Fully coupled electric-thermo-mechanical model for predicting the response of a SMA wire activated by electrical input

Shape Memory Alloys (SMAs) are becoming increasingly used in actuator technologies thanks to the generation of high specific power and reliability. These features are obtained by extremely simple architecture and actuation mechanisms that exploit the thermal-induced shape recovery properties of SMAs. Thanks to the high specific power, small diameter wires can be directly used as linear actuators whose activation can be obtained by electric currents, exploiting the Joule effect. Despite the simplicity of the actuator, the complex constitutive behaviour of such material does not allow to easily model its mechanical behavior due to the interdependency of the alloy parameters, especially when electric-thermal phonemena are also involved. In this paper, a fully coupled electricthermo-mechanical model is proposed to predict the thermal and mechanical response of Shape Memory Alloy (SMA) wires when electrically actuated with the aim to provide user guidelines for properly design/select SMA based wire actuators for engineering applications. The model takes into account the latent heats linked to phase transformations, conduction and convective heat exchanges phenomena as well as the dependency of the resistivity from the thermo-mechanical parameter of the alloy. The implementation consists in two submodels: the electric-thermal and the thermo-mechanical one. Because of the marked dependence of the volume fraction of martensite with both temperature, generated by Joule effect, and mechanical stress, the submodels were coupled. Due to the complexity of the problem, a Matlab/Simulink code was implemented to numerically solve the governing equations. Temperature evolution, generated by the electric input, was investigated during both the heating and cooling stage and its effect on the mechanical response of the SMA actuator was studied. Results were validated with experimental measurements carried out on nickel-titanium (NiTi) wires. It was shown that the proposed model is suitable in predicting the temperature evolution of the wire, even catching phase transitions, as well as the actuation response for different loading conditions. Finally, the SMA actuators performances, in terms of input current to use, actuation time and efficiency, were investigated.