Scaling of the energy for thin martensitic films
Nirmalendu Chaudhuri and Stefan Müller
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Submission date: 20. Sep. 2004
published in: SIAM journal on mathematical analysis, 38 (2006) 2, p. 468-477
DOI number (of the published article): 10.1137/04061581X
MSC-Numbers: 74K20, 74N10, 74B20
Keywords and phrases: martensitic films, phase transformation
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We study the scaling behaviour of thin martensitic films. Specifically we consider an elastic energy with two SO(3) invariant wells which are strongly incompatible in the sense of Matos and Sverák, but whose two-dimensional projections are compatible. We show that in a thin film of thickness the energy per unit height scales like h. This scaling lies in between the classical membrane theory (where the energy per unit height is of order 1) and the Kirchhoff bending theory, which corresponds to a scaling of .