and *ELASTIC
*ELASTIC or the combination of *EOS and
*EOS SHEAR, TYPE=ELASTIC
Enhancements for plasticity options:
Option
*BRITTLE
FAILURE
*SHEAR FAILURE
*POROUS METAL
PLASTICITY
*POTENTIAL
*RATE
DEPENDENT
*INELASTIC HEAT
FRACTION
Requires
*BRITTLE CRACKING and *BRITTLE
SHEAR
*PLASTIC
*PLASTIC
*PLASTIC
*DRUCKER PRAGER or *FOAM or
*PLASTIC
*PLASTIC and *SPECIFIC HEAT
Enhancement for elasticity or plasticity options:
Option
Requires
*TENSILE FAILURE *PLASTIC or *EOS
Hydrostatic fluid property:
Option
*FLUID DENSITY
Requires
8.2 General properties
8.2.1 Density
Mass density is defined by using the *DENSITY option.
References
· *DENSITY
· ``Material library: overview,'' Section 8.1.1
Overview
A material's mass density:
· must be defined for all materials except hydrostatic fluids; and
· can be specified as a function of temperature and predefined field variables.
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Materials: Introduction
Defining density
Density can be defined as a function of temperature and field variables; however, the density is a
function of the initial conditions only. It will not be updated if temperatures and field variables change
during the analysis.
Usage: Use either of the following options:
*DENSITY
*DENSITY, DEPENDENCIES=n
Units
Since ABAQUS has no built-in dimensions, the user must ensure that the density is given in consistent
units. The use of consistent units, and density in particular, is discussed in ``Conventions,'' Section
1.2.2. If American or English units are used, the user must be particularly careful that the density used
is in units of ML¡3 , where mass is defined in units of FT2 L¡1 .
Elements
A nonzero mass density must be defined for all elements in ABAQUS/Explicit that are not part of a
rigid body. The *DENSITY option is used to specify mass density for all elements, except hydrostatic
fluid elements and rigid elements. Mass density for hydrostatic fluid elements is defined with the
*FLUID DENSITY option, and mass density for rigid elements is specified using the DENSITY
parameter on the *RIGID BODY option.
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Elastic Mechanical Properties
9. Elastic Mechanical Properties
9.1 Overview
9.1.1 Elastic behavior: overview
The ABAQUS/Explicit material library includes several models of elastic behavior:
Linear elasticity: Linear elasticity (``Linear elastic behavior,'' Section 9.2.1) is the simplest form
of elasticity available in ABAQUS/Explicit. The linear elastic model can define isotropic,
orthotropic, or anisotropic material behavior and is valid for small elastic strains.
Plane stress orthotropic failure: Failure theories are provided (``Plane stress orthotropic failure
measures,'' Section 9.2.2) for use with linear elasticity. They can be used to obtain postprocessed
output requests.
Hyperelasticity: For rubberlike material at finite strain the hyperelastic model ( ``Hyperelastic
behavior,'' Section 9.3.1) provides a general strain energy potential to describe the material
behavior for nearly incompressible elastomers. This nonlinear elasticity model is valid for large
elastic strains.
Foam hyperelasticity: The hyperfoam model (``Elastomeric foam behavior,'' Section 9.3.2)
provides a general capability for elastomeric compressible foams at finite strains. This nonlinear
elasticity model is valid for large strains (especially large volumetric changes). The foam plasticity
model should be used for foam materials that undergo permanent deformation (``Crushable foam
plasticity model,'' Section 10.3.3).
Viscoelasticity: The viscoelastic model is used to specify time-dependent material behavior
(``Viscoelasticity,'' Section 9.4.1). It must be combined with linear elasticity, hyperelasticity, or
foam hyperelasticity.
Equation of state: The equation of state in ABAQUS/Explicit provides a hydrostatic material
model in which the pressure is defined as a function of the density and the internal energy
(``Equation of state,'' Section 9.5.1). The material modeled by an equation of state may have no
deviatoric strength or may have either isotropic elastic or Newtonian viscous deviatoric behavior.
This model can be used by itself or in conjunction with the Mises or the Johnson-Cook plasticity
models to model elastic-plastic hydrodynamic materials.
Thermal strain
Thermal expansion can be introduced for any of the elasticity models ( ``Thermal expansion,'' Section
11.1.2) except the equation of state model.
Elastic strain magnitude
Except in the hyperelasticity models, the stresses are always assumed to be small compared to the
tangent modulus of the elasticity relationship; that is, the elastic strain must be small. The total strain
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Elastic Mechanical Properties
can be arbitrarily large if inelastic response such as metal plasticity is included in the material
definition.
For finite-strain calculations where the large strains are purely elastic, the hyperelastic model (for
rubberlike behavior) or the foam hyperelasticity model (for elastomeric foams) should be used. The
hyperelasticity models are the only models that give realistic predictions of actual material behavior at
large elastic strains.
9.2 Linear elasticity
9.2.1 Linear elastic behavior
Linear elasticity is defined by using the *ELASTIC option.
References
· *ELASTIC
· ``Material library: overview,'' Section 8.1.1
· ``Elastic behavior: overview,'' Section 9.1.1
Overview
A linear elastic material model:
· is valid for small elastic strains (normally less than 5%);
· can be isotropic, orthotropic, or fully anisotropic; and
· can have properties that depend on temperature and/or other field variables.
Defining linear elastic material behavior
The total stress is defined from the total elastic strain as
¾ = Del "el ;
where ¾ is the total stress ("true," or Cauchy stress in finite-strain problems), Del is the fourth-order
elasticity tensor, and "el is the total elastic strain (log strain in finite-strain problems). Do not use the
linear elastic material definition when the elastic strains may become large; use a hyperelastic model
instead. Even in finite-strain problems the elastic strains should still be small (less than 5%).
Defining linear elastic response for viscoelastic materials
The elastic response of a viscoelastic material ( ``Viscoelasticity,'' Section 9.4.1) can be specified by
defining either the instantaneous response or the long-term response of the material. To define the
instantaneous response, experiments to determine the elastic constants have to be performed within
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Elastic Mechanical Properties
time spans much shorter than the characteristic relaxation time of the material. These data define the
elastic response when the following option is used:
Usage: *ELASTIC, MODULI=INSTANTANEOUS
If, on the other hand, the long-term elastic response is used, data from experiments have to be collected
after time spans much longer than the characteristic relaxation time of the viscoelastic material. These
data define the elastic response when the following option is used:
Usage: *ELASTIC, MODULI=LONG TERM
Directional dependence of linear elasticity
Depending on the number of symmetry planes for the elastic properties, a material can be classified as
either isotropic (an infinite number of symmetry planes passing through every point) or anisotropic (no
symmetry planes). Some materials have a restricted number of symmetry planes passing through every
point; for example, orthotropic materials have two orthogonal symmetry planes for the elastic
properties. The number of independent components of the elasticity tensor Del depends on such
symmetry properties. The level of anisotropy and mode of defining the elastic properties are chosen by
the TYPE parameter on the *ELASTIC option, as described below. If the material is anisotropic, the
*ORIENTATION option must be used to define the direction of anisotropy.
Stability of a linear elastic material
Linear elastic materials must satisfy the conditions of material or Drucker stability (see the discussion
on material stability in ``Hyperelastic behavior,'' Section 9.3.1). Stability requires that the tensor Del
be positive definite, which leads to certain restrictions on the values of the elastic constants. The
stress-strain relations for several different classes of material symmetries are given below. The
appropriate restrictions on the elastic constants stemming from the stability criterion are also given.
Defining isotropic elasticity
The simplest form of linear elasticity is the isotropic case, and the stress-strain relationship is given by
9 2
8
"11 >
1=E
>
>
>
>
>
"
¡º=E
>
>
6
>
= 6
< 22 >
"33
6 ¡º=E
=6
°
>
>
6 0
12 >
>
>
>
4
>
>
>
0
;
: °13 >
°23
0
¡º=E
1=E
¡º=E
0
0
0
¡º=E
¡º=E
1=E
0
0
0
0
0
0
1=G
0
0
0
0
0
0
1=G
0
9
38
¾11 >
0
>
>
>
0 7>
>
> ¾22 >
>
=
<
7>
0 7 ¾33
:
7
0 7>
¾12 >
>
>
>
5>
>
>
>
0
;
: ¾13 >
¾23
1=G
The elastic properties are completely defined by giving the Young's modulus, E, and the Poisson's
ratio, º. The shear modulus, G, can be expressed in terms of E and º as G = E=2(1 + º ) . These
parameters can be given as functions of temperature and of other predefined fields, if necessary.
Usage: *ELASTIC, TYPE=ISOTROPIC
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Elastic Mechanical Properties
Stability
The stability criterion requires that E > 0, G > 0, and ¡1 < º < 0:5 . Values of Poisson's ratio
approaching 0.5 result in nearly incompressible behavior. Except for plane stress cases (including
membranes and shells) or beams and trusses, values of Poisson's ratio approaching 0.5 generate high
frequency noise in explicit dynamics steps and result in excessively small stable time increments.
Defining orthotropic elasticity by specifying the engineering
constants
Linear elasticity in an orthotropic material is most easily defined by giving the "engineering constants":
the three moduli E1 , E2 , E3 ; Poisson's ratios º12 , º13 , º23 ; and the shear moduli G12 , G13 , and G23
associated with the material's principal directions. These moduli define the elastic compliance
according to
8
9 2
"11 >
1=E1
>
>
>
>
>
" > 6 ¡º12 =E1
>
>
< 22 >
= 6
"33
6 ¡º =E
= 6 13 1
°12 >
>
0
6
>
>
>
>
4
>
>
>
>
°
0
: 13 ;
°23
0
¡º21 =E2
1=E2
¡º23 =E2
0
0
0
¡º31 =E3
¡º32 =E3
1=E3
0
0
0
0
0
0
1=G12
0
0
0
0
0
0
1=G13
0
9
38
¾11 >
0
>
>
>
0 7>
¾22 >
>
>
>
>
=
7<
0 7 ¾33
:
7
0 7>
¾12 >
>
>
>
5>
>
>
>
0
;
: ¾13 >
¾23
1=G23
The quantity ºij has the physical interpretation of the Poisson's ratio that characterizes the transverse
strain in the j-direction, when the material is stressed in the i-direction. In general, ºij is not equal to
ºji : they are related by ºij =Ei =ºji =Ej . The engineering constants can also be given as functions of
temperature and other predefined fields, if necessary.
Usage: *ELASTIC, TYPE=ENGINEERING CONSTANTS
Stability
Material stability requires
E1 ; E2 ; E3 ; G12 ; G13 ; G23 > 0;
jº12 j < (E1 =E2 )1=2 ;
jº13 j < (E1 =E3 )1=2 ;
jº23 j < (E2 =E3 )1=2 ;
1 ¡ º12 º21 ¡ º23 º32 ¡ º31 º13 ¡ 2º21 º32 º13 > 0:
When the left-hand side of the inequality approaches zero, the material exhibits incompressible
behavior. Using the relations ºij =Ei =ºji =Ej , the second, third, and fourth restrictions in the above set
can also be expressed as
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Elastic Mechanical Properties
jº21 j < (E2 =E1 )1=2 ;
jº31 j < (E3 =E1 )1=2 ;
jº32 j < (E3 =E2 )1=2 :
Defining transversely isotropic elasticity
A special subclass of orthotropy is transverse isotropy, which is characterized by a plane of isotropy at
every point in the material. Assuming the 1-2 plane to be the plane of isotropy at every point,
transverse isotropy requires that E1 =E2 =Ep , º31 =º32 =ºtp , º13 =º23 =ºpt , and G13 =G23 =Gt , where p
and t stand for "in-plane" and "transverse," respectively. Thus, while ºtp has the physical interpretation
of the Poisson's ratio that characterizes the strain in the plane of isotropy resulting from stress normal
to it, ºpt characterizes the transverse strain in the direction normal to the plane of isotropy resulting
from stress in the plane of isotropy. In general, the quantities ºtp and ºpt are not equal and are related
by ºtp =Et =ºpt =Ep . The stress-strain laws reduce to
9 2
8
"11 >
1=Ep
>
>
>
>
>
" > 6 ¡ºp =Ep
>
>
= 6
< 22 >
"33
6 ¡º =E
= 6 pt p
°12 >
>
0
6
>
>
>
>
4
>
>
>
0
;
: °13 >
°23
0
¡ºp =Ep
1=Ep
¡ºpt =Ep
0
0
0
¡ºtp =Et
¡ºtp =Et
1=Et
0
0
0
0
0
0
1=Gp
0
0
0
0
0
0
1=Gt
0
9
38
¾11 >
0
>
>
>
0 7>
¾22 >
>
>
>
>
=
7<
0 7 ¾33
;
7
0 7>
¾12 >
>
>
>
5>
>
>
>
0
;
: ¾13 >
¾23
1=Gt
where Gp =Ep =2(1 + ºp ) and the total number of independent constants is only five.
Usage: *ELASTIC, TYPE=ENGINEERING CONSTANTS
Stability
In the transversely isotropic case the stability relations for orthotropic elasticity simplify to
Ep ; Et ; Gp ; Gt > 0;
jºp j < 1;
jºpt j < (Ep =Et )1=2 ;
jºtp j < (Et =Ep )1=2 ;
1 ¡ ºp 2 ¡ 2ºtp ºpt ¡ 2ºp ºtp ºpt > 0:
Defining orthotropic elasticity in plane stress
Under plane stress conditions, such as in a shell element, only the values of E1 , E2 , º12 , G12 , G13 ,
and G23 are required to define an orthotropic material. (In all of the plane stress elements in ABAQUS
the (1; 2) surface is the surface of plane stress, so that the plane stress condition is ¾33 = 0.) The shear
moduli G13 and G23 are included because they may be required for modeling transverse shear
deformation in a shell.
2-454
Elastic Mechanical Properties
Usage: *ELASTIC, TYPE=LAMINA
Stability
Material stability for plane stress requires
E1 ; E2 ; G12 ; G13 ; G23 > 0;
jº12 j < (E1 =E2 )1=2 :
Defining orthotropic elasticity by specifying the terms in the
elastic stiffness matrix
Linear elasticity in an orthotropic material can also be defined by giving the nine independent elastic
stiffness parameters, as functions of temperature and other predefined fields, if necessary. In this case
the stress-strain relations are of the form
8
9 2
¾11 >
D1111
>
>
>
>
>
¾ > 6
>
>
< 22 >
= 6
¾33
6
=6
¾12 >
>
6
>
>
>
>
4
>
>
>
>
¾
: 13 ;
¾23
D1122
D2222
D1133
D2233
D3333
0
0
0
D1212
sym
0
0
0
0
D1313
9
8
9
38
"11 >
"11 >
>
>
>
>
>
>
>
"22 >
"22 >
>
>
>
>
7>
>
>
>
>
=
<
=
<
7
"
7 "33
33
el
:
= [D ]
7
°12 >
°12 >
>
7>
>
>
>
>
>
>
>
5>
>
>
>
>
>
>
;
: °13 >
;
: °13 >
D2323
°23
°23
0
0
0
0
0
For an orthotropic material the engineering constants define the D matrix as
D1111 = E1 (1 ¡ º23 º32 )¨;
D2222 = E2 (1 ¡ º13 º31 )¨;
D3333 = E3 (1 ¡ º12 º21 )¨;
D1122 = E1 (º21 + º31 º23 )¨ = E2 (º12 + º32 º13 )¨;
D1133 = E1 (º31 + º21 º32 )¨ = E3 (º13 + º12 º23 )¨;
D2233 = E2 (º32 + º12 º31 )¨ = E3 (º23 + º21 º13 )¨;
D1212 = G12 ;
D1313 = G13 ;
D2323 = G23 ;
where
¨=
1 ¡ º12 º21 ¡ º23 º32
1
:
¡ º31 º13 ¡ 2º21 º32 º13
When the material stiffness parameters (the Dijkl ) are given directly, ABAQUS imposes the constraint
¾33 = 0 for the plane stress case to reduce the material's stiffness matrix as required.
2-455
Elastic Mechanical Properties
Usage: *ELASTIC, TYPE=ORTHOTROPIC
Stability
The restrictions on the elastic constants due to material stability are
D1111 ; D2222 ; D3333 ; D1212 ; D1313 ; D2323 > 0;
jD1122 j < (D1111 D2222 )1=2 ;
jD1133 j < (D1111 D3333 )1=2 ;
jD2233 j < (D2222 D3333 )1=2 ;
det(Del ) > 0:
The last relation leads to
D1111 D2222 D3333 + 2D1122 D1133 D2233 ¡ D2222 D1133 2 ¡ D1111 D2233 2 ¡ D3333 D1122 2 > 0:
These restrictions in terms of the elastic stiffness parameters are equivalent to the restrictions in terms
of the "engineering constants." Incompressible behavior results when the left-hand side of the
inequality approaches zero.
Defining fully anisotropic elasticity
For fully anisotropic elasticity 21 independent elastic stiffness parameters are needed. The stress-strain
relations are as follows:
8
9 2
¾11 >
D1111
>
>
>
>
>
¾
>
>
6
>
< 22 >
= 6
¾33
6
=6
¾
>
>
6
12 >
>
>
>
4
>
>
>
: ¾13 >
;
¾23
D1122
D2222
D1133
D2233
D3333
D1112
D2212
D3312
D1212
sym
D1113
D2213
D3313
D1213
D1313
9
8
9
38
"11 >
D1123 > "11 >
>
>
>
>
>
>
D2223 7 >
" >
>
>
>
> "22 >
>
>
=
< 22 >
=
<
7>
D3323 7 "33
"33
el
:
= [D ]
7
D1223 7 >
°12 >
°12 >
>
>
>
>
>
>
>
>
5>
>
>
>
>
>
D1323 >
;
: °13 >
;
: °13 >
D2323
°23
°23
When the material stiffness parameters (the Dijkl ) are given directly, ABAQUS imposes the constraint
¾33 = 0 for the plane stress case to reduce the material's stiffness matrix as required.
Usage: *ELASTIC, TYPE=ANISOTROPIC
Stability
The restrictions imposed upon the elastic constants by stability requirements are too complex to
express in terms of simple equations. However, the requirement that Del is positive definite requires
that all of the eigenvalues of the elasticity matrix [D el ] be positive.
Elements
2-456
Elastic Mechanical Properties
Linear elasticity can be used with any stress/displacement or coupled temperature-displacement
element in ABAQUS/Explicit.
9.2.2 Plane stress orthotropic failure measures
Plane stress orthotropic failure is defined by the *FAIL STRESS or the *FAIL STRAIN options.
References
· *FAIL STRAIN
· *FAIL STRESS
· *ELASTIC
· ``Material library: overview,'' Section 8.1.1
· ``Elastic behavior: overview,'' Section 9.1.1
· ``Linear elastic behavior,'' Section 9.2.1
Overview
The orthotropic plane stress failure measures:
· are indications of material failure (normally used for fiber-reinforced composite materials);
· can be used only in conjunction with the *ELASTIC and the *ORIENTATION options;
· can be used for any element that uses a plane stress formulation; that is, for plane stress continuum
elements, shell elements, and membrane elements;
· are postprocessed output requests and do not cause any material degradation; and
· take values that are greater than or equal to 0.0, with values that are greater than or equal to 1.0
implying failure.
Failure theories
Five different failure theories are provided: four stress-based theories and one strain-based theory.
We denote orthotropic material directions by 1 and 2, with the 1-material direction aligned with the
fibers and the 2-material direction transverse to the fibers. For the *FAIL STRESS and the *FAIL
STRAIN options to work correctly, the 1- and 2-directions of the material constants defined in the
*ELASTIC option must align with the fiber and the transverse-to-fiber directions, respectively. For
applications other than fiber-reinforced composites, the 1- and 2-material directions should represent
the strong and weak orthotropic-material directions, respectively.
In all cases tensile values must be positive and compressive values must be negative.
2-457
Elastic Mechanical Properties
Stress-based failure theories
The input data for the stress-based failure theories are tensile and compressive stress limits, Xt and
Xc , in the 1-direction; tensile and compressive stress limits, Yt and Yc , in the 2-direction; and shear
strength (maximum shear stress), S, in the X-Y plane.
Usage: *FAIL STRESS
All four stress-based theories are defined and available with a single use of the *FAIL STRESS option;
the desired output is chosen by the output variables described at the end of this section.
Maximum stress theory
If ¾11 > 0, X = Xt ; otherwise, X = Xc . If ¾22 > 0, Y = Yt ; otherwise, Y = Yc . The maximum
stress failure criterion requires that
IF = max
³¾
11
X
;
¾22 ¯¯ ¾12 ¯¯´
;¯
¯ < 1:0 :
Y
S
Tsai-Hill theory
If ¾11 > 0, X = Xt ; otherwise, X = Xc . If ¾22 > 0, Y = Yt ; otherwise, Y = Yc . The Tsai-Hill
failure criterion requires that
2
2
2
¾11 ¾22
¾11
¾22
¾12
IF = 2 ¡
+ 2 + 2 < 1:0 :
X
X2
Y
S
Tsai-Wu theory
The Tsai-Wu failure criterion requires that
2
2
2
+ F22 ¾22
+ F66 ¾12
+ 2F12 ¾11 ¾22 < 1:0 :
IF = F1 ¾11 + F2 ¾22 + F11 ¾11
The Tsai-Wu coefficients are defined as follows:
F1 =
1
1
+
;
Xt
Xc
F2 =
1
1
+
;
Yt
Yc
F11 = ¡
1
;
Xt Xc
F22 = ¡
1
;
Yt Yc
F66 =
¾biax is the equibiaxial stress at failure. If it is known, then
F12 =
1
2
2¾biax
∙
¶
µ
¶
¸
µ
1
1
1
1
1
1
2
¾biax +
¾biax ;
1¡
+
+
+
+
Xt
Xc
Yt
Yc
Xt Xc
Yt Yc
otherwise,
¤p
F12 = f
F11 F22 ;
2-458
1
:
S2
Elastic Mechanical Properties
¤
¤
¤
where ¡1:0 ∙ f ∙ 1:0 . The default value of f is zero. For the Tsai-Wu failure criterion either f or
¤
¾biax must be given as input data. The coefficient f is ignored if ¾biax is given.
Azzi-Tsai-Hill theory
The Azzi-Tsai-Hill failure theory is the same as the Tsai-Hill theory, except that the absolute value of
the cross product term is taken:
IF =
2
2
2
j¾11 ¾22 j ¾22
¾11
¾12
¡
+
+
< 1:0 :
X2
X2
Y2
S2
This difference between the two failure criteria shows up only when ¾11 and ¾22 have opposite signs.
Stress-based failure measures--failure envelopes
To illustrate the four stress-based failure measures, Figure 9.2.2-1, Figure 9.2.2-2, and Figure 9.2.2-3
show each failure envelope (i.e., IF = 1:0) in (¾11 -¾22 ) stress space compared to the Tsai-Hill
envelope for a given value of in-plane shear stress. In each case the Tsai-Hill surface is the piecewise
continuous elliptical surface with each quadrant of the surface defined by an ellipse centered at the
origin. The parallelogram in Figure 9.2.2-1 defines the maximum stress surface. In Figure 9.2.2-2 the
Tsai-Wu surface appears as the ellipse. In Figure 9.2.2-3 the Azzi-Tsai-Hill surface differs from the
Tsai-Hill surface only in the second and fourth quadrants, where it is the outside bounding surface (i.e.,
further from the origin). Since all of the failure theories are calibrated by tensile and compressive
failure under uniaxial stress, they all give the same values on the stress axes.
Figure 9.2.2-1 Tsai-Hill versus maximum stress failure envelope (IF = 1:0).
Figure 9.2.2-2 Tsai-Hill versus Tsai-Wu failure envelope (IF = 1:0, F12 = 0:0).
2-459
Elastic Mechanical Properties
Figure 9.2.2-3 Tsai-Hill versus Azzi-Tsai-Hill failure envelope (IF = 1:0).
Strain-based failure theory
The input data for the strain-based theory are tensile and compressive strain limits, X"t and X"c , in the
1-direction; tensile and compressive strain limits, Y"t and Y"c , in the 2-direction; and shear strain limit,
S" , in the X-Y plane.
Usage: *FAIL STRAIN
Maximum strain theory
If "11 > 0, X" = X"t ; otherwise, X" = X"c . If "22 > 0, Y" = Y"t ; otherwise, Y" = Y"c . The
maximum strain failure criterion requires that
IF = max
µ
¯¶
¯
"11 "22 ¯¯ "12 ¯¯
;
;
< 1:0 :
X" Y" ¯ S" ¯
Elements
The plane stress orthotropic failure measures can be used with any plane stress, shell, or membrane
element in ABAQUS/Explicit.
Output
ABAQUS provides output of the failure index if failure measures are defined with the material
description. The definition of the failure index, R, and the different output variables are described
below.
Output failure indices
Each of the stress-based failure theories defines a failure surface surrounding the origin in the
three-dimensional space f¾11 ; ¾22 ; ¾12 g. Failure occurs any time a state of stress is either on or outside
this surface. The failure index, R, is used to measure the proximity to the failure surface. R is defined
as the scaling factor such that, for the given stress state f¾11 ; ¾22 ; ¾12 g,
n¾
11
R
;
¾22 ¾12 o
;
R R
)
IF = 1:0 ;
that is, 1=R is the scaling factor with which we need to multiply all of the stress components
2-460
Elastic Mechanical Properties
simultaneously to lie on the failure surface. Values R < 1:0 indicate that the state of stress is within
the failure surface, while values R ¸ 1:0 indicate failure. For the maximum stress theory R ´ IF .
The failure index R is defined similarly for the maximum strain failure theory. R is the scaling factor
such that, for the given strain state f"11 ; "22 ; "12 g,
n"
"22 "12 o
;
R R R
11
;
)
IF = 1:0 :
For the maximum strain theory R ´ IF .
Output variables
Output variables MSTRS, TSAIH, TSAIW, and AZZIT for the individual stress theories and output
variable MSTRN for the strain theory can be written to the output database ( .odb) file using the
*OUTPUT, FIELD option.
9.3 Hyperelasticity
9.3.1 Hyperelastic behavior
Hyperelasticity is defined by using the *HYPERELASTIC option and, optionally, the *UNIAXIAL
TEST DATA, the *BIAXIAL TEST DATA, the *PLANAR TEST DATA, and the *VOLUMETRIC
TEST DATA options.
References
· *HYPERELASTIC
· *UNIAXIAL TEST DATA
· *BIAXIAL TEST DATA
· *PLANAR TEST DATA
· *VOLUMETRIC TEST DATA
· ``Material library: overview,'' Section 8.1.1
· ``Elastic behavior: overview,'' Section 9.1.1
Overview
The hyperelastic material model:
· is isotropic and nonlinear;
· is valid for materials that exhibit instantaneous elastic response up to large strains (such as rubber,
solid propellant, or other elastomeric materials); and
2-461
Elastic Mechanical Properties
· requires that geometric nonlinearity be accounted for during the analysis step (``Procedures:
overview,'' Section 6.1.1), since it is intended for finite-strain applications.
Compressibility
Most elastomers (solid, rubberlike materials) have very little compressibility compared to their shear
flexibility. This behavior is not a problem with plane stress analysis, shells, or membranes. However, it
can be a problem in other cases (three-dimensional solids, plane strain, and axisymmetric analysis).
For example, in applications where the material is not highly confined, it would be quite satisfactory to
assume that the material is fully incompressible: the volume of the material cannot change except for
thermal expansion. In cases where the material is highly confined (such as an O-ring used as a seal),
the compressibility must be modeled correctly to obtain accurate results.
Except for plane stress cases, it is not possible to assume that the material is fully incompressible in
ABAQUS/Explicit because the program has no mechanism for imposing such a constraint at each
material calculation point. Instead, we must provide some compressibility. The difficulty is that, in
many cases, the actual material behavior provides too little compressibility for the algorithms to work
efficiently. Thus, except for plane stress, the user must provide enough compressibility for the code to
work, knowing that this makes the bulk behavior of the model softer than that of the actual material.
Some judgment is, therefore, required to decide whether or not the solution is sufficiently accurate, or
whether the problem can be modeled at all with ABAQUS/Explicit because of this numerical
limitation.
We can assess the relative compressibility of a material by the ratio of its initial bulk modulus, K0 , to
its initial shear modulus, ¹0 . This ratio can also be expressed in terms of Poisson's ratio, º, since
º=
3K0 =¹0 ¡ 2
:
6K0 =¹0 + 2
The table below provides some representative values:
K0 =¹0
Poisson's ratio
0.452
10
0.475
20
0.490
50
0.495
100
0.4995
1000
10,000
0.49995
If no value is given for the material compressibility in the hyperelastic option, by default
ABAQUS/Explicit assumes K0 =¹0 = 20, corresponding to Poisson's ratio of 0.475. Since typical
unfilled elastomers have K0 =¹0 ratios in the range of 1,000 to 10,000 ( º = 0:4995 to º = 0:49995 )
and filled elastomers have K0 =¹0 ratios in the range of 50 to 200 (º = 0:490 to º = 0:497 ), this
default provides much more compressibility than is available in most elastomers. However, if the
elastomer is relatively unconfined, this softer modeling of the material's bulk behavior usually provides
quite accurate results. Unfortunately, in cases where the material is highly confined--such as when it is
in contact with stiff, metal parts and has a very small amount of free surface, especially when the
2-462
Elastic Mechanical Properties
loading is highly compressive--it may not be feasible to obtain accurate results with
ABAQUS/Explicit.
If the user is defining the compressibility rather than accepting the default value, an upper limit of 100
is suggested for the ratio of K0 =¹0 . Larger ratios introduce high frequency noise into the dynamic
solution and require the use of excessively small time increments.
Another class of rubberlike materials is elastomeric foam, which is elastic but very compressible.
Elastomeric foams are discussed in ``Elastomeric foam behavior,'' Section 9.3.2.
Isotropy assumption
The initial orientation of the long-chain molecules in elastomeric materials is assumed to be random;
therefore, the material is initially isotropic. As the material is stretched, the molecules orient
themselves, giving rise to anisotropy. However, the development of this anisotropy follows the
direction of straining; hence, the material can be considered to be isotropic throughout the deformation
history. As a consequence, the strain energy potential can be formulated as a function of the strain
invariants.
Strain energy potentials
Hyperelastic materials are described in terms of a "strain energy potential," U ("), which defines the
strain energy stored in the material per unit of reference volume (volume in the initial configuration) as
a function of the strain at that point in the material. There are several forms of strain energy potentials
available in ABAQUS/Explicit to model approximately incompressible isotropic elastomers: the
Arruda-Boyce form, the Mooney-Rivlin form, the neo-Hookean form, the Ogden form, the polynomial
form, the reduced polynomial form, the Yeoh form, and the Van der Waals form. As will be pointed
out below, the reduced polynomial and Mooney-Rivlin models can be viewed as particular cases of the
polynomial model; the Yeoh and neo-Hookean potentials, in turn, can be viewed as special cases of the
reduced polynomial model. Thus, we will occasionally refer collectively to these models as
"polynomial models."
Generally, when data from multiple experimental tests are available (typically, this requires at least
uniaxial and equibiaxial test data), the Ogden and Van der Waals forms are more accurate in fitting
experimental results. If limited test data are available for calibration (usually uniaxial tension data
only), the Arruda-Boyce, Van der Waals, Yeoh, or reduced polynomial forms provide reasonable
behavior and are recommended.
Arruda-Boyce form
The form of the Arruda-Boyce strain energy potential is
½
1
11
1
2
3
(I 1 ¡ 3) +
(I 1 ¡ 9) +
(I 1 ¡ 27)
2
4
2
20¸m
1050¸m
¶
µ 2
¾
19
519
1 Je`
¡1
4
5
+
(I ¡ 81) +
(I ¡ 243) + : : : +
¡ ln Je` ;
7000¸6m 1
673750¸8m 1
D
2
U =¹
2-463
Elastic Mechanical Properties
where U is the strain energy per unit of reference volume; ¹, ¸m , and D are temperature-dependent
material parameters; I 1 is the first deviatoric strain invariant defined as
2
2
2
I 1 = ¸1 + ¸2 + ¸3 ;
1
where the deviatoric stretches ¸i = J ¡ 3 ¸i ; J is the total volume ratio; J e` is the elastic volume ratio
as defined below in "Thermal expansion;" and ¸i are the principal stretches. The initial shear modulus
is given directly by ¹, while the initial bulk modulus is related to D with the expression
K0 =
2
:
D
Mooney-Rivlin form
The form of the Mooney-Rivlin strain energy potential is
U = C10 (I 1 ¡ 3) + C01 (I 2 ¡ 3) +
1
(J e` ¡ 1)2 ;
D1
where U is the strain energy per unit of reference volume; C10 , C01 , and D1 are
temperature-dependent material parameters; I 1 and I 2 are the first and second deviatoric strain
invariants defined as
2
2
2
I 1 = ¸1 + ¸2 + ¸3
and
(¡2)
I 2 = ¸1
(¡2)
+ ¸2
(¡2)
+ ¸3
;
1
where the deviatoric stretches ¸i = J ¡ 3 ¸i ; J is the total volume ratio; J e` is the elastic volume ratio
as defined below in "Thermal expansion;" and ¸i are the principal stretches. The initial shear modulus
and bulk modulus are given by
¹0 = 2(C10 + C01 );
K0 =
2
:
D1
Neo-Hookean form
The form of the neo-Hookean strain energy potential is
U = C10 (I 1 ¡ 3) +
1
(J e` ¡ 1)2 ;
D1
where U is the strain energy per unit of reference volume; C10 and D1 are temperature-dependent
material parameters; I 1 is the first deviatoric strain invariant defined as
2
2
2
I 1 = ¸1 + ¸2 + ¸3 ;
2-464
Elastic Mechanical Properties
1
where the deviatoric stretches ¸i = J ¡ 3 ¸i ; J is the total volume ratio; J e` is the elastic volume ratio
as defined below in "Thermal expansion;" and ¸i are the principal stretches. The initial shear modulus
and bulk modulus are given by
¹0 = 2C10 ;
K0 =
2
:
D1
Ogden form
The form of the Ogden strain energy potential is
N
N
X
X
2¹i ®i
1
®i
®i
U=
(¸1 + ¸2 + ¸3 ¡ 3) +
(J e` ¡ 1)2i ;
2
®i
Di
i=1
i=1
1
where ¸i are the deviatoric principal stretches ¸i = J ¡ 3 ¸i ; ¸i are the principal stretches; N is a
material parameter; and ¹i , ®i , and Di are temperature-dependent material parameters. The initial
shear modulus and bulk modulus for the Ogden form are given by
¹0 =
N
X
¹i ;
K0 =
i=1
2
:
D1
The particular material models described above--the Mooney-Rivlin and neo-Hookean forms--can also
be obtained from the general Ogden strain energy potential for special choices of ¹i and ®i .
Polynomial form
The form of the polynomial strain energy potential is
N
X
N
X
1 e`
U=
Cij (I 1 ¡ 3) (I 2 ¡ 3) +
(J ¡ 1)2i ;
D
i
i+j=1
i=1
i
j
where U is the strain energy per unit of reference volume; N is a material parameter; Cij and Di are
temperature-dependent material parameters; I 1 and I 2 are the first and second deviatoric strain
invariants defined as
2
2
2
I 1 = ¸1 + ¸2 + ¸3
and
(¡2)
I 2 = ¸1
(¡2)
+ ¸2
(¡2)
+ ¸3
1
;
where the deviatoric stretches ¸i = J ¡ 3 ¸i ; J is the total volume ratio; J e` is the elastic volume ratio
as defined below in "Thermal expansion;" and ¸i are the principal stretches. The initial shear modulus
and bulk modulus are given by
¹0 = 2(C10 + C01 );
K0 =
2
:
D1
2-465
Elastic Mechanical Properties
For cases where the nominal strains are small or only moderately large (< 100%), the first terms in the
polynomial series usually provide a sufficiently accurate model. Some particular material models--the
Mooney-Rivlin, neo-Hookean, and Yeoh forms--are obtained for special choices of Cij .
Reduced polynomial form
The form of the reduced polynomial strain energy potential is
U=
N
X
i=1
N
X
1 e`
Ci0 (I 1 ¡ 3) +
(J ¡ 1)2i ;
D
i
i=1
i
where U is the strain energy per unit of reference volume; N is a material parameter; Ci0 and Di are
temperature-dependent material parameters; I 1 is the first deviatoric strain invariant defined as
2
2
2
I 1 = ¸1 + ¸2 + ¸3 ;
1
where the deviatoric stretches ¸i = J ¡ 3 ¸i ; J is the total volume ratio; J e` is the elastic volume ratio
as defined below in "Thermal expansion;" and ¸i are the principal stretches. The initial shear modulus
and bulk modulus are given by
¹0 = 2C10 ;
K0 =
2
:
D1
Van der Waals form
The form of the Van der Waals strain energy potential is
U =¹
½
¡(¸2m
∙
¶3¾
¶
µ 2
¸
µ~
1 Je`
2
I ¡3 2
¡1
¡ 3) ln(1 ¡ ´) + ´ ¡ a
+
¡ ln Je` ;
3
2
D
2
where
I~ = (1 ¡ ¯ )I 1 + ¯I 2
and
´=
s
I~ ¡ 3
:
¸2m ¡ 3
Here, U is the strain energy per unit of reference volume; ¹ is the initial shear modulus; ¸m is the
locking stretch; a is the global interaction parameter; ¯ is an invariant mixture parameter; and D
governs the compressibility. These parameters can be temperature-dependent. I 1 and I 2 are the first
and second deviatoric strain invariants defined as
2
2
2
I 1 = ¸1 + ¸2 + ¸3
and
(¡2)
I 2 = ¸1
(¡2)
+ ¸2
(¡2)
+ ¸3
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Elastic Mechanical Properties
1
where the deviatoric stretches ¸i = J ¡ 3 ¸i ; J is the total volume ratio; J e` is the elastic volume ratio
as defined below in "Thermal expansion;" and ¸i are the principal stretches. The initial shear modulus
and bulk modulus are given by
¹0 = ¹;
K0 =
2
:
D
Yeoh form
The form of the Yeoh strain energy potential is
U =C10 (I 1 ¡ 3) + C20 (I 1 ¡ 3)2 + C30 (I 1 ¡ 3)3
1
1
1
+
(J e` ¡ 1)2 +
(J e` ¡ 1)4 +
(J e` ¡ 1)6 ;
D1
D2
D3
where U is the strain energy per unit of reference volume; Ci0 and Di are temperature-dependent
material parameters; I 1 is the first deviatoric strain invariant defined as
2
2
2
I 1 = ¸1 + ¸2 + ¸3 ;
1
where the deviatoric stretches ¸i = J ¡ 3 ¸i ; J is the total volume ratio; J e` is the elastic volume ratio
as defined below in "Thermal expansion;" and ¸i are the principal stretches. The initial shear modulus
and bulk modulus are given by
¹0 = 2C10 ;
K0 =
2
:
D1
Thermal expansion
Only isotropic thermal expansion is permitted with the hyperelastic material model.
The elastic volume ratio, J e` , relates the total volume ratio, J , and the thermal volume ratio, J th :
J e` =
J
:
J th
J th is given by
J th = (1 + "th )3 ;
where "th is the linear thermal expansion strain that is obtained from the temperature and the isotropic
thermal expansion coefficient (``Thermal expansion,'' Section 11.1.2).
Determining the hyperelastic material parameters
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The mechanical response of a material is defined by choosing the parameters in the strain energy
potential to fit the particular material. Since hyperelastic materials are usually almost incompressible,
the approach is to use data from experiments involving simple deformations to define the coefficients
governing the deviatoric behavior (Cij for the polynomial models--including the reduced polynomial
model and the "named" Mooney-Rivlin, neo-Hookean, and Yeoh options; ( ¹i , ®i ) for the Ogden
model; (¹, ¸m ) for the Arruda-Boyce model; and (¹, ¸m , a, and ¯) for the Van der Waals model)
assuming that the material is fully incompressible. If compressibility is important, volumetric
compression data are used to determine the Di for the (general) polynomial and Ogden models or D
for the Arruda-Boyce and Van der Waals models. Two options are provided for defining the material
parameters: the user can specify the hyperelastic material parameters directly on the data lines or
specify test data and allow ABAQUS to calculate the material parameters.
The properties of rubberlike materials can vary significantly from one batch to another; therefore, if
data are used from several experiments, all of the experiments should be performed on specimens
taken from the same batch of material, regardless of whether the coefficients are computed by the user
or by ABAQUS.
The elastic response of viscoelastic materials ( ``Viscoelasticity,'' Section 9.4.1) can be specified by
defining either the instantaneous response or the long-term response of such materials. To define the
instantaneous response, the experiments outlined in the "Experimental tests" section that follows have
to be performed within time spans much shorter than the characteristic relaxation times of these
materials. These data define the elastic response when the following option is used:
Usage: *HYPERELASTIC, MODULI=INSTANTANEOUS
If, on the other hand, the long-term elastic response is used, data from experiments have to be collected
after time spans much longer than the characteristic relaxation times of these materials. These data
define the elastic response when the following option is used:
Usage: *HYPERELASTIC, MODULI=LONG TERM
Data line specification
The parameters of the hyperelastic strain energy potentials can be given as functions of temperature.
Usage: Use one of the following options:
*HYPERELASTIC,
*HYPERELASTIC,
*HYPERELASTIC,
*HYPERELASTIC,
*HYPERELASTIC,
*HYPERELASTIC,
*HYPERELASTIC,
*HYPERELASTIC,
ARRUDA-BOYCE
MOONEY-RIVLIN
NEO HOOKE
OGDEN, N=n (n ∙ 6)
POLYNOMIAL, N=n (n ∙ 6)
REDUCED POLYNOMIAL, N=n (n ∙ 6)
VAN DER WAALS
YEOH
Test data specification
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Elastic Mechanical Properties
The value of N and experimental stress-strain data can be specified for up to four simple tests:
uniaxial, equibiaxial, planar, and a volumetric compression test. ABAQUS will then compute the
material parameters. The material constants are determined through a least-squares-fit procedure,
which minimizes the relative error in stress. For the n nominal-stress-nominal-strain data pairs, the
relative error measure E is minimized, where
E=
n µ
X
i=1
1¡
Tith =Titest
¶2
:
Titest is a stress value from the test data, and Tith comes from one of the nominal stress expressions
derived below (see "Experimental tests"). ABAQUS minimizes the relative error rather than an
absolute error measure since this provides a better fit at lower strains. This method is available for all
strain energy potentials and any order of N except for the polynomial form, where a maximum of
N = 2 is allowed. The polynomial models are linear in terms of the constants Cij ; therefore, a linear
least-squares procedure can be used. The Arruda-Boyce, Ogden, and Van der Waals potentials are
nonlinear in some of their coefficients, thus necessitating the use of a nonlinear least-squares
procedure. ``Fitting of hyperelastic and hyperfoam constants,'' Section 4.6.2 of the ABAQUS Theory
Manual, contains a detailed derivation of the related equations.
It is generally best to obtain data from several experiments involving different kinds of deformation
over the range of strains of interest in the actual application and to use all of these data to determine
the parameters. This is particularly true for the phenomenological models; i.e., the Ogden and the
polynomial models. It has been observed that to achieve good accuracy and stability, it is necessary to
fit these models using test data from more than one deformation state. In some cases, especially at
large strains, removing the dependence on the second invariant may alleviate this limitation. The
Arruda-Boyce, neo-Hookean, and Van der Waals models offer a physical interpretation and provide a
better prediction of general deformation modes when the parameters are based on only one test. An
extensive discussion of this topic can be found in ``Hyperelastic material behavior,'' Section 4.6.1 of
the ABAQUS Theory Manual.
This method does not allow the hyperelastic properties to be temperature dependent. However, if
temperature-dependent test data are available, several curve fits can be conducted by performing a
datacheck analysis on a simple input file. The temperature-dependent coefficients determined by
ABAQUS can then be entered directly in the actual analysis run.
Optionally, the parameter ¯ in the Van der Waals model can be set to a fixed value while the other
parameters are found using a least-squares curve fit.
Usage: Use one of the following options to select the strain energy potential:
*HYPERELASTIC,
*HYPERELASTIC,
*HYPERELASTIC,
*HYPERELASTIC,
*HYPERELASTIC,
TEST
TEST
TEST
TEST
TEST
DATA
DATA
DATA
DATA
DATA
INPUT,
INPUT,
INPUT,
INPUT,
INPUT,
ARRUDA-BOYCE
MOONEY-RIVLIN
NEO HOOKE
OGDEN, N=n (n ∙ 6)
POLYNOMIAL, N=n (n ∙ 2)
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Elastic Mechanical Properties
*HYPERELASTIC,
*HYPERELASTIC,
*HYPERELASTIC,
*HYPERELASTIC,
TEST
TEST
TEST
TEST
DATA
DATA
DATA
DATA
INPUT,
INPUT,
INPUT,
INPUT,
REDUCED POLYNOMIAL, N=n (n ∙ 6)
VAN DER WAALS
VAN DER WAALS, BETA=¯ (0 ∙ ¯ ∙ 1)
YEOH
In addition, use at least one and up to four of the following options to give the test data (see
"Experimental tests" below):
*UNIAXIAL TEST DATA
*BIAXIAL TEST DATA
*PLANAR TEST DATA
*VOLUMETRIC TEST DATA
As many data points as required can be entered from each test. It is recommended that data from all
four tests (on samples taken from the same piece of material) be included and that the data points cover
the range of nominal strains expected to arise in the actual loading. For the (general) polynomial and
Ogden models and for the coefficient ¯ in the Van der Waals model, the planar test data must be
accompanied by either the uniaxial test data, the biaxial test data, or both of these types of test data;
otherwise, the solution to the least-squares fit will not be unique.
The strain data should be given as nominal strain values (change in length per unit of original length).
For the uniaxial, equibiaxial, and planar tests stress data are given as nominal stress values (force per
unit of original cross-sectional area). These tests allow for entering both compression and tension data.
Compressive stresses and strains are entered as negative values.
The Di or D are computed from pure volumetric compression test data; if no such data are given,
default values are used. For these compression tests the stress data are given as pressure values.
Experimental tests
For a homogeneous material, homogeneous deformation modes suffice to characterize the material
constants. ABAQUS accepts test data from the following deformation modes:
· Uniaxial tension and compression
· Equibiaxial tension and compression
· Planar tension and compression (also known as pure shear)
· Volumetric tension and compression
These modes are illustrated schematically in Figure 9.3.1-1 and are described below.
Figure 9.3.1-1 Schematic illustrations of deformation modes.
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Elastic Mechanical Properties
The most commonly performed experiments are uniaxial tension, uniaxial compression, and planar
tension. Combine data from these three test types to get a good characterization of the hyperelastic
material behavior.
For the incompressible version of the material model, the stress-strain relationships for the different
tests are developed using derivatives of the strain energy function with respect to the strain invariants.
We define these relations in terms of the nominal stress (the force divided by the original, undeformed
area) and the nominal, or engineering, strain defined below.
The deformation gradient, expressed in the principal directions of stretch, is
2
¸1
4
F= 0
0
0
¸2
0
3
0 5;
¸3
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Elastic Mechanical Properties
where ¸1 , ¸2 , and ¸3 are the principal stretches: the ratios of current length to length in the original
configuration in the principal directions of a material fiber. The principal stretches, ¸i , are related to
the principal nominal strains, ²i , by
¸ i = 1 + ²i :
Because we assume incompressibility and isothermal response, J = det(F) = 1 and, hence,
¸1 ¸2 ¸3 = 1. The deviatoric strain invariants in terms of the principal stretches are then
I 1 = ¸1 2 + ¸2 2 + ¸3 2 ;
and
I 2 = ¸1 ¡2 + ¸2 ¡2 + ¸3 ¡2 :
Uniaxial tests
The uniaxial deformation mode is characterized in terms of the principal stretches, ¸i , as
¸1 = ¸U ;
¸2 = ¸3 = 1=
p
¸U ;
where ¸U is the stretch in the loading direction. The nominal strain is defined by "U = ¸U ¡ 1:
To derive the uniaxial nominal stress TU , we invoke the principle of virtual work:
±U = TU ±¸U ;
so that
µ
¶
@U
@U
@U
¡3
:
= 2(1 ¡ ¸U ) ¸U
+
TU =
@¸U
@I 1
@I 2
The uniaxial tension test is the most common of all the tests and is usually performed by pulling a
"dog-bone" specimen. The uniaxial compression test is performed by loading a compression button
between lubricated surfaces. The loading surfaces are lubricated to minimize any barreling effect in the
button that would cause deviations from a homogeneous uniaxial compression stress-strain state.
Usage: *UNIAXIAL TEST DATA
Equibiaxial tests
The equibiaxial deformation mode is characterized in terms of the principal stretches, ¸i , as
¸1 = ¸2 = ¸B ;
¸3 = 1=¸2B ;
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Elastic Mechanical Properties
where ¸B is the stretch in the two perpendicular loading directions. The nominal strain is defined by
"B = ¸B ¡ 1:
To develop the expression for the equibiaxial nominal stress, TB , we again use the principle of virtual
work (assuming that the stress perpendicular to the loading direction is zero),
±U = 2TB ±¸B ;
so that
¡
¢
1 @U
= 2 ¸B ¡ ¸¡5
TB =
B
2 @¸B
µ
@U
@U
+ ¸2B
@I 1
@I 2
¶
:
In practice, the equibiaxial compression test is rarely performed because of experimental setup
difficulties. In addition, this deformation mode is equivalent to a uniaxial tension test, which is
straightforward to conduct.
A more common test is the equibiaxial tension test, in which a stress state with two equal tensile
stresses and zero shear stress is created. This state is usually achieved by stretching a square sheet in a
biaxial testing machine. It can also be obtained by inflating a circular membrane into a spheroidal
shape (like blowing up a balloon). The stress field in the middle of the membrane then closely
approximates equibiaxial tension, provided that the thickness of the membrane is very much smaller
than the radius of curvature at this point. However, the strain distribution will not be quite uniform,
and local strain measurements will be required. Once the strain and radius of curvature are known, the
nominal stress can be derived from the inflation pressure.
Usage: *BIAXIAL TEST DATA
Planar tests
The planar deformation mode is characterized in terms of the principal stretches, ¸i , as
¸1 = ¸S ; ¸2 = 1; ¸3 = 1=¸S ;
where ¸S is the stretch in the loading direction. Then, the nominal strain in the loading direction is
"S = ¸S ¡ 1:
This test is also called a "pure shear" test since, in terms of logarithmic strains,
"1 = ln ¸1 = ¡ln ¸3 = ¡"3 ;
"2 = ln ¸2 = 0;
which corresponds to a state of pure shear at an angle of 45° to the loading direction.
The principle of virtual work gives
±U = TS ±¸S ;
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Elastic Mechanical Properties
where TS is the nominal planar stress, so that
@U
TS =
= 2(¸S ¡ ¸¡3
S )
@¸S
µ
@U
@U
+
@I 1
@I 2
¶
:
For the (general) polynomial and Ogden models and for the coefficient ¯ in the Van der Waals model
this equation alone will not determine the constants uniquely. The planar test data must be augmented
by uniaxial test data and/or biaxial test data to determine the material parameters.
Planar tests are usually done with a thin, short, and wide rectangular strip of material fixed on its wide
edges to rigid loading clamps that are moved apart. If the separation direction is the 1-direction and the
thickness direction is the 3-direction, the comparatively long size of the specimen in the 2-direction
and the rigid clamps allow us to use the approximation ¸2 = 1; that is, there is no deformation in the
wide direction of the specimen. This deformation mode could also be called planar compression if the
3-direction is considered to be the primary direction. All forms of incompressible plane strain behavior
are characterized by this deformation mode. Consequently, if plane strain analysis is performed, planar
test data represent the relevant form of straining of the material.
Usage: *PLANAR TEST DATA
Volumetric tests
Since ABAQUS/Explicit requires some compressibility in the material model (except for plane stress
cases), the Di or D (for the Arruda-Boyce and Van der Waals models) must also be given. However,
as discussed under "Compressibility" above, for most elastomers the actual compressibility is too little
for the code to work well. The following discussion describes procedures for obtaining Di values (or
D, for the Arruda-Boyce and Van der Waals models) corresponding to the actual material behavior.
With these values the user can compare the material's initial bulk modulus, K0 = 2=D1 , to its initial
PN
shear modulus (¹0 = 2(C10 + C01 ) for the polynomial model, ¹0 = i=1 ¹i for Ogden's model) and
then judge whether Di values that will provide results are sufficiently realistic. The material's actual
Di values can be calculated from data obtained in pure volumetric compression of a specimen
(volumetric tension tests are much more difficult to perform). In a pure volumetric test
¸1 = ¸2 = ¸3 = ¸V ; therefore, I 1 = I 2 = 3 and J = ¸V 3 = V =V0 (the volume ratio). Using the
polynomial form of the strain energy potential, the total pressure stress on the specimen is obtained as
p=¡
µ
¾1 + ¾2 + ¾3
3
¶
=¡
N
X
i=1
2i
1
(¸V 3 ¡ 1)2i¡1 :
Di
This equation can be used to determine the Di . If we are using a second-order polynomial series for U ,
we have N = 2, and so two Di are needed. Therefore, a minimum of two points on the
pressure-volume ratio curve are required to give two equations for the Di . For the Ogden and reduced
polynomial potentials Di can be determined for up to N = 6. A linear least-squares fit is performed
when more than N data points are provided.
An approximate way of conducting a volumetric test consists of using a cylindrical rubber specimen
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Elastic Mechanical Properties
that fits snugly inside a rigid container and whose top surface is compressed by a rigid piston.
Although both volumetric and deviatoric deformation are present, the deviatoric stresses will be
several orders of magnitude smaller than the hydrostatic stresses (because the bulk modulus is much
higher than the shear modulus) and can be neglected. The compressive stress imposed by the rigid
piston is effectively the pressure, and the volumetric strain in the rubber cylinder is computed from the
piston displacement.
Nonzero values of Di affect the uniaxial, equibiaxial, and planar stress results. However, since the
material is assumed to be only slightly compressible, the techniques described for obtaining the
deviatoric coefficients should give sufficiently accurate values even though they assume that the
material is fully incompressible.
Usage: *VOLUMETRIC TEST DATA
Equivalent experimental tests
The superposition of a tensile or compressive hydrostatic stress on a loaded, fully incompressible
elastic body results in different stresses but does not change the deformation. Thus, Figure 9.3.1-2
shows that some apparently different loading conditions are actually equivalent in their deformations
and, therefore, are equivalent tests:
Figure 9.3.1-2 Equivalent deformation modes through superposition of hydrostatic stress.
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Elastic Mechanical Properties
· Uniaxial tension () Equibiaxial compression
· Uniaxial compression () Equibiaxial tension
· Planar tension () Planar compression
On the other hand, the tensile and compressive cases of the uniaxial and equibiaxial modes are
independent from each other: uniaxial tension and uniaxial compression provide independent data.
Model prediction of material behavior versus experimental data
Once the hyperelastic constants are determined, the behavior of the hyperelastic model in ABAQUS is
established. However, the quality of this behavior must be assessed: the prediction of material behavior
under different deformation modes must be compared against the experimental data. The user must
judge whether the hyperelastic constants determined by ABAQUS are acceptable, based on the
correlation between the ABAQUS predictions and the experimental data. Single-element test cases can
be used to derive the nominal stress-nominal strain response of the material model.
See ``Fitting of rubber test data,'' Section 3.1.4 of the ABAQUS Benchmarks Manual, which illustrates
the entire process of fitting hyperelastic constants to a set of test data.
Hyperelastic material stability
An important consideration in judging the quality of the fit to experimental data is the concept of
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Elastic Mechanical Properties
material or Drucker stability. ABAQUS checks the Drucker stability of the material for the first three
deformation modes described above.
The Drucker stability condition for an incompressible material requires that the change in the stress,
¾ , following from any infinitesimal change in the logarithmic strain, d"", satisfies the inequality
d¾
¾ : d"" > 0:
d¾
¾ = D : d"" , where D is the tangent material stiffness, the inequality becomes
Using d¾
d"" : D : d"" > 0;
thus requiring the tangential material stiffness to be positive-definite.
For an isotropic elastic formulation the inequality can be represented in terms of the principal stresses
and strains,
d¾1 d"1 + d¾2 d"2 + d¾3 d"3 > 0:
As before, since the material is assumed to be incompressible, we can choose any value for the
hydrostatic pressure without affecting the strains. A convenient choice for the stability calculation is
¾3 = d¾3 = 0, which allows us to ignore the third term in the above equation.
The relation between the changes in stress and in strain can then be obtained in the form of the matrix
µ
d¾1
d¾2
¶
=
µ
D11
D21
D12
D22
¶µ
d"1
d"2
¶
;
where Dij = Dij (¸1 ; ¸2 ; ¸3 ) . For material stability D must be positive-definite; thus, it is necessary
that
D11 + D22 > 0;
D11 D22 ¡ D12 D21 > 0:
This stability check is performed for the polynomial models, the Ogden potential, and the Van der
Waals form. The Arruda-Boyce form is always stable for positive values of (¹, ¸m ); hence, it suffices
to check the material coefficients to ensure stability.
The user should be careful when defining the Cij or (¹i ; ®i ) for the polynomial models or the Ogden
form: especially when N > 1, the behavior at higher strains is strongly sensitive to the values of the
Cij or (¹i ; ®i ), and unstable material behavior may result if these values are not defined correctly.
When some of the coefficients are strongly negative, instability at higher strain levels is likely to
occur.
ABAQUS performs a check on the stability of the material for six different forms of loading--uniaxial
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Elastic Mechanical Properties
tension and compression, equibiaxial tension and compression, and planar tension and
compression--for 0:1 ∙ ¸1 ∙ 10:0 (nominal strain range of ¡0:9 ∙ ²1 ∙ 9:0 ) at intervals
¢¸1 = 0:01 . If an instability is found, ABAQUS issues a warning message and prints the lowest
absolute value of ²1 for which the instability is observed. Ideally, no instability occurs. If instabilities
are observed at strain levels that are likely to occur in the analysis, it is strongly recommended that the
user either change the material model or carefully examine and revise the material input data.
Improving the accuracy and stability of the test data fit
Unfortunately, the initial fit of the models to experimental data may not come out as well as expected.
This is particularly true for the most general models, such as the (general) polynomial model and the
Ogden model. For some of the simpler models, stability is assured by following some simple rules.
· For positive values of the initial shear modulus, ¹, and the locking stretch, ¸m , the Arruda-Boyce
form is always stable.
· For positive values of the coefficient C10 the neo-Hookean form is always stable.
· Given positive values of the initial shear modulus, ¹, and the locking stretch, ¸m , the stability of
the Van der Waals model depends on the global interaction parameter, a.
· For the Yeoh model stability is assured if all Ci0 > 0. Typically, however, C20 will be negative,
since this helps capture the S-shape feature of the stress-strain curve. Thus, reducing the absolute
value of C20 or magnifying the absolute value of C10 will help make the Yeoh model more stable.
In all cases the following suggestions may improve the quality of the fit:
· Both tension and compression data are allowed; compressive stresses and strains are entered as
negative values. Use compression or tension data depending on the application: it is difficult to fit
a single material model accurately to both tensile and compressive data.
· Always use many more experimental data points than unknown coefficients.
· If N ¸ 3 is used, experimental data should be available to at least 100% tensile strain or 50%
compressive strain.
· Perform different types of tests (e.g., compression and simple shear tests). Proper material
behavior for a deformation mode requires test data to characterize that mode.
· Check for warning messages about material instability or error messages about lack of
convergence in fitting the test data. This check is especially important with new test data; a simple
finite element model with the new test data can be run through the solver input file processor to
check the material stability.
· Perform one-element simulations for simple deformation modes, and compare the ABAQUS
results against the experimental data. The X-Y plotting options in ABAQUS/Viewer can be used
for this comparison.
· Delete some data points at very low strains if large strains are anticipated. A disproportionate
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Elastic Mechanical Properties
number of low strain points may unnecessarily bias the accuracy of the fit toward the low strain
range and cause greater errors in the large strain range.
· Delete some data points at the highest strains if small to moderate strains are expected. The high
strain points may force the fitting to lose accuracy and/or stability in the low strain range.
· Pick data points at evenly spaced strain intervals over the expected range of strains, which will
result in similar accuracy throughout the entire strain range.
· The higher the order of N , the more oscillations are likely to occur, leading to instabilities in the
stress-strain curves. If the (general) polynomial model is used, lower the order of N from 2 to 1 (3
to 2 for Ogden), especially if the maximum strain level is low (say, less than 100% strain).
· If multiple types of test data are used and the fit still comes out poorly, some of the test data
probably contain experimental errors. New tests may be needed. One way of determining which
test data are erroneous is to first calibrate the initial shear modulus ¹test
of the material. Then fit
0
each type of test data separately in ABAQUS and compute the shear modulus, ¹f0 it , from the
material constants using the relations
¹f0 it
= 2(C10 + C01 )
(polynomial form)
or
¹f0 it
=
N
X
¹i
(Ogden form):
i=1
Alternatively, the initial Young's modulus, E0test , can be calibrated and compared with
E0f it
= 6(C10 + C01 )
(polynomial form)
or
E0f it
=3
N
X
¹i
(Ogden form):
i=1
or E0test indicate the erroneous test
The values of ¹f0 it or E0f it that are most different from ¹test
0
data.
Elements
The hyperelastic material model can be used with solid (continuum) elements, shells, and membranes.
It cannot be used with one-dimensional elements (beams).
Procedures
Hyperelasticity must always be used with geometrically nonlinear analyses; the NLGEOM parameter
must be set to YES on the *STEP option (``Procedures: overview,'' Section 6.1.1).
9.3.2 Elastomeric foam behavior
Elastomeric foams are modeled using the *HYPERFOAM option and, optionally, the *UNIAXIAL
TEST DATA, the *BIAXIAL TEST DATA, the *PLANAR TEST DATA, the *SIMPLE SHEAR
TEST DATA, and the *VOLUMETRIC TEST DATA options.
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References
· *HYPERFOAM
· *UNIAXIAL TEST DATA
· *BIAXIAL TEST DATA
· *PLANAR TEST DATA
· *VOLUMETRIC TEST DATA
· *SIMPLE SHEAR TEST DATA
· ``Material library: overview,'' Section 8.1.1
· ``Elastic behavior: overview,'' Section 9.1.1
Overview
The elastomeric foam material model:
· is isotropic and nonlinear;
· is valid for cellular solids whose porosity permits very large volumetric changes;
· can deform elastically to large strains, up to 90% strain in compression; and
· requires that geometric nonlinearity be accounted for during the analysis step (``Procedures:
overview,'' Section 6.1.1), since it is intended for finite-strain applications.
Mechanical behavior of elastomeric foams
Cellular solids are made up of interconnected networks of solid struts or plates that form the edges and
faces of cells. Foams are made up of polyhedral cells that pack in three dimensions. The foam cells can
either be open (e.g., sponge) or closed (e.g., flotation foam). Common examples of elastomeric foam
materials are cellular polymers such as cushions, padding, and packaging materials that utilize the
excellent energy absorption properties of foams: the energy absorbed by foams is substantially greater
than by ordinary stiff elastic materials for a certain stress level.
Another class of foam materials is crushable foams, which undergo permanent (plastic) deformation.
Crushable foams are discussed in ``Crushable foam plasticity model,'' Section 10.3.3.
Foams are commonly loaded in compression. Figure 9.3.2-1 shows a typical compressive stress-strain
curve.
Figure 9.3.2-1 Typical compressive stress-strain curve.
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Elastic Mechanical Properties
Three stages can be distinguished during compression:
1. At small strains (< 5%) the foam deforms in a linear elastic manner due to cell wall bending.
2. The next stage is a plateau of deformation at almost constant stress, caused by the elastic buckling
of the columns or plates that make up the cell edges or walls. In closed cells the enclosed gas
pressure and membrane stretching increase the level and slope of the plateau.
3. Finally, a region of densification occurs, where the cell walls crush together, resulting in a rapid
increase of compressive stress. Ultimate compressive nominal strains of 0.7 to 0.9 are typical.
The tensile deformation mechanisms for small strains are similar to the compression mechanisms, but
they differ for large strains. Figure 9.3.2-2 shows a typical tensile stress-strain curve. There are two
stages during tension:
1. At small strains the foam deforms in a linear, elastic manner as a result of cell wall bending,
similar to that in compression.
2. The cell walls rotate and align, resulting in rising stiffness. The walls are substantially aligned at a
tensile strain of about 1=3. Further stretching results in increased axial strains in the walls.
At small strains for both compression and tension, the average experimentally observed Poisson's ratio,
º, of foams is 1=3. At larger strains it is commonly observed that Poisson's ratio is effectively zero
during compression: the buckling of the cell walls does not result in any significant lateral
deformation. However, º is nonzero during tension, which is a result of the alignment and stretching of
the cell walls.
Figure 9.3.2-2 Typical tensile stress-strain curve.
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The manufacture of foams often results in cells with different principal dimensions. This shape
anisotropy results in different loading responses in different directions. However, the hyperfoam model
does not take this kind of initial anisotropy into account.
Strain energy potential
In the elastomeric foam material model the elastic behavior of the foams is based on the strain energy
function
¸
∙
N
X
¢
1 ¡ e` ¡®i ¯i
2¹i ^ ®i ^ ®i ^ ®i
U=
¸1 + ¸2 + ¸3 ¡ 3 +
(J )
¡1 ;
2
®
¯
i
i
i=1
where N is a material parameter; ¹i , ®i , and ¯i are temperature-dependent material parameters;
^ i = (J th )¡ 13 ¸i
¸
!
^1 ¸
^2 ¸
^ 3 = J e` ;
¸
and ¸i are the principal stretches. The elastic and thermal volume ratios, J e` and J th , are defined
below.
The coefficients ¹i are related to the initial shear modulus, ¹0 , by
¹0 =
N
X
¹i ;
i=1
while the initial bulk modulus, K0 , follows from
K0 =
N
X
i=1
1
2¹i ( + ¯i ):
3
For each term in the energy function, the coefficient ¯i determines the degree of compressibility. ¯i is
related to the Poisson's ratio, ºi , by the expressions
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Elastic Mechanical Properties
¯i =
ºi
;
1 ¡ 2ºi
ºi =
¯i
:
1 + 2¯i
Thus, if ¯i is the same for all terms, we have a single effective Poisson's ratio, º. This effective
Poisson's ratio is valid for finite values of the logarithmic principal strains "1 ; "2 ; "3 ; in uniaxial
tension "2 = "3 = ¡º"1 .
Thermal expansion
Only isotropic thermal expansion is permitted with the hyperfoam material model.
The elastic volume ratio, J e` , relates the total volume ratio (current volume/reference volume), J , and
the thermal volume ratio, J th :
J e` =
J
:
J th
J th is given by
J th = (1 + "th )3 ;
where "th is the linear thermal expansion strain that is obtained from the temperature and the isotropic
thermal expansion coefficient (``Thermal expansion,'' Section 11.1.2).
Determining the hyperfoam material parameters
The response of the material is defined by the parameters in the strain energy function, U ; these
parameters must be determined to use the hyperfoam model. Two options are provided for defining the
material parameters: the user can specify the hyperfoam material parameters directly on the data lines
or specify test data and allow ABAQUS to calculate the material parameters.
The elastic response of a viscoelastic material ( ``Viscoelasticity,'' Section 9.4.1) can be specified by
defining either the instantaneous response or the long-term response of such a material. To define the
instantaneous response, the experiments outlined in the "Experimental tests" section that follows have
to be performed within time spans much shorter than the characteristic relaxation time of the material.
These data define the elastic response when the following option is used:
Usage: *HYPERFOAM, MODULI=INSTANTANEOUS
If, on the other hand, the long-term elastic response is used, data from experiments have to be collected
after time spans much longer than the characteristic relaxation time of the viscoelastic material. These
data define the elastic response when the following option is used:
Usage: *HYPERFOAM, MODULI=LONG TERM
Data line specification
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The parameters N , ¹i , ®i , and ºi can be specified as functions of temperature.
Usage: *HYPERFOAM, N=n (n ∙ 6)
The default value of ºi is zero, which corresponds to an effective Poisson's ratio of zero. The
incompressible limit corresponds to all ºi ! 0:5. However, this material model should not be used for
approximately incompressible materials: use of the hyperelastic model ( ``Hyperelastic behavior,''
Section 9.3.1) is recommended if the effective Poisson's ratio ºef f > 0:45 .
Test data specification
The value of N and the experimental stress-strain data can be specified for up to five simple tests:
uniaxial, equibiaxial, simple shear, planar, and volumetric. ABAQUS contains a capability for
obtaining the ¹i , ®i , and ¯i for the hyperfoam model with up to six terms (N =6) directly from test
data. Poisson effects can either be included by means of a constant Poisson's ratio or through
specification of volumetric test data and/or lateral strains in the other test data options.
It is important to recognize that the properties of foam materials can vary significantly from one batch
to another. Therefore, all of the experiments should be performed on specimens taken from the same
batch of material.
This method does not allow the properties to be temperature dependent.
Usage: Use the first option to define an effective Poisson's ratio ( ºi = º for all i), or use the second
option to define the lateral strains as part of the test data input:
*HYPERFOAM, N=n, POISSON=º , TEST DATA INPUT (n ∙ 6)
*HYPERFOAM, N=n, TEST DATA INPUT (n ∙ 6).
In addition, use at least one and up to five of these additional options to give the experimental
stress-strain data (see "Experimental tests" below):
*UNIAXIAL TEST DATA
*BIAXIAL TEST DATA
*PLANAR TEST DATA
*SIMPLE SHEAR TEST DATA
*VOLUMETRIC TEST DATA
As many data points as required can be entered from each test. ABAQUS will then compute ¹i , ®i ,
and, if necessary, ºi . The technique uses a least squares fit to the experimental data so that the relative
error in the nominal stress is minimized.
It is recommended that data from the uniaxial, biaxial, and simple shear tests (on samples taken from
the same piece of material) be included and that the data points cover the range of nominal strains
expected to arise in the actual loading. The planar and volumetric tests are optional.
For all tests the strain data, including the lateral strain data, should be given as nominal strain values
(change in length per unit of original length). For the uniaxial, equibiaxial, simple shear, and planar
tests, stress data are given as nominal stress values (force per unit of original cross-sectional area). The
tests allow for both compression and tension data; compressive stresses and strains should be entered
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Elastic Mechanical Properties
as negative values. For the volumetric tests the stress data are given as pressure values.
Experimental tests
For a homogeneous material, homogeneous deformation modes suffice to characterize the material
parameters. ABAQUS accepts test data from the following deformation modes:
· Uniaxial tension and compression
· Equibiaxial tension and compression
· Planar tension and compression (pure shear)
· Simple shear
· Volumetric tension and compression
The stress-strain relations are defined in terms of the nominal stress (the force divided by the original,
undeformed area) and the nominal, or engineering, strains, ²i . The principal stretches, ¸i , are related to
the principal nominal strains, ²i , by
¸ i = 1 + ²i :
Uniaxial, equibiaxial, and planar tests
The deformation gradient, expressed in the principal directions of stretch, is
2
¸1
4
F= 0
0
0
¸2
0
3
0
0 5;
¸3
where ¸1 , ¸2 , and ¸3 are the principal stretches: the ratios of current length to length in the original
configuration in the principal directions of a material fiber. The deformation modes are characterized
in terms of the principal stretches, ¸i , and the volume ratio, J = det(F) . The elastomeric foams are
not incompressible, so that J = ¸1 ¸2 ¸3 6= 1. The transverse stretches, ¸2 and/or ¸3 , are independently
specified in the test data either as individual values from the measured lateral deformations or through
the definition of an effective Poisson's ratio.
The three deformation modes use a single form of the nominal stress-stretch relation,
N
2 X ¹ i ®i
@U
TL =
=
(¸L ¡ J ¡®i ¯i );
@¸L
¸L i=1 ®i
where TL is the nominal stress and ¸L is the stretch in the loading direction. Because of the
compressible behavior, the planar mode does not result in a state of pure shear. In fact, if the effective
Poisson's ratio is zero, planar deformation is identical to uniaxial deformation.
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Uniaxial mode
In uniaxial mode ¸1 = ¸U , ¸2 = ¸3 , and J = ¸U ¸22 .
Usage: *UNIAXIAL TEST DATA
Equibiaxial mode
In equibiaxial mode ¸1 = ¸2 = ¸B and J = ¸2B ¸3 .
Usage: *BIAXIAL TEST DATA
Planar mode
In planar mode ¸1 = ¸P , ¸2 = 1, and J = ¸P ¸3 . Planar test data must be augmented by either
uniaxial or biaxial test data.
Usage: *PLANAR TEST DATA
Simple shear tests
Simple shear is described by the deformation gradient
2
1
4
F= 0
0
°
1
0
3
0
05;
1
where ° is the shear strain. For this deformation J = det(F) = 1 . A schematic illustration of simple
shear deformation is shown in Figure 9.3.2-3.
Figure 9.3.2-3 Simple shear test.
The nominal shear stress, TS , is
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Elastic Mechanical Properties
¾
2 ½
N
X
X
@U
2°
¹ i ®i
TS =
=
(¸j ¡ 1) ;
2
2
@°
2(
¸
¡
1)
¡
°
®
i
j
j=1
i=1
where ¸j are the principal stretches in the plane of shearing, related to the shear strain ° by
¸1;2 =
s
°2
1+
§°
2
r
1+
°2
:
4
The stretch in the direction perpendicular to the shear plane is ¸3 = 1: The transverse (tensile) stress,
TT , developed during simple shear deformation due to the Poynting effect, is
2
X
@U
TT =
=
@"
j=1
(
)
N
X
2(¸2j ¡ 1)
¹ i ®i
(¸ ¡ 1) :
2¸4j ¡ ¸2j (° 2 + 2) i=1 ®i j
Usage: *SIMPLE SHEAR TEST DATA
Volumetric tests
The deformation gradient, F, is the same for volumetric tests as for uniaxial tests. The volumetric
deformation mode consists of all principal stretches being equal;
¸1 = ¸2 = ¸3 = ¸V ; J = ¸3V :
The pressure-volumetric ratio relation is
N
2 X ¹ i 1 ®i
@U
¡p =
=
(J 3 ¡ J ¡®i ¯i ):
@J
J i=1 ®i
A volumetric compression test is illustrated in Figure 9.3.2-4. The pressure exerted on the foam
specimen is the hydrostatic pressure of the fluid, and the decrease in the specimen volume is equal to
the additional fluid entering the pressure chamber. The specimen is sealed against fluid penetration.
Figure 9.3.2-4 Volumetric compression test.
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Elastic Mechanical Properties
Usage: *VOLUMETRIC TEST DATA
Difference between compression and tension deformation
For small strains (< 5%) foams behave similarly for both compression and tension. However, at large
strains the deformation mechanisms differ for compression (buckling and crushing) and tension
(alignment and stretching). Therefore, accurate hyperfoam modeling requires that the experimental
data used to define the material parameters correspond to the dominant deformation modes of the
problem being analyzed. If compression dominates, the pertinent tests are:
· Uniaxial compression
· Simple shear
6 0)
· Planar compression (if Poisson's ratio º =
· Volumetric compression (if Poisson's ratio º 6= 0)
If tension dominates, the pertinent tests are:
· Uniaxial tension
· Simple shear
6 0)
· Biaxial tension (if Poisson's ratio º =
· Planar tension (if Poisson's ratio º 6= 0)
Lateral strain data can also be used to define the compressibility of the foam. Measurement of the
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Elastic Mechanical Properties
lateral strains may make other tests redundant; for example, providing lateral strains for a uniaxial test
eliminates the need for a volumetric test. However, if volumetric test data are provided in addition to
the lateral strain data for other tests, both the volumetric test data and the lateral strain data will be
used in determining the compressibility of the foam. The hyperfoam model may not accurately fit
Poisson's ratio if it varies significantly between compression and tension.
Model prediction of material behavior versus experimental data
Once the elastomeric foam constants are determined, the behavior of the hyperfoam model in
ABAQUS is established. However, the quality of this behavior must be assessed: the prediction of
material behavior under different deformation modes must be compared against the experimental data.
The user must judge whether the elastomeric foam constants determined by ABAQUS are acceptable,
based on the correlation between the ABAQUS predictions and the experimental data. Single-element
test cases can be used to calculate the nominal stress-nominal strain response of the material model.
See ``Fitting of elastomeric foam test data,'' Section 3.1.5 of the ABAQUS Benchmarks Manual, which
illustrates the entire process of fitting elastomeric foam constants to a set of test data.
Elastomeric foam material stability
As with incompressible hyperelasticity, ABAQUS checks the Drucker stability of the material for the
deformation modes described above. The Drucker stability condition for a compressible material
requires that the change in the Kirchhoff stress, d¿¿ , following from an infinitesimal change in the
logarithmic strain, d"", satisfies the inequality
d¿¿ : d"" > 0;
¾ . Using d¿¿ = D : d"" , the inequality becomes
where the Kirchhoff stress ¿ = J¾
d"" : D : d"" > 0:
This restriction requires that the tangential material stiffness D be positive definite.
For an isotropic elastic formulation the inequality can be represented in terms of the principal stresses
and strains
d¿1 d"1 + d¿2 d"2 + d¿3 d"3 > 0:
Thus, the relation between changes in the stress and changes in the strain can be obtained in the form
of the matrix equation
8
9 2
D11
< d¿1 =
4
d¿2 = D21
:
;
d¿3
D31
D12
D22
D32
9
38
D13 < d"1 =
D23 5 d"2 ;
;
:
D33
d"3
where Dij = Dij (¸1 ; ¸2 ; ¸3 ):
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Elastic Mechanical Properties
Since D must be positive definite, it is necessary that
D11 + D22 + D33 > 0;
2
2
2
¡ D13
¡ D12
> 0;
D11 D22 + D22 D33 + D33 D11 ¡ D23
det(D) > 0:
The user should be careful about defining the parameters ¹i , ®i , and ºi : especially when N > 1, the
behavior at higher strains is strongly sensitive to the values of these parameters, and unstable material
behavior may result if these values are not defined correctly. When some of the coefficients are
strongly negative, instability at higher strain levels is likely to occur. ABAQUS performs a check on
the stability of the material for nine different forms of loading--uniaxial tension and compression,
equibiaxial tension and compression, simple shear, planar tension and compression, and volumetric
tension and compression--for 0:1 ∙ ¸1 ∙ 10:0 (nominal strain range of ¡0:9 ∙ ²1 ∙ 9:0 ), at intervals
¢¸1 = 0:01 . If an instability is found, ABAQUS issues a warning message and prints the lowest
absolute value of ²1 for which the instability is observed. Ideally, no instability occurs. If instabilities
are observed at strain levels that are likely to occur in the analysis, it is strongly recommended that the
user carefully examine and revise the material input data.
Improving the accuracy and stability of the test data fit
``Hyperelastic behavior,'' Section 9.3.1, contains suggestions for improving the accuracy and stability
of elastomeric modeling. ``Fitting of elastomeric foam test data,'' Section 3.1.5 of the ABAQUS
Benchmarks Manual, illustrates the process of fitting elastomeric foam test data.
Elements
The hyperfoam model can be used with solid (continuum) elements, shells, and membranes. However,
it cannot be used with beam elements.
Procedures
The hyperfoam model must always be used with geometrically nonlinear analyses; the NLGEOM
parameter must be set to YES on the *STEP option (``Procedures: overview,'' Section 6.1.1).
9.4 Viscoelasticity
9.4.1 Viscoelasticity
Viscoelastic materials--materials in which dissipative losses are primarily caused by "viscous"
(internal damping) effects--are defined by the *VISCOELASTIC option and, optionally, the *SHEAR
TEST DATA, the *VOLUMETRIC TEST DATA, the *COMBINED TEST DATA, and the *TRS
options.
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References
· *VISCOELASTIC
· *SHEAR TEST DATA
· *VOLUMETRIC TEST DATA
· *COMBINED TEST DATA
· *TRS
· ``Material library: overview,'' Section 8.1.1
· ``Elastic behavior: overview,'' Section 9.1.1
Overview
The viscoelastic material model:
· describes isotropic rate-dependent material behavior;
· assumes that the shear (deviatoric) and volumetric behaviors are independent in multiaxial stress
states (except when used for an elastomeric foam);
· can be used only in conjunction with either ``Linear elastic behavior,'' Section 9.2.1; ``Hyperelastic
behavior,'' Section 9.3.1; or ``Elastomeric foam behavior,'' Section 9.3.2, to define the elastic
material properties; and
· can be used in large-strain problems.
Defining the shear behavior
Time domain viscoelasticity is available in ABAQUS for small-strain applications where the
rate-independent elastic response can be defined with a linear elastic material model and for
large-strain applications where the rate-independent elastic response must be defined with a
hyperelastic or hyperfoam material model.
Small strain
Consider a shear test at small strain, in which a time varying shear strain, ° (t), is applied to the
material. The response is the shear stress ¿ (t). The viscoelastic material model defines ¿ (t) as
¿ (t) =
Z
t
0
GR (t ¡ s)°_ (s) ds;
where GR (t) is the time-dependent "shear relaxation modulus" that characterizes the material's
response. This constitutive behavior can be illustrated by considering a relaxation test in which a strain
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Elastic Mechanical Properties
° is suddenly applied to a specimen and then held constant for a long time. The beginning of the
experiment, when the strain is suddenly applied, is taken as zero time, so that
¿ (t) =
Z
t
0
GR (t ¡ s)°_ (s) ds = GR (t)°
(since °_ = 0 for t > 0),
where ° is the fixed strain. The viscoelastic material model is "long-term elastic" in the sense that,
after having been subjected to a constant strain for a very long time, the response settles down to a
constant stress; i.e., GR (t) ! G1 as t ! 1.
The shear relaxation modulus can be written in dimensionless form:
gR (t) = GR (t)=G0 ;
where G0 = GR (0) is the instantaneous shear modulus, so that the expression for the stress takes the
form
¿ (t) = G0
Z
t
0
gR (t ¡ s)°_ (s) ds:
The dimensionless relaxation function has the limiting values gR (0) = 1 and gR (1) = G1 =G0 .
Large strain
The equation for the stress can be transformed by using integration by parts:
µ
¿ (t) = G0 ° ¡
Z
t
0
¶
g_ R (s)° (t ¡ s) ds :
It is convenient to write this equation in the form
¿ (t) = ¿0 (t) ¡
Z
t
0
g_ R (s)¿0 (t ¡ s) ds;
where ¿0 (t) is the instantaneous shear stress at time t. This form allows a straightforward
generalization to nonlinear elastic deformations by replacing the linear elastic relation ¿0 = G0 ° by
the nonlinear elasticity relation ¿0 = ¿0 (° ) . This generalization yields a linear viscoelasticity model, in
the sense that the dimensionless stress relaxation function is independent of the magnitude of the
deformation.
In the above equation the instantaneous stress, ¿0 , applied at time t ¡ s influences the stress, ¿ , at time
t. Therefore, to create a proper finite-strain formulation, it is necessary to map the stress that existed in
the configuration at time t ¡ s into the configuration at time t. In ABAQUS this is done by means of a
mixed "push-forward" transformation with the relative deformation gradient Ft¡s (t):
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Elastic Mechanical Properties
Ft¡s (t) =
@x(t)
:
@x(t ¡ s)
To ensure that the stress remains symmetric, ABAQUS uses the integral form:
¿ = ¿ 0 ¡ SYM
"Z
t
0
#
G_ R (s) ¡1
Ft (t ¡ s) ¢ ¿ 0 (t ¡ s) ¢ Ft (t ¡ s) ds ;
G0
where ¿ is the deviatoric part of the Kirchhoff stress.
The finite-strain theory is described in more detail in ``Finite-strain viscoelasticity,'' Section 4.7.2 of
the ABAQUS Theory Manual.
Defining the volumetric behavior
The volumetric behavior can be written in a form that is similar to the shear behavior:
p(t) = ¡K0
Z
t
0
kR (t ¡ s) "_vol (s) ds;
where p is the hydrostatic pressure, K0 is the instantaneous elastic bulk modulus, kR (t) is the
dimensionless bulk relaxation modulus, and "vol is the volume strain.
The above expansion applies to small as well as finite strain since the volume strains are generally
small and there is no need to map the pressure from time t ¡ s to time t.
Temperature effects
The effect of temperature, µ, on the material behavior is introduced through the dependence of the
instantaneous stress, ¿0 , on temperature and through a reduced time concept. The expression for the
linear-elastic shear stress is rewritten as
µ
¿ (t) = G0 (µ) ° ¡
Z
t
g_ R
0
¡
¶
¢
» (s) ° (t ¡ s) ds ;
where the instantaneous shear modulus G0 is temperature dependent, g_ R (» ) = dgR =d», and » (t) is the
reduced time, defined by
» (t) =
Z
t
0
ds
¡
¢;
A µ(s)
¢
¡
where A µ(t) is a shift function at time t. This reduced time concept for temperature dependence is
usually referred to as thermo-rheologically simple (TRS) temperature dependence. Often the shift
function is approximated by the Williams-Landell-Ferry (WLF) form:
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Elastic Mechanical Properties
log(A) = ¡
C1 (µ ¡ µ0 )
;
C2 + (µ ¡ µ0 )
where µ0 is the reference temperature at which the relaxation data are given and C1 , C2 are calibration
constants obtained at this temperature. If µ ∙ µ0 ¡ C2 , deformation changes will be elastic, based on
the instantaneous moduli.
The reduced time concept is also used for the volumetric behavior and the large-strain formulation. For
additional information on the WLF equation, see ``Viscoelasticity,'' Section 4.7.1 of the ABAQUS
Theory Manual.
Numerical implementation
ABAQUS assumes that the viscoelastic material is defined by a Prony series expansion of the
dimensionless relaxation modulus:
gR (t) = 1 ¡
N
X
i=1
G
g¹iP (1 ¡ e¡t=¿i );
where N , g¹iP , and ¿iG , i = 1; 2; : : : ; N , are material constants. Substitution in the small-strain
expression for the shear stress yields
Ã
¿ (t) = G0
°¡
N
X
°i
i=1
!
;
where
g¹P
°i = iG
¿i
Z
t
G
e¡s=¿i ° (t ¡ s) ds:
0
The °i are interpreted as state variables that control the stress relaxation, and
°
cr
=
N
X
°i
i=1
is the "creep" strain: the difference between the total mechanical strain and the instantaneous elastic
strain (the stress divided by the instantaneous elastic modulus).
A similar Prony series expansion is used for the volumetric response, which is valid for both smalland finite-strain applications:
p = ¡K0
Ã
"vol ¡
N
X
i=1
"vol
i
!
;
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Elastic Mechanical Properties
where
"vol
i
Z t
K
k¹iP
= K
e¡s=¿i "vol (t ¡ s) ds:
¿i 0
ABAQUS assumes that ¿iG = ¿iK = ¿i .
The Prony series expansion, in combination with the finite-strain expression for the shear stress,
produces the following large-strain shear model:
¿ = ¿0 ¡
N
X
¿ i;
i=1
where
∙
g¹P
¿ i = SYM iG
¿i
Z
t
¡s=¿iG
e
0
F¡1
t (t
¸
¡ s) ¢ ¿ 0 (t ¡ s) ¢ Ft (t ¡ s) ds :
The ¿ i are interpreted as state variables that control the stress relaxation.
If the instantaneous material behavior is defined by linear elasticity or hyperelasticity, the bulk and
shear behavior can be defined independently. However, if the instantaneous behavior is defined by the
hyperfoam model, the deviatoric and volumetric constitutive behavior are coupled and it is necessary
to use the same relaxation data for both behaviors.
G
In all of the above expressions temperature dependence is readily introduced by replacing e¡s=¿i by
G
K
K
e¡»(s)=¿i and e¡s=¿i by e¡»(s)=¿i .
Determination of viscoelastic material parameters
The above equations are used to model the time-dependent shear and volumetric behavior of a
viscoelastic material. The relaxation parameters can be defined in one of three ways: direct
specification of the Prony series parameters, inclusion of creep test data, or inclusion of relaxation test
data. Temperature effects are included in the same manner regardless of the method used to define the
viscoelastic material.
Direct specification
The Prony series parameters g¹iP , k¹iP , and ¿i can be defined directly. The data line is repeated as often
as needed to define the first, second, third, etc. terms in the Prony series. There is no restriction on the
number of terms that can be used. If a relaxation time is associated with only one of the two moduli,
leave the other one blank or enter a zero. The lines should be given in ascending order of the relaxation
time. The number of lines given in the option defines the number of terms in the Prony series, N . If
this option is used in conjunction with the *HYPERFOAM option, the two modulus ratios have to be
the same (g¹iP = k¹iP ).
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Elastic Mechanical Properties
Usage: *VISCOELASTIC, TIME=PRONY
Creep test data
If creep test data are specified, ABAQUS will calculate the terms in the Prony series automatically.
The normalized shear and bulk compliances are defined as
jS (t) = G0 JS (t)
jK (t) = K0 JK (0);
and
where JS (t) = ° (t)=¿0 is the shear compliance, ° (t) is the total shear strain, and ¿0 is the constant
shear stress in a shear creep test; JK (t) = "vol (t)=p0 is the volumetric compliance, "vol (t) is the total
volumetric strain, and p0 is the constant pressure in a volumetric creep test. At time t = 0,
jS (0) = jK (0) = 1 .
The creep data are converted to relaxation data through the convolution integrals
Z
t
0
gR (s)jS (t ¡ s)ds = t
and
Z
t
0
kR (s)jK (t ¡ s)ds = t:
ABAQUS then uses the normalized shear modulus gR (t) and normalized bulk modulus kR (t) in a
nonlinear least-squares fit to determine the Prony series parameters.
The shear test data and volumetric test data options can be used consecutively to define the normalized
shear and bulk compliances as functions of time. A separate least-squares fit is performed on each data
giP ; ¿iG ) and (k¹iP ; ¿iK ), are merged into one
set, and the two derived sets of Prony series parameters, (¹
giP ; k¹iP ; ¿i ) .
set of parameters, (¹
Usage: Use the following three options. The first option is required. Only one of the second and third
options is required. For an elastomeric foam the third option cannot be used.
*VISCOELASTIC, TIME=CREEP TEST DATA
*SHEAR TEST DATA
*VOLUMETRIC TEST DATA
Alternatively, the combined test data option can be used to specify the normalized shear and bulk
compliances simultaneously as functions of time. A single least-squares fit is performed on the
giP ; k¹iP ; ¿i ) .
combined set of test data to determine one set of Prony series parameters, (¹
Usage: Use both of the following options:
*VISCOELASTIC, TIME=CREEP TEST DATA
*COMBINED TEST DATA
Relaxation test data
As with creep test data, ABAQUS will calculate the Prony series parameters automatically from
relaxation test data. Again, the shear test data and volumetric test data options can be used
consecutively to define the relaxation moduli as functions of time. A separate nonlinear least-squares
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giP ; ¿iG ) and
fit is performed on each data set, and the two derived sets of Prony series parameters-- (¹
(k¹iP ; ¿iK )--are merged into one set of parameters, (¹
giP ; k¹iP ; ¿i ) .
Usage: Use the following three options. The first option is required. Only one of the second and third
options is required. For an elastomeric foam the third option cannot be used.
*VISCOELASTIC, TIME=RELAXATION TEST DATA
*SHEAR TEST DATA
*VOLUMETRIC TEST DATA
Alternatively, the combined test data option can be used to specify the relaxation moduli
simultaneously as functions of time. A single least-squares fit is performed on the combined set of test
giP ; k¹iP ; ¿i ) .
data to determine one set of Prony series parameters, (¹
Usage: Use both of the following options:
*VISCOELASTIC, TIME=RELAXATION TEST DATA
*COMBINED TEST DATA
Calibrating the Prony series parameters
Two optional parameters ERRTOL and NMAX can be given on the *VISCOELASTIC option line.
ERRTOL is the allowable average root-mean-square error of data points in the least-squares fit, and its
default value is 0:01; NMAX is the maximum number of terms N in the Prony series, and its default
and maximum value is 13. ABAQUS will perform the least-squares fit from N = 1 to N = NMAX
until convergence is achieved for the lowest N with respect to ERRTOL.
The following are some guidelines for determining the number of terms in the Prony series from test
data. Based on these guidelines, the user can choose NMAX.
· There should be enough data pairs for determining all the parameters in the Prony series terms.
Thus, assuming that N is the number of Prony series terms, there should be a total of at least 2N
data points in *SHEAR TEST DATA, 2N data points in *VOLUMETRIC TEST DATA, and 3N
data points in *COMBINED TEST DATA.
· The number of terms in the Prony series should be typically not more than the number of
logarithmic "decades" spanned by the test data. The number of logarithmic "decades" is defined as
log 10 (tmax =tmin ), where tmax and tmin are the maximum and minimum time in the test data,
respectively.
Temperature effects
Regardless of the method used to define the viscoelastic behavior, thermo-rheologically simple
temperature effects can be included by specifying the method used to define the shift function. The
shift function can be defined by the Williams-Landell-Ferry (WLF) approximation.
Usage: *TRS
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Defining the rate-independent part of the material response
In all cases elastic moduli must be specified to define the rate-independent part of the material
behavior. Small-strain linear elastic behavior is defined by the *ELASTIC option, and
large-deformation behavior is defined by the *HYPERELASTIC or the *HYPERFOAM options. The
rate-independent elasticity can be defined in terms of either instantaneous elastic moduli or long-term
elastic moduli. The MODULI parameter on the *ELASTIC, *HYPERELASTIC, and *HYPERFOAM
options is used for this purpose. The choice of defining the elasticity in terms of instantaneous or
long-term moduli is a matter of convenience only; it does not have an effect on the solution.
The effective relaxation moduli are obtained by multiplying the instantaneous elastic moduli with the
dimensionless relaxation functions as described below.
Linear elastic materials
For linear elastic material behavior
Ã
GR (t) = G0
1¡
N
X
k=1
!
g¹kP (1 ¡ e¡t=¿k )
and
Ã
KR (t) = K0
1¡
N
X
k=1
!
k¹kP (1 ¡ e¡t=¿k )
;
where G0 and K0 are the instantaneous shear and bulk moduli determined from the values of the
instantaneous elastic moduli E0 and º0 defined using the *ELASTIC, MODULI=INSTANTANEOUS
option: G0 = E0 =2(1 + º0 ) and K0 = E0 =3(1 ¡ 2º0 ) .
If long-term elastic moduli are defined using the *ELASTIC, MODULI=LONG TERM option, the
instantaneous moduli are determined from
G1 = G0
Ã
1¡
N
X
g¹kP
k=1
!
and
K1 = K0
Ã
1¡
N
X
k=1
k¹kP
!
:
Hyperelastic materials
For hyperelastic material behavior the relaxation coefficients are applied to the constants that define
the energy function. For the polynomial function and its particular cases (reduced polynomial,
Mooney-Rivlin, neo-Hookean, and Yeoh)
R
0
Cij
(t) = Cij
Ã
1¡
N
X
k=1
!
g¹kP (1 ¡ e¡t=¿k ) ;
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for the Ogden function
0
¹R
i (t) = ¹i
Ã
1¡
N
X
k=1
!
g¹kP (1 ¡ e¡t=¿k )
;
and for the Arruda-Boyce and Van der Waals functions
R
¹ (t) = ¹
0
Ã
1¡
N
X
g¹kP (1
k=1
¡t=¿k
¡e
!
)
:
For the coefficients governing the compressible behavior of the polynomial models and the Ogden
model
Ã
DiR (t) = Di0 = 1 ¡
N
X
k=1
!
k¹kP (1 ¡ e¡t=¿k )
;
whereas for the Arruda-Boyce and Van der Waals functions
Ã
D R (t) = D 0 = 1 ¡
N
X
k=1
!
k¹kP (1 ¡ e¡t=¿k )
:
If long-term elastic moduli are defined using the *HYPERELASTIC, MODULI=LONG TERM option,
the instantaneous moduli are determined from
1
0
Cij
= Cij
Ã
1¡
N
X
g¹kP
k=1
!
0
; or ¹1
i = ¹i
Ã
1¡
N
X
g¹kP
k=1
!
; or ¹1 = ¹0
Ã
1¡
N
X
k=1
g¹kP
!
;
while the instantaneous bulk compliance moduli are obtained from
Di1
=
Di0 =
Ã
1¡
N
X
k=1
k¹kP
!
; or D
1
0
Ã
=D = 1¡
N
X
k=1
k¹kP
!
:
Elastomeric foams
For elastomeric foam material behavior the instantaneous shear and bulk relaxation coefficients are
assumed to be equal and are applied to the material constants ¹i in the energy function:
0
¹R
i (t) = ¹i
Ã
1¡
N
X
k=1
!
g¹kP (1 ¡ e¡t=¿k )
= ¹0i
Ã
1¡
N
X
k=1
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!
k¹kP (1 ¡ e¡t=¿k )
:
Elastic Mechanical Properties
If long-term elastic moduli are defined using the *HYPERFOAM, MODULI=LONG TERM option,
the instantaneous moduli are determined from
0
¹1
i = ¹i
Ã
1¡
N
X
k=1
g¹kP
!
= ¹0i
Ã
1¡
N
X
k=1
k¹kP
!
:
Use with other material options
The viscoelastic material option must be combined in a material data block with an elasticity option. It
is used with the isotropic linear elasticity model ( ``Linear elastic behavior,'' Section 9.2.1) to define
classical, linear, small-strain, viscoelastic behavior or with the hyperelastic ( ``Hyperelastic behavior,''
Section 9.3.1) or hyperfoam (``Elastomeric foam behavior,'' Section 9.3.2) models to define
large-deformation, nonlinear, viscoelastic behavior. The elastic properties defined by these options can
be temperature dependent.
Viscoelasticity cannot be combined with any of the plasticity options. See ``Combining material
properties,'' Section 8.1.3, for more details.
Elements
The viscoelastic material model can be used with any stress/displacement or coupled temperaturedisplacement element in ABAQUS/Explicit.
9.5 Equations of state
9.5.1 Equation of state
Equations of state are defined in ABAQUS/Explicit using the *EOS option and, for JWL equation of
state models, the *DETONATION POINT option.
References
· *EOS
· *EOS SHEAR
· *DETONATION POINT
· *TENSILE FAILURE
· ``Elastic behavior: overview,'' Section 9.1.1
· ``Material library: overview,'' Section 8.1.1
Overview
Equations of state in ABAQUS/Explicit:
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· provide a hydrodynamic material model in which the material's volumetric strength is determined
by an equation of state;
· determine the pressure (positive in compression) as a function of the density, ½, and the specific
energy (the internal energy per unit mass), Em : p = f (½; Em );
· are available as Mie-Gruniesen equations of state, thus providing the linear Us ¡ Up Hugoniot
form or the JWL high explosive equations of state;
· are also available in the form of an ideal gas;
· assume an adiabatic condition unless a dynamic coupled temperature-displacement analysis is
used;
· can be used to model a material that has only volumetric strength (the material is assumed to have
no shear strength) or a material that also has isotropic elastic or Newtonian viscous deviatoric
behavior;
· can be used with the Mises (``Classical metal plasticity,'' Section 10.2.1) or the Johnson-Cook
(``Johnson-Cook plasticity,'' Section 10.2.4) plasticity models; and
· can be used with the tensile failure model ( ``Failure models,'' Section 10.2.5) to model dynamic
spall or a pressure cutoff.
Energy equation and Hugoniot curve
The equation for conservation of energy equates the increase in internal energy per unit mass, Em , to
the rate at which work is being done by the stresses and the rate at which heat is being added. In the
absence of heat conduction the energy equation can be written as
½
@Em
1 @½
_
= (p ¡ pbv )
+ S : e_ + ½Q;
@t
½ @t
where p is the pressure stress defined as positive in compression, pbv is the pressure stress due to the
bulk viscosity, S is the deviatoric stress tensor, e_ is the deviatoric part of strain rate, and Q_ is the heat
rate per unit mass.
The equation of state is assumed for the pressure as a function of the current density, ½, and the
internal energy per unit mass, Em :
p = f (½; Em );
which defines all the equilibrium states that can exist in a material. The internal energy can be
eliminated from the above equation to obtain a p versus V relationship (where V is the current
volume) or, equivalently, a p versus 1=½ relationship that is unique to the material described by the
equation of state model. This unique relationship is called the Hugoniot curve and is the locus of p-V
states achievable behind a shock (see Figure 9.5.1-1).
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Figure 9.5.1-1 A schematic representation of a Hugoniot curve.
The Hugoniot pressure, pH , is a function of density only and can be defined, in general, from fitting
experimental data.
Mie-Gruniesen equations of state
A Mie-Gruniesen equation of state is linear in energy. The most common form is
p ¡ pH = ¡½(Em ¡ EH );
where pH and EH are the Hugoniot pressure and specific energy (per unit mass) and are functions of
density only, and ¡ is the Gruniesen ratio defined as
¡ = ¡0
½0
;
½
where ¡0 is a material constant and ½0 is the reference density.
The Hugoniot energy, EH , is related to the Hugoniot pressure by
EH =
pH ´
;
2½0
where ´ = 1 ¡ ½0 =½ is the nominal volumetric compressive strain. Elimination of ¡ and EH from the
above equations yields
p = pH
µ
¡0 ´
1¡
2
¶
+ ¡0 ½0 Em :
The equation of state and the energy equation represent coupled equations for pressure and internal
energy. ABAQUS/Explicit solves these equations simultaneously at each material point.
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Elastic Mechanical Properties
Linear equations of state can always be written in the form
p = f + gEm ;
where f (½) and g (½) are functions of density only and depend on the particular equation of state
model.
Linear Us ¡ Up Hugoniot form
A common fit to the Hugoniot data is given by
pH
½0 c20 ´
=
;
(1 ¡ s´ )2
where c0 and s define the linear relationship between the linear shock velocity, Us , and the particle
velocity, Up , as follows:
Us = c0 + sUp :
With the above assumptions the linear Us ¡ Up Hugoniot form is written as
p=
½0 c20 ´
¡0 ´
) + ¡0 ½0 Em ;
(1
¡
(1 ¡ s´)2
2
where ½0 c20 is equivalent to the elastic bulk modulus at small nominal strains.
There is a limiting compression given by the denominator of this form of the equation of state
´lim =
1
s
or
½lim =
s½0
:
s¡1
At this limit there is a tensile minimum; thereafter, negative sound speeds are calculated for the
material.
Set the parameter TYPE=USUP in the *EOS option to request this model; the variables c0 , s, and ¡0
are defined in this option.
Usage: *EOS, TYPE=USUP
Initial state
The initial state of the material is determined by the initial specific energy, Em0 ; the initial density, ½,
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specified on the *DENSITY option; and either a specified relative density or the initial pressure stress.
The initial nonzero specific energy, Em0 , can be defined using the *INITIAL CONDITIONS,
TYPE=SPECIFIC ENERGY option. Use the *INITIAL CONDITIONS, TYPE=RELATIVE DENSITY
option to define the initial relative density, ½=½0 . Alternatively, use the *INITIAL CONDITIONS,
TYPE=STRESS option to define an initial nonzero pressure directly. ABAQUS will then determine
the reference density, ½0 , that satisfies the equation of state. If both options are specified, the value for
initial relative density will be used to define the equation of state and the value for initial stress will be
used only to initialize the deviatoric behavior if it exists. If no option is specified, the initial pressure
will be zero and the reference density, ½0 , will be adjusted to satisfy the equation of state.
Usage: Use some or all of the following options, as required:
*INITIAL CONDITIONS, TYPE=SPECIFIC ENERGY
*INITIAL CONDITIONS, TYPE=RELATIVE DENSITY
*INITIAL CONDITIONS, TYPE=STRESS
JWL high explosive equation of state
The Jones-Wilkens-Lee (or JWL) equation of state models the pressure generated by the release of
chemical energy in an explosive. This model is implemented in a form referred to as a programmed
burn, which is requested by setting the parameter TYPE=JWL in the *EOS option. A programmed
burn means that the reaction and initiation of the explosive is not determined by shock in the material.
Instead, the initiation time is determined by a geometric construction using the detonation wave speed
and the distance of the material point from the detonation points.
The JWL equation of state can be written in terms of the initial energy per unit mass, Em0 , as
µ
!½
p=A 1¡
R1 ½0
¶
µ
½0
exp ¡R1
½
¶
µ
!½
+B 1¡
R2 ½0
¶
µ
½0
exp ¡R2
½
¶
+
!½2
Em0 ;
½0
where A; B; R1 ; R2 ; and ! are material constants that are defined in the *EOS, TYPE=JWL option.
Usage: *EOS, TYPE=JWL
Arrival time of detonation wave
ABAQUS/Explicit calculates the arrival time of the detonation wave at a material point (tmp
d ) as the
distance from the material point to the nearest detonation point divided by the detonation wave speed:
tmp
d
∙
Á ¸
q
N
N
N
mp
mp
= min td + (x ¡ xd ) ¢ (x ¡ xd ) Cd ;
N
where xmp is the position of the material point, xN
d is the position of the N th detonation point, td is
the detonation delay time of the N th detonation point, and Cd is the detonation wave speed of the
explosive material. The minimum in the above formula is over the N detonation points that apply to
the material point.
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Burn fraction
To spread the burn wave over several elements, a burn fraction, Fb , is computed as
∙
¸
(t ¡ tmp
d )Cd
;
Fb = min 1;
Bs le
where Bs is a constant that controls the width of the burn wave (set to a value of 2.5) and le is the
characteristic length of the element. If the time is less than tmp
d , the pressure is zero in the explosive;
otherwise, the pressure is given by the product of Fb and the pressure determined from the JWL
equation above.
Defining detonation points
Use the *DETONATION POINT option to define any number of detonation points for the explosive
material. Coordinates of the points must be defined along with a detonation delay time. Each material
point responds to the first detonation point that it sees. The detonation arrival time at a material point
is based upon the time that it takes a detonation wave (traveling at the detonation wave speed Cd ) to
reach the material point plus the detonation delay time for the detonation point. If there are multiple
detonation points, the arrival time is based on the minimum arrival time for all the detonation points.
In a body with curved surfaces care should be taken that the detonation arrival times are meaningful.
The detonation arrival times are based on the straight line of sight from the material point to the
detonation point. In a curved body the line of sight may pass outside of the body.
Usage: Use both of the following options:
*EOS, TYPE=JWL
*DETONATION POINT
Initial state
Explosive materials generally have some nominal volumetric stiffness before detonation. It may be
useful to incorporate this stiffness when elements modeled with a JWL equation of state are subjected
to stress before initiation of detonation by the arriving detonation wave. The user can define the
pre-detonation bulk modulus, Kpd , on the data line of the *EOS option. The pressure will be computed
from the volumetric strain and Kpd until detonation, at which time the pressure will be determined by
the procedure outlined above.
If a nonzero value of Kpd is provided, an initial stress state for the explosive materials can be defined
using the *INITIAL CONDITIONS, TYPE=STRESS option.
The initial relative density (½=½0 ) used in the JWL equation is assumed to be unity by default. Other
values can be defined by using the *INITIAL CONDITIONS, TYPE=RELATIVE DENSITY option.
This relative density affects only the JWL equation and not the pre-detonation response.
The nonzero values of initial specific energy, Em0 , can be specified using the *INITIAL
CONDITIONS, TYPE=SPECIFIC ENERGY option.
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Usage: Use some or all of the following options, as required:
*INITIAL CONDITIONS, TYPE=SPECIFIC ENERGY
*INITIAL CONDITIONS, TYPE=RELATIVE DENSITY
*INITIAL CONDITIONS, TYPE=STRESS
Ideal gas equation of state
An ideal gas equation of state can be written in the form of
¡
¢
p + pA = ½R µ ¡ µZ ;
where pA is the ambient pressure, R is the gas constant, µ is the current temperature, and µZ is the
absolute zero on the temperature scale being used. It is an idealization to real gas behavior and can be
used to model any gases approximately under appropriate conditions (e.g., low pressure and high
temperature).
One of the important features of an ideal gas is that its specific energy depends only upon its
temperature; therefore, the specific energy can be integrated numerically as
Em = Em0 +
Z
µ¡µ Z
cv (T )dT;
µ0 ¡µ Z
where Em0 is the initial specific energy at the initial temperature µ0 and cv is the specific heat at
constant volume (or the constant volume heat capacity), which depends only upon temperature for an
ideal gas.
Modeling with an ideal gas equation of state is typically performed adiabatically; the temperature
increase is calculated directly at the material integration points according to the adiabatic thermal
energy increase caused by the work pdv, where v is the specific volume (the volume per unit mass,
v = 1=½). Therefore, unless a coupled temperature-displacement analysis is performed, an adiabatic
condition is always assumed in ABAQUS/Explicit.
When performing a coupled temperature-displacement analysis, the pressure stress and specific energy
are updated based on the evolving temperature field. The energy increase due to the change in state
will be accounted for in the heat equation and will be subject to heat conduction.
Set the parameter TYPE=IDEAL GAS in the *EOS option to request this model; the gas constant, R,
and the ambient pressure, pA , are defined in this option. For an ideal gas R can be determined from the
~ and the molecular weight, M W , as follows:
universal gas constant, R,
R=
~
R
:
MW
In general, the value R for any gas can be estimated by plotting pv=(µ ¡ µZ ) as a function of state
(e.g., pressure or temperature). The ideal gas approximation is adequate in any region where this value
is constant. The specific heat at constant volume, cv , must be specified using the *SPECIFIC HEAT
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option. For an ideal gas cv is related to the specific heat at constant pressure, cp , by
R = cp ¡ cv :
Usage: Use both of the following options:
*EOS, TYPE=IDEAL GAS
*SPECIFIC HEAT, DEPENDENCIES=n
Initial state
The initial state of the gas is determined from the initial density, ½, specified on the *DENSITY option
and either the initial pressure stress, p0 , or the initial temperature, µ0 . The user can choose between
specifying initial pressure or temperature using the *INITIAL CONDITIONS option with the TYPE
parameter set to STRESS or TEMPERATURE, respectively. If both are specified, the value for stress
will be used to initialize the state of the gas. For those material points that have zero or no pressure
stress specified on the *INITIAL CONDITIONS option, the initial state is determined from the initial
density and the initial temperature. When a non-absolute temperature scale is used, the value of
absolute zero temperature must be specified using the *PHYSICAL CONSTANTS option.
The initial specific energy, Em0 , can be defined using the *INITIAL CONDITIONS, TYPE=SPECIFIC
ENERGY option. The initial specific energy for an ideal gas equation of state affects only the output of
the total specific energy and should be mathematically equivalent to
Em0 =
Z
µ0 ¡µ Z
cv (T )dT:
0
Usage: Use some or all of the following options, as required:
*DENSITY, DEPENDENCIES=n
*INITIAL CONDITIONS, TYPE=SPECIFIC ENERGY
*INITIAL CONDITIONS, TYPE=STRESS
*INITIAL CONDITIONS, TYPE=TEMPERATURE
The value of absolute zero
The value of absolute zero is specified using the ABSOLUTE ZERO parameter on the *PHYSICAL
CONSTANTS option.
Usage: *PHYSICAL CONSTANTS, ABSOLUTE ZERO=µZ
A special case
In the case of an adiabatic analysis with constant specific heat (both cv and cp are constant), the
specific energy is linear in temperature
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Elastic Mechanical Properties
¡
¢
Em = cv µ ¡ µZ :
The pressure stress can, therefore, be recast in the common form of
p + pA = (° ¡ 1)½Em ;
where ° = cp =cv is the ratio of specific heats and can be defined as
°=
n+2
;
n
where
n=3
for a monatomic;
n=5
for a diatomic; and
n=6
for a polyatomic gas.
Comparison with the hydrostatic fluid model
The ideal gas equation of state can be used to model wave propagation effects and the dynamics of a
spatially varying state of a gaseous region. For cases in which the inertial effects of the gas are not
important and the state of the gas can be assumed to be uniform throughout a region, the hydrostatic
fluid model (``Hydrostatic fluid model,'' Section 11.3.1) is a simpler, more computationally efficient
alternative.
Deviatoric behavior
The equation of state defines only the material's hydrostatic behavior. It can be used by itself, in which
case the material has only volumetric strength (the material is assumed to have no shear strength).
Alternatively, ABAQUS/Explicit allows the user to define deviatoric behavior, assuming that the
deviatoric and volumetric responses are uncoupled. Two models, a linear isotropic deviatoric model or
a Newtonian viscous deviatoric model, are available and can be defined by using the *EOS SHEAR
option. The material's volumetric response is governed then by the equation of state model, while its
deviatoric response is governed by either the linear isotropic elastic model or the Newtonian viscous
fluid model.
The *EOS SHEAR option must be used in conjunction with the *EOS option. The elastic shear
modulus, ¹, or the viscosity, ´, must be provided on the data lines of the *EOS SHEAR option. For the
elastic shear behavior the increment in the deviatoric stress is defined from the deviatoric elastic strain
increment as
S = 2¹eel ;
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where S is the deviatoric stress and eel is the deviatoric elastic strain; for the Newtonian viscous shear
behavior the deviatoric stress is related to the deviatoric strain rate by the Navier-Poisson law of a
Newtonian fluid
_
S = 2´ e;
where S is the deviatoric stress and e_ is the deviatoric part of the strain rate.
Usage: Use both of the following options in the case of elastic shear behavior:
*EOS
*EOS SHEAR, TYPE=ELASTIC
or use both of the following options in the case of viscous shear behavior:
*EOS
*EOS SHEAR, TYPE=VISCOUS
Use with the Mises or the Johnson-Cook plasticity models
An equation of state model can be used with the Mises ( ``Classical metal plasticity,'' Section 10.2.1) or
the Johnson-Cook (``Johnson-Cook plasticity,'' Section 10.2.4) plasticity models to model
elastic-plastic behavior. In this case the elastic part of the shear behavior must be defined by using the
*EOS SHEAR, TYPE=ELASTIC option. The material's volumetric response is governed by the
equation of state model, while the deviatoric response is governed by the linear elastic shear and the
plasticity model.
Usage: Use the following options:
*EOS
*EOS SHEAR, TYPE=ELASTIC
*PLASTIC
Use with the tensile failure model
An equation of state model (except the ideal gas equation of state) can also be used with the tensile
failure model (``Failure models,'' Section 10.2.5) to model dynamic spall or a pressure cutoff. The
tensile failure model uses the hydrostatic pressure stress as a failure measure and offers a number of
failure choices. The hydrostatic cutoff stress must be provided on the data line of the *TENSILE
FAILURE option.
The SHEAR parameter on the *TENSILE FAILURE option is used to fail the deviatoric stresses when
the tensile failure criterion is met. In the case where the material's deviatoric behavior is not defined
(the *EOS option is used by itself), the SHEAR parameter is meaningless and is, therefore, ignored.
The tensile failure model in ABAQUS/Explicit is designed for high-strain-rate dynamic problems in
which inertia effects are important. Therefore, the *TENSILE FAILURE option should be used only
for such situations. Improper use of the tensile failure model may result in an incorrect simulation.
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Usage: Use the following options:
*EOS
*EOS SHEAR
*TENSILE FAILURE
Adiabatic assumption
An adiabatic condition is always assumed for materials modeled with an equation of state unless a
dynamic coupled temperature-displacement procedure is used. In other words, neither the
ADIABATIC parameter on the *DYNAMIC option nor the *TEMPERATURE option has any effect
on the behavior of this model.
Modeling fluids
A linear Us ¡ Up equation of state model can be used to model incompressible viscous and inviscid
laminar flow governed by the Navier-Stokes equation of motion. The volumetric response is governed
by the equations of state, where the bulk modulus acts as a penalty parameter for the incompressible
constraint.
To model a viscous laminar flow that follows the Navier-Poisson law of a Newtonian fluid, use the
*EOS SHEAR, TYPE=VISCOUS option and define the viscosity as the real linear viscosity of the
fluid. Appropriate initial conditions for velocity and stress are essential to get an accurate solution for
this class of problem.
To model an incompressible inviscid fluid such as water in ABAQUS/Explicit, it is useful to define a
small amount of shear resistance to suppress shear modes that can otherwise tangle the mesh. Here the
shear stiffness or shear viscosity acts as a penalty parameter. The shear modulus or viscosity should be
small because flow is inviscid; a high shear modulus or viscosity will result in an overly stiff response.
To avoid an overly stiff response, the internal forces arising due to the deviatoric response of the
material should be kept several orders of magnitude below the forces arising due to the volumetric
response. This can be done by choosing an elastic shear modulus that is several orders of magnitude
lower than the bulk modulus. If the viscous model is used, the shear viscosity specified should be on
the order of the shear modulus, calculated as above, scaled by the stable time increment. The expected
stable time increment can be obtained from a datacheck analysis of the model. This method is a
convenient way to approximate a shear resistance that will not introduce excessive viscosity in the
material.
If a shear model is defined by using the *EOS SHEAR option, the hourglass control forces are
calculated based on the shear resistance of the material. Thus, in materials with extremely low or zero
shear strengths such as inviscid fluids, the hourglass forces calculated based on the default parameters
are insufficient to prevent spurious hourglass modes. Therefore, a sufficiently high hourglass scaling
factor is recommended to increase the resistance to such modes.
Elements
Equations of state can be used with any solid (continuum) elements except plane stress elements.
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Additional references
· Dobratz, B. M., "LLNL Explosives Handbook, Properties of Chemical Explosives and Explosive
Simulants," UCRL-52997, Lawrence Livermore National Laboratory, Livermore, California,
January 1981.
· Lee, E., M. Finger, and W. Collins, "JWL Equation of State Coefficients for High Explosives,"
UCID-16189, Lawrence Livermore National Laboratory, Livermore, California, January 1973.
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10. Inelastic Mechanical Properties
10.1 Overview
10.1.1 Inelastic behavior
The ABAQUS/Explicit material library includes several models of inelastic behavior:
Classical metal plasticity: The yield and inelastic flow of a metal at relatively low temperatures,
for which loading is relatively monotonic, can typically be described with the classical metal
plasticity models (``Classical metal plasticity,'' Section 10.2.1). In ABAQUS/Explicit these models
use standard Mises or Hill yield surfaces with associated plastic flow. Perfect plasticity and
isotropic hardening definitions are both available in the classical metal plasticity models. Common
applications include crash analyses, metal forming, and general collapse studies; the models are
simple and adequate for such cases.
Rate-dependent yield: As strain rates increase, many materials show an increase in their yield
strength. Rate dependence (``Rate-dependent yield,'' Section 10.2.2) can be defined in
ABAQUS/Explicit for a number of plasticity models. Applicable models include classical metal
plasticity, extended Drucker-Prager plasticity, and crushable foam plasticity.
Anisotropic yield: ABAQUS provides an anisotropic yield model (``Anisotropic yield,'' Section
10.2.3), which is available for use with materials modeled with classical metal plasticity
(``Classical metal plasticity,'' Section 10.2.1) that exhibit different yield stresses in different
directions. This model allows for the specification of different stress ratios for each stress
component to define the initial anisotropy. The model is not adequate for cases in which the
anisotropy changes significantly as the material deforms as a result of loading.
Johnson-Cook plasticity: The Johnson-Cook plasticity model (``Johnson-Cook plasticity,''
Section 10.2.4) is particularly suited to model high-strain-rate deformation of metals. This model
is a particular type of Mises plasticity that includes analytical forms of the hardening law and rate
dependence. It is generally used in adiabatic transient dynamic analysis.
Failure models: Two types of failure models are offered in ABAQUS/Explicit for the Mises and
Johnson-Cook plasticity models (``Failure models,'' Section 10.2.5). One is the shear failure
model, where the failure criterion is based on the accumulated equivalent plastic strain. Another is
the tensile failure model, which uses the hydrostatic pressure stress as a failure measure to model
dynamic spall or a pressure cutoff. Both models offer a number of failure choices including
element removal and are applicable mainly in truly dynamic situations.
Porous metal plasticity: The porous metal plasticity model (``Porous metal plasticity,'' Section
10.2.6) is used to model materials that exhibit damage in the form of void initiation and growth,
and it can also be used for some powder metal process simulations at high relative densities
(relative density is defined as the ratio of the volume of solid material to the total volume of the
material). The model is based on Gurson's porous metal plasticity theory with void nucleation and
is intended for use with materials that have a relative density that is greater than 0.9. The model is
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adequate for relatively monotonic loading.
Extended Drucker-Prager plasticity: The extended Drucker-Prager plasticity model (``Extended
Drucker-Prager model,'' Section 10.3.1) describes the behavior of granular materials or polymers
in which the yield behavior depends on the equivalent pressure stress. The inelastic deformation
may sometimes be associated with frictional mechanisms such as sliding of particles across each
other. The model uses smoothed Mohr-Coulomb yield surfaces in the deviatoric plane, associated
inelastic flow in the deviatoric plane, and separate dilation and friction angles.
Modified Drucker-Prager/Cap plasticity: The modified Drucker-Prager/Cap plasticity model
(``Modified Drucker-Prager/Cap model,'' Section 10.3.2) can be used to simulate geological
materials that exhibit pressure-dependent yield. The addition of a cap yield surface helps control
volume dilatancy when the material yields in shear and provides an inelastic hardening mechanism
to represent plastic compaction.
Crushable foam plasticity: The foam plasticity model (``Crushable foam plasticity model,''
Section 10.3.3) is intended for modeling crushable foams that are typically used as energy
absorption structures; however, other crushable materials such as balsa wood can also be
simulated with this model. The model is a modification of the critical state theory.
Cracking model for concrete: The brittle cracking model in ABAQUS/Explicit (``Cracking
model for concrete,'' Section 10.4.1) is designed to provide a capability for modeling plain and
reinforced concrete (as well as other similarly brittle materials) in all types of structures: beams,
shells and solids. The model is designed for applications in which the concrete behavior is
dominated by tensile cracking. A simple brittle failure criteria is available to allow the removal of
elements from a mesh.
Plasticity theories
Most materials of engineering interest initially respond elastically. Elastic behavior means that the
deformation is fully recoverable: when the load is removed, the specimen returns to its original shape.
If the load exceeds some limit (the "yield load"), the deformation is no longer fully recoverable. Some
part of the deformation will remain when the load is removed, as, for example, when a paperclip is
bent too much or when a billet of metal is rolled or forged in a manufacturing process. Plasticity
theories model the material's mechanical response as it undergoes such nonrecoverable deformation in
a ductile fashion. The theories have been developed most intensively for metals, but they are also
applied to soils, concrete, rock, ice, crushable foam, and so on. These materials behave in very
different ways. For example, large values of pure hydrostatic pressure cause very little inelastic
deformation in metals, but quite small hydrostatic pressure values may cause a significant,
nonrecoverable volume change in a soil sample. Nonetheless, the fundamental concepts of plasticity
theories are sufficiently general that models based on these concepts have been developed successfully
for a wide range of materials.
Incremental plasticity models
The plasticity models in ABAQUS/Explicit are "incremental" theories in which the mechanical strain
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rate is decomposed into an elastic part and a plastic (inelastic) part.
Incremental plasticity models are usually formulated in terms of
· a yield surface, which generalizes the concept of "yield load" into a test function that can be used
to determine if the material responds purely elastically at a particular state of stress, temperature,
etc;
· a flow rule, which defines the inelastic deformation that occurs if the material point is no longer
responding purely elastically; and
· evolution laws that define the hardening--the way in which the yield and/or flow definitions
change as inelastic deformation occurs.
Elastic response
The ABAQUS plasticity models also need an elasticity definition to deal with the recoverable part of
the strain. In ABAQUS/Explicit the elasticity is defined by including the *ELASTIC option in the
same material definition block (see ``Material data definition,'' Section 8.1.2). In the case of the Mises
and Johnson-Cook plasticity models the elasticity can alternatively be defined using an equation of
state with associated deviatoric behavior (see ``Equation of state,'' Section 9.5.1).
ABAQUS/Explicit assumes that the plastic strains dominate the deformation and that the elastic strains
are small. This restriction is imposed by the elasticity models that ABAQUS uses. It is justified
because most materials have a well-defined yield point that is a very small percentage of their Young's
modulus; for example, the yield stress of metals is typically less than 1% of the Young's modulus of
the material. Therefore, the elastic strains will also be less than this percentage, and the elastic
response of the material can be modeled quite accurately as being linear.
Stress and strain measures
Most materials that exhibit ductile behavior (large inelastic strains) yield at stress levels that are orders
of magnitude less than the elastic modulus of the material, which implies that the relevant stress and
strain measures are "true" stress (Cauchy stress) and logarithmic strain. Material data for all of these
models should, therefore, be given in these measures.
If the user has nominal stress-strain data for a uniaxial test and the material is isotropic, a simple
conversion to true stress and logarithmic plastic strain is
¾true = ¾nom (1 + "nom );
"pl
ln = ln(1 + "nom ) ¡
¾true
;
E
where E is the Young's modulus.
Example of stress-strain data input
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The example below illustrates the input of material data for the classical metal plasticity model
(``Classical metal plasticity,'' Section 10.2.1). Stress-strain data representing the material hardening
behavior are necessary to define the model. An experimental hardening curve might appear as that
shown in Figure 10.1.1-1. First yield occurs at 200 MPa (29000 lb/in 2). The material then hardens to
300 MPa (43511 lb/in 2) at one percent strain, after which it is perfectly plastic. Assuming that the
Young's modulus is 200000 MPa ( 29 £ 106 lb/in2), the plastic strain at the one percent strain point is
:01 ¡ 300=200000 = :0085 . When the units are Newtons and millimeters, the input is
*PLASTIC
200., 0.
300., .0085
Figure 10.1.1-1 Experimental hardening curve.
Plastic strain values, not total strain values, are used in defining the hardening behavior. Furthermore,
the first data pair must correspond with the onset of plasticity (the plastic strain value must be zero in
the first pair). These concepts are applicable when hardening data are defined in a tabular form for any
of the following plasticity models:
· ``Classical metal plasticity,'' Section 10.2.1.
· ``Porous metal plasticity,'' Section 10.2.6.
· ``Extended Drucker-Prager model,'' Section 10.3.1.
· ``Modified Drucker-Prager/Cap model,'' Section 10.3.2.
· ``Crushable foam plasticity model,'' Section 10.3.3.
The options required to define hardening are discussed in the referenced sections.
10.2 Metal plasticity
10.2.1 Classical metal plasticity
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The classical metal plasticity models are defined using the *PLASTIC and, optionally, the *RATE
DEPENDENT and the *POTENTIAL options.
References
· *PLASTIC
· *RATE DEPENDENT
· *POTENTIAL
· ``Rate-dependent yield,'' Section 10.2.2
· ``Anisotropic yield,'' Section 10.2.3
· ``Johnson-Cook plasticity,'' Section 10.2.4
· ``Failure models,'' Section 10.2.5
· ``Material library: overview,'' Section 8.1.1
· ``Inelastic behavior,'' Section 10.1.1
Overview
The classical metal plasticity models:
· use Mises or Hill yield surfaces with associated plastic flow, which allow for isotropic and
anisotropic yield, respectively;
· use perfect plasticity or isotropic hardening behavior;
· are intended for applications such as crash analyses, metal forming, and general collapse studies;
· can be used such that plastic dissipation results in the heating of a material;
· can be used when rate-dependent effects are important;
· can be used in conjunction with the *SHEAR FAILURE option to provide a simple ductile failure
criterion that allows for the removal of elements from the mesh;
· can be used in conjunction with the *TENSILE FAILURE option to provide a tensile spall
criterion offering a number of failure choices and removal of elements from the mesh; and
· must be used in conjunction with either the linear elastic material model ( ``Linear elastic
behavior,'' Section 9.2.1) or the equation of state material model (``Equation of state,'' Section
9.5.1).
Yield surfaces
The Mises and Hill yield surfaces assume that yielding of the metal is independent of the equivalent
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pressure stress: this observation is confirmed experimentally for most metals (except voided metals)
under positive pressure stress but may be inaccurate for metals under conditions of high triaxial
tension when voids may nucleate and grow in the material. Such conditions can arise in stress fields
near crack tips and in some extreme thermal loading cases such as those that might occur during
welding processes. A porous metal plasticity model is provided in ABAQUS for such situations. This
model is described in ``Porous metal plasticity,'' Section 10.2.6.
The Mises yield surface is used to define isotropic yielding. It is defined by giving the value of the
uniaxial yield stress as a function of uniaxial equivalent plastic strain, temperature, and/or field
variables on the data lines of the *PLASTIC option.
The Hill yield surface allows anisotropic yielding to be modeled. A reference yield stress, ¾ 0 , must be
given using the *PLASTIC option, and a set of yield ratios, Rij , must be defined by the *POTENTIAL
option. These options define the yield stress corresponding to each stress component as Rij ¾ 0 . Hill's
potential function is discussed in detail in ``Anisotropic yield,'' Section 10.2.3. The *POTENTIAL
option can be used to define three common forms of anisotropy associated with sheet metal forming:
transverse anisotropy, planar anisotropy, and general anisotropy.
Hardening
Three types of work hardening are provided: perfect plasticity, isotropic hardening, and Johnson-Cook
hardening.
Perfect plasticity
Perfect plasticity means that the yield stress does not change with plastic strain. It can be defined in
tabular form for a range of temperatures and/or field variables; a single yield stress value per
temperature and/or field variable specifies the onset of yield.
Usage: *PLASTIC
Isotropic hardening
Isotropic hardening means that the yield surface changes size uniformly in all directions such that the
yield stress increases (or decreases) in all stress directions as plastic straining occurs. ABAQUS
provides an isotropic hardening model, which is useful for cases involving gross plastic straining or in
cases where the straining at each point is essentially in the same direction in strain space throughout
the analysis. Although the model is referred to as a "hardening" model, strain softening or hardening
followed by softening can be defined. Isotropic hardening plasticity is discussed in more detail in
``Isotropic elasto-plasticity,'' Section 4.3.2 of the ABAQUS Theory Manual.
If isotropic hardening is defined, the yield stress, ¾ 0 , must be given as a tabular function of plastic
strain, and, if required, of temperature and/or other predefined field variables. The yield stress at a
given state is simply interpolated from this table of data, and it remains constant for plastic strains
exceeding the last value given as tabular data. ABAQUS/Explicit will regularize the data into tables
that are defined in terms of even intervals of the independent variables. In some cases where the yield
stress is defined at uneven intervals of the independent variable (plastic strain) and the range of the
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independent variable is large compared to the smallest interval, ABAQUS/Explicit may fail to obtain
an accurate regularization of the user's data in a reasonable number of intervals. In this case the
program will stop after all data are processed with an error message that the user must redefine the
material data. See ``Material library: overview,'' Section 8.1.1, for a more detailed discussion of data
regularization.
Usage: *PLASTIC, HARDENING=ISOTROPIC (default)
Johnson-Cook hardening
Johnson-Cook hardening is a particular type of isotropic hardening where the yield stress is given as an
analytical function of equivalent plastic strain, strain rate, and temperature. This hardening law is
suited for modeling high-rate deformation of many materials including most metals. The
*POTENTIAL option cannot be used with Johnson-Cook hardening. For more details, see
``Johnson-Cook plasticity,'' Section 10.2.4.
Usage: *PLASTIC, HARDENING=JOHNSON COOK
Flow rule
Associated plastic flow is used. Therefore, as the material yields, the inelastic deformation rate is in the
direction of the normal to the yield surface (the plastic deformation is volume invariant). This
assumption is generally acceptable for most calculations with metals; the most obvious case where it is
not appropriate is the detailed study of the localization of plastic flow in sheets of metal as the sheet
develops texture and eventually tears apart. So long as the details of such effects are not of interest (or
can be inferred from less detailed criteria, such as reaching a forming limit that is defined in terms of
strain), the associated flow models in ABAQUS used with the smooth Mises or Hill yield surfaces
generally predict the behavior accurately.
Rate dependence
As strain rates increase, many materials show an increase in their yield strength. This effect becomes
important in many metals when the strain rates range between 0.1 and 1 per second; and it can be very
important for strain rates ranging between 10 and 100 per second, which are characteristic of
high-energy dynamic events or manufacturing processes.
There are two ways to introduce a strain-rate-dependent yield stress.
Direct tabular data
Test data can be provided as tables of yield stress values versus equivalent plastic strain at different
pl
equivalent plastic strain rates ( "¹_ ); one table per strain rate. Direct tabular data cannot be used with
Johnson-Cook hardening. The guidelines that govern the entry of this data are provided in
``Rate-dependent yield,'' Section 10.2.2.
pl
Usage: *PLASTIC, RATE="¹_
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Yield stress ratios
The *RATE DEPENDENT option can be used in conjunction with the *PLASTIC option. This
combination allows the user to enter only one hardening curve, the static hardening curve, and then to
express the rate-dependent hardening curves in terms of the static relation; that is, we assume that
pl
pl
¾
¹ (¹
"pl ; "¹_ ) = ¾ 0 (¹
"pl )R("¹_ );
pl
where ¾ 0 is the static yield stress, "¹pl is the equivalent plastic strain, "¹_ is the equivalent plastic strain
pl
rate, and R is a ratio, defined as R = 1:0 at "¹_ = 0:0. The *RATE DEPENDENT option is described
further in ``Rate-dependent yield,'' Section 10.2.2.
Usage: Use both of the following options:
*PLASTIC
*RATE DEPENDENT
Shear failure
The *SHEAR FAILURE option can be used in conjunction with the metal plasticity material models in
ABAQUS/Explicit to define shear failure of the material. The shear failure model provides a simple
failure criterion that is suitable for high-strain-rate deformation of many materials including most
metals. It offers two failure choices, including the removal of elements from the mesh as a result of
tearing or ripping of the structure. The shear failure criterion is based on the value of the equivalent
plastic strain and is applicable mainly to high-strain-rate, truly dynamic problems. For more details,
see ``Failure models,'' Section 10.2.5.
Usage: Use both of the following options:
*PLASTIC
*SHEAR FAILURE
Tensile failure
The *TENSILE FAILURE option can be used in conjunction with the metal plasticity material models
in ABAQUS/Explicit to define tensile failure of the material. The tensile failure model uses the
hydrostatic pressure stress as a failure measure to model dynamic spall or a pressure cutoff. It offers a
number of failure choices including element removal. Similarly to the shear failure model, the
ABAQUS/Explicit tensile failure model is suitable for high-strain-rate deformation of metals and is
applicable to truly dynamic problems. For more details, see ``Failure models,'' Section 10.2.5.
Usage: Use both of the following options:
*PLASTIC
*TENSILE FAILURE
Heat generation by plastic work
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ABAQUS/Explicit allows for an adiabatic stress analysis to be performed in which heat generated by
plastic straining of a material is calculated. An adiabatic stress analysis is specified by including the
ADIABATIC parameter in the *DYNAMIC, EXPLICIT option. The option is typically used in the
simulation of bulk metal forming or high speed manufacturing processes involving large amounts of
inelastic strain, where the heating of the material caused by its deformation is an important effect
because of temperature dependence of the material properties.
This effect is introduced by defining the fraction of the rate of inelastic dissipation that appears as a
heat flux per volume.
Usage: Use all of the following parameters in the same material data block:
*PLASTIC
*SPECIFIC HEAT
*DENSITY
*INELASTIC HEAT FRACTION
Elements
Classical metal plasticity can be used with any elements that include mechanical behavior (elements
that have displacement degrees of freedom).
Output
In addition to the standard output identifiers available in ABAQUS/Explicit (``Output variable
identifiers,'' Section 4.2.1), the following variable has special meaning for the classical metal plasticity
models:
R t q 2 pl pl
pl
PEEQ
Equivalent plastic strain, "¹ = 0 3 "_ : "_ dt:
10.2.2 Rate-dependent yield
Strain rate dependence can be defined directly or with the *RATE DEPENDENT option when using
the *PLASTIC option, the *DRUCKER PRAGER HARDENING option, or the *FOAM
HARDENING option.
References
· *RATE DEPENDENT
· ``Classical metal plasticity,'' Section 10.2.1
· ``Johnson-Cook plasticity,'' Section 10.2.4
· ``Extended Drucker-Prager model,'' Section 10.3.1
· ``Crushable foam plasticity model,'' Section 10.3.3
· ``Material library: overview,'' Section 8.1.1
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Inelastic Mechanical Properties
· ``Inelastic behavior,'' Section 10.1.1
Overview
Rate-dependent yield:
· is needed to define a material's yield behavior accurately when the yield strength depends on the
rate of straining and the anticipated strain rates are significant;
· is available only for the isotropic hardening metal plasticity models (Mises and Johnson-Cook) ,
the extended Drucker-Prager plasticity model, and the crushable foam plasticity model;
· can be conveniently defined on the basis of work hardening parameters and field variables for
*PLASTIC, HARDENING=ISOTROPIC and *DRUCKER PRAGER HARDENING by providing
tabular data for these options; and
· can be defined using the *RATE DEPENDENT option in conjunction with the *PLASTIC, the
*DRUCKER PRAGER HARDENING, or the *FOAM HARDENING options through
specification of user-defined overstress power law parameters or yield stress ratios.
Work hardening dependencies
¹ (or f for the foam model), is dependent on work hardening,
Generally, a material's yield stress, ¾
which for isotropic hardening models is usually represented by a suitable measure of equivalent plastic
pl
strain, "¹pl ; the inelastic strain rate, "¹_ ; temperature, µ; and predefined field variables, fi :
pl
¾
¹=¾
¹ (¹
"pl ; "¹_ ; µ; fi ):
Many materials show an increase in their yield strength as strain rates increase; this effect becomes
important in many metals and polymers when the strain rates range between 0.1 and 1 per second, and
it can be very important for strain rates ranging between 10 and 100 per second, which are
characteristic of high-energy dynamic events or manufacturing processes.
Defining hardening dependencies for various material models
Strain rate dependence can be defined by entering hardening curves at different strain rates directly or
by using the *RATE DEPENDENT option to define yield stress ratios.
Direct entry of test data
For both the isotropic hardening Mises plasticity model and the extended Drucker-Prager plasticity
model, work hardening dependencies can be given quite generally. The tabular data can be provided
through the *PLASTIC, HARDENING=ISOTROPIC option and the *DRUCKER PRAGER
HARDENING option. The test data are entered as tables of yield stress values versus equivalent plastic
strain at different equivalent plastic strain rates. The yield stress must be given as a function of the
equivalent plastic strain and, if required, of temperature and of other predefined field variables. In
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Inelastic Mechanical Properties
defining this dependence at finite strains, "true" (Cauchy) stress and log strain values should be used.
The hardening curve at each temperature must always start at zero plastic strain. For perfect plasticity
only one yield stress, with zero plastic strain, should be defined at each temperature. It is possible to
define the material to be strain softening as well as strain hardening. The work hardening data are
repeated as often as needed to define stress-strain curves at different strain rates. The yield stress at a
given strain and strain rate is interpolated directly from these tables.
Usage: Use one of the following options:
pl
*PLASTIC, HARDENING=ISOTROPIC, RATE="¹_
pl
*DRUCKER PRAGER HARDENING, RATE="¹_
Using yield stress ratios
Alternatively, and as the only means of defining rate-dependent yield stress for the Johnson-Cook and
the crushable foam plasticity models, the strain rate behavior can be assumed to be separable, so that
the stress-strain dependence is identical at all strain levels:
pl
¾
¹ = ¾ 0 (¹
"pl ; µ; fi )R("¹_ ; µ; fi );
"pl ; µ; fi ) (or f0 (¹
"pl ; µ; fi ) in the foam model) is the static stress-strain behavior and
where ¾ 0 (¹
pl
R("¹_ ; µ; fi ) is the ratio of the yield stress at nonzero strain rate to the static yield stress (so that
R(0; µ; fi ) = 1:0 ).
To specify such a definition, the *RATE DEPENDENT option must be used in conjunction with the
*PLASTIC option, the *DRUCKER PRAGER HARDENING option, or the *FOAM HARDENING
option. Three methods are offered by the *RATE DEPENDENT option to define R: specifying an
overstress power law, defining R directly as a tabular function, or specifying an analytical
Johnson-Cook form.
Overstress power law
The overstress power law has the form
pl
"¹_ = D (R ¡ 1)n
for
¾
¹ ¸ ¾0
(or
f ¸ f0
in the foam model);
where D (µ; fi ) and n(µ; fi ) are material parameters that can be functions of temperature and, possibly,
of other predefined field variables.
Usage: *RATE DEPENDENT, TYPE=POWER LAW
Tabular function
pl
Alternatively, R can be entered directly as a tabular function of the equivalent plastic strain rate, "¹_ ;
temperature, µ; and field variables, fi .
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Inelastic Mechanical Properties
Usage: *RATE DEPENDENT, TYPE=YIELD RATIO
Johnson-Cook rate dependence
Johnson-Cook rate dependence has the form
∙
1
"¹_ = "_0 exp
(R ¡ 1)
C
pl
¸
for
¾
¹ ¸ ¾0 ;
where "_0 and C are material constants that do not depend on temperature and are assumed not to
depend on predefined field variables. Johnson-Cook rate dependence must be used with Johnson-Cook
hardening (it cannot be used in conjunction with the *PLASTIC, HARDENING=ISOTROPIC option,
the *DRUCKER PRAGER HARDENING option, or the *FOAM HARDENING option). For more
details, see ``Johnson-Cook plasticity,'' Section 10.2.4.
Usage: *RATE DEPENDENT, TYPE=JOHNSON COOK
Elements
Rate-dependent yield can be used with all elements that include mechanical behavior (elements that
have displacement degrees of freedom).
10.2.3 Anisotropic yield
Anisotropic yield is defined by using the *POTENTIAL option in conjunction with the *PLASTIC
option.
References
· *POTENTIAL
· ``Material library: overview,'' Section 8.1.1
· ``Inelastic behavior,'' Section 10.1.1
Overview
Anisotropic yield:
· can be used for materials that exhibit different yield behavior in different directions;
· is introduced through user-defined stress ratios that are applied in Hill's potential function; and
· can be used only in conjunction with the *PLASTIC option.
Yield stress ratios
Anisotropic yield behavior is modeled through the use of yield stress ratios, Rij . The yield ratios are
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Inelastic Mechanical Properties
defined with respect to a reference yield stress, ¾ 0 (given on the *PLASTIC option) such that if ¾ij is
applied as the only nonzero stress, the corresponding yield stress is Rij ¾ 0 .
Yield stress ratios can be defined as constants or as tabular functions of temperature and predefined
field variables using the *POTENTIAL option. This option must appear immediately after the
*PLASTIC material option data to which it applies. The *ORIENTATION option must be used to
define the direction of anisotropy.
Usage: *POTENTIAL
Anisotropic yield
Hill's potential function is a simple extension of the Mises function, which can be expressed in terms
of rectangular Cartesian stress components as
f (¾ ) =
p
F (¾22 ¡ ¾33 )2 + G(¾33 ¡ ¾11 )2 + H (¾11 ¡ ¾22 )2 + 2L¾23 2 + 2M ¾31 2 + 2N ¾12 2 ;
where F; G; H; L; M; and N are constants obtained by tests of the material in different orientations.
They are defined as
F =
(¾ 0 )2 1
1
1 1
1
1
1
( 2 + 2 ¡ 2 ) = ( 2 + 2 ¡ 2 );
2
¾
¹22
¾
¹33
¾
¹11
2 R22
R33
R11
G=
(¾ 0 )2 1
1
1 1
1
1
1
( 2 + 2 ¡ 2 ) = ( 2 + 2 ¡ 2 );
2
¾
¹33
¾
¹11
¾
¹22
2 R33
R11
R22
H=
1
1
(¾ 0 )2 1
1
1 1
1
( 2 + 2 ¡ 2 ) = ( 2 + 2 ¡ 2 );
2
¾
¹11
¾
¹22
¾
¹33
2 R11
R22
R33
2
3 ¿0
3
L= (
) =
;
2
2 ¾
¹23
2R23
2
M=
3 ¿0
3
(
) =
;
2 ¾
¹13
2R213
N=
3 ¿0
3
(
) =
;
2 ¾
¹12
2R212
2
where each ¾
¹ij is the measured yield stress value when ¾ij is applied as the only nonzero stress
component; ¾ 0 is the reference yield stress specified on the *PLASTIC option; R11 , R22 , R33 , R12 ,
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Inelastic Mechanical Properties
p
R13 , and R23 are anisotropic yield stress ratios; and ¿ 0 = ¾ 0 = 3. The six yield stress ratios are,
therefore, defined as follows (in the order in which they must be provided by the user):
¾
¹11
;
¾0
¾
¹22
;
¾0
¾
¹33
;
¾0
¾
¹12
;
¿0
¾
¹13
;
¿0
¾
¹23
:
¿0
Because of the form of the yield function, all of these ratios must be positive.
The flow rule is
d""pl = d¸
@f
d¸
b;
=
¾
@¾
f
where, from the definition of f above,
2
3
¡G(¾33 ¡ ¾11 ) + H (¾11 ¡ ¾22 )
6 F (¾22 ¡ ¾33 ) ¡ H (¾11 ¡ ¾22 ) 7
6
7
6 ¡F (¾22 ¡ ¾33 ) + G(¾33 ¡ ¾11 ) 7
b=6
7:
2N¾12
6
7
4
5
2M ¾31
2L¾23
Usage: Use both of the following options:
*PLASTIC
*POTENTIAL
Defining anisotropic yield behavior on the basis of strain ratios
As discussed above, Hill's anisotropic plasticity potential is defined in ABAQUS from user input
consisting of ratios of yield stress in different directions with respect to a reference stress. However, in
some cases, such as sheet metal forming applications, it is common to find the anisotropic material
data given in terms of ratios of width strain to thickness strain. Mathematical relationships are then
necessary to convert the strain ratios to stress ratios that can be input into ABAQUS.
In sheet metal forming applications we are generally concerned with plane stress conditions. Consider
x; y to be the "rolling" and "cross" directions in the plane of the sheet; z is the thickness direction.
From a design viewpoint, the type of anisotropy usually desired is that in which the sheet is isotropic
in the plane and has an increased strength in the thickness direction, which is normally referred to as
transverse anisotropy. Another type of anisotropy is characterized by different strengths in different
directions in the plane of the sheet, which is called planar anisotropy.
In a simple tension test performed in the x-direction in the plane of the sheet, the flow rule for this
potential (given above) defines the incremental strain ratios (assuming small elastic strains) as
d"11 : d"22 : d"33 = G + H : ¡H : ¡G:
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Inelastic Mechanical Properties
Therefore, the ratio of width to thickness strain, known as the r-value, is
rx =
d"22
H
= :
d"33
G
Similarly, for a simple tension test performed in the y-direction in the plane of the sheet, the
incremental strain ratios are
d"11 : d"22 : d"33 = ¡H : F + H : ¡F;
and
ry =
d"11
H
= :
d"33
F
Transverse anisotropy
A transversely anisotropic material is one where rx = ry . If we define ¾ 0 in the *PLASTIC option to
¹11 , then
be equal to ¾
R11 = R22 = 1
and, using the relationships above
R33 =
r
rx + 1
:
2
If rx = 1 (isotropic material), R33 = 1 and the Mises isotropic plasticity model is recovered.
Planar anisotropy
In the case of planar anisotropy rx and ry are different and R11 ; R22 ; R33 will all be different. If we
¹11 ,
define ¾ 0 in the *PLASTIC option to be equal to ¾
R11 = 1;
and, using the relationships above, we obtain
R22 =
s
ry (rx + 1)
;
rx (ry + 1)
R33 =
s
ry (rx + 1)
:
(rx + ry )
Again, if rx = ry = 1, R22 = R33 = 1 and the Mises isotropic plasticity model is recovered.
General anisotropy
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Inelastic Mechanical Properties
Thus far, we have only considered loading applied along the axes of anisotropy. To derive a more
general anisotropic model in plane stress, the sheet must be loaded in one other direction in its plane.
Suppose we perform a simple tension test at an angle ® to the x-direction; then, from equilibrium
considerations we can write the nonzero stress components as
¾11 = ¾ cos2 ®;
¾22 = ¾ sin2 ®;
¾12 = ¾ sin® cos®;
where ¾ is the applied tensile stress. Substituting these values in the flow equations and assuming
small elastic strains yields
d"11 = [(G + H )cos2 ® ¡ H sin2 ®]
¾
d¸;
f
d"22 = [(F + H )sin2 ® ¡ H cos2 ®]
¾
d¸;
f
d"33 = ¡[F sin2 ® + G cos2 ®]
d°12 = [N sin® cos®]
¾
d¸; and
f
¾
d¸:
f
Assuming small geometrical changes, the width strain increment (the increment of strain at right angles
to the direction of loading, ®) is written as
d"®+ ¼2 = d"11 sin2 ® + d"22 cos2 ® ¡ 2 d°12 sin® cos®;
and the r-value for loading at an angle ® is
r® =
d"®+ ¼2
H + (2N ¡ F ¡ G ¡ 4H )sin2 ® cos2 ®
:
=
d"33
F sin2 ® + G cos2 ®
One of the more commonly performed tests is that in which the loading direction is at 45°. In this case
r45 =
2N ¡ (F + G)
2(F + G)
or
1
N
rx
= (r45 + )(1 + ):
G
2
ry
¹11 in the *PLASTIC option, R11 = 1. R22 ; R33 are as defined before for transverse
If ¾ 0 is equal to ¾
or planar anisotropy and, using the relationships above,
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Inelastic Mechanical Properties
R12 =
s
3(rx + 1)ry
:
(2r45 + 1)(rx + ry )
Elements
Anisotropic yield can be defined for any element that can be used with the classical metal plasticity
models (``Classical metal plasticity,'' Section 10.2.1).
Output
The standard output identifiers available in ABAQUS/Explicit (``Output variable identifiers,'' Section
4.2.1) and all output variables associated with the classical metal plasticity models (``Classical metal
plasticity,'' Section 10.2.1) are available when anisotropic yield is defined.
The following variable has special meaning if anisotropic yield is defined:
R t pl
R t _ pl
PEEQ
Equivalent plastic strain, "¹pl = 0 "¹_ dt = 0 ¾ :"¾0 dt :
10.2.4 Johnson-Cook plasticity
The Johnson-Cook plasticity model is defined by using the *PLASTIC, HARDENING=JOHNSON
COOK option and, optionally, the *RATE DEPENDENT, TYPE=JOHNSON COOK option.
References
· *PLASTIC
· *RATE DEPENDENT
· *SHEAR FAILURE
· *TENSILE FAILURE
· ``Classical metal plasticity,'' Section 10.2.1
· ``Rate-dependent yield,'' Section 10.2.2
· ``Equation of state,'' Section 9.5.1
· ``Failure models,'' Section 10.2.5
· ``Material library: overview,'' Section 8.1.1
· ``Inelastic behavior,'' Section 10.1.1
Overview
The Johnson-Cook plasticity model:
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Inelastic Mechanical Properties
· is a particular type of Mises plasticity model with analytical forms of the hardening law and rate
dependence;
· is suitable for high-strain-rate deformation of many materials, including most metals;
· is typically used in adiabatic transient dynamic simulations;
· can be used in conjunction with the *SHEAR FAILURE, TYPE=JOHNSON COOK option to
model shear failure;
· can be used in conjunction with the *TENSILE FAILURE option to model tensile spall or a
pressure cutoff; and
· must be used in conjunction with either the linear elastic material model ( ``Linear elastic
behavior,'' Section 9.2.1) or the equation of state material model (``Equation of state,'' Section
9.5.1).
Yield surface and flow rule
A Mises yield surface with associated flow is used in the Johnson-Cook plasticity model.
Johnson-Cook hardening
Johnson-Cook hardening is a particular type of isotropic hardening where the static yield stress, ¾ 0 , is
assumed to be of the form
h
´
¡ ¢n i³
¾ 0 = A + B "¹pl
1 ¡ µ^m ;
where "¹pl is the equivalent plastic strain and A, B, n and m are material parameters measured at or
below the transition temperature, µtransition . µ^ is the nondimensional temperature defined as
µ^ ´
8
>
<
>
:
0
(µ ¡ µtransition )=(µmelt ¡ µtransition )
1
for
µ < µtransition
for
µtransition ∙ µ ∙ µmelt ;
for
µ > µmelt
where µ is the current temperature, µmelt is the melting temperature, and µtransition is the transition
temperature defined as the one at or below which there is no temperature dependence on the
expression of the yield stress. The material parameters must be measured at or below the transition
temperature.
The Johnson-Cook model is valid up to the melting temperature. When the temperature reaches or
exceeds the melting temperature, the material will be melted and will behave like a fluid (there will be
no shear resistance). Therefore, the material point fails, and all the stress components will be set to
zero.
The values of A, B, n, m, µmelt , and µtransition are provided by the user on the data line of the
*PLASTIC, HARDENING=JOHNSON COOK option.
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Inelastic Mechanical Properties
Usage: *PLASTIC, HARDENING=JOHNSON COOK
Johnson-Cook strain rate dependence
Johnson-Cook strain rate dependence assumes that
pl
¾
¹ = ¾ 0 (¹
"pl ; µ)R("¹_ )
and
∙
1
"¹_ = "_0 exp
(R ¡ 1)
C
pl
¸
for
¾
¹ ¸ ¾0 ;
where
¾
¹
is the yield stress at nonzero strain rate;
pl
"¹_
is the equivalent plastic strain rate;
"_0 and C
are material parameters measured at or below the transition temperature, µtransition ;
"pl ; µ)
¾ 0 (¹
is the static yield stress; and
pl
R("¹_ )
is the ratio of the yield stress at nonzero strain rate to the static yield stress (so that
R("_0 ) = 1:0 ).
The yield stress is, therefore, expressed as
"
à pl !#
i
´
³
¢
"¹_
n
¾
¹ = A + B "¹pl
1 + C ln
1 ¡ µ^m :
"_0
h
¡
The values of C and "_0 are provided by the user on the data line of the *RATE DEPENDENT,
TYPE=JOHNSON COOK option.
The use of Johnson-Cook hardening does not necessarily require the use of Johnson-Cook strain rate
dependence, but the use of Johnson-Cook strain rate dependence does require the use of Johnson-Cook
hardening.
Usage: Use both of the following options:
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Inelastic Mechanical Properties
*PLASTIC, HARDENING=JOHNSON COOK
*RATE DEPENDENT, TYPE=JOHNSON COOK
Johnson-Cook shear failure
The option *SHEAR FAILURE, TYPE=JOHNSON COOK can be used in conjunction with the
Johnson-Cook plasticity model to define shear failure of the material. The Johnson-Cook shear failure
model is based on the value of the equivalent plastic strain at element integration points; failure is
assumed to occur when the damage parameter exceeds 1. The damage parameter, !, is defined as
!=
X
Ã
pl
¢¹
"
"¹pl
f
!
;
"pl is an increment of the equivalent plastic strain, "¹pl
where ¢¹
f is the strain at failure, and the
summation is performed over all increments in the analysis. The strain at failure, "¹pl
f , is assumed to be
pl
dependent on a nondimensional plastic strain rate, "¹_ ="_0 ; a dimensionless pressure-deviatoric stress
ratio, p=q (where p is the pressure stress and q is the Mises stress); and the nondimensional
^ defined earlier in the Johnson-Cook hardening model. The dependencies are assumed
temperature, µ,
to be separable and are of the form
∙
µ
p
"¹pl
f = d1 + d2 exp d3
q
¶¸ "
Ã
pl
"¹_
1 + d4 ln
"_0
!#
´
³
1 + d5 µ^ ;
where d1 -d5 are failure parameters measured at or below the transition temperature, µtransition , and "_0
is the reference strain rate.
When this failure criterion is met, the deviatoric stress components are set to zero and remain zero for
the rest of the analysis. Depending on the user's choice, the pressure stress may also be set to zero for
the rest of calculation (if this is the case, the ELEMENT DELETION=YES parameter must be used
and the element will be deleted) or it may be required to remain compressive for the rest of the
calculation (if this is the case, the ELEMENT DELETION=NO parameter must be used). The
ELEMENT DELETION parameter has a default value of YES.
The Johnson-Cook shear failure model is suitable for high-strain-rate deformation of metals; therefore,
it is most applicable to truly dynamic situations. For quasi-static problems that require element
removal, strain softening or the Gurson metal plasticity model are recommended.
The values of d1 -d5 are provided by the user on the data line of the option *SHEAR FAILURE,
TYPE=JOHNSON COOK.
The use of the Johnson-Cook shear failure model requires the use of Johnson-Cook hardening but does
not necessarily require the use of Johnson-Cook strain rate dependence. However, the rate-dependent
term in the Johnson-Cook shear failure criterion will be included only if the option *RATE
DEPENDENT, TYPE=JOHNSON COOK has been used.
Usage: Use both of the following options:
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Inelastic Mechanical Properties
*PLASTIC, HARDENING=JOHNSON COOK
*SHEAR FAILURE, TYPE=JOHNSON COOK, ELEMENT DELETION=YES or NO
Tensile failure
The *TENSILE FAILURE option can be used in conjunction with the Johnson-Cook plasticity model
to define tensile failure of the material. The tensile failure model uses the hydrostatic pressure stress as
a failure measure to model dynamic spall or a pressure cutoff and offers a number of failure choices
including element removal. Similar to the Johnson-Cook shear failure model, the ABAQUS/Explicit
tensile failure model is suitable for high-strain-rate deformation of metals and is most applicable to
truly dynamic problems. For more details, see ``Failure models,'' Section 10.2.5.
Usage: Use both of the following options:
*PLASTIC, HARDENING=JOHNSON COOK
*TENSILE FAILURE
Heat generation by plastic work
ABAQUS/Explicit allows for an adiabatic stress analysis to be performed in which heat generated by
plastic straining of a material is calculated. An adiabatic stress analysis is specified by including the
ADIABATIC parameter on the option *DYNAMIC, EXPLICIT. Adiabatic analyses are typically used
in the simulation of bulk metal forming or high-speed manufacturing processes involving large
amounts of inelastic strain, where the heating of the material caused by its deformation is an important
effect because of temperature dependence of the material properties. Since the Johnson-Cook plasticity
model is motivated by high-strain-rate transient dynamic applications, temperature change in this
model is generally computed by assuming adiabatic conditions (no heat transfer between elements).
Heat is generated in an element by plastic work, and the resulting temperature rise is computed using
the specific heat of the material.
This effect is introduced by defining the fraction of the rate of inelastic dissipation that appears as a
heat flux per volume.
Usage: Use all of the following options in the same material data block:
*PLASTIC, HARDENING=JOHNSON COOK
*SPECIFIC HEAT
*DENSITY
*INELASTIC HEAT FRACTION
Elements
The Johnson-Cook plasticity model can be used with any elements that include mechanical behavior
(elements that have displacement degrees of freedom).
Output
In addition to the standard output identifiers available in ABAQUS/Explicit (``Output variable
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Inelastic Mechanical Properties
identifiers,'' Section 4.2.1), the following variables have special meaning for the Johnson-Cook
plasticity model:
R t q 2 pl pl
pl
PEEQ
Equivalent plastic strain, "¹ = 0 3 "_ : "_ dt:
STATUS
Status of element. The status of an element is 1.0 if the element is active and 0.0 if
the element is not.
10.2.5 Failure models
A shear failure model and a tensile failure model are offered in ABAQUS/Explicit. The shear failure
model is defined by using the *SHEAR FAILURE option in conjunction with the *PLASTIC option;
the tensile failure model is defined by using the *TENSILE FAILURE option in conjunction with the
*PLASTIC and/or the *EOS options. Both models can be used for the same material.
References
· *EOS
· *EOS SHEAR
· *PLASTIC
· ``Equation of state,'' Section 9.5.1
· ``Classical metal plasticity,'' Section 10.2.1
· ``Rate-dependent yield,'' Section 10.2.2
· ``Johnson-Cook plasticity,'' Section 10.2.4
· ``Material library: overview,'' Section 8.1.1
· ``Inelastic behavior,'' Section 10.1.1
Overview
ABAQUS/Explicit offers two deviatoric failure models. One is driven by plastic yielding--the shear
failure model invoked by the *SHEAR FAILURE option. The other model is driven by tensile
loading--the tensile failure model invoked by the *TENSILE FAILURE option.
The shear failure model:
· is designed for high-strain-rate deformation of many materials, including most metals;
· uses the equivalent plastic strain as a failure measure;
· offers two failure choices including the removal of elements from the mesh;
· can be used in conjunction with either the Mises or the Johnson-Cook plasticity models; and
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Inelastic Mechanical Properties
· can be used in conjunction with the tensile failure model.
The tensile failure model:
· is designed for high-strain-rate deformation of many materials, including most metals;
· uses the hydrostatic pressure stress as a failure measure to model dynamic spall or a pressure
cutoff;
· offers a number of failure choices including the removal of elements from the mesh;
· can be used in conjunction with either the Mises or the Johnson-Cook plasticity models, or the
equation of state material model; and
· can be used in conjunction with the shear failure model.
Shear failure model
The *SHEAR FAILURE option can be used in conjunction with the Mises or the Johnson-Cook
plasticity models in ABAQUS/Explicit to define shear failure of the material.
Shear failure criterion
The shear failure model is based on the value of the equivalent plastic strain at element integration
points; failure is assumed to occur when the damage parameter exceeds 1. The damage parameter, !, is
defined as
!=
X
Ã
¢¹
"pl
"¹pl
f
!
;
"pl is an increment of the equivalent plastic strain, "¹pl
where ¢¹
f is the strain at failure, and the
summation is performed over all increments in the analysis.
pl
¹_ ; a dimensionless
The strain at failure, "¹pl
f , is assumed to depend on the plastic strain rate, "
pressure-deviatoric stress ratio, p=q (where p is the pressure stress and q is the Mises stress);
temperature; and predefined field variables. There are two ways to define the strain at failure, "¹pl
f . One
is to use direct tabular data, where the dependencies are given in a tabular form on the data lines of the
option *SHEAR FAILURE, TYPE=TABULAR. Alternatively, the analytical form proposed by
Johnson and Cook can be invoked by using *SHEAR FAILURE, TYPE=JOHNSON COOK (see
``Johnson-Cook plasticity,'' Section 10.2.4, for more details).
When *SHEAR FAILURE, TYPE=TABULAR is used, the strain at failure, "¹pl
f , must be given as a
tabular function of the equivalent plastic strain rate, the pressure-deviatoric stress ratio, temperature,
and predefined field variables. This option requires the use of the Mises plasticity model.
With *SHEAR FAILURE, TYPE=JOHNSON COOK, the user must specify the failure parameters,
d1 -d5 (see ``Johnson-Cook plasticity,'' Section 10.2.4 for more details on these parameters). It should
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Inelastic Mechanical Properties
be emphasized that the shear failure data must be calibrated at or below the transition temperature,
µtransition , defined in ``Johnson-Cook plasticity,'' Section 10.2.4. The use of this option requires the
use of the Johnson-Cook plasticity model.
Usage: Use both of the following options for the Mises plasticity model:
*PLASTIC, HARDENING=ISOTROPIC
*SHEAR FAILURE, TYPE=TABULAR
or use both of the following options for the Johnson-Cook plasticity model:
*PLASTIC, HARDENING=JOHNSON COOK
*SHEAR FAILURE, TYPE=JOHNSON COOK
Element deletion
When the shear failure criterion is met at an element integration point, all the stress components will
be set to zero and the material point fails. If all of the material points in an element fail, by default, the
element is removed from the mesh. For example, in a first-order reduced-integration solid element
removal of the element takes place as soon as its only integration point fails. However, in a shell
element all through-the-thickness integration points must fail before the element is removed from the
mesh. This default failure choice corresponds to using the ELEMENT DELETION=YES parameter on
the *SHEAR FAILURE option.
An alternative failure choice is to set ELEMENT DELETION=NO on the *SHEAR FAILURE option.
In this case, when the shear failure criterion is met at a material point, the deviatoric stress components
will be set to zero for that point and will remain zero for the rest of the calculation. The pressure stress
is then required to remain compressive; that is, if a negative pressure stress is computed in a failed
material point in an increment, it is reset to zero.
The ELEMENT DELETION=NO parameter is not allowed when using plane stress, shell, membrane,
beam, and truss elements because the structural constraints may be violated.
Determining when to use the shear failure model
The shear failure model in ABAQUS/Explicit is suitable for high-strain-rate dynamic problems where
inertia is important. Improper use of the shear failure model may result in an incorrect simulation.
For quasi-static problems that may require element removal, a strain-softening model or the Gurson
porous metal plasticity model are recommended.
Tensile failure model
The *TENSILE FAILURE option can be used in conjunction with either the Mises or the
Johnson-Cook plasticity models or the equation of state material model in ABAQUS/Explicit to define
tensile failure of the material.
Tensile failure criterion
The ABAQUS/Explicit tensile failure model uses the hydrostatic pressure stress as a failure measure to
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Inelastic Mechanical Properties
model dynamic spall or a pressure cutoff. The tensile failure criterion assumes that failure occurs when
the pressure stress, p, becomes more tensile than the specified hydrostatic cutoff stress, ¾cuto® . The
hydrostatic cutoff stress must be provided on the data lines of the *TENSILE FAILURE option, and
may be a function of temperature and predefined field variables. There is no default value for this
stress.
The *TENSILE FAILURE option can be used with either the Mises or the Johnson-Cook plasticity
models or the equation of state material model.
Usage: Use both of the following options for the Mises or Johnson-Cook plasticity models:
*PLASTIC
*TENSILE FAILURE
or use both of the following options for the equation of state material model:
*EOS
*TENSILE FAILURE
Failure choices
When the tensile failure criterion is met at an element integration point, the material point fails. Five
failure choices are offered for the failed material points: the default choice, which includes element
removal, and four different spall models. These failure choices are described below.
Element removal
The default failure choice includes element removal. If all of the material points in an element fail, the
element will be removed from the mesh. For example, in a first-order reduced-integration solid
element removal of the element takes place as soon as its only integration point fails. However, in a
shell element all through-the-thickness integration points must fail before the element is removed from
the mesh.
Usage: *TENSILE FAILURE, ELEMENT DELETION=YES (default)
Spall models
An alternative failure choice is to set ELEMENT DELETION=NO on the *TENSILE FAILURE
option. When the tensile failure criterion is met at a material point, the deviatoric stress components
may be unaffected or may be required to be zero, and the pressure stress may be limited by the
hydrostatic cutoff stress or may be required to be compressive. Therefore, there are four possible
failure combinations (see Figure 10.2.5-1, where "O" is the stress that would exist if the *TENSILE
FAILURE option was not used).
Figure 10.2.5-1 Tensile failure choices.
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Inelastic Mechanical Properties
These failure combinations are determined by using the SHEAR and PRESSURE parameters as
follows:
· SHEAR=DUCTILE and PRESSURE=DUCTILE: this choice corresponds to point 1 in Figure
10.2.5-1 and models the case in which the deviatoric stress components are unaffected and the
pressure stress is limited by the hydrostatic cutoff stress; i.e., p = max(¡¾cuto® ; p).
· SHEAR=BRITTLE and PRESSURE=DUCTILE: this choice corresponds to point 2 in Figure
10.2.5-1 and models the case in which the deviatoric stress components are set to zero and remain
zero for the rest of the calculation, and the pressure stress is limited by the hydrostatic cutoff
stress; i.e., p = max(¡¾cuto® ; p).
· SHEAR=BRITTLE and PRESSURE=BRITTLE: this choice corresponds to point 3 in Figure
10.2.5-1 and models the case in which the deviatoric stress components are set to zero and remain
zero for the rest of the calculation, and the pressure stress is required to be compressive; i.e.,
p = max(0; p).
· SHEAR=DUCTILE and PRESSURE=BRITTLE: this choice corresponds to point 4 in Figure
10.2.5-1 and models the case in which the deviatoric stress components are unaffected and the
pressure stress is required to be compressive; i.e., p = max(0; p).
There are no default values for the SHEAR and PRESSURE parameters. They must be specified when
using ELEMENT DELETION=NO. If the material's deviatoric behavior is not defined (for example,
the *EOS option is used without the *EOS SHEAR option), the SHEAR parameter is meaningless and
will be ignored. The ELEMENT DELETION=NO parameter is not allowed when using plane stress,
shell, membrane, beam, and truss elements.
Determining when to use the tensile failure model
The tensile failure model in ABAQUS/Explicit is suitable for high-strain-rate dynamic problems in
which inertia effects are important. Improper use of the tensile failure model may result in an incorrect
simulation.
Using the failure models with rebar
It is possible to use the shear failure and/or the tensile failure models in elements for which rebars are
also defined. When such elements fail according to the failure criterion, the base material contribution
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Inelastic Mechanical Properties
to the element stress carrying capacity is removed or adjusted depending on the type of failure chosen,
but the rebar contribution to the element stress carrying capacity is not removed. However, if the user
also includes the failure option in the rebar material definition, the rebar contribution to the element
stress carrying capacity will also be removed or adjusted if the failure criterion specified for the rebar
is met.
Elements
The shear and tensile failure models with the parameter ELEMENT DELETION=YES can be used
with any elements that include mechanical behavior (elements that have displacement degrees of
freedom). The shear and tensile failure models with the parameter ELEMENT DELETION=NO can be
used only with plane strain, axisymmetric, and three-dimensional solid (continuum) elements.
Output
In addition to the standard output identifiers available in ABAQUS/Explicit (``Output variable
identifiers,'' Section 4.2.1), the following variable has special meaning for the shear and tensile failure
models:
STATUS
Status of element (the status of an element is 1.0 if the element is active, 0.0 if the
element is not).
10.2.6 Porous metal plasticity
Porous metal plasticity is defined by using the *POROUS METAL PLASTICITY option and,
optionally, the *VOID NUCLEATION and *POROUS FAILURE CRITERIA options.
References
· *POROUS METAL PLASTICITY
· *VOID NUCLEATION
· *POROUS FAILURE CRITERIA
· ``Material library: overview,'' Section 8.1.1
· ``Inelastic behavior,'' Section 10.1.1
Overview
The porous metal plasticity model:
· is used to model materials with a dilute concentration of voids in which the relative density is
greater than 0.9;
· is based on Gurson's porous metal plasticity theory (Gurson, 1977) with void nucleation and a
failure definition; and
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Inelastic Mechanical Properties
· defines the inelastic flow of the porous metal on the basis of a potential function that characterizes
the porosity in terms of a single state variable, the relative density.
Elastic and plastic behavior
The elastic part of the response is specified on the *ELASTIC option. Only linear isotropic elasticity
can be specified.
The hardening behavior of the fully dense matrix material is specified with the *PLASTIC option.
Only isotropic hardening can be specified. The hardening curve must describe the yield stress of the
fully dense matrix material as a function of plastic strain in the fully dense matrix material.
Rate dependency effects for the matrix material can be modeled with the *RATE DEPENDENT option
pl
or the *PLASTIC, RATE="¹_ option (``Rate-dependent yield,'' Section 10.2.2).
Yield condition
The relative density of a material, r, is defined as the ratio of the volume of solid material to the total
volume of the material. The relationships defining the model are expressed in terms of the void volume
fraction, f , which is defined as the ratio of the volume of voids to the total volume of the material. It
follows that f = 1 ¡ r: For a metal containing a dilute concentration of voids, Gurson (1977)
proposed a yield condition as a function of the void volume fraction. This yield condition was later
modified by Tvergaard (1981) to the form
©=
µ
q
¾y
¶2
µ
3p
+ 2q1 f cosh ¡q2
2¾y
¤
¶
³
´
¡ 1 + q3 f ¤ 2 = 0;
where
S = pI + ¾
is the deviatoric part of the Cauchy stress tensor ¾ ;
q
q = 32 S : S
is the effective Mises stress;
p = ¡ 13 ¾ : I
is the hydrostatic pressure;
¾y (¹
"pl
m)
is the yield stress of the fully dense matrix material as a function of "¹pl
m , the equivalent plastic
strain in the matrix; and
q1 , q2 , q3
are material parameters.
The Cauchy stress is defined as the force per "current unit area," comprised of voids and the solid
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Inelastic Mechanical Properties
(matrix) material. The model is described in detail in ``Porous metal plasticity,'' Section 4.3.6 of the
ABAQUS Theory Manual, along with a discussion of its numerical implementation.
Failure criteria
The function f ¤ (f ) models the rapid loss of stress carrying capacity that accompanies void
coalescence. This function is defined in terms of the void volume fraction:
f¤ =
8
f
>
>
>
<
if f ∙ fc ;
fc +
>
>
>
:¹
fF
f¹F ¡ fc
(f ¡ fc ) if fc < f < fF ;
fF ¡ fc
if f ¸ fF ,
where
q1 +
f¹F =
p
q12 ¡ q3
q3
:
In the above relationship, fc is a critical value of the void volume fraction, and fF is the value of void
volume fraction at which there is a complete loss of stress carrying capacity in the material. The
parameters fc and fF model the material failure when fc < f < fF , due to mechanisms such as micro
fracture and void coalescence. These parameters are directly specified by the user on the data lines of
the *POROUS FAILURE CRITERIA option. When f ¸ fF total failure at the material point occurs.
In ABAQUS/Explicit an element is removed once all of its material points have failed.
f = 0 (r = 1) implies that the material is fully dense, and the Gurson yield condition reduces to the
Mises yield condition. f = 1 (r = 0) implies that the material is completely voided, and has no stress
carrying capacity. The model generally only gives physically reasonable results for f < 0:1 (r > 0:9).
Usage: *POROUS FAILURE CRITERIA
Specifying q1 , q2 , and q3
The parameters q1 , q2 , and q3 are specified directly by the user on the data lines of the *POROUS
METAL PLASTICITY option. For typical metals the ranges of the parameters reported in the literature
are q1 = 1:0 to 1.5, q2 = 1:0, and q3 = q12 = 1:0 to 2.25 (see ``Necking of a round tensile bar,'' Section
1.1.9 of the ABAQUS Benchmarks Manual). The original Gurson model is recovered when
q1 = q2 = q3 = 1:0 . These parameters can be defined by the user as tabular functions of temperature
and/or field variables.
Usage: *POROUS METAL PLASTICITY
At material points
The initial relative density can be specified as part of the material definition by using the RELATIVE
DENSITY parameter with the *POROUS METAL PLASTICITY option.
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Inelastic Mechanical Properties
Usage: *POROUS METAL PLASTICITY, RELATIVE DENSITY=r0
At nodes
Alternatively, the initial relative density at nodes can be defined with the *INITIAL CONDITIONS
option (``Initial conditions,'' Section 18.2.1); these values are interpolated to the material points. The
initial conditions are applied only if the RELATIVE DENSITY parameter does not appear on the
*POROUS METAL PLASTICITY option. When a discontinuity of the initial relative density field
occurs at the element boundaries, separate nodes must be used to define the elements at these
boundaries, with *MPCs applied to make the nodal displacements and rotations equivalent.
Usage: *INITIAL CONDITIONS, TYPE=RELATIVE DENSITY
Flow rule and hardening
The presence of pressure in the yield condition results in nondeviatoric plastic strains. Plastic flow is
assumed to be normal to the yield surface:
"_ pl = ¸_
@©
:
¾
@¾
The hardening of the fully dense matrix material is described through ¾y = ¾y (¹
"pl
m ). The evolution of
the equivalent plastic strain in the matrix material is obtained from the following equivalent plastic
work expression:
pl
(1 ¡ f )¾y "¹_ m = ¾ : "_ pl :
The model is illustrated in Figure 10.2.6-1, where the yield surfaces for different levels of void volume
fraction are shown in the p-q plane.
Figure 10.2.6-1 Schematic of the yield surface in the p-q plane.
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Inelastic Mechanical Properties
Figure 10.2.6-2 compares the behavior of a porous material (whose initial yield stress is ¾y0 ) in tension
and compression against the behavior of the perfectly plastic matrix material. In compression the
porous material "hardens" due to closing of the voids, and in tension it "softens" due to growth and
nucleation of the voids.
Figure 10.2.6-2 Schematic of uniaxial behavior of a porous metal (perfectly plastic matrix material
with initial volume fraction of voids = f0 ).
Void growth and nucleation
The total change in void volume fraction is given as
f_ = f_gr + f_nucl ;
where f_gr is change due t