A recursive asymptotic homogenization scheme for multi-phase fibrous elastic composites

A multi-phase elastic composite is considered here. A periodic hexagonal array of concentric circular cylindrical fibers is dealt with, wherein the constituents exhibit transverse isotropy. The geometrical and transversely isotropic axes are parallel. Based on certain analytical formulae derived recently for biphasic materials using the asymptotic homogenization method, a recursive scheme is set up to determine the overall properties of this multi-phase material. Comparisons with experimental data, variational bounds and some other models are presented in order to show the efficiency of the employed scheme.