Multiphysics design of programmable shape-memory alloy-based smart structures via topology optimization

We present a novel multiphysics and multimaterial computational design framework for shape-memory alloy-based smart structures. The proposed framework uses topology optimization to optimally distribute multiple material candidates within the design domain, and leverages a nonlinear phenomenological constitutive model for shape-memory alloys (SMAs), along with a coupled transient heat conduction model. In most practical scenarios, SMAs are activated by a nonuniform temperature field or a nonuniform stress field. This framework accurately captures the coupling between the phase transformation process and the evolution of the local temperature field. Thus, the resulting design framework is able to optimally tailor the two-way shape-memory effect and the superelasticity response of SMAs more precisely than previous algorithms that have relied on the assumption of a uniform temperature distribution. We present several case studies, including the design of a self-actuated bending beam and a gripper mechanism. The results show that the proposed framework can successfully produce SMA-based designs that exhibit targeted displacement trajectories and output forces. In addition, we present an example in which we enforce material-specific thermal constraints in a multimaterial design to enhance its thermal performance. In conclusion, the proposed framework provides a systematic computational approach to consider the nonlinear thermomechanical response of SMAs, thereby providing enhanced programmability of the SMA-based structure.