Closed-form expressions for the effective coefficients of fibre-reinforced composite with transversely isotropic constituents. I: Elastic and hexagonal symmetry

The purpose of this paper is to determine the effective elastic, piezoelectric and dielectric properties of reinforced piezoelectric composite materials with unidirectional cylindrical fibres periodically distributed in two directions at an angle π/3 by means of the asymptotic homogenization method. Each periodic cell of the medium is a binary piezoelectric composite wherein both constituents are homogeneous piezoelectric materials with transversely isotropic properties. This paper makes use of some results obtained in Part I. Relatively simple closed-form expressions for the overall properties are obtained by means of potential methods of a complex variable and Weierstrass elliptic and related functions. Schulgasser universal type of relations are derived in a simple new way by means of the homogenized asymptotic method. The number of local problems to get all coefficients is two. The numerical computation of these effective properties is simple.

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