A duality-based path-following semismooth Newton method for elasto-plastic contact problems

A Fenchel dualization scheme for the one-step time-discretized contact problem of quasi-static elasto-plasticity with combined kinematic–isotropic hardening is considered. The associated path is induced by a coupled Moreau–Yosida/Tikhonov regularization of the dual problem. The sequence of solutions to the regularized problems is shown to converge strongly to the optimal displacement–stress–strain triple of the original elasto-plastic contact problem in the space-continuous setting. This property relies on the density of the intersection of certain convex sets which is shown as well. It is also argued that the mappings associated with the resulting problems are Newton—or slantly differentiable. Consequently, each regularized subsystem can be solved mesh-independently at a local superlinear rate of convergence. For efficiency purposes, an inexact path-following approach is proposed and a numerical validation of the theoretical results is given.