Numerical modeling of the elastic behavior of fiber-reinforced composites with inhomogeneous interphases

This paper describes a numerical approach for modeling the micromechanical behavior and macroscopic properties of multi-phase fiber-reinforced composites with inhomogeneous interphases. The interphases are modeled as functionally graded elastic layers with the Young's modulus and Poisson's ratio varying in the radial direction. In general, the fibers can have different elastic properties and sizes and can, if desired, be randomly distributed. The approach is based on the numerical solution of a complex boundary integral equation in which the boundary parameters are expressed in terms of complex Fourier series. All the integration can be done analytically and thus the method allows for accurate calculation of the elastic fields anywhere within the material, including inside the fibers and interphases. Explicit expressions for the effective elastic constants can be obtained from general relations between the average stresses and strains. Numerical experiments and comparisons with the numerical benchmark results available in the literature have demonstrated the versatility, accuracy, and efficiency of the presented approach.