Poisson's Ratio of Ber-reinforced Composites

Poisson's ratio ow diagrams, that is, the Poisson's ratio versus the ber fraction , are obtained numerically for hexagonal arrays of elastic circular bers in an elastic matrix. High numerical accuracy is achieved through the use of an interface integral equation method. Questions concerning xed point theorems and the validity of existing asymptotic relations are investigated and partially resolved. Our ndings for the transverse eeective Poisson's ratio, together with earlier results for random systems by other authors, make it possible to formulate a general statement for Poisson's ratio ow diagrams: For composites with circular bers and where the phase Poisson's ratios are equal to 1/3, the system with the lowest stiiness ratio has the highest Poisson's ratio. For other choices of the elastic moduli for the phases, no simple statement can be made.