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Hyperelastic equibiaxial tension test

Overview

The aim of this case is to validate the following functions:

  • Hyperelasticity for equibiaxial tension test

The simulation results of SimScale were compared to the results presented in [Tre44]. The mesh used in the study is a hexahedral mesh with only one element imported to SimScale platform.

Import equibiaxial tension test validation project into workspace

Geometry

Cube-geometry

Cube geometry

The cube (ABCDEFGH) has the dimension of:

Cube length 1 m
Cube width 1 m
Cube height 1 m

Analysis type and Domain

Tool Type : Calculix (CCX), Code_Aster (CA)

Analysis Type : Static

Mesh and Element types :

Mesh type Number of nodes Element type
linear hexahedral 8 3D isoparametric
Cube-mesh

Cube mesh

Simulation Setup

Important

All displacement and load components are referred to the coordinate system in the figure of the geometry section.

Important

All the material model values below are calculated through a curve fitting with Treloar test data presented in [Tre44].

Equibiaxial test:

Material:

Material model   \(C_{10}\) \(C_{01}\) \(C_{20}\) \(C_{11}\) \(C_{02}\) \(C_{30}\) \(D_1\) \(D_2\) \(D_3\)
\(\mathrm{Neo\ Hookean^{(CCX/CA)}}\) \(2.398485\) \(1e-8\ ^{(CCX)} - 1e-6\ ^{(CA)}\)
\(\mathrm{Mooney\ Rivlin^{(CCX/CA)}}\) \(1.751252\) \(0.046253\) \(1e-8\ ^{(CCX)} - 1e-6\ ^{(CA)}\)
\(\mathrm{Yeoh^{(CCX)}}\) \(2.097527\) \(-0.008231\) \(0.000321\) \(1e-8\) \(1e-8\) \(1e-8\)
\(\mathrm{Red\ Poly\ 2^{(CCX)}}\) \(1.816315\) \(0.011638\) \(1e-8\) \(1e-8\)
\(\mathrm{Poly\ 2^{(CCX)}}\) \(2.997394\) \(-0.644725\) \(0.152000\) \(0.001504\) \(-1.678833\) \(1e-8\) \(1e-8\)
\(\mathrm{Signorini^{(CA)}}\) \(5.364642\) \(-2.477353\) \(0.633690\) \(1e-6\)
    \(\mu_1\) \(\mu_2\) \(\mu_3\) \(\alpha_1\) \(\alpha_2\) \(\alpha_3\)      
\(\mathrm{Ogden\ 1^{(CCX)}}\) \(3.526919\) \(2.375063\) \(1e-8\)
\(\mathrm{Ogden\ 2^{(CCX)}}\) \(4.144658\) \(0.038056\) \(1.683416\) \(5.472163\) \(1e-8\) \(1e-8\)
\(\mathrm{Ogden\ 3^{(CCX)}}\) \(3.391535\) \(0.038065\) \(0.753115\) \(1.683378\) \(5.472015\) \(0.753115\) \(1e-8\) \(1e-8\) \(1e-8\)
  \(\lambda_m\) \(\mu\)                
\(\mathrm{Arruda-Boyce^{(CCX)}}\) \(5.312373\) \(3.654976\) \(1e-8\)

Constraints:

  • Face ABFE zero x-displacement
  • Face AEHD zero y-displacement
  • Face ABCD zero z-displacement
  • Face DCGH 4m x-displacement
  • Face BFGC 4m y-displacement

Results

Comparison of the nominal stress vs. the nominal strain calculated on the node of edge AB and AE. The values of the reference [Tre44] in all figures were extracted with WebPlotDigitizer.

Equibiaxial_results

Comparison of the Equibiaxial results with Treloar test data using CCX and CA

References

[Tre44](1, 2, 3) L. R. G. Treloar. Stress-strain data for vulcanised rubber under various types of deformation. Trans. Faraday Soc., 40:59–70, 1944.