Scaling of the energy for thin martensitic films

Nirmalendu Chaudhuri and Stefan Müller

Contact the author: Please use for correspondence this email.
Submission date: 20. Sep. 2004
Pages: 15
published in: SIAM journal on mathematical analysis, 38 (2006) 2, p. 468-477 
DOI number (of the published article): 10.1137/04061581X
Bibtex
MSC-Numbers: 74K20, 74N10, 74B20
Keywords and phrases: martensitic films, phase transformation
Download full preprint: PDF (163 kB), PS ziped (161 kB)

Abstract:
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 .