Documentation

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

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].

Equibiaxial test:

Material:

Material model C10

C10

 

C01

C01

 

C20

C20

 

C11

C11

 

C02

C02

 

C30

C30

 

D1

D1

 

D2

D2

 

D3

D3

 

Neo Hookean(CCX/CA)

Neo Hookean(CCX/CA)

 

2.398485

2.398485

 

1e8 (CCX)1e6 (CA)

1e8 (CCX)1e6 (CA)

 

Mooney Rivlin(CCX/CA)

Mooney Rivlin(CCX/CA)

 

1.751252

1.751252

 

0.046253

0.046253

 

1e8 (CCX)1e6 (CA)

1e8 (CCX)1e6 (CA)

 

Yeoh(CCX)

Yeoh(CCX)

 

2.097527

2.097527

 

0.008231

0.008231

 

0.000321

0.000321

 

1e8

1e8

 

1e8

1e8

 

1e8

1e8

 

Red Poly 2(CCX)

Red Poly 2(CCX)

 

1.816315

1.816315

 

0.011638

0.011638

 

1e8

1e8

 

1e8

1e8

 

Poly 2(CCX)

Poly 2(CCX)

 

2.997394

2.997394

 

0.644725

0.644725

 

0.152000

0.152000

 

0.001504

0.001504

 

1.678833

1.678833

 

1e8

1e8

 

1e8

1e8

 

Signorini(CA)

Signorini(CA)

 

5.364642

5.364642

 

2.477353

2.477353

 

0.633690

0.633690

 

1e6

1e6

 

μ1

μ1

 

μ2

μ2

 

μ3

μ3

 

α1

α1

 

α2

α2

 

α3

α3

 

Ogden 1(CCX)

Ogden 1(CCX)

 

3.526919

3.526919

 

2.375063

2.375063

 

1e8

1e8

 

Ogden 2(CCX)

Ogden 2(CCX)

 

4.144658

4.144658

 

0.038056

0.038056

 

1.683416

1.683416

 

5.472163

5.472163

 

1e8

1e8

 

1e8

1e8

 

Ogden 3(CCX)

Ogden 3(CCX)

 

3.391535

3.391535

 

0.038065

0.038065

 

0.753115

0.753115

 

1.683378

1.683378

 

5.472015

5.472015

 

0.753115

0.753115

 

1e8

1e8

 

1e8

1e8

 

1e8

1e8

 

λm

λm

 

μ

μ

 

ArrudaBoyce(CCX)

ArrudaBoyce(CCX)

 

5.312373

5.312373

 

3.654976

3.654976

 

1e8

1e8

 

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.

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

References

[Tre44] (123) L. R. G. Treloar. Stress-strain data for vulcanised rubber under various types of deformation. Trans. Faraday Soc., 40:59–70, 1944.
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