An algorithm for gradient-regularized plasticity coupled to damage based on a dual mixed FE-formulation Original Research Article

A thermodynamically consistent theory of gradient-regularized plasticity with coupling to isotropic damage was presented by Svedberg and Runesson [23]. Its main purpose was to describe the successive development of the localization zone that is pertinent to the softening regime due to excessive damage close to failure. Explicit constitutive relations were established for a model problem based on von Mises plasticity with isotropic hardening of two types: local and gradient-enhanced. The main purpose of this paper is to describe a new numerical algorithm for the gradient-enhanced formulation. Using the Backward Euler rule leads to a gradient-enhanced format of the classical Closest-Point-Projection-Method. The plastic multiplier increment is solved via a dual mixed method, which is a convenient feature in the present context. This leads to an unambiguous representation of the constitutive relations in the equilibrium equation. Moreover, the classical local algebraic Kuhn-Tucker conditions are obtained in a straightforward fashion in the limit case of local theory. The developed algorithm was implemented in the educational finite element package [5]. Numerical results are shown for the extension of a plate in plane stress. These results demonstrate the convergence characteristics with mesh refinement, as well as the salient features of the adopted damage-based constitutive model.