Closed-form expressions for the effective coefficients of a fiber-reinforced composite with transversely isotropic constituents - II. Piezoelectric and square symmetry

A composite material with unidirectional cylindrical fibers periodically di stributed is considered here, where each periodic cell is a binary homogene ous piezoelectric medium with square symmetry in welded contact at the inte rface. This paper makes use of some results obtained for a similar elastic composite in Rodriguez-Ramos et al. [Mech. Mater. 33 (2001) 223-235]. Relat ively simple closed-form expressions for the overall properties are obtaine d by the asymptotic homogenization method. The local problems that arise ar e solved by means of potentials methods of a complex variable and Weierstra ss elliptic and related functions. Benveniste and Dvorak universal type of relations for some of the overall properties are derived in a simple new wa y without solving any local problem, The number of local problems to get al l coefficients is 3. The numerical computation of the effective properties is simple, Averaged properties of these piezo-composites relevant to hydros tatic and medical imaging transducer applications are computed and compared with existing experimental results. The comparison shows quite a good agre ement with experimental data. (C) 2001 Elsevier Science Ltd. All rights res erved.