Development and implementation of an effective constitutive model for architected cellular iron

Using architected cellular iron-based shape memory alloys (AC Fe-SMAs) can help compensate the relatively higher density of the base material compared to NiTi-based and Cu-based shape memory alloys, while providing good shape recovery, lower production cost, and greater energy dissipation. This article is dedicated to the development of an effective and pressure-dependent constitutive model that predicts the thermomechanical response of AC Fe-SMAs. We first simulate the behavior of the cellular material using the dense model that was previously developed by the authors, along with different unit cells (UCs) subject to periodic boundary. The shape memory effect is simulated by compressing the UCs by 2% of their height, followed by mechanical unloading, and heating above the austenite finish temperature. The results highlight stress concentration, maximum phase transformation, and maximum plastic deformation at the geometry discontinuities or strands necks. Post-processing the ABAQUS ODB files with Python scripts shows that the bending-dominated unit cell with the highest maximum local values of state variables exhibits the lowest volume-averaged outputs. Comparison of the unit cell to cubic multi-cell structures points out an asymptotic vanishing of the effects of the free boundaries as the number of cells in the multi-cell structure increases. The results of the unit cells are used to calibrate the parameters of the pressure-dependent effective model. The ratios of the inelastic hydrostatic strains to the equivalent total inelastic strains indicate higher pressure effects in the bending-dominated cellular lattice than in the stretch-dominated structures. The force-displacement and “dissipated energy”-temperature curves of the cellular beam and its equivalent bulk structure obtained by simulations of 4-point bending tests are found to be close enough that the effective model can be considered as an efficient design tool for architected cellular iron-based shape memory alloy structures