Uniaxial Elastic-Plastic Wave Propagation

Abstract

This article considers the uniaxial elastic-plastic response of a solid slab subject to a velocity applied to one boundary, over time scales on which both elastic and plastic waves can propagate. We briefly describe a simple model in which the amplitudes are small enough for these waves to satisfy linear wave equations, although the full problem is still non-linear because of the presence of an unknown free boundary separating elastic and plastic regions. Examples are given which show that the presence of residual stress can cause the pattern of elastic and plastic regions in the |$(X,t)$|-plane to be surprisingly complicated.