Effective piezoelectric coefficients of ferroelectric 0-3 composites

We studied theoretically the effective piezoelectric strain coefficients of a 0-3 composite comprising spherical ferroelectric inclusions dispersed in a ferroelectric matrix. Tensile loading and hydrostatic loading conditions were considered. Explicit expressions for the effective d(31), d(33) and d(h) coefficients were derived for the case of low volume concentration of dispersed particles in terms of the electro-mechanical properties of the constituents. The theoretical predictions of the piezoelectric coefficients were compared with experimental data from previous works and good agreement was obtained.