Homogenization and Pseudoelastic Behavior of Composite Materials Reinforced with Shape Memory Alloy Fibers

Pseudoelastic behavior of cylindrical shape memory alloy (SMA) fiber embedded in a polymer matrix is investigated by using micromechanic approaches. A homogenization scheme based on Eshelby's equivalent inclusion method is adopted to derive the expressions for strains in the fiber and matrix in terms of the average strain in the composite. The constitutive laws for the SMA fiber and matrix are also expressed in terms of the average strain in the composite. The expressions for the SMA composite stiffness and the inelastic strains tensors are derived using dilute distribution theory and rule of mixtures approach. The composite stiffness and inelastic strain tensors are used in the generalized Hooke's law to compute the transformation stresses and associated hysteresis of the SMA composite. A comparison is also made with the strain energy approach. The computational results in terms of the composite stiffness and the stresses are presented within different fiber volume fraction, using the proposed methods. Finally, the modifications in the modeling approaches are highlighted with analytical case studies involving hysteretic stress—strain behaviors.