Hello,

I was wondering if anyone could help me create a VUMAT for St Venant-Kirchhoff model, which is a basic hyper elastic model.

S(E) = lambda*tr(E)*I + 2*mu*E

The reference says a hyper elastic material in VUMAT must be defined in terms of right stretch tensor to avoid applying rotation twice. So the model is written in terms of U rather than E.

S(U) = lambda*tr(1/2*(U*U-I))*I + 2*mu*(1/2*(U*U-I))

and the new stress is defined by

newStress = oldStress + dS/dU*stretchInc

Then the problem is how do I find increment of stretch? As you know there is predefined "strainInc" variable. Is the "strainInc" the Lagrange strain?

Another issue is,

When I convert the Second Piola-Kirchhoff stress to Cauchy stress, there happen for deformation gradient F to be involved. Does violate the rotation problem?

Welcome any advice or example. Thanks all community!