MULTIDISCIPLINARY ANALYSIS, INVERSE DESIGN, ROBUST OPTIMIZATION AND CONTROL
(MAIDROC) LABORATORY
DEPARTMENT OF MECHANICAL AND MATERIALS ENGINEERING
Presents an Invited Lecture
MODELING CONTACT IN MULTI-MATERIAL FRAMEWORKS
Professor David L. Littlefield
Department of Mechanical engineering
The University of Alabama at Birmingham, Birmingham AL 35294
littlefield@uab.edu
Date:
Time:
Room:
June 16, 2006 (FRIDAY)
1:15 p.m.
EC 3327 - MME Conference Room
Realistic and accurate modeling of contact in the presence of large deformations and severe distortions is beset
with many computational challenges. Relevant applications where this situation arises include vehicle crash
dynamics, ballistic penetration and perforation, structure-blast interaction, warhead fracture and fragmentation,
and orbital debris impact. The natural framework for description of surfaces afforded by Lagrangian finite
element methods makes it the method of choice for many applications in this class. However, the large
distortions often result in elements that develop large aspect ratios, twist, or even invert; making the
application of traditional finite element approaches impossible in many cases. Due to this deficiency, Eulerian
and arbitrary Lagrangian-Eulerian (ALE) methods have become popular, particularly in the last decade. The
tradeoff with Eulerian or ALE approaches is the added complexity associated with permitting multiple
materials to occupy a single finite element.
One of the difficulties associated with allowing multiple materials in a single element is satisfying contact
constraints at the interface between the materials. Historically this problem has been sidestepped by replacing
the materials present in the element with an equivalent single material. The heuristic techniques applied to
determine the material properties of this fictitious material usually have little or nothing to do with contact and
as a result, often result in unphysical behavior. Recently several researchers have investigated alternatives in
an attempt to correct this deficiency. The simplest technique is to set the shear stresses at interfaces equal to
zero [1] which, in effect, replaces the contact boundary with a fluid layer one element wide. Benson [2]
developed a mixture theory approach that accounts for friction at the interface by introducing additional
internal state variables to describe the slip. A third alternative [3], demonstrated for rigid objects penetrating
deforming bodies, uses a penalty method to prevent the Eulerian material from penetrating the rigid body. A
common feature to all these approaches is the use of a single velocity field for all deforming materials. This
limits applicability to contact problems, which by their very nature require distinct velocity fields for each
material.
An alternative approach, recently introduced by the author [4,5], uses distinct velocity fields for each material.
No mixed-element thermodynamic or constitutive models are used in the formulation. Instead, the governing
equations are solved for each material, with the appropriate inequality constraints applied at intermediate
locations within the elements. What arises from this is a set of coupled equations that are approximated by an
uncoupled, reduced form. Recent results from development of this technique will be presented in this talk.
REFERENCES
[1] Walker, J. D. and Anderson, C. E., “Multi-material velocities for mixed cells”, High Pressure Science and
Technology – 1993, American Institute of Physics Press, pp. 1773–1776, 1994.
[2] Benson, D. J., “A mixture theory for contact in multi-material Eulerian formulations”, Comput. Methods
Appl. Mech. Engng., 140, pp. 59 – 86, 1997.
[3] Benson, D. J. and Okazawa, S., “Contact in a multi-material Eulerian finite element formulation”, Comput.
Methods Appl. Mech. Engng., 193, pp. 4277 – 4298, 2004.
[4] Littlefield, D. L., “A method for treatment of dynamic contact-impact in multi-material frameworks”,
Proceedings of the Fifth World Congress on Computational Mechanics, Jul 7 – 12, Vienna Austria, 2002.
[5] Littlefield, D. L. “A technique for modeling interfaces in multi-material CSM applications”, presented at
the Seventh U.S. National Congress on Computational Mechanics, Jul 27 – 31, Albuquerque NM, 2003.
A Biographical Sketch of the Invited Lecturer:
David Littlefield is professor of Mechanical Engineering at the University of Alabama at Birmingham (UAB). He is
also the Functional Area Point-of-Contact (FAPOC) for Computational Structural Mechanics (CSM) for the
Programming Environment and Training (PET) Program sponsored by the Department of Defense High Performance
Computing Modernization Program (DoD HPCMP). Dr. Littlefield’s primary technical interests are in the areas of
computational solid mechanics and computational magnetohydrodynamics. He has authored or co-authored over 100
papers and technical reports in these areas. In his role as FAPOC in the PET program, Dr. Littlefield leads a team of
university researchers, scientists and DoD laboratory on-site personnel that is tasked with technology transfer of
computer modeling applications, algorithms, methods, and tools into the user community. He has participated in both
material and managerial roles on many projects since assuming the role of FAPOC in July 2002. Technical work he
has been involved in includes advanced finite element methods, global error estimation and adaptive mesh
refinement, goal-oriented error estimation, code coupling algorithms, improved interface tracking methods, and
equations of state for energetic materials. Dr. Littlefield’s graduate studies were in Mechanical Engineering. He
received his MSME degree from Georgia Institute of Technology in 1984. His Ph.D. in Mechanical Engineering was
awarded in 1989, also from Georgia Institute of Technology. Dr. Littlefield as a member of the American Society of
Mechanical Engineers, and was elected to fellow grade in 2002. He is also a member of the United States
Association for Computational Mechanics, the Hypervelocity Impact Society and the National Defense Industrial
Association.
For further information please contact Prof. Dulikravich at (305) 348-7016 or at dulikrav@fiu.edu.