This is a very complex constitutive model. The yield function is assumed to be Mohr-Coulomb type with zero cohesion. The friction angle will increase or decrease (after peak) with the development of the hardening parameter, a modified plastic work. This friction angle-plastic work relation is stress-dependent. For simplicity, the potential function is assumed to be Drucker-Prager type. The dilatancy angle used in the potential function varies with the friction angle. In addition, cross-anisotropic elastic model which is stress-dependent is used in the model.

I have tried the cutting plane method and the closed point projection method. However, it only works with one-element simulation of the PSC test. It diverges when I perform multi-elements simulation of the same PSC test. Then I found that even the perfect-plastic MC model does not work well when simulating the PSC test with multi-elements. I did not deal with the corners and apex of the MC model and I guess this is one reason. However, I am not sure about it. So, my questions are:

(1)  Must the corners and apex of the MC model be dealt with? And how?

(2)  Are the backward-Euler methods suitable for the hardening-softening model I described? I read a lot papers dealing with perfect-plasticity, but I cannot find a proper case for my model. Could anyone give me some suggestions on the algorithm aspect? Thank you!