TY  - GEN
T1  - The behaviour of microstructures with small shears of the austenite-martensite interface in martensitic phase transformations
A1  - Fuchs,Martin
A1  - Elfanni,Abdellah
Y1  - 2011/11/22
N2  - 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.
CY  - Saarbrücken
PB  - Universitäts- und Landesbibliothek
AD  - Postfach 151141, 66041 Saarbrücken
UR  - http://scidok.sulb.uni-saarland.de/volltexte/2011/4352
ER  -