Modeling bending behavior of shape memory alloy wire-reinforced composites: Semi-analytical model and finite element analysis

In this study, we propose a novel and simple exact semi-analytical model for superelastic Shape Memory Alloy (SMA) wire reinforced composites subjected to bending loads. In order to study the mechanical response of the composite during loading/unloading, a Representative Volume Element (RVE) is extracted to examine the bending response of the composite. Analytical moment–curvature, and shear force-shear strain relations are derived based on a 3-Dimensional (3D) thermomechanical SMA model and Timoshenko beam theory. The composite Simpson’s rule is adopted to numerically solve the exact analytical moment–curvature and shear force-shear strain relationships. Results including the moment–curvature response, axial stress distribution along the vertical and longitudinal directions, martensite volume fraction, and the tip deflection are reported and validated against 3D finite element simulations. The influence of temperature, martensite volume fraction distribution, and matrix stiffness on the mechanical performance of the composite is also investigated. In particular, the composite is found to behave superelastically under certain conditions of temperature, SMA volume fraction, and elastic stiffness of the matrix. Such behavior is advantageous in applications requiring large recoverable strains or high energy dissipation density.