A variational limit defined on the space of bi-dimensional gradient Young measures is obtained from three-dimensional elasticity via dimension reduction. The obtained limit problem uniquely determines the energy density of the thin film. Our result might be used to compute the microstructure in membranes made of phase transforming material.
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Lorenzo Freddi, Roberto Paroni, The energy density of martensitic thin films via dimension reduction. Interfaces Free Bound. 6 (2004), no. 4, pp. 439–459DOI 10.4171/IFB/109