Validation Case: Hyperelastic Uniaxial Tension Test

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

• Hyperelasticity under uniaxial 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 consists of one eight nodes hexahedral element, computed locally and updated to the platform.

Case	Mesh Type	Number of Nodes	Element Type
ALL	1st Order Hexahedral	8	Standard

Simulation Setup

Material:

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

• Mooney-Rivlin:
  • \(C_{10} = \) 4.103 \(Pa\)
  • \(C_{01} = \) -7.486 \(Pa\)
  • \(D_{1} = \) 1e-6 \(1/Pa\)
• Neo Hooke:
  • \(C_{10} = \) 2.881 \(Pa\)
  • \(D_{1} = \) 1e-6 \(1/Pa\)
• Signorini:
  • \(C_{10} = \) -1.432 \(Pa\)
  • \(C_{01} = \) 5.578 \( Pa\)
  • \(C_{20} = \) 3.781e-2 \(Pa\)
  • \(D_{1} = \) 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 7 \(m\) 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 force on the faces with zero displacement, versus the reference data is shown in Figure 3:

Following is a plot of the final deformed shape from the Signorini case results:

Last updated: May 19th, 2021