Martensitic thin films are being used as the active element in actuators, sensors, and micromachines. Single-crystal martensitic thin films have recently been grown in the laboratory by Palmstrøm and theoretically offer even larger displacements during the solid-solid phase transformation.
Bhattacharya and James have derived a thin film variational principle from the three-dimensional elastic energy for martensitic crystals with the surface energy density modeled by the square of the strain gradient. We give a derivation of an alternative thin film variational principle in which the interfacial energy is modeled by the total variation of the deformation gradient. Deformations of finite energy can have sharp interfaces with our model, and more efficient finite element approximations can be used for the deformation.
We will present numerical methods and computational results for the simulation of the deformation of a martensitic single crystal thin film during thermally activated and stress induced phase changes.