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# 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.

## 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: Figure 3: Nominal stress-strain curves comparison with Treloar $$^1$$

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: Figure 4: Final deformed shape of the cube, with color representing deformation magnitude for the Signorini case

References

• L. R. G. Treloar, “Stress-strain data for vulcanised rubber under various types of deformation”, Trans. Faraday Soc., 40:59–70, 1944.

Note

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Last updated: July 28th, 2021