Finite deformation plasticity coupled with isotropic damage: Formulation in principal axes and applications

Abstract

A local, isotropic damage coupled hyperelastic–plastic framework is formulated in principal axes. It is shown that, in a functional setting, treatment of many damage growth models, including those originated from phenomenological models (with formal thermodynamical derivations), micro-mechanics or fracture criteria, proposed in the literature, is possible. As a model problem, a Lemaitre-variant damage model with quasi-unilateral damage evolutionary forms is given with special emphasis on the feasibility of formulations in principal axes. To this end, closed form expression for the inelastic tangent moduli, consistent with the linearization of the closest point projection algorithm, is derived. It is shown that, generally, even in the absence of quasi-unilateral damage evolutionary conditions, the consistent tangent moduli are unsymmetric. The model is implemented as a user defined material subroutine (UMAT) for ABAQUS/Standard. The predictive capability of the selected model problem is studied through axi-symmetric application problems involving forward extrusion of a cylindrical billet, upsetting of a tapered specimen and tension of a notched specimen, in which characteristic failure mechanisms are observed.