Effective transverse elastic moduli of three-phase hybrid fiber-reinforced composites with randomly located and interacting aligned circular fibers of distinct elastic properties and sizes

Abstract

A higher-order multi-scale structure for three-phase hybrid fiber-reinforced composites containing randomly located yet unidirectionally aligned circular fibers is proposed to predict effective transverse elastic moduli based on the probabilistic spatial distribution of circular fibers, the pairwise fiber interactions, and the ensemble-area homogenization method. Specifically, the two inhomogeneity phases feature distinct elastic properties and sizes. Two non-equivalent formulations are considered in detail to derive effective transverse elastic moduli of three-phase composites leading to new higher-order bounds. Numerical examples and comparisons among our theoretical predictions and other analytical predictions are rendered to illustrate the potential capability of the present method.