Cylindrical and spherical elastoplastic stress waves by a unified direct analysis method.

Abstract

A unified general solution of cylindrical and spherical elastoplastic stress waves for the small deformation theory is presented herein. A discrete formulation of analysis based directly on the underlying physical laws rather than the differential equations deducible from these laws has been used. The internal pressure pulse is an arbitrary, but nondecreasing function of time, and the material is assumed to strain-harden linearly beyond the yield point. The stress wave solution yields the respective static solutions by damping out the particle motion. The direct analysis has thus synthesized solutions of four separate problems which are usually formulated by four different differential equations for mathematical approaches. New illustrative results are presented for cylindrical elastoplastic waves for a step pressure pulse. For the static case, the agreement between results obtained by the direct analysis and the available mathematical analysis is close.