Striped Periodic Minimizers of a Two-Dimensional Model for Martensitic Phase Transitions |
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| Authors: | Email author" target="_blank">Alessandro?GiulianiEmail author Stefan?Müller |
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| Institution: | 1.Dipartimento di Matematica di Roma Tre,Roma,Italy;2.Hausdorff Center for Mathematics & Institute for Applied Mathematics,Universit?t Bonn,Bonn,Germany |
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| Abstract: | In this paper we consider a simplified two-dimensional scalar model for the formation of mesoscopic domain patterns in martensitic
shape-memory alloys at the interface between a region occupied by the parent (austenite) phase and a region occupied by the
product (martensite) phase, which can occur in two variants (twins). The model, first proposed by Kohn and Müller (Philos
Mag A 66(5):697–715, 1992), is defined by the following functional:
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(E)(u) = 2pb||u(0,·)||2(H)\dot]1/2(0,h]) + ò0L dx ò0h dy ( |ux|2 + \frace2|uyy| ),\mathcal (E)(u) = 2\pi\beta||u(0,\cdot)||^2_{\dot H^{1/2}(0,h])} + \int_{0}^{L} dx \int_0^h dy\, \big( |u_x|^2 + \frac{\varepsilon}2|u_{yy}| \big), |
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