Connecting Microsoft Excel
as a solver to optiSLang
Tutorial:
Using MS Excel as a solver to fit true stress /
true strain curves of metallic materials
Background
• Material Parameters can be determined in practical tensile tests.
• The result of these tests is a true stress / true strain curve of the
material.
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Tutorial: Using MS Excel as a solver for fitting stress/strain curves with optiSLang
Background
• To perform FE-Analyses it is often necessary to define material
properties that are fittet to a tensile test measurement.
• As a result of the measurement, you get the data points of a
σ-ε-plot.
• You can fit a generated curve according to the Gosh-Equation:
σY(εp) = k • (ε0 + εp)n – p
• At first, you have to determine the start values of the parameters
k,n,p and ε0.
• These parameters can be taken out of the given reference curve.
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Tutorial: Using MS Excel as a solver for fitting stress/strain curves with optiSLang
Take a look at a given reference curve
Epsilon
•
•
You get a reference curve usually
as an Excel sheet.
•
•
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Sigma
σY
0
745.0994718
0.0005
747.8550844
0.00053949
748.0678985
0.00058209
748.2967565
0.00062806
748.5428066
0.00067766
748.8072696
calculate n = ln(σY/k) / ln(εP)
0.00073118
749.0914423
Notice: to get a good result, take
an average of n between εP = 0
and εP = 0.2!
0.73783423
1052.653937
0.79610271
1059.104677
and finally ε0 = (σY/k)1/n
0.85897278
1065.601572
0.92680784
1072.14451
1
1078.733406
To determine the start values
of the gosh parameters, you
can take out:
k = the Value of εP = 1
•
•
εP
Set the parameter p = 0
Tutorial: Using MS Excel as a solver for fitting stress/strain curves with optiSLang
Calculating the start value of n
• Sum up the desired values for „n“
• Divide it by the number of considered
values.
• This leads to your first approximation
of „n“
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Tutorial: Using MS Excel as a solver for fitting stress/strain curves with optiSLang
Generating a first approximation curve
• Generate the input section with the four parameters
• Create the new true stress true strain curve with the GoshEquation and set the reference of the values for k,n,p, ε0 to the
input section!
• To check the accurance of the fitting, create a new column:
the quadratic error: (σapprox. – σY)2
• Finally sum up the quadratic errors and calculate an average value
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Tutorial: Using MS Excel as a solver for fitting stress/strain curves with optiSLang
Preparing the worksheet for optiSLang
• Input Variables are read in in rows
• Output Variables are read out in columns
• The used macro needs some references. So you have to mark the
first input variable als „inputParams“, the first output variable as
„outputParams“ and the second output variable as „outputParams2“
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Tutorial: Using MS Excel as a solver for fitting stress/strain curves with optiSLang
Working with the macro
• To work with the extraction macro, you have to allow using
macros in your Excel settings!
• Start the MS Visual Basic-Editor to have a look at the macro
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Tutorial: Using MS Excel as a solver for fitting stress/strain curves with optiSLang
The macro
• In the macro you find:
• The input file names
• The output file names
• The Names of the references,
that you have to set in Excel
(see sheet 7)
• Some settings
• The extraction routine
(as shown beside)
• Note:
The macro is pre-defined
for one input file and two
output files for each one
column. If you want to
extract more, please adapt
the macro to your needs.
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Tutorial: Using MS Excel as a solver for fitting stress/strain curves with optiSLang
Creating the input deck
• Close and save your completed Excel Worksheet!
• Define an input.txt where you define the input variables:
n
ε0
k
p
• Open the given jscript file and modify the name of your
worksheet!
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Tutorial: Using MS Excel as a solver for fitting stress/strain curves with optiSLang
Start the reference run
• You start the calculation and extraction of the both outputs in
the following way:
• Write a „start.bat“ file with the command line:
cscript G:\Projekte\Excel_Solver\test\kurve_optislang.js //B
 modify this according to your system 
• Make sure that Java-Script is not deactivated on your computer!
• You‘ll get now the following structure in your directory:
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Tutorial: Using MS Excel as a solver for fitting stress/strain curves with optiSLang
Create the optiSLang project
• Create a new optiSLang project in your working directory
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Tutorial: Using MS Excel as a solver for fitting stress/strain curves with optiSLang
Parametrize the input variables
• Start a new parametrization of the 4 input variables n, ε0 , k, p
• Fill in the lower and upper bounds and the formats as shown below
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Tutorial: Using MS Excel as a solver for fitting stress/strain curves with optiSLang
Parametrize the outputs
• First open the output2.txt to parametrize the average quadratic
error (last value at the end of the file) as an output variable.
• You need at least one output variable to finish a parametrization.
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Tutorial: Using MS Excel as a solver for fitting stress/strain curves with optiSLang
Preparing the signal parameters
• The fitting of the curves will be done with signals in optiSLang.
• Therefore, you have to create the reference curve in two text files
by copying the values from the given excel sheet.
The textfile „epsilon.txt“ is also needed to get the values for εY!
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Tutorial: Using MS Excel as a solver for fitting stress/strain curves with optiSLang
Creating signal parameters
• At first, you have to define the block markers. These markers
represent the array of values that you allocate to a vector.
• Create the markers as shown below
• For the output2.txt, you have to define an end in the marker,
because after the single values, the sum and average of the
quadratic error follows and this should not be extracted here!
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Tutorial: Using MS Excel as a solver for fitting stress/strain curves with optiSLang
Creating signal parameters
• Repeat this for the additional textfiles sigma.txt and epsilon.txt
• Notice: Here you have to set the start line as „2“ because the
values begin in row 2.
• Now you have to define the parameter vectors
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Tutorial: Using MS Excel as a solver for fitting stress/strain curves with optiSLang
Creating parameter vectors
• Mark the first value of the output files and add them as vectors
• Set the reference to the output-file-marker and insert a
reasonable name (examples are shown below).
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Tutorial: Using MS Excel as a solver for fitting stress/strain curves with optiSLang
Defining the reference vectors
• Repeat this for all the desired output vectors.
• The Sigma.txt contains the reference value of σY.
• The vector in Epsilon.txt has to be defined twice – one of them
is used as a reference vector.
• To make a vector a reference vector, you have to set them as
constant:
• Double-click on the vector element and mark it as constant
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Tutorial: Using MS Excel as a solver for fitting stress/strain curves with optiSLang
Defining signal objects
• After you have now defined all the needed vectors, you can now
create the signal objects to start the analysis.
• Do this for the Sigma_Epsilon, the quadratic error and the
reference curve. Mark the reference curve as constant so that it is
treated as the reference by optiSLang.
• Save the parametrization and close it.
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Tutorial: Using MS Excel as a solver for fitting stress/strain curves with optiSLang
Design of Experiments
• To get an overview of the variation space, it can be useful to perform
a sensitivity study at first.
• Here you can see the output variation and wheather your target
value is located inside of the variation space.
• For the DoE, first add two lines to your start.bat file:
copy "G:\Projekte\Referenzkurve\optislang\sigma.txt" .
copy "G:\Projekte\Referenzkurve\optislang\epsilon.txt" .
Modify the path when it differs from your settings!
• Use the predefined problem specification
• Use the start.bat as starting script
• Calculate about 100 designs – it doesn‘t take long (~ 1.6 s /design)
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Tutorial: Using MS Excel as a solver for fitting stress/strain curves with optiSLang
DoE Postprocessing
• You see that the reference curve is within the variation space. So
it shall be possible to fit the four Gosh-parameters for an optimal
fitting of the calculated curve.
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Tutorial: Using MS Excel as a solver for fitting stress/strain curves with optiSLang
Defining the objective in optiSLang
• To start a curve fitting, you have to define an objective in
optiSLang.
• Just re-open the parametrization to add a signal function at first
• Choose then as function the SIG_DIF_EUCLID_SLOT function
This functions determines the euclidian norm between two curves in
a defined slot. The slot is chosen because for large strain values
(ε > 0.4), the curve fitting has not to be verry accurate.
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Tutorial: Using MS Excel as a solver for fitting stress/strain curves with optiSLang
Defining the objective in optiSLang
• Enter a reasonable name for the signal function. This name will be
used for the objective.
• Define the objective function just by inserting the signal function
name. The effect of the optimization is that the value of this
function will be minimized.
• As an alternative, you may use the integral-difference function
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Tutorial: Using MS Excel as a solver for fitting stress/strain curves with optiSLang
Starting an optimization run (ARSM)
• Because we have only 4 parameters, a ARSM-Optimization would
be a fast method to create a best design.
• Define a new ARSM run with the modified problem-specification
file and the start script.
• To scan a wider design space, set the start range up to 75%.
• To avoid endless calculations, set a maximum ARSM iteration
number of 75.
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Tutorial: Using MS Excel as a solver for fitting stress/strain curves with optiSLang
Postprocessing ARSM
• After 75 Iterations, it was possible to achieve an excellent curve
fitting.
• Get the design values for the Goshequation as a result
• See the very small difference between
the curves (Kurvenfitting)
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Tutorial: Using MS Excel as a solver for fitting stress/strain curves with optiSLang
Signal data of the ARSM
• The best design is hardly to distinguish from the reference curve.
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Tutorial: Using MS Excel as a solver for fitting stress/strain curves with optiSLang
Excel Sheet
•
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Comparision of the two curves in MS Excel – See the accurate fitting
Tutorial: Using MS Excel as a solver for fitting stress/strain curves with optiSLang
Excel Sheet
•
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With the optimization it was possible to reduce the quadratic error
significantly!
Tutorial: Using MS Excel as a solver for fitting stress/strain curves with optiSLang
Conclusion
• Performing a parametric optimization with MS Excel as a solver,
it was now possible to determine the parameters that have to
fill in into a Gosh-Equation for calculating true stress true strain
curves.
• Because of the fast calculation speed it is possible to get good
results in a short time.
• The determined parameters can now transfered to a FE-Analysis
programm like ANSYS or LS-Dyna.
• For this case, the Gosh-Equation has the following values:
σY(εp) = k • (ε0 + εp)n – p
σY(εp) = 1109 • (0.0099 + εp)0.0766 – 34.8
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Tutorial: Using MS Excel as a solver for fitting stress/strain curves with optiSLang
Contact Information
For further informations according to optiSLang or the
used Excel macro, please contact us.
DYNARDO GmbH
Luthergasse 1D
D-99423 Weimar
Fon: +49 (0)3643 900830
Fax: +49 (0)3643 900839
support@dynardo.de
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Tutorial: Using MS Excel as a solver for fitting stress/strain curves with optiSLang