Please use this identifier to cite or link to this item: doi:10.22028/D291-26210
Title: Microstructures corresponding to curved austenite-martensite interfaces
Author(s): Elfanni, Abdellah
Fuchs, Martin
Language: English
Year of Publication: 2002
Free key words: elastic energy
minimizing sequences
Young measures
DDC notations: 510 Mathematics
Publikation type: Other
Abstract: Let \Omega\subset\mathbb{R}^{2} denote a bounded Lipschitz domain and consider some portion \Gamma_{0} of \partial\Omega representing the austenite-twinned martensite interface which is not assumed to be a straight segment. We prove \underset{u\in\mathcal{W}(\Omega)}{inf}\int_{\Omega}\varphi(\nabla u(x,y))dxdy=0 for an elastic energy density \varphi:\mathbb{R}^{2}\rightarrow[0,\infty) such that \varphi(0,\pm1)=0. Here \mathcal{W}(\Omega) consist of all functions u from the Sobolev class W^{1,\infty}(\Omega) such that \left|u_{y}\right|=1 a.e. on \Omega together with u=0 on \Gamma_{0}. Moreover some minimizing sequences vanishing on the whole boundary \partial\Omega are constructed, that is, one can even take \Gamma_{0}=\partial\Omega. We also show that the existence or nonexistence of minimizers depends on the shape of the austenite-twinned martensite interface \Gamma_{0}.
Link to this record: urn:nbn:de:bsz:291-scidok-43857
Series name: Preprint / Fachrichtung Mathematik, Universität des Saarlandes
Series volume: 60
Date of registration: 2-Dec-2011
Faculty: MI - Fakultät für Mathematik und Informatik
Department: MI - Mathematik
Collections:SciDok - Der Wissenschaftsserver der Universität des Saarlandes

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