A Free Energy Model for Thin-film Shape Memory Alloys

Thin-film shape memory alloys (SMAs) have become excellent candidates for microactuator fabrication in MEMS. We develop a material model based on a combination of free energy principles in combination with stochastic homogenization techniques. In the first step of the development, we construct free energies and develop phase fraction and thermal evolution laws for homogeneous, single-crystal SMAs. Second, we extend the single-crystal model to accommodate material inhomogeneities and polycrystalline compounds. The combined model predicts rate-dependent, uniaxial SMA deformations due to applied stress and temperature. Moreover, the model admits a low-order formulation that is suitable for subsequent control design. We illustrate aspects of the model through comparison with thin-film NiTi superelastic hysteresis data.