Piezoelectric composites consisting of spherically anisotropic piezoelectric inclusions ͑i.e., piezoceramic material͒ in an infinite nonpiezoelectric matrix under a uniform electric field are theoretically investigated. Analytical solutions for the elastic displacements and the electric potentials are derived exactly. Taking account of the coupling effects of elasticity, permittivity, and piezoelectricity, formulas are derived for the effective dielectric and piezoelectric responses in the dilute limit. A piezoelectric response mechanism is revealed, in which the effective piezoelectric response vanishes irrespective of how much spherically anisotropic piezoelectric inclusions are inside. Moreover, the effective coupled responses of the piezoelectric composites show that the effective dielectric responses decrease ͑increase͒ as the inclusion elastic ͑piezoelectric͒ constants increase.

The transformation field theory is developed to investigate the effective properties of piezoelectric composites consisting of anisotropic inclusions having arbitrary geometrical shapes in unit cell. The complicated boundary problem of arbitrary geometrical shapes of anisotropic inclusions is solved by introducing the transformation strain and electric fields. Motivated by theoretical investigation of the effective properties of piezoelectric composites, as an example, the effective dielectric, elastic, and piezoelectric constants of spherical periodic piezoelectric composites are discussed, and a good agreement is obtained by comparing the calculation results with the experimental data in the dilute limit.

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