How to implement hyperelastic and viscoelastic constitutive laws?

[Qin-Shaowen]

Hi, thanks for this great library.

I am simulating a rubber cord undergoing very large torsion (up to ~100 full turns) and releasing it. At such large shear strains, the default constant youngs_modulus and shear_modulus are not sufficient to capture the nonlinear material behavior. I need two things:

1. Hyperelasticity: The torque-twist relation becomes nonlinear at large twists, and the bending stiffness may also depend on the local twist due to the Poynting effect (axial-torsional coupling inherent to rubber-like materials). I would like to use a strain energy density function (e.g., neo-Hookean, Mooney-Rivlin, or Ogden) to compute the internal forces and moments.

2. Viscoelasticity: Rubber damping is significant and strain-rate dependent. I need to add viscous stress components to the internal forces/torques.

Is there a way to customize the constitutive law within PyElastica’s Cosserat rod model? Specifically:

• Can I override the stress resultant calculation (bending/twisting moments and shear/tensile forces) with a user-defined function?
• Is there a mechanism to make bend_matrix and shear_matrix depend on the local strains (curvature, twist, shear) or to update them at each time step?
• For viscoelasticity, can I add damping torques proportional to the strain rates?

If not yet implemented, could you point me to the relevant part of the source code where the internal forces are assembled, so I can try to subclass and override it?

Thanks for any guidance!