Mathematical modelling of elastoplasticity at high stress

Abstract

This paper describes a simple mathematical model for one-dimensional elastoplastic wave propagation in a metal in the regime where the applied stress greatly exceeds the yield stress. Attention is focussed on the increasing ductility that occurs in the over-driven limit when the plastic wave speed approaches the elastic wave speed. Our model predicts that a plastic compression wave is unable to travel faster than the elastic wave speed, and instead splits into a compressive elastoplastic shock followed by a plastic expansion wave.