An analytical method for the plane problem of doubly periodic circular cross-section fiber composite materials
双周期圆截面纤维复合材料平面问题的解析法

Combining the theory of doubly periodic and doubly quasi-periodic Riemann boundary value problems and Eshelby's equivalent inclusion method, an analytical method for the plane problem of composite materials with a doubly periodic array of circular cross-section fibers is presented. The stresses expressions in series are obtained in the fibers and matrix and a comparison with the finite element calculations is done. The transverse tensile and shear moduli are predicted for a unidirectional fiber-reinforced composite with an doubly periodic array of circular fibers. It is found that for a composite with hard fibers and a soft matrix under a same fiber volume fraction, the effective moduli for a square array of fibers are larger than those for a hexagonal array of fibers. The present method provides an efficient tool for analyzing the mechanical properties of inhomogeneous materials and designing microstructures of composite materials, and can also be used to evaluate the precision of other numerical and approximate methods such as the finite element method.