Study of discontinuities in solutions of the Prandtl–Reuss elastoplasticity equations

Abstract

Relations across shock waves propagating through Prandtl–Reuss elastoplastic materials with hardening are investigated in detail. It is assumed that the normal and tangent velocities to the front change across shock waves. In addition to conservation laws, shock waves must satisfy additional relations implied by their structure. The structure of shock waves is studied assuming that the principal dissipative mechanism is determined by stress relaxation, whose rate is bounded. The relations across shock waves are subject to a qualitative analysis, which is illustrated by numerical results obtained for quantities across shocks.