Theory and numerics of a thermodynamically consistent framework for geometrically linear gradient plasticity

The paper presents the theory and the numerics of a thermodynamically consi stent formulation of gradient plasticity at small strains. Starting from th e classical local continuum formulation, which fails to produce physically meaningful and numerically converging results within localization computati ons, a thermodynamically motivated gradient plasticity formulation is envis ioned. The model is based on an assumption for the Helmholtz free energy in corporating the gradient of the internal history variable, a yield conditio n and the postulate of maximum dissipation resulting in an associated struc ture. As a result the driving force conjugated to the hardening evolution i s identified as the quasi-non-local drag stress which incorporates besides the strictly local drag stress essentially the divergence of a vectorial ha rdening flux. At the numerical side, besides the balance of linear momentum , the algorithmic consistency condition has to be solved in weak form. Ther eby, the crucial issue is the determination of the active constraints exhib iting plastic loading which is solved by an active set search algorithm bor rowed from convex non-linear programming. Moreover, different discretizatio n techniques are proposed in order to compare the FE-performance in local p lasticity with the advocated gradient formulation both for hardening and so ftening. Copyright (C) 2001 John Wiley & Sons, Ltd.