The simulation of localized failure in elastic-plastic solids, e.g. in the form of shear bands, yields the typical mesh dependent postcritical results within standard finite element formulations. We here propose a new relaxation technique based on a micromechanically motivated approach which overcomes this problem. The key idea is the introduction of a micro structure at a typical Gauss-point of the finite element mesh which bifurcates in the form of an assumed fluctuation field when macroscopic localization occurs. The method can be understood as an approximated quasi-convexification of a non-convex incremental stress potential function.
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