Coupled behavior of SMA wires and elastic composite structures—numerical modeling and experiments

The present work describes the numerical implementation of a micromechanics-based constitutive model for polycrystalline shape memory alloy (SMA) wires and its finite elements adaptation for the simulation of shape-morphing structures incorporating embedded SMA actuators. In a previous work, the authors developed a one-dimensional thermomechanical model based on micromechanical arguments, yielding closed-form solutions for simple loading paths. It successfully captures the nonlinear hardening behavior of a SMA wire under tensile loading, arising from its polycrystalline texture. By introducing both texture and time discretizations, this model is reformulated as a Linear Complementarity Problem which can be solved through numerical optimization techniques. The algorithm has been implemented as a user-defined material behavior for the finite elements software ABAQUS, enabling the simulation of the coupled mechanical response of an embedded one-dimensional SMA wire together with its 3-dimensional host structure. Furthermore, a novel integration method for embedding SMA wire actuators into laminated fiber reinforced polymers has been proposed and tested on morphing blades exhibiting a temperature-dependent curvature. The mechanical response of these SMA hybrid composites has been confronted to the finite elements simulations and demonstrated the predictive capability of the model.