Theoretical and computational aspects of a thermodynamically consistent framework for geometrically linear gradient damage

This paper presents the theory and the numerics of an isotropic gradient da mage formulation within a thermodynamical background. The main motivation i s provided by localization computations whereby classical local continuum f ormulations fail to produce physically meaningful and numerically convergin g results. We propose a formulation in terms of the Helmholtz free energy i ncorporating the gradient of the damage field, a dissipation potential and the postulate of maximum dissipation. As a result, the driving force conjug ated to damage evolution is identified as the quasi-nonlocal energy release rate, which essentially incorporates the divergence of a vectorial damage flux besides the strictly local energy release rate, On the numerical side, besides balance of linear momentum, the algorithmic consistency condition must be solved in weak form, Thereby, the crucial issue is the selection of active constraints which is solved by an active set search algorithm borro wed from convex nonlinear programming. In the examples, we compare the beha vior in local damage with the performance of the gradient formulation. (C) 2001 Elsevier Science B.V. All rights reserved.