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Title: A mathematical framework for standard generalized materials in the rate-independent case
Authors: Mielke, Alexander
Issue Date: 2006
Published in: Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik , Volume 1123, ISSN 0946-8633
Publisher: Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
Abstract: Standard generalized materials are described by an elastic energy density and a dissipation potential. The latter gives rise to the evolution equation (flow law) for the internal variables. The energetic formulation provides a very weak, derivative-free form of this flow law. It is based on a global stability condition and an energy balance. Using time-incremental minimization problems, which allow for the usage of the rich theory in the direct method of the calculus of variations, it is possible to establish general, abstract existence results as well as convergence for numerical approximations. Applications to shape-memory materials and to magnetostrictive or piezoelectric materials are surveyed.
Keywords: Rate-independence; energetic formulation; Gamma-convergence; relaxation; shape-memory material; magnetostriction; piezoelectricity
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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