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Abstract
A fibre-reinforced periodic elastic composite, where the constituents exhibit transverse isotropic properties, is considered here. The fibre cross-section is circular and the periodicity is the same in two orthogonal directions. Analytical formulae are obtained for the effective thermoelastic properties of this composite by means of the Asymptotic Homogenization Method. This method has been applied for a new derivation of Hill's type of universal relations, involving thermal coefficient for fibrous composite, without solving any local problem. The solution of the required resulting local problems makes use of potential methods of a complex variable and properties of Weierstrass elliptic and related functions. Comparisons with experimental data and others approaches are shown.
Acknowledgements
The authors would like to thank Professor Gerard A. Maugin at the Laboratoire de Modélisation in Mécanique, Université Pierre et Marie Curie, Paris, France, for helpful discussions during the course of this work, and the reviewers for their comments and suggestions. This work was sponsored by FENOMEC and PAPIIT, DGAPA, UNAM-México, under grant IN101705. Thanks also to the project CITMA, Ciencias Básicas IBMFQC 09-2004, Cuba.