An alternative mathematical theory of elastoplastic behaviour

TL;DR

This paper introduces a new mathematical framework for modeling elastoplastic materials that do not rely on a reference configuration, featuring hypoelastic equations, emergent hardening, and a stress space limit surface.

Contribution

It proposes an alternative elastoplastic theory that avoids deformation decomposition and incorporates a limit surface for hardening and softening regions.

Findings

Existence of a limit surface dividing stress space into hardening and softening regions.

Plastic response governed by solutions to hypoelastic differential equations.

Hardening emerges naturally from the theory without explicit rules.

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.