Mechanical Nonlin 13.0 WS 07A Hyperelasticity

8/12/2019 Mechanical Nonlin 13.0 WS 07A Hyperelasticity

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Customer Training Material

Hyperelastic Curve Fitting

Structural Nonlinearities

WS7A-1ANSYS, Inc. Proprietary

2010 ANSYS, Inc. All rights reserved.Release 13.0

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ANSYS Mechanical Structural Nonlinearities

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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Steps to Follow:

Restore Archive browse for file W7A-hyper.wbpz

Save as

File name: W7A-hyper

*



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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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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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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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Preview the mesh:

The default mesh should be swept with hexahedral elements



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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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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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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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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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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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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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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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Execute Solve Curve Fit.

Expand the Yeoh 3rd Order Cell

Highlight the Curve Fitting Cell

> o ve urve t



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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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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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,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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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.

Mechanical Nonlin 13.0 WS 07A Hyperelasticity

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