

Preprint 68/2006
A Γ-convergence result for thin martensitic films in linearized elasticity
Peter Hornung
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Submission date: 28. Jul. 2006 (revised version: February 2007)
Pages: 32
Bibtex
MSC-Numbers: 74B05, 74M25
Keywords and phrases: linearized elasticity, martensitic materials
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Abstract:
The linearly elastic energy of a thin film
of thickness h with displacement u is given by the functional
.
We consider materials whose energy density W is linearly frame indifferent and vanishes on two
linearized wells which are compatible in the plane but incompatible in the thickness direction.
We prove compactness of displacement sequences satisfying
and show that
the limiting two-dimensional displacements can only have two different interface directions.
Our main result is the derivation of the
-limit of the functionals
as
.
It is given by a weighted sum over the lengths of the interfaces.