Bending model for functionally graded porous shape memory alloy/poroelastic composite cantilever beams

A new model is developed for bending of functionally graded (FG) porous shape memory alloy (SMA)/poroelastic composite cantilever beams. The model generalizes the ZM model for dense SMAs to cases involving potentially high degrees of porosity. The accuracy of the proposed model is verified against experimental data as well as simulations involving finite element analysis (FEA) of porous architected SMAs with fully detailed geometries. Using the new model, a bending theory is derived for a porous composite cantilever beam reinforced with a FG porous (FGP) SMA layer. The derivation involves expressing the effective material parameters of the porous SMA as polynomial functions of porosity, which facilitates analytical treatment of the bending theory. Moreover, the theory accounts for the distribution of solid phases within a beam cross section as a function of applied load during a complete loading cycle. Results such as the load-deflection behavior of the beam, as well as the location of the neutral axis and distribution of axial stress as a function of the applied load are validated against FEA data. The validated theory is further utilized to investigate the influence of several parameters on the behavior of the composite beam, including the index gradient, temperature, and thickness of the SMA layer.