## N. Chaudhuri - S. MÃ¼ller

# Scaling of the energy for thin martensitic films

created on 02 Nov 2004

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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 $h^2$.

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