Shock Propagation in a Strain-Hardening Material

Abstract

Weak shock theory is used to analyze the propagation of the stress waves which are induced by nonuniform, instantaneous, internal heating of a nonlinearly elastic, semi-infinite solid. The material nonlinearity considered is caused by the increase in bulk modulus which occurs as the hydrodynamic stress component increases. Heating is assumed to occur instantaneously. Since the shock is assumed to be weak, the entropy change across it is negligible, and therefore the wave form both behind and in front of the shock is found by using a coordinate perturbation method to solve the nonlinear equations for constant entropy. This solution predicts a multivalued material state in the vicinity of the shock front without locating the front itself. The location of the shock front is found separately by using the principle of momentum conservation. If the front is then inserted at this location, a wave form is obtained for which the material state is everywhere single-valued. The results and conclusions which are presented are based on a comparison of the perturbation solution found in this paper, and a simple wave solution and on an assessment of shock strength.