Understanding parameter value for Ogden/Mooney-Rivlin model

[YanzhouWang]

I'm trying to assign a hyperelastic material model (Ogden or Mooney-Rivlin) to a soft material. As mentioned here, Ogden.h implements a 1-term Ogden material model; taking a look at the strain energy density function, it seems that only two parameters (mu and alpha) is enough to completely describe the 1-term Ogden hyperelastic behavior, so I was surprised to see a third parameter, k, included in the parameter list. Same thing goes for Mooney-Rivlin.

Could someone explain what does this k (k0 rather in the actual implementation file) stands for?

[hugtalbot]

Hi @YanzhouWang

Thank you for your question and welcome to the SOFA GitHub forum!
I just created a new doc page for the TetrahedronHyperelasticityFEMForceField (not yet merged) but you can access it here: https://github.com/sofa-framework/doc/blob/4002fa45bec5721d83629e01f636ed61da0350da/30_Components/30_ForceFields/30_TetrahedronHyperelasticityFEMForceField.md

It will soon be available here : https://www.sofa-framework.org/community/doc/components/forcefields/tetrahedronhyperelasticityfemforcefield (for future readers)

Regarding your precise question about k or k0, it corresponds to the material parameter related to the incompressibility term.
Does this make sense?

Best.

[YanzhouWang]

Hi @hugtalbot

Thanks! I was correct in assuming that. I checked out the new doc page, which looks very comprehensive; as a suggestion though it might be worth listing the actual strain energy function implemented in SOFA such that there will be no ambiguity in terms of parameters like k0.

Best,
Yanzhou