Riemann Problems for an Elastoplastic Model for Antiplane Shearing With a Nonassociative Flow Rule

Abstract

A system of partial differential equations describing antiplane shearing of an elastoplastic material is studied. The constitutive relations for plastic deformation include a nonassociative flow rule and strain hardening. Nonassociativity leads to the equations becoming ill-posed after sufficient strain hardening, which is commonly used as an indication of the formation of shear bands in the material. However, it also results in the existence of regions in stress space where the speed of plastic waves exceeds the speed of elastic waves. It is shown that a consequence of this ordering of wave speeds is that the Riemann problem cannot be solved for certain initial data. A modification of the model, which retains the occurrence of ill-posedness but removes the problem of reverse ordering of wave speeds, is presented.