Pressurized shape memory thin films

We study the behavior of a martensitic thin film with a hydrostatic pressure applied underneath the film. The problem is formulated in 3-D for a single crystal film of thickness h, and a Cosserat membrane theory is derived by Γ-convergence techniques in the limit h → 0. The membrane theory is further simplified using a second Γ-convergence argument based on hard moduli. The resulting theory supports energy minimizing "tunnels": structures having the shape of part of a cylinder cut by a plane parallel to its axis, obtained by releasing the film from the substrate along a strip with a certain orientation. As the temperature is raised (at fixed pressure) the energy minimizing shape collapses gradually to the substrate, accompanied by a martensite-to-austenite phase transformation. During this process the tunnel supports a microstructure consisting of fine bands of austenite parallel to the axis of the tunnel, alternating with bands of a single variant of martensite. Formulas for the associated volume-temperature-pressure relation are given: in these the latent heat of transformation plays an important role.