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Customer Training Material
Hyperelastic Curve Fitting
Structural Nonlinearities
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Customer Training MaterialWorkshop 7A - Hyperelastic Curve Fitting
Goal
Use curve-fitting tool to create a hyperelastic material model from
test data.
na yze ens e ru er es spec men
Plot and graph results
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Customer Training Material Workshop 7A - Hyperelastic Curve Fitting
Model Description
3D large deflection with nonlinear material
(hyperelastic)
ree p anes o symme ry o e ac ua mo e
Loads and Boundary Conditions:
Frictionless supports on each plane of symmetry
Displacement load to elongate one end.
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Customer Training Material Workshop 7A - Hyperelastic Curve Fitting
Steps to Follow:
Restore Archive browse for file W7A-hyper.wbpz
Save as
File name: W7A-hyper
*
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Customer Training Material Workshop 7A - Hyperelastic Curve Fitting
The project Schematic should look like the
picture to the right.
From this Schematic, you can see that
ng neer ng ma er a a a an eome ry
have already been defined (green checkmarks).
It remains to set up and run the FE model in
Mechanical
Highlight the Engineering Data Cell and open
(RMB)=>Edit to verify the default linear
material properties.
Verify that the units are in Metric
, , . ,clicking on
Utility Menu=>Units=>Metric(Tonne,
mm,)
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Customer Training Material Workshop 7A - Hyperelastic Curve Fitting
Click on Return to Project
Double click on the Model Cell to open the FE Model (Mechanical
Session) (or RMB=>Edit)
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Customer Training Material Workshop 7A - Hyperelastic Curve Fitting
Once inside the Mechanical application, verify the working unit system
Unit > Metric (mm,kg,N,s,mV,mA)
Open the folders beneath the model branch to become familiar with the
- .
Confirm the three frictionless boundary conditions.
Confirm the displacement load of 19mm on the far end.
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Customer Training Material Workshop 7A - Hyperelastic Curve Fitting
Preview the mesh:
The default mesh should be swept with hexahedral elements
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Customer Training Material Workshop 7A - Hyperelastic Curve Fitting
ntro uce ypere ast c mater a test ata
Return to the Project Schematic
Open the Engineering Data Cell
RMB duplicate.
Change the name of the duplicated material
to Elastomer and the description to test
specimen
Verify metric units are active
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Customer Training Material Workshop 7A - Hyperelastic Curve Fitting
With the Elastomer material highlighted, insert hyperelastic material test
data
From the Toolbox, expand the Experimental Stress Strain Data Folder
,
Repeat for: Biaxial Test Data
Shear Test Data
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Customer Training Material Workshop 7A - Hyperelastic Curve Fitting
ecome am ar w e proper y a es an c ar
a Properties Outline Dialogue box should now include three additional cells for the
hyperelastic test data
b The Table of Pro erties re resents the data for the cell that is hi hli hted in a.
c The Engineering Data Chart is a graphical display of the tabulated data in b.
Note:
cThe question mark nextto each cell indicates
that no data has been
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Customer Training Material Workshop 7A - Hyperelastic Curve Fitting
Read in material test data
Browse for and open tension-uni.xls
This spread sheet contains two columns of data that
represent uniaxial strain-stress data
Highlight the two columns and copy them with Ctrl-C
Return to the Table of Properties Row 9: Uniaxial Test
a a n e ng neer ng a a e
Highlight the asterisk * at the bottom of the Uniaxial Test
Data Table and RMB>Paste to the insert data
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Customer Training Material Workshop 7A - Hyperelastic Curve Fitting
The Table of Properties should now display the Uniaxial Test Data in
tabular form. The Chart should display of the data in graphical form.
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Customer Training Material Workshop 7A - Hyperelastic Curve Fitting
Repeat procedure for biaxial test data and shear test data using excel files
tension-eb.xls and tension-pt.xls respectively.
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Customer Training Material Workshop 7A - Hyperelastic Curve Fitting
From the Toolbox, open the Hyperelasticity Folder and highlight Yeoh 3rd
Order with RMB> Include Property.
You should now see a Yeoh 3rd order cell in the Properties Dialogue box with
, .
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Customer Training Material Workshop 7A - Hyperelastic Curve Fitting
Execute Solve Curve Fit.
Expand the Yeoh 3rd Order Cell
Highlight the Curve Fitting Cell
> o ve urve t
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Customer Training Material Workshop 7A - Hyperelastic Curve Fitting
When complete, the Engineering Data Chart will display all three modes oftest data in dot-dash lines. Superimposed on this is the predicted Yeohbehavior in solid lines for comparison.
Note: The Coefficients have been calculated, but no material model has been savedto the Engineering Data yet. This is by design. If you are not satisfied with the
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resulting curve fit, you can try other functions, or perhaps suppress a less dominatemode of loading and rerun the curve fitting routine for a better result.
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Customer Training Material Workshop 7A - Hyperelastic Curve Fitting
ange t e rror orm rom orma ze rror to so ute rror an run
the curve fitting routine again.
Recall the normalized error approach gives equal weight to all data points while the
absolute error a roach ives more wei ht to lar er strain values.
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This results in a slightly improved curve fit at higher strain values.
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Customer Training Material Workshop 7A - Hyperelastic Curve Fitting
,properties Highlight Curve Fitting RMB> Copy Calculated Values to Property
The Yeoh coefficients are now copied to the Properties Table. Notice the D
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.will be fully incompressible if no volumetric strain data is read into the curvefitter.
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Customer Training Material Workshop 7A - Hyperelastic Curve Fitting
From the Utility Menu: Click on Refresh Project
highlight the 3 bodies that make up thispart and change the default material
Elastomer
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e urn o e ec an ca ess on an spec y na ys s e ngs as s ownbelow:
Specify enough substeps
to enhance convergence
Turn on Large Deflection
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Execute the Solve
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Model converges very nicely in less then 20 iterations
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Post process results (i.e. deformation, stress, strain,etc).
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e ec er ex as s own an nser ser e ne resu s o pos processstress and strain along x direction
Expression for x direction of stress is SX
Expression for x direction of strain is EPELX
Refer to documentation on PRNSOL command for syntax of user defined
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c ar oo an nser an user e ne resu s as o ec sfor plotting stress vs strain as shown below.
Q. Wh doesnt this curve match u exactl with the tensile test data curve?
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A. The test data is engineering stress-strain, the results are post processed as true
stress-strain.
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Change the displacement load to 50mm and re-run the solution.
- Model still converges without trouble in 22 iterations, no bisections, even
though the loading is outside of the bounds of the original test data.
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Notice the dramatic stress stiffening effects at higher strain values, acommon characteristic of most elastomers.
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eturn to ng neer ng ata
Insert a Response Function from the
toolbox
automatically suppressed
now the active material. The test data
previously read in is automatically
included under this material model, butno curve fitting solution is required.
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Refresh the Project, return to Mechanical and rerun the Solution withoutmaking any other changes. Notice the solution now fails to converge atabout 40% of the full load due to excessive element distortion
Tr ad ust the time ste ran e and executin a
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restart.- Solution still fails to converge.
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e uce t e sp acement oa ac to mm, reset t e or g na t me steprange and rerun solution.
- Solution now converges successfully to same results as Yeoh 3rd order model
-
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curve fit, but is only effective for loading inside the test data range and typically
involves a longer run time as compared with the traditional strain energy functions.