VISCOPLASTIC RELAXATION - CONVERGENCE AND LOCALIZATION

A visco-plastic shear-strain softening constitutive model is introduce d as a regularization of the unstable elasto-plastic softening model. Mathematical analysis demonstrates that, in spite of softening, the so lution of the visco-plastic model has bounded energy; furthermore, the solution (in particular the stress) converges, in an appropriate sens e, to the solution of the elasto-plastic model. A computational scheme based on a high-order Godunov method is then used to compute numerica l solutions to the visco-plastic problem. In this scheme, the computat ional timestep is not limited by the visco-plastic relaxation time, bu t only by the elastic wavespeed.