On a Regularising Convex Potential Related to a Variational Formulation of an Elastoplastic-Damage Constitutive Model

Abstract

In this work we have proposed the definition of a regularising convex potential to be used in numerical analysis involving a certain class of constitutive elastoplastic-damage models. All the mathematical aspects discussed here are based on convex analysis, aiming at a variational formulation of the regularising elastopastic-damage potential and its conjugate potential. It is shown that the constitutive relations for the considered class of damage models are derived from those potentials by means of the respective sub-differentials sets. Furthermore, the potentials are defined in such a way that the complementarity and consistency conditions present in the local form of the damage model are satisfied. The optimality conditions of the resulting minimisation problem represents, in particular, a linear complementary problem. The numerical integration of the latter set of equations is exact if the time step does not includes damage followed by unloading.