A justification of the theory of martensitic thin films in the absence of an interfacial energy

In the framework of Nonlinear Elasticity, the asymptotic behavior of the free energy of a martensitic material is studied as the height of the sample tends to zero. The effective thin film energy is identified in terms of parametrized probability measures, which allows for a justification of the kinematic compatibility conditions proposed in Bhattacharya and James' theory of thin films of martensitic materials, in the absence of higher order interfacial energy contributions to the three-dimensional bulk energy.