On the theorem with uniqueness of solution in dynamics problem according to the theory of small elastoplastic deformations

Abstract

In dynamics, the uniqueness of solutions was presented for elastic problem [1] and for rigid plastic problem based on the theory of plastic flow [2]. In this paper the theorem with uniqueness of solution in the dynamics problem according to the theory of small elastoplastic deformations is presented for a class of bodies subjected to time - dependent surface tractions with two impotant assumptions so that the theory of small elastoplastic deformations may be used.

First, displacement will be assumed sufficiently small, that the original geomeuy may be used in writing the equilibrium equations.

Second, external loads from the moment of their application increase proportionaly to the single parameter.