: Nowadays, cellular materials have found several industrial applications due to exceptional properties such as low weight and high strength. During last decades, shape memory alloys have attracted attention of researchers because of outstanding mechanical and biological properties, and attempts for fabricating cellular samples of these materials get increased. Cellular shape memory alloys combine the advantages of both cellular materials and shape memory alloys which makes them promising candidates for several industrial applications. Since fabrication and characterization of cellular shape memory alloys is time consuming and expensive, developing powerful modeling approaches to predict their mechanical properties is of great importance. The main aim of this thesis is to develop a suitable modeling approach for predicting the mechanical response of shape memory alloys cellular lattice structures. To do so, three main steps are followed. First, modeling of the mechanical response of general cellular lattice structures are investigated and the effects of bulk material as well as microstructural imperfections are assessed. The results of these investigations show that both bulk material and microstructural imperfections can severely affect the mechanical response of these materials. However, considering these imperfections in geometric models can significantly increase the computational cost. To compel these difficulties, a computationally efficient modeling approach is proposed and validated by experimental findings. In the second step, a three-dimensional constitutive model is presented based on microplane theory. Then, this model is extended to take material asymmetry into account. After validating the proposed constitutive equation through uniaxial tension-compression tests as well as four-point bending of NiTi tubes, in the third step, the effects of this material asymmetry as well as microstructural imperfections on the mechanical response of cellular samples are assessed. The results of these assessments show that both the imperfections and material asymmetric response affects the mechanical response of cellular shape memory alloys. In addition, the effects of material asymmetry are decreased by decreasing the value of porosity and increasing the portion of axial deformation mechanisms. Keywords Shape memory alloys, Porous materials, Cellular materials, Constitutive model, Tension-compression asymmetry, Microstructural imperfections, Microstructural defects.
