Effective initial and subsequent loading surfaces for phase transformation in TPMS-SMAS

In this paper, the effective behavior of shape memory alloy (SMA) triply periodic minimal surface (TPMS) structures is investigated by means of finite element analysis and numerical homogenization. For this purpose, the onset and subsequent thresholds of phase transformation are determined considering TPMS primitive, gyroid, and diamond unit cells subjected to different loading conditions. At all relative densities studied, the initial phase transformation loading surfaces corresponding to the different geometries considered are found to be reasonably well represented by the anisotropic Hill's and von Misses yield criterions. The observed surfaces, either shrink or expand as the effective martensite volume fraction increases, depending on TPMS geometry. The determination of subsequent loading surfaces as a function of the effective volume fraction of martensite shows a nonlinear hardening behavior, which seems to follow a unique trend for the different geometries considered. Ultimately, the loading surfaces are found to reach an asymptotic state with distinctly different features compared to their initial shapes.