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

The endochronic theory, developed in the early seventies, 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 pseudo-potentials, indicator functions, sub-differentials, 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 pseudo-potential definition allowing a very general damage evolution is given. CE DATABASE SUBJECT HEADINGS: Plasticity, Thermodynamics, Damage, Constitutive models Preprint submitted to J.Eng.Mech. ∗ Researcher, Université Paris-Est, UR Navier, Ecole des Ponts, LAMI, 6 et 8 av. B. Pascal, Cité Descartes, Champs-sur-Marne, 77455 Marne-la-Vallée, Cedex 2, France (corresponding author). E-mail: [email protected] ∗∗Professor, Conservatoire National des Arts et Métiers (CNAM), Spécialité Mathématiques (442), 292 rue Saint-Martin, 75141 Paris, Cedex 03, France. E-mail: [email protected]