This dissertation presents a one-dimensional thermomechanical constitutive model for shape memory alloys based on basic concepts of thermodynamics and phase transformation kinetics. Compared with other developed constitutive relations, this thermomechanical constitutive relation not only reflects the physical essence of shape memory alloys, i.e., the martensitic phase transformation involved, but also provides an easy-to-use design tool for engineers. It can predict and describe the behavior of SMA quantitatively. A multi-dimensional constitutive relation for shape memory alloys is further developed based on the one-dimensional model. It can be used to study the mechanical behavior including shape memory effect of complex SMA structures that have never been analytically studied, and provide quantitative analysis for many diverse applications of shape memory alloys.

A general design method for shape memory alloy actuators has also been developed based on the developed constitutive relation and transient thermal considerations. The design methodology provides a quantitative approach to determine the design parameters of shape memory alloy force actuators, including both bias spring SMA force actuators and differential SMA force actuators.