NUMERICAL INVESTIGATION OF THE MECHANICAL BEHAVIOR OF SHAPE MEMORY ALLOY TRIPLY PERIODIC MINIMAL SURFACE PRIMITIVE LATTICES

This work investigates the mechanical behavior of a Schwarz primitive (SP) triply periodic minimal surface (TPMS) lattice made from superelastic nitinol shape memory alloy. The investigation uses numerical homogenization to determine the effective response of a unit nitinol SP cell subjected to a reduced set of periodic boundary conditions that account for the cubic symmetry of the considered SP topology. The simulation of the mechanical behavior of the unit cell is carried out by means of finite element analysis using an implementation of the Zaki-Moumni (ZM) model for shape memory alloys. The analysis considers the influence of temperature and relative density on the mechanical and phase transformation behavior of the SMA SP lattice. The effective stress-strain response of the lattice, in the superelastic temperature range, shows smooth phase transitions characterized by less abrupt changes in the slope of the stress-strain curve compared to dense nitinol. Moreover, later stages of the material phase transformation from austenite to martensite are shown to approach completion in an asymptotic fashion in terms of the applied load, with full transformation corresponding to asymptotically high applied strain. The onset of phase transformation is found to describe an ellipsoidal hypersurface in stress space, which is shown to adequately fit an extended Hill's loading surface that accounts for the influence of hydrostatic pressure. Moreover, the loading surface is found to evolve with the applied load in a way similar to isotropic hardening, whereby the center of the surface remains fixed whereas the size of the elastic domain increases monotonically with increased cumulated phase transformation, defined as the integral from zero of the magnitude of the differential increment in martensite volume fraction as the load applied to the nitinol lattice cell is varied. The reported findings contribute to understanding the behavior of architected nitinol lattice metamaterials and provide an important element in developing constitutive models that can describe their complex mechanical and functional response.