Towards effective simulation of effective elastoplastic evolution

Summary. This paper summarises the general strategy for time evolving finite elastoplasticity and outlines encountered computational challenges in form of nu-merical 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 for-mulations from the relaxation finite element method (RFEM). For single-slip finite plasticity, one requires to relax numerically with laminates or semiconvexity notions. Acknowledgement. The authors thank: S.Conti, A.Mielke and A.Orlando for stim-ulating discussions and collaborations and the DFG for support via the FG797