Homogenization and localization of imperfectly bonded periodic fiber-reinforced composites

Abstract

An elasticity-based micromechanics model is derived analytically to investigate the homogenized and localized responses of unidirectional composites with imperfect interfaces. To mimic the perturbation of the inclusion positioning caused by the consolidation process, an arbitrarily parallelogram-shaped repeating unit cell (RUC) is developed with periodic boundary conditions. Different from the finite-element/volume approaches which solve a boundary-value problem in the discretized domain, the present work avoids the complicated mesh discretization and instead adopts the Trefftz concept that employs the complete elastic solutions with unknown coefficients to represent the internal trial displacement/stress fields. The solutions of the unknown coefficients are obtained by applying the flexible separation relations along the fiber/matrix interface that govern the interfacial traction reciprocities and displacement discontinuities, as well as the periodic balanced variational principle at the circumference of microstructures. The homogenization equations are then applied to generate the effective properties of composite materials with different architectures over a wide range of fiber volume fractions. In addition to validating the effective properties and underpinning stress fields against other micromechanical techniques in the literature, new results are generated extensively aiming at demonstrating the effects of the interfacial stiffness, radius of fiber and shape of the unit cell on the homogenized and localized composite responses. The analytical framework developed in this communication also facilitates the identification of the interfacial stiffness that minimizes the difference between the effective moduli and targeted material properties through the incorporation of Particle Swarm Optimization algorithm.