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.