An accurate dynamic model for polycrystalline shape memory alloy wire actuators and sensors

Thermal shape memory alloy (SMA) wires exhibit a mechanical hysteresis of which the shape depends on both temperature and loading rate. Commercially available actuator wires typically exhibit polycrystalline behavior, which also depends on training effects. Polycrystallinity may lead to complex hysteresis loops, differing substantially from standard box shapes often employed in modeling attempts. In addition, actuation often results in loading trajectories leading through the interior of the hysteresis, making accurate modeling and control of SMA systems a highly challenging task. In this paper, we present a novel dynamic model for polycrystalline SMA actuator wires based on a modified version of the Müller-Achenbach-Seelecke model. The model permits to predict time evolution of stress and resistance of a one-dimensional SMA wire under arbitrary input strain and Joule heating profiles. The constitutive equations are developed by properly exploiting the concept of a representative single-crystal, resulting in an optimal trade-off between physical interpretation and computational efficiency. After developing constitutive model equations, experimental validation is performed by means of two case studies, given by a superelastic NiTi wire and a quasi-plastic NiTi wire, respectively. The experiments are intended to illustrate the model capabilities in predicting internal hysteresis loops, loading rate effects, as well as actuation and sensing behavior at the same time. A remarkable accuracy is observed in all of the investigated experimental scenarios, making the model particularly suitable for high-precision control and self-sensing applications.