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 distributed is considered here, where each periodic cell is a binary homogeneous piezoelectric medium with square symmetry in welded contact at the interface. This paper makes use of some results obtained for a similar elastic composite in Rodriguez-Ramos et al. [Mech. Mater. 33 (2001) 223-235]. Relatively simple closed-form expressions for the overall properties are obtained by the asymptotic homogenization method. The local problems that arise are solved by means of potentials methods of a complex variable and Weierstrass elliptic and related functions. Benveniste and Dvorak universal type of relations for some of the overall properties are derived in a simple new way without solving any local problem, The number of local problems to get all coefficients is 3. The numerical computation of the effective properties is simple, Averaged properties of these piezo-composites relevant to hydrostatic and medical imaging transducer applications are computed and compared with existing experimental results. The comparison shows quite a good agreement with experimental data. (C) 2001 Elsevier Science Ltd. All rights reserved.