An Infinite-Dimensional Semismooth Newton Method for Elasto-Plastic Contact Problems

A Fenchel dualization scheme for the one-step time-discretized elasto-plastic contact problem with kinematic or isotropic hardening is considered. The associated path is induced by a combined Moreau-Yosida / Tichonov regularization of the dual problem. The sequence of solutions to the regularized problems is shown to converge strongly to the solution of the original problem. This property relies on the density of the intersection of certain convex sets. The corresponding conditions are worked out and customary regularization approaches are shown to be valid in this context. It is also argued that without higher regularity assumptions on the data the resulting problems possess Newton differentiable optimality systems in infinite dimensions 2]. Consequently, each regularized subsystem can be solved mesh-independently at a local superlinear rate of convergence 6]. Numerically the problems are solved using conforming finite elements. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)