Francois Ebobisse

Existence and uniqueness for rate-independent infinitesimal gradient plasticity with isotropic hardening and plastic spin

Existence and uniqueness for infinitesimal dislocation based rate-independent gradient plasticity with linear isotropic hardening and plastic spin are shown using convex analysis and variational inequality methods. The dissipation potential is extended non-uniquely from symmetric plastic rates to non-symmetric plastic rates and three qualitatively different formats for the dissipation potential are distinguished.

Some properties of the dissipative model of strain-gradient plasticity

A theoretical and computational investigation is carried out of a dissipative model of rate-independent strain-gradient plasticity and its regularisation. It is shown that the flow relation, when expressed in terms of the Cauchy stress, is necessarily global. The most convenient approach to formulating the flow relation is through the use of a dissipation function. It is shown, however, that the task of obtaining the dual version, in the form of a normality relation, is a complex one. A numerical investigation of problems in two space dimensions casts further light on the response using the dissipative theory in situations of non-proportional loading. The elastic gap, a feature reported in recent investigations, is observed in situations in which passivation has been imposed. The computational study indicates that the gap may be regarded as an efficient path between a load-deformation response corresponding to micro-free boundary conditions, and that corresponding to micro-hard boundary conditions, in which plastic strains are set equal to zero on all or part of the boundary.

On the Mathematical Formulations of a Model of Strain Gradient Plasticity

In this paper we study two mathematical formulations of a model of infinitesimal strain gradient plasticity for plastically irrotational materials proposed by Gurtin and Anand. The first formulation which exploits the context of convex analysis leads to a variational inequality whose well-posedness is studied. Due to the inability of this formulation to accommodate softening behaviour, a promising second formulation is proposed following the energetic approach for rate-independent processes developed by Mielke.

Stability of some unilateral free-discontinuity problems in two-dimensional domains

The purpose of this paper is to study the stability of some unilateral free-discontinuity problems, under perturbations of the discontinuity sets in the Hausdorff metric.

Flow Relations and Yield Functions for Dissipative Strain-Gradient Plasticity

In this work we carry out a theoretical investigation of a dissipative model of rate-independent strain-gradient plasticity. The work builds on the investigation in [1], which in turn was inspired by the investigations in [4] of responses to non-proportional loading in the form of surface passivation. We recall the global nature of the flow relation when expressed in terms of the Cauchy stress and dissipation function. We highlight the difficulties encountered in attempts to obtain dual forms of the flow relation and associated yield functions, for the continuous and discrete problems, and derive upper bounds on the global yield function.