On simple waves in an elastic-ideal plastic medium

Abstract

Elastic-plastic flow is described by a non-linear hyperbolic /1/ system of equations and an inequality (non-negativity of the factor in the associated law) that is the loading condition. There are overturning waves among the simple waves (SW) of this system of equations. However, only those SW that are not overturning satisfy the loading condition. This fact is known for the case when Hooke's law for elastic deformation and the Mises flow criterion /2/ are assumed; its foundation substantially utilized these particular properties. The absence of SW overturning is established below for a body with an arbitrary smooth flow surface and linear anisotropic elasticity. In this case jumps do not occur from the elastic-plastic SW, which indicates the possibility of solving the problem of the decay of an arbitrary discontinuity without the insertion of jumps of any new kinds that require the search for additional conditions.