Validation Case: Hyperelastic Planar Tension Test

This validation case belongs to solid mechanics. The aim of this test case is to validate the following parameters:

Hyperelasticity under planar tension

The simulation results of SimScale were compared to the results derived from [Treloar]\(^1\).

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Geometry

The geometry used for the case is below:

cube geometrical model — Figure 1: Geometry model for the cube

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

Table 1: Finite element model for each case

tetrahedral mesh for planar tension validation case simscale — Figure 2: Tetrahedral element mesh for the cube

Simulation Setup

Material:

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

Neo Hooke:
- \(C_{10} = \) 1.684 \(Pa\)
- \(D_{1} = \) 1e-6 \(1/Pa\)
Mooney-Rivlin:
- \(C_{10} = \) -99.16 \(Pa\)
- \(C_{01} = \) 100.8 \(Pa\)
- \(D_{1} = \) 1e-6 \(1/Pa\)
Signorini:
- \(C_{10} = \) 1 \(Pa\)
- \(C_{01} = \) 0.6809 \(Pa\)
- \(C_{20} = \) 1.19e-4 \(Pa\)
- \(D_{1} = \) 1e-6 \(1/Pa\)

Boundary Conditions:

Constraints:
- Face ABFE with zero x-displacement
- Face AEHD with zero y-displacement
- Face BFGC with zero y-displacement
- Face ABCD with zero z-displacement
- Face DCGH with imposed 4 \(m\) x-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 forces on the faces with zero displacements, versus the reference data is shown in Figure 3: