Some Recent Results in the Theory of an Ideal Plastic Body

Abstract

Publisher Summary This chapter discusses some aspects of the mathematical theory of a perfectly plastic body. The “general and complete” plane problem of perfectly plastic isotropic body is defined. The main problem considered is an introduction to the theory of the “general and complete” plane problem. To study general yield conditions or to study the plane problem under assumption of a general yield condition must be derived from a physically correct three-dimensional setup. The chapter discusses simple waves, stress and velocity, the theory of the characteristics of the complete problem, the approximate solution of some initial value problems in case of real characteristics, and boundary value problems based on the theory exposed on the assumption of plane strain. Some specific features of boundary value problems of plasticity theory are illustrated. It is preferable to derive the plane problem as a particular solution of the three-dimensional one to make sure that the important cases of plane stress and plane strain are taken care of and that enough generality is achieved, together with necessary restrictions.