An enhanced SMA phenomenological model: I. The shortcomings of the existing models

This paper provides an enhanced phenomenological model for shape memory alloys (SMAs), to better model their behavior in cases where the temperature and stress states change simultaneously. The phenomenological models for SMAs, consisting of a thermodynamics-based-constitutive and a phase transformation kinetics model, are the most widely used models for engineering applications. The existing phenomenological models are formulated to qualitatively predict the behavior of SMA systems for simple loadings. In this study, we have shown that there are certain situations in which these models are either not correctly formulated, and therefore are not able, to predict the behavior of SMA wires or the formulation is not straightforward for engineering applications. Such cases most often occur when the temperature and stress of the SMA wire change simultaneously, such as the case of rotary SMA actuators. To this end, a rotary SMA-actuated robotic arm is modeled using the existing constitutive models. The model is verified against the experimental results to document that the model is not able to predict the behavior of the SMA-actuated manipulator, under certain conditions.