A micromechanical constitutive model for responding the macroscopic behavior of porous shape memory alloys (SMA) has been proposed in this work. According to the micromechanical method, the stiffness tensor of the porous SMA is obtained. The critical stresses are calculated by elastic mechanics. Based on the general concept of secant moduli method, the effective secant moduli of the porous SMA is given in terms of the secant moduli of dense SMA and the volume fraction of pores. The model takes account of the tensile-compressive asymmetry of SMA materials and the effect of the hydrostatic stress. Only the material parameters of dense SMA are needed for numerical calculation, and can degenerate to dense material. Examples for the uniaxial response of porous SMA materials at constant temperature are then used to illustrate one possible application of the constitutive model. The numerical results have been compared with the experiment data for porous SMA, which show that the modeling results are in good agreement with the experiments.

According to micromechanics, consider the porous shape memory alloy (SMA) as a composite-sphere model. Isolate a constant thickness spherical shell which is composed of SMA, and is traction free on its inner surface and subjected to the uniform hydrostatic pressure and the deviatoric stress on its external surface. Then, a constitutive model for porous SMA considering hydrostatic stress is proposed by elasticity solution. The stress distribution of the spherical shell was calculated. Corresponding to different applied stresses, the spherical shell is divided into different regions of pure austenite, pure martenite, and austenite/martensite mixture under isothermal circumstances. The martensite volume fraction is then obtained. The predicted results have been compared with the obtained experimental data by Zhao and Sia Nemat-Nasser. It shows that the modeling results are in good agreement with the experiments and the initial phase transition point for porous SMA is lower than the dense SMA.

Shape Memory Alloy (SMA) composites are being used in an ever-expanding set of applications. For new applications, SMA composites are being developed as metal-ceramic Functionally Graded Materials (FGMs) utilizing SMA as the metallic phase, which contain both high temperature resistance of the ceramic phase and the mechanical properties of SMA composites. Three models including Averaging Technique of Composites (ATC), Mixture Rule (MR) and Mori-Tanaka (MT) scheme are used to calculate the stress distributions of the system subjected to thermal loading, respectively. The results obtained from the analyses of an SMA-ceramic graded composite show that after transformation the stress in the SMA composite is lower than in the case of pure elastic composite under the same thermal loading. This decrease stress can result in an increase in temperature resistance and improved mechanical properties of SMA composites. This work will be explored through a parametric study to understand their influence on SMA composite design.