Nonlinear, negative stiffness materials solver

[Satiar]

hi everyone
I want to model a nonlinear elastic with negative stiffness behavior, however, I cannot find a good solver for it. I tried Riks method but it doesn't work since the displacement is too large, Do you have any suggestion!?
Thank you so much in advance

 

[superfea]

Instead of solving the static, solve it using explicit. For my understanding, negative stiffness means material/structure is going to fail/collapse.