Universal connections of elastic fibrous composites: some new results

Universal connections between the overall moduli of elastic ®brous composites are explored. For any medium that can be represented by certain characterization functions, we show that its e€ective modulus tensors follow similar constraints as those for Hillʹs connections for a two-phase ®brous composite. Some new standpoints are proposed, which reveal that the connections remain valid for media containing cavities or rigid inclusions. In addition, connections are devised to accomodate the case in which the composite consists of phases with identical eigenmoduli. We show that, in this particular case, it often provides additional constraints to the overall moduli of the composite. Speci®c results are given in analytic forms for two-phase ®brous composites with transversely isotropic phases, and with square-symmetric phases