Thermomechanical topology optimization of shape-memory alloy structures using a transient bilevel adjoint method

We present a novel method for computational design of adaptive shape-memory alloy (SMA) structures via topology optimization. By optimally distributing a SMA within the prescribed design domain, the proposed algorithm seeks to tailor the two-way shape-memory effect (TWSME) and pseudoelasticity response of the SMA materials. Using a phenomenological material model, the thermomechanical response of the SMA structure is solved through inelastic finite element analysis, while assuming a transient but spatially uniform temperature distribution. The material distribution is parameterized via a SIMP formulation, with gradient-based optimization used to perform the optimization search. We derive a transient, bilevel adjoint formulation for analytically computing the design sensitivities. We demonstrate the proposed design framework using a series of two-dimensional thermomechanical benchmark problems. These examples include design for optimal displacement due to the TWSME, and design for maximum mechanical advantage while accounting for pseudoelasticity.