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

Please always quote using this URN:urn:nbn:de:0296-matheon-12507
  • A Fenchel dualization scheme for the one-step time-discretized contact problem of quasi-static elasto-plasticity 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 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.

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Metadaten
Author:Michael Hintermüller, Simon Rösel
URN:urn:nbn:de:0296-matheon-12507
Referee:Fredi Tröltzsch
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2013/10/08
Release Date:2013/10/08
Tag:Elasto-plastic contact, Variational inequality of the 2nd kind, Fenchel duality, Moreau-Yosida/Tichonov regularization, Path-following, Semismooth Newton
Institute:Research Center Matheon
Humboldt-Universität zu Berlin
MSC-Classification:49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] / 49Mxx Numerical methods [See also 90Cxx, 65Kxx] / 49M15 Newton-type methods
Preprint Number:1036
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