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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 andŠverák, 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 adoi:10.1137/04061581x fatcat:h5cc7m6rpvbvdouexmhfw7ddea