Modelling the Stress-dependent Hysteresis of Shape Memory Alloys

Shape memory alloy (SMA) actuators are becoming increasingly popular in many industrial application fields like automotive, medical devices, robotics or smartphones. However, the behavior of SMA material is non-linear and displays a pronounced hysteresis. In order to optimize the performance of SMA actuators already early during design, mathematical models capturing the complex behavior with a high degree of accuracy are needed. Such models will also provide the basis for advanced model-based control schemes. This paper proposes a novel transformation function that is able to capture the rounded and asymmetric hysteresis shape found in commercial SMA wires. It uses two additional parameters to adapt the curvature and asymmetry of the hysteresis to experimental data. Dependency of the additional parameters on the stress level in the SMA wire is investigated, and the fit with measurements is analyzed for ‘constant force’ and ‘constant power’ experiments.