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The strain energy absorption of shape memory alloy (SMA) bars and beams under tension and bending loading was studied. A theoretical model is presented that can give quantitative relations between the martensite fraction, the applied load, and the strain energy absorbed in the shape memory alloy (SMA). It was found analytically that the super-elastic SMA demonstrates a high strain energy absorption capability. The closed- form solution of the strain energy absorption capability of SMA bars is a simple and useful tool in the design of energy absorption applications of super-elastic SMA. The nonlinear equations for SMA hybrid composite plates, which can be used for low velocity impact or quasi-static contact loading, are derived. The governing equations include the transverse shear deformation to the first-order, large deformation of the plates, and SMA/epoxy lamina. The equations are derived in the general form with general boundary conditions and general stack of angle ply. The equations can be simplified to special forms in the specific applications. A theoretical study of the impact force and the strain energy absorption of an SMA/graphite/epoxy composite beam under a low-velocity impact has been performed. The contact deformation, the global bending deformation, the transverse shear deformation, and the martensitic phase transformation of the super-elastic SMA fibers are studied. The energy absorbed by the SMA hybrid composite is calculated for each task of the absorption mechanisms: contact deformation, global bending deformation, and The analysis methods and models developed in this dissertation are the first reported research in modeling SMA composite under low velocity impact and quasi-static loading. The models and methods developed here can be used for further study and design of SMA composites for low velocity impact or quasi-static loading in failure process. / Ph. D.