An adaptive finite element algorithm for gradient theory of plasticity with coupling to damage

In this paper, an adaptive finite element algorithm is proposed for resolving localization zones in plastic solids with coupling to damage, whereby the solution is regularized via the introduction of gradient theory. It is possible to avoid the mesh dependence that otherwise would become inevitable when the localization narrows progressively due to the development of damage. The adaptive method is based on an a posteriori error computation in energy norm for the plastic multiplier based on the constitutive subproblem, which is solved via a mixed finite element formulation. The performance of the proposed method is investigated for a few simple numerical examples in 1D and 2D.