Analytical procedures are developed for a composite system consisting
of shape memory alloy fibers within an elastic matrix subject to unifo
rm temperature. A three-phase concentric cylinder model is developed f
or the analysis of local stresses, which includes the fiber, the matri
x, and the surrounding homogenized composite, The solution addresses t
he complexities induced by the nonlinear dependence of the in situ mar
tensite fraction of the fibers on the local stresses and temperature a
nd the local stresses developed from interactions between the fibers a
nd matrix during the martensitic and reverse phase transformations. Re
sults are presented for a Ni-44.8wt% Ti/epoxy composite. The applicati
ons illustrate the response of the composite in isothermal longitudina
l loading and unloading. The local stresses developed in the composite
under various stages of the martensitic and reverse phase transformat
ions are also shown.