A Γ-Convergence Result for Thin Martensitic Films in Linearized Elasticity

The elastic energy of a thin film Ωh of thickness h with displacement u : Ωh → R is given by the functional E(u) = ∫ Ωh W (∇u). 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 u : Ωh → R satisfying E(u) ≤ Ch and we derive the Γ-limit of the functionals 1 h2E h as h→ 0.