Validation Case: Hyperelastic Equibiaxial Tension Test

This validation case belongs to an hyperelastic equibiaxial tension test in solid mechanics. The aim of this test case is to validate the following parameters:

• Hyperelasticity under equibiaxial tension

The simulation results of SimScale were compared to the results derived from [Treloar]${}^1$.

Geometry

The geometry used for the case is as follows:

The cube has an edge length of 1 $m$.

Analysis Type and Mesh

Tool Type: Code_Aster

Analysis Type: Static Non-Linear

Mesh and Element Types:

The mesh for the cube geometry was computed using SimScale’s Standard meshing algorithm.

Case	Mesh Type	Number of Nodes	Element Type
All	Standard	1184	1st order tetrahedral

Simulation Setup

Material:

Hyperelasticity material, with the following parameters for each type of law:

• Neo Hooke:
  • $C_{10}=$ 2.398 $Pa$
  • $D_1=$ 1e-6 $1/Pa$
• Mooney-Rivlin:
  • $C_{10}=$ 1.751 $Pa$
  • $C_{01}=$ 4.625e-2 $Pa$
  • $D_1=$ 1e-6 $1/Pa$
• Signorini:
  • $C_{10}=$ 5.365 $Pa$
  • $C_{01}=$ -2.477 $Pa$
  • $C_{20}=$ 6.337e-1 $Pa$
  • $D_1=$ 1e-6 $1/Pa$

Boundary Conditions:

• Constraints:
  • Face ABFE with zero x-displacement
  • Face AEHD with zero y-displacement
  • Face ABCD with zero z-displacement
  • Face DCGH with imposed 4 $m$ x-displacement
  • Face BFGC with imposed 4 $m$ y-displacement

Reference Solution

The reference solution is of the experimental type and was extracted from [Treloar]${}^1$. It corresponds with the nominal stress-strain material curve. The values were extracted using WebPlotDigitizer.

Result Comparison

Comparison of the nominal stress-strain curves computed from reaction force on the faces with zero displacement, versus the reference data is shown in Figure 3:

Following are the contours of the final deformed shape and the von Mises stress from the Signorini case results, where the hyperelastic equibiaxial tension load effect can be appreciated:

Last updated: July 28th, 2021