Antiplane shear flows in visco-plastic solids exhibiting isotropic and kinematic hardening

Abstract

Abstract: "The authors consider antiplane shearing motions of an incompressible visco-plastic 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, LΓéé 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.