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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]\(^1\).


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.

CaseMesh TypeNumber of
Element Type
AllStandard11841st 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


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:

nominal stress strain result curves comparison for planar validation case
Figure 3: Nominal stress-strain curves comparison

Following is a plot of the final deformed shape from the Neo-Hooke case results:

deformed shape color plot for planar validation case
Figure 4: Final deformed shape of the cube, with color representing deformation magnitude for the Neo-Hooke case


  • 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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Last updated: August 2nd, 2021