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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.

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A constitutive model for magnetic shape memory alloys is developed through a combined consideration of micromechanical and thermodynamic theories. Of special concern is the influence of different temperatures on field-induced reorientation strain for a NiMnGa single-crystal specimen. The theoretical results are found to be in general agreement with experimental data. It is shown that the method is accurate and simple.

Based on thermodynamic theory, a phenomenological model of shape memory alloy is provided. Simulations under different loading illustrate the influence of large-strain deformation and small-strain deformation on the characteristics of the model. The results indicate that the difference between the two methods is small under uniaxial tension case, while the influence is very large under shear deformation case.