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Hyperelastic Uniaxial Tension Test

Overview

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

  • Hyperelasticity for uniaxial 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 uniaxial 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].

Uniaxial 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)

 

2.881331

2.881331

 

1e8 (CCX)1e6 (CA)

1e8 (CCX)1e6 (CA)

 

Mooney Rivlin(CCX/CA)

Mooney Rivlin(CCX/CA)

 

4.1034451

4.1034451

 

7.486014

7.486014

 

1e8 (CCX)1e6 (CA)

1e8 (CCX)1e6 (CA)

 

Yeoh(CCX)

Yeoh(CCX)

 

1.813706

1.813706

 

0.019586

0.019586

 

0.000464

0.000464

 

1e8

1e8

 

1e8

1e8

 

1e8

1e8

 

Red Poly 2(CCX)

Red Poly 2(CCX)

 

0.618107

0.618107

 

0.026944

0.026944

 

1e8

1e8

 

1e8

1e8

 

Poly 2(CCX)

Poly 2(CCX)

 

20.465522

20.465522

 

26.340633

26.340633

 

0.185894

0.185894

 

1.474968

1.474968

 

9.051008

9.051008

 

1e8

1e8

 

1e8

1e8

 

Signorini(CA)

Signorini(CA)

 

1.432189

1.432189

 

5.578092

5.578092

 

0.037811

0.037811

 

1e6

1e6

 

μ1

μ1

 

μ2

μ2

 

μ3

μ3

 

α1

α1

 

α2

α2

 

α3

α3

 

Ogden 1(CCX)

Ogden 1(CCX)

 

0.308812

0.308812

 

3.883934

3.883934

 

1e8

1e8

 

Ogden 2(CCX)

Ogden 2(CCX)

 

2.747783

2.747783

 

1.009837 e6

1.009837 e6

 

2.199164

2.199164

 

10.319457

10.319457

 

1e8

1e8

 

1e8

1e8

 

Ogden 3(CCX)

Ogden 3(CCX)

 

0.000241

0.000241

 

3.234478

3.234478

 

2.982735 e92

2.982735 e92

 

7.508369

7.508369

 

10.319457

10.319457

 

2.982735 e92

2.982735 e92

 

1e8

1e8

 

1e8

1e8

 

1e8

1e8

 

λm

λm

 

μ

μ

 

ArrudaBoyce(CCX)

ArrudaBoyce(CCX)

 

4.441020

4.441020

 

2.366097

2.366097

 

1e8

1e8

 

Constraints:

  • Face ABFE zero x-displacement
  • Face AEHD zero y-displacement
  • Face ABCD zero z-displacement
  • Face DCGH 7m 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 uniaxial 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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