Pseudo-potentials and loading surfaces for an endochronic plasticity theory with isotropic damage

TL;DR

This paper formulates an endochronic plasticity model with isotropic damage using convex analysis tools, introducing pseudopotentials and loading surfaces, and compares it with classical plasticity models.

Contribution

It develops a novel endochronic damage model using convex analysis, defining damage pseudopotentials and loading surfaces, and offers a comparison with classical models.

Findings

A damage pseudopotential for general damage evolution is proposed.

Loading surfaces for the endochronic model are characterized and compared.

The model bridges endochronic theory with classical plasticity tools.

Abstract

The endochronic theory, developed in the early 70s, allows the plastic behavior of materials to be represented by introducing the notion of intrinsic time. With different viewpoints, several authors discussed the relationship between this theory and the classical theory of plasticity. Two major differences are the presence of plastic strains during unloading phases and the absence of an elastic domain. Later, the endochronic plasticity theory was modified in order to introduce the effect of damage. In the present paper, a basic endochronic model with isotropic damage is formulated starting from the postulate of strain equivalence. Unlike the previous similar analyses, in this presentation the formal tools chosen to formulate the model are those of convex analysis, often used in classical plasticity: namely pseudopotentials, indicator functions, subdifferentials, etc. As a result, the notion of loading surface for an endochronic model of plasticity with damage is investigated and an insightful comparison with classical models is made possible. A damage pseudopotential definition allowing a very general damage evolution is given.