A phenomenological constitutive model for Functionally Graded Porous Shape Memory Alloy

Functionally Graded Porous Shape Memory Alloy (FGP-SMA), whose porosity varies continuously along gradient direction, has attracted wide attention in the field of smart materials. Considering the Gibbs free energy, a phenomenological constitutive model which can be used to predict the mechanical behaviors of FGP-SMA is presented here by using the theory of thermodynamics. A new transformation function considering the effect of hydrostatic stress is proposed. A finite element model is also provided to investigate the mechanical properties of a FGP-SMA cylinder. The uniaxial compression test of the FGP-SMA cylinder is simulated by using those two models mentioned above. Numerical results show a reasonable agreement with experimental results, which implies that the models established in this work are valid. What’s more, the average stress–strain relation, the stress distribution on the cross section and the energy absorption properties of the FGP-SMA cylinder are investigated in detail. The results obtained demonstrate several interesting features of this new material, which may have potential applications in practice.