A hybrid dynamical simulation framework for polycrystalline SMA-based wire actuators

Shape Memory Alloys (SMAs) are a class of smart materials with thermo-mechanical properties different from conventional metals. In fact, heating a SMA causes crystal lattice transformations in the material that result in a macroscopic change in shape, typically ranging from 4-6%. This effect can be exploited to design unconventional actuators that respond to external thermal stimuli by undergoing a contraction in length. In most actuator applications, SMA material is shaped as a thin wire, since thermal activation can be easily induced using electric current. Despite the many advantages such as high energy density, direct linear motion, and lightweight, the material characteristic is highly nonlinear and therefore challenging to model and control. The main reason behind the nonlinearities lies in the hysteretic thermo-electro-mechanical characteristic whose shape depends on external load, temperature, and actuation rate. Effective exploitation of SMA technology in engineering applications requires accurate models for hysteresis compensation. In this paper, a hybrid dynamical modeling framework for polycrystalline SMA-driven actuators is presented and implemented in Matlab/Simulink environment. The goal of this work is to provide an accurate and numerically efficient model, which can be used to perform simulations, model-based design optimization, and tests of control schemes for complex structures based on polycrystalline SMA material. The model adopted in this framework is a hybrid dynamical reformulation of the Müller-Achenbach-Seelecke (MAS) model extended for polycrystalline materials. A simple case study is analyzed consisting of a SMA wire coupled with a biasing mechanism, highlighting numerical accuracy and physical interpretability in predicting experimentally observed behaviors.