Towards effective simulation of effective elastoplastic evolution

Carsten Carstensen , Robert Huth

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 9 pp.

MSC 2000

65M60 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods

Abstract
This paper summarises the general strategy for time evolving finite elastoplasticity and outlines encountered computational challenges in form of numerical benchmarks. Each time-step of some natural implicit time-discretisation is eventually recast into a possibly non-convex minimisation problem. Finite plasticity seems to imply the lack of lower semicontinuity of the energy functional and so leads to enforced fine strain oscillations called microstructures with required generalised solution concepts. The adaptive spacial discretisation is possible for convexified formulations from the relaxation finite element method (RFEM). For single-slip finite plasticity, one requires to relax numerically with laminates or semiconvexity notions.