The behaviour of microstructures with small shears of the austenite-martensite
interface in martensitic phase transformations |
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Authors: | A Elfanni M Fuchs |
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Institution: | (1) Universität des Saarlandes, Fachbereich 6.1-Mathematik, 151150, 66041 Saarbrücken, Germany;(2) Universität des Saarlandes, Fachbereich 6.1-Mathematik, 151150, 66041 Saarbrücken, Germany |
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Abstract: | Let $\Omega \subset \Bbb{R}^2$ denote a bounded domain whose boundary
$\partial \Omega$ is Lipschitz and contains a segment $\Gamma_0$ representing
the austenite-twinned martensite interface. We prove
$$\displaystyle{\inf_{{u\in \cal W}(\Omega)} \int_\Omega \varphi(\nabla
u(x,y))dxdy=0}$$ for any elastic energy density $\varphi : \Bbb{R}^2
\rightarrow 0,\infty)$ such that $\varphi(0,\pm 1)=0$. Here
${\cal W}(\Omega)$ consists of all Lipschitz functions $u$ with
$u=0$ on $\Gamma_0$ and $|u_y|=1$ a.e. Apart from the trivial case
$\Gamma_0 \subset \reel \times \{a\},~a\in \Bbb{R}$, this result is
obtained through the construction of suitable minimizing sequences
which differ substantially for vertical and non-vertical
segments. |
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Keywords: | 49 74 |
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