RIEMANN PROBLEMS FOR AN ELASTOPLASTIC MODEL FOR ANTIPLANE SHEARING WITH A NONASSOCIATIVE FLOW RULE

A system of partial differential equations describing antiplane sheari ng 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 indic ation of the formation of shear bands in the material. However, it als o 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 prob lem cannot be solved for certain initial data. A modification of the m odel, which retains the occurrence of ill-posedness but removes the pr oblem of reverse ordering of wave speeds, is presented.