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 hdl:20.500.11880/26247 http://dx.doi.org/10.22028/D291-26191 |
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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preprint_34_01.pdf | 212,28 kB | Adobe PDF | View/Open |
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