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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;

  • C10
  • C01
  • D1

Note

Note that some sources (including CalculiX) uses 1 ⁄ D1 in the equation for the strain energy potential, while other sources use D1. This is somewhat confusing.

In the way CalculiX defines it, D1 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 D1 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 C10 and C01 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.


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