A gradient model for finite strain elastoplasticity coupled with damage

Abstract

This paper describes the formulation of an implicit gradient damage model for finite strain elastoplasticity problems including strain softening. The strain softening behavior is modeled through a variant of Lemaitre's damage evolution law. The resulting constitutive equations are intimately coupled with the finite element formulation, in contrast with standard local material models. A 3D finite element including enhanced strains is used with this material model and coupling peculiarities are fully described. The proposed formulation results in an element which possesses spatial position variables, nonlocal damage variables and also enhanced strain variables. Emphasis is put on the exact consistent linearization of the arising discretized equations. A numerical set of examples comparing the results of local and the gradient formulations relative to the mesh size influence is presented and some examples comparing results from other authors are also presented, illustrating the capabilities of the present proposal.