An alternative mathematical theory of elastoplastic behaviour

Abstract

This paper presents a theory for the behaviour of isotropic-hardening/softening elastoplastic materials that do not have a preferred reference configuration. In spite of important differences, many ingredients of classical plasticity are present. Main features are: the elastic and plastic responses are given by solutions of hypoelastic differential equations, no decomposition of the deformation into elastic and plastic parts is done from the start, the hardening rule is an outcome, and the principle of material objectivity is obeyed. An important result is the existence of a limit surface that divides the stress space into regions of hardening and softening and is composed of equilibrium points of the differential equation of plastic response.