Unified analytical formulae for the effective properties of periodic fibrous composites

Two-phase fibre-reinforced elastic composites with transversely isotropic constituents and two types of fibres periodic distribution (square and hexagonal arrays) with perfect contact conditions at the interface are considered. Unified simple analytical formulae for their effective properties are given. Such formulae involve two orders of approximation of semi-analytical expressions obtained via asymptotic homogenization. The limit case of empty fibres is also presented. The influence of each approximation is illustrated. Theoretical and experimental comparisons are included. The objective is to provide information at hand which could be useful for applications to bone mechanics and ultrasonic transducers, and for validation of numerical codes.

► Easy to evaluate rational functions are provided for effective properties.
► Very good estimates of properties from asymptotic homogenization.
► Useful for applications to bones and magneto-electro-elastic structures.
► Formulae could be handy for validation of numerical codes and experiments.