Domain decomposition in Plasticity ?

Carsten Carstensen

Mathematisches Seminar II der C-A-Universität zu Kiel

Abstract

After a brief introduction to plasticity, we consider its primal formulation which consists of a minimization problem with a non-smooth functional. We make the observation that the non-smooth material law is local, i.e., the variables appearing in this relation belong to L^{2}(Ω) rather than H^{1}(Ω). Therefore, a non-overlapping domain decomposition is feasible for those variables while an overlapping decomposition is to be used for the displacements. We follow the following philosophy: If there is no overlap in the decomposition of some components, then the functional is allowed to be non-smooth in these components. P.L. Lion’s work on Schwarz alternating method for convex minimization problems is generalized to verify a precise form of our philosophy.