On the general equation and the general solution in problems for plastodynamics with rigid-plastic material

Abstract

This work is the continuation of the discussion of refs. [1–2]. We discuss the dynamics problems of ideal rigid — plastic material in the flow theory of plasticity in this paper. From introduction of the theory of functions of complex variable under Dirac-Pauli representation we can obtain a group of the so-called “general equations” (i.e. have two scalar equations) expressed by the stream function and the theoretical ratio. In this paper we also testify that the equation of evolution for time in plastodynamics problems is neither dissipative nor disperive, and the eigen-equation in plastodynamics problems is a stationary Schrodinger equation, in which we take partial tensor of stress-increment as eigenfunctions and take theoretical ratio as eigenvalues. Thus, we turn nonlinear plastodynamics problems into the solution of linear stationary Schrodinger equation, and from this we can obtain the general solution of plastodynamics problems with rigid-plastic material.