Dynamics of Unloading and Elastic Waves in a Medium with Accumulated Plastic Pre-Deformations

Abstract

Approaches that allow one to describe the elastic dynamics of a medium (including unloading and elastic loading) in the presence of irreversible pre-deformations are proposed for a model of large elastoplastic deformations. Formulas based on a rotation tensor are obtained for calculating the redistribution of plastic strains. For dynamic elastic processes generating shock waves in an elastoplastic medium, the possible rates and types of plane shock waves are determined. It is shown that elastic shock waves create jumps in the field of plastic pre-deformations. Relations for calculating such discontinuities are obtained. The main properties of modeling self-similar solutions taking into account the proposed approach to the description of the kinematics of the medium and the possibility of distinguishing between elastic and plastic strains are considered.