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Title: Rate-independent elastoplasticity at finite strains and its numerical approximation
Authors: Mielke, AlexanderRoubíc̆ek, Tomáš
Issue Date: 2016
Published in: Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik , Volume 2210, ISSN 2198-5855
Publisher: Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
Abstract: Gradient plasticity at large strains with kinematic hardening is analyzed as quasistatic rate-independent evolution. The energy functional with a frame-indifferent polyconvex energy density and the dissipation are approximated numerically by finite elements and implicit time discretization, such that a computationally implementable scheme is obtained. The non-selfpenetration as well as a possible frictionless unilateral contact is considered and approximated numerically by a suitable penalization method which keeps polyconvexity and simultaneously by-passes the Lavrentiev phenomenon. The main result concerns the convergence of the numerical scheme towards energetic solutions. In the case of incompressible plasticity and of nonsimple materials, where the energy depends on the second derivative of the deformation, we derive an explicit stability criterion for convergence relating the spatial discretization and the penalizations.
Keywords: Plasticity; quasistatic evolution; energetic solutions; dissipation distance; hardening; polyconvexity; Ciarlet-Neˇcas condition; Signorini contact; finite-element approximation; Gamma-convergence; Lavrentiev phenomenon; 2nd-grade nonsimple materials
DDC: 510
License: This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.
Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.
Appears in Collections:Mathematik



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