Shape Memory Alloys (SMA’s) are used in a wide range of engineering and medical applications such as biomechanics, robotics, aerospace, and civil engineering due to particular characteristics of such metals. Exceptional behaviors of such materials are not predictable by the conventional models, and the theoretical and experimental investigation on modeling of shape memory alloys are consequently in progress. In order to enhance the existing approaches to the modeling of SMA’s, in this thesis the constitutive equations for such kind of materials are investigated. A three dimensional model based on “microplane” theory is proposed and further developed, to simulate the real behaviors of shape memory alloys under nonproportional multiaxial loading paths. Results obtained from the model show considerable advantages of the proposed model over the existing ones especially in case of nonproportional loadings. A fully coupled thermomechanical model for SMA wires is then developed in order to take the effects of strain rate into account. The model is formulated within a continuum framework, in which the heat transfer from an SMA wire to the surrounding medium is more accurately than the existing models taken into consideration. The comparison of the results from the present model and those of the other theoretical and experimental date shows that the present model is able to predict the SMA behaviors at different conditions more accurately, and is more efficient than the existing approaches especially in case of cyclic loadings.
