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

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:292

Article

Hintermueller, M.¹  Roesel, S.¹ 

[1] Humboldt Univ, Dept Math, D-10099 Berlin, Germany

关键词: Elasto-plastic contact;    Variational inequality of the 2nd kind;    Fenchel duality;    Moreau-Yosida/Tikhonov regularization;    Path-following;    Semismooth Newton;   

DOI  :  10.1016/j.cam.2015.06.010

来源: Elsevier

【 摘 要 】

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. (C) 2015 Elsevier B.V. All rights reserved.

【 授权许可】

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