Analytical expressions of effective constants for a piezoelectric composite reinforced with square cross-section fibres

The purpose of this paper is to present analytical expresiion of the effective elastic, piezoelectric and dielectric constants of reinforced piezoelectric composite materials with unidirectional fibers periodically distributed in a square matrix, as obtained by means of the "double asymptotic homogenization" method. The cross-section of the fibers is square. Each periodic cell of the medium is a binary piezoelectric composite wherein both phases are homogeneous piezoelectric materials with transversely isotropic properties. Comparison between the derived theoretical predictions of characteristic parameters and the existing experimental results shows a rather good agreement. The results obtained in the present paper were verified by means of the universal relations of Schulgasser. Numerical computation of the effective properties can be realized without difficulties.