Some Properties of Elastic Dynamics of a Medium with Preliminary Large Irreversible Deformations

Abstract

The nonstationary dynamics of a medium without additional accumulation of plastic strains over preexisting ones is considered in the framework of a model of large elastoplastic deformations. For such a case, it is shown that the velocities and types of arising elastic shock waves completely repeat the wave pattern for a nonlinearly-elasticmedium, whereas the compatibility conditions for discontinuities do not depend on the plastic strains. Some general formulas for calculating the rotation and redistribution of plastic deformations are obtained. The results are illustrated by relatively simple example with the plane one-dimensional shock waves. For an isotropic nonlinear relation between the stresses and elastic strains, it is shown that the plane elastic shock waves are divided into quasi-longitudinal, quasi-transverse, and rotational ones. It is also shown that, in the general case, some jump rotation of plastic deformations can occur on each of the elastic waves.