Effective phase transformation behavior of NiTi triply periodic minimal surface architectures

The effective behavior of shape memory alloy triply periodic minimal surface (TPMS) structures is investigated using finite element analysis and numerical homogenization. The TPMS unit cells considered are primitive, IW-P, gyroid, and diamond subjected to different loading conditions. Under uniaxial displacement-driven loading, the results show a dramatic increase in effective stress and martensite volume fraction with increased relative density of the TPMS unit cell. Comparison among the four types of TPMS unit cells shows that diamond has superior mechanical performance for the loading cases considered. Based on numerical homogenization results, the onset and subsequent thresholds of phase transformation are determined for all four unit cells considering multiaxial loading. At lower relative density, the loading surfaces corresponding to the onset of phase transformation were reasonably well represented by either von Mises or Hill’s criteria. The observed fit with the von Mises model degenerated with increased effective martensite volume fraction, while a proper fit was maintained with Hill’s criterion. Subsequent loading surfaces, corresponding to monotonically increasing martensite volume fraction, show a nonlinear hardening behavior, which seems to follow a similar trend regardless of geometry. The loading surfaces were found to reach asymptotic states with distinctly different features compared to their initial shapes.