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

A two-phase parallel fibre-reinforced periodic elastic composite is conside red wherein the constituents exhibit transverse isotropy. The fibre cross-s ection is circular and the periodicity is the same in two directions at an angle pi /3. Simple closed-form expressions are obtained for the effective properties of this composite by means of the asymptotic homogenization meth od. Numerical computation of these is easy. The analytical solution of the required resulting plane-and antiplane-strain local problems, which turns o ut to be only two, makes use of potential methods of a complex variable and properties of Weierstrass elliptic and related functions of periods (1,0) and (cos pi /3, sin pi /3). Hill's universal type of relations for this com posite are easily derived in an elementary new way. Comparison with known b ounds is shown, (C) 2001 Elsevier Science Ltd. All rights reserved.