An enhanced patch based stress recovery for elastoplasticity

An important part in the development of numerical strategies for the solution of physical problems consists in evaluating the quality of the solution, for example via the estimation of the associated error. Error estimation requires the availability of a more accurate (numerical) solution, to be used for comparison. Within the context of finite element modelling, a number of recovery procedures have been recently proposed, aimed at providing such accurate solutions at a reasonable computational cost. Most of the available recovery procedures were formulated within the context of linear elastic material models, their extension to nonlinear cases becoming crucial to broaden the spectrum of model verification techniques. A particularly promising recovery technique is the Recovery by Compatibility in Patches. The RCP is based on the enforcement of the compatibility condition in weak form over patches of elements centered around a given element or node. Each patch is treated as a subproblem, with imposed displacement boundary conditions deriving from the original finite element solution. Improved local stresses are then computed by minimizing the complementary energy of the patch, among an assumed set of equilibrated stress fields. The procedure has been shown to be simple, efficient, robust and numerically stable. A first extension of the RCP to elastoplastic material behavior was presented in a previous work. Here, we focus on the choice of the interpolation for the plastic multiplier. The simplest choice consists in taking a constant approximation over the patch. This leads to a single integral consistency condition over the whole patch, which may cause an excessive averaging of the originally local plasticity effects. A further possibility is here considered, consisting in elementwise constant approximation functions. This choice implies a variable number of integral consistency conditions over the patch, one for each plastified element, while still allowing to easily verify the positiveness of the plastic multiplier. Results obtained via the two approximations are presented and discussed, evaluating the effect of the plastic multiplier description on the convergence rate and on the quality of the recovered quantities.