# Hyperelastic planar tension test¶

## Overview¶

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

• Hyperelasticity for planar (pure shear) 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 planar (pure shear) tension test validation project into workspace

## 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

## 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].

Planar (pure shear) test:

Material:

Material model   $$C_{10}$$ $$C_{01}$$ $$C_{20}$$ $$C_{11}$$ $$C_{02}$$ $$C_{30}$$ $$D_1$$ $$D_2$$ $$D_3$$
$$\mathrm{Neo\ Hookean^{(CCX/CA)}}$$ $$1.684244$$ $$1e-8\ ^{(CCX)} - 1e-6\ ^{(CA)}$$
$$\mathrm{Mooney\ Rivlin^{(CCX/CA)}}$$ $$-99.157878$$ $$100.842122$$ $$1e-8\ ^{(CCX)} - 1e-6\ ^{(CA)}$$
$$\mathrm{Yeoh^{(CCX)}}$$ $$1.884809$$ $$-0.023045$$ $$0.000951$$ $$1e-8$$ $$1e-8$$ $$1e-8$$
$$\mathrm{Red\ Poly\ 2^{(CCX)}}$$ $$1.680890$$ $$0.000119$$ $$1e-8$$ $$1e-8$$
$$\mathrm{Poly\ 2^{(CCX)}}$$ $$-3342.294056$$ $$3343.974945$$ $$-29.075454$$ $$52.176771$$ $$-23.101198$$ $$1e-8$$ $$1e-8$$
$$\mathrm{Signorini^{(CA)}}$$ $$1$$ $$0.680889$$ $$0.000119$$ $$1e-6$$
$$\mu_1$$ $$\mu_2$$ $$\mu_3$$ $$\alpha_1$$ $$\alpha_2$$ $$\alpha_3$$
$$\mathrm{Ogden\ 1^{(CCX)}}$$ $$3.170002$$ $$2.057305$$ $$1e-8$$
$$\mathrm{Ogden\ 2^{(CCX)}}$$ $$0.270802$$ $$2.366077$$ $$3.652417$$ $$-0.38567$$ $$1e-8$$ $$1e-8$$
$$\mathrm{Ogden\ 3^{(CCX)}}$$ $$1.160174$$ $$2.366074$$ $$-0.889366$$ $$3.650165$$ $$-0.385663$$ $$-0.889366$$ $$1e-10$$ $$1e-10$$ $$1e-10$$
$$\lambda_m$$ $$\mu$$
$$\mathrm{Arruda-Boyce{(CCX)}}$$ $$11.185037$$ $$3.148984$$ $$1e-8$$

Constraints:

• Face ABFE zero x-displacement
• Face AEDH and BFGC zero y-displacement
• Face ABCD zero z-displacement
• Face DCGH 4m x-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.

Comparison of the Planar (pure shear) 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.