# Mooney-Rivlin rubber data for CalculiX

Recently I was looking for material data for 60 Shore A rubber for a simulation. This article describes what I found and how I transformed that to material data.

There is a lot of research available about rubbers. One thing is clear from that; a standard isotropic material doesn’t describe rubber very well.

After doing some reading, I found that CalculiX supports such material using
the `*HYPERELASTIC`

keyword. After some seaching I found data for
Mooney-Rivlin variant of this model.
This has three parameters;

*C*_{10}*C*_{01}*D*_{1}

Note

Note that some sources (including CalculiX) uses 1 ⁄ *D*_{1} in
the equation for the strain energy potential, while other sources use
*D*_{1}. This is somewhat confusing.

In the way CalculiX defines it, *D*_{1} would be equal to 2 ⁄ *k*,
where *k* is the bulk modulus.
The bulk modulus for rubbers is in the order of 1−2 GPa.
That would mean a *D*_{1} significantly smaller than CalculiX’ default
value of 0.8446e-07. So we will use the latter.

In this 2018 paper I found a table of values for *C*_{10} and
*C*_{01} for rubbers of different hardness.
From that, the following material data was generated.

```
*MATERIAL, NAME=Mrubber_55ShoreA
*HYPERELASTIC, MOONEY-RIVLIN
** C10,C01,D1
0.382e6,0.096e6,0.8446e-07
*MATERIAL, NAME=Mrubber_58ShoreA
*HYPERELASTIC, MOONEY-RIVLIN
0.436e6,0.109e6,0.8446e-07
*MATERIAL, NAME=Mrubber_60ShoreA
*HYPERELASTIC, MOONEY-RIVLIN
0.474e6,0.118e6,0.8446e-07
*MATERIAL, NAME=Mrubber_65ShoreA
*HYPERELASTIC, MOONEY-RIVLIN
0.586e6,0.147e6,0.8446e-07
*MATERIAL, NAME=Mrubber_70ShoreA
*HYPERELASTIC, MOONEY-RIVLIN
0.738e6,0.184e6,0.8446e-07
```

As of this date I have not been able to properly verify these by experiment, but at least for 60 Shore A rubber calculations using these values converge nicely. And they seem to produce a realistic deformation response.

For comments, please send me an e-mail.

## Related articles

- Corrugation against buckling
- Approximating elliptical arcs in CalculiX Graphics
- Hex versus tet meshes in FEA
- Singularities versus stress concentrations in FEA
- Automating CalculiX with make(1)