Development of a torsional theory for radially functionally graded porous shape memory alloy circular bars

This work develops a novel torsional theory for a radially functionally graded (FG) porous shape memory alloy (SMA) circular bar. Prior to the theoretical development, the effective three-dimensional (3D) phenomenological constitutive model for SMAs with high porosity is proposed. To help derive successfully the theory, the pure shear-driven material parameters in the effective model are expressed in the cubic polynomial. Subsequently, the torsional theory for radially FG porous SMA circular bar is derived considering the evolution of effective phase evolution in the bar. This phase evolution consideration guarantees the accuracy of the developed theory. Indeed, the soundness of effective constitutive model is confirmed by 3D finite element method (FEM) simulation of porous SMA structure in Abaqus using the well-established ZM's model for dense SMAs. Specifically, the simulating results in terms of the shear stress-shear strain response obtained from two prediction methods considering a variation of SMA volume fraction and temperature are in good agreement. Furthermore, accuracy of torsional theory is validated by 3D FEM simulation using the 3D effective constitutive model with a good agreement observed. It is found that the superelasticity of the bar can be enhanced by increasing the gradient index and decreasing the temperature and wall thickness.