# Scaling of the energy for thin martensitic films

created on 02 Nov 2004

[BibTeX]

Submitted Paper

Inserted: 2 nov 2004

Year: 2004

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 Sverak, 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 $h^2$.