A homogenized free energy model for hysteresis in thin-film shape memory alloys

Thin-film shape memory alloys (SMAs) have become excellent candidates for microactuator fabrication in microelectromechanical systems due to their capability to achieve very high work densities, produce large deformations, and generate high stresses. In general, the material behavior of SMAs is nonlinear and hysteretic. To achieve the full potential of SMA actuators, it is necessary to develop models that characterize the nonlinearities and hysteresis inherent to the constituent materials. We develop a model that quantifies the nonlinearities and hysteresis inherent to SMAs. The fully thermomechanical model is based on free energy principles combined with stochastic homogenization techniques. It predicts rate-dependent, polycrystalline SMA behavior, and it accommodates heat transfer issues pertinent to thin-film SMAs. The main advantages of this model are that it admits a simple, low-order formulation suitable for implementation and subsequent control design, and that most of the model parameters are identifiable directly from standard measurements. We illustrate aspects of the model through comparison with thin-film SMA superelastic and shape memory effect hysteresis data.