Antiplane shear flows in viscoplastic solids exhibiting isotropic and kinematic hardening

The authors consider antiplane shearing motions of an incompressible viscoplastic solid. The particular constitutive equation employed assumes that the stress tensor has an "elastic" component and a component which can exhibit hysteresis. The model exhibits both "kinematic" and "isotropic" hardening. Our results consist of a set of energy type estimates for the resulting system, L-2 contractivity estimates for the solution operator, and finally an analysis of the approach of our system to a "rate independent" model as a distinguished parameter describing our flow rule approaches zero. We also include some computational results for simple piecewise constant data.