Orthogonality constrained gradient reconstruction for superconvergent linear functionals

Abstract

The post-processing of the solution of variational problems discretized with Galerkin finite element methods is particularly useful for the computation of quantities of interest. Such quantities are generally expressed as linear functionals of the solution and the error of their approximation is bounded by the error of the solution itself. Several a posteriori recovery procedures have been developed over the years to improve the accuracy of post-processed results. Nonetheless such recovery methods usually deteriorate the convergence properties of linear functionals of the solution and, as a consequence, of the quantities of interest as well. The paper develops an enhanced gradient recovery scheme able to both preserve the good qualities of the recovered gradient and increase the accuracy and the convergence rates of linear functionals of the solution.

Generalized radial‐return mapping algorithm for anisotropic von Mises plasticity framed in material eigenspace

“…Anisotropic plasticity, however, typically precludes the use of radial‐return like algorithms for associative plasticity because the predictor and corrector flow directions (ie, the trial and actual surface normals) are not equivalent due to the yield surface no longer being a hyper‐sphere. Ensuring associative flow, ie, enforcing the normality condition, can be achieved by simultaneously solving for the amount and direction of the plastic flow within the return mapping algorithm, ie, the so‐called closest‐point projection (CPP) type algorithms; however, the additional computational expense of this approach can make it an unrealistic option for large scale computations where efficiency of numerical algorithms is paramount …”