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Numerical methods for finite micromorphic elasticity problems

Micromorphic elasticity models are applied in the description of cellular materials, metallic foams or material inhomogeneities. They also help to model size effects in a natural way, i.e., small samples of a material behave comparatively stiffer than large samples which has important applications in the mechanics of nano devices. The micromorphic models considered here consist of a coupled system of nonlinear partial differential equations which are discretized by finite elements and are solved by a staggered algorithm. Each of the subproblems arising from this algorithm again require sophisticated numerical methods for their solution, including robust nonlinear solvers and domain decomposition techniques suitable for parallel computing. Joint work with Prof. Dr. Patrizio Neff, Lehrstuhl für Nichtlineare Analysis und Modellierung, and Dr. Stefanie Vanis, Lehrstuhl für Numerische Mathematik, Fakultät für Mathematik, Universität Duisburg-Essen, and Prof. Dr. Oliver Rheinbach, Institut für Numerische Mathematik und Optimierung, TU Freiberg.

A metal foam. Image from S. Vanis, O. Rheinbach, A. Klawonn, O. Prymak, M. Epple, Mat.-wiss. u. Werkstofftechn., Vol. 37, No. 6, (2006)