A discontinuous Galerkin formulation for classical and gradient plasticity. Part 2: Algorithms and numerical analysis

Abstract

This work is the second of a two-part investigation into the use of discontinuous Galerkin methods for obtaining approximate solutions to problems of classical and gradient plasticity. Part I [J.K. Djoko, F. Ebobisse, A.T. McBride, B.D. Reddy, A discontinuous Galerkin formulation for classical and gradient plasticity. Part 1: Formulation and analysis, Comput. Methods Appl. Mech. Engrg., 196 (2007) 3881–3897] presented the formulation and analysis of such problems. This part focusses on algorithmic and computational aspects of the problem. In particular, it is shown that the predictor–corrector algorithms of classical plasticity are readily extended to the case of gradient plasticity, and to discontinuous Galerkin formulations. Conditions for convergence of the algorithms are presented, for the elastic, secant, and consistent tangent predictors. The form of the consistent tangent modulus is established for the case of gradient plasticity. A selection of numerical examples is presented and discussed with a view to illustrating aspects of the approximation scheme and algorithms, as well as features of the model of gradient plasticity adopted here.