kinematic ahrdening

Hi, I’m trying to implement a mixed hardening J2 plasticity model. The idea is to use the Ludwik law to represent the isotropic hardening and the Amstrong-Frederick law for the kinematic hardening, both combine in a J2 classic von Mises model.

I need some advice for the return mapping algorithm.

Once that I have check that the elastic trial state is not plastically admissible I have to solve a three equation system, where the first two are a tensor equations and the third one is the J2 yield function equation.