Please use this identifier to cite or link to this item: doi:10.22028/D291-26191
Title: The behaviour of microstructures with small shears of the austenite-martensite interface in martensitic phase transformations
Author(s): Fuchs, Martin
Elfanni, Abdellah
Language: English
Year of Publication: 2001
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 domain whose boundary \partial\Omega is Lipschitz and contains a segment \Gamma_{0} representing the austenite-twinned martensite interface. We prove \underset{u\in\mathcal{W}(\Omega)}{inf}\int_{\Omega}\varphi(\nabla u(x,y))dxdy=0 for any elastic energy density \varphi:\mathbb{R}^{2}\rightarrow[0,\infty) such that \varphi(0,\pm1)=0. Here \mathcal{W}(\Omega)consists of all Lipschitz functions u with u=0 on \Gamma_{0} and \left|u_{y}\right|=1 a.e. Apart from the trivial case \Gamma_{0}\subset\mathbb{R}x\{a\}, a\in\mathbb{R}, this result is obtained through the construction of suitable minimizing sequences which differ substantially for vertical and non-vertical segments.
Link to this record: urn:nbn:de:bsz:291-scidok-43527
Series name: Preprint / Fachrichtung Mathematik, Universität des Saarlandes
Series volume: 34
Date of registration: 22-Nov-2011
Faculty: MI - Fakultät für Mathematik und Informatik
Department: MI - Mathematik
Collections:SciDok - Der Wissenschaftsserver der Universität des Saarlandes

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