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.
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