  The linear strong--property--fluctuation theory (SPFT) was developed in order
to estimate the constitutive parameters of certain homogenized composite
materials (HCMs) in the long--wavelength regime. The component materials of the
HCM were generally orthorhombic $mm2$ piezoelectric materials, which were
randomly distributed as oriented ellipsoidal particles. At the second--order
level of approximation, wherein a two--point correlation function and its
associated correlation length characterize the component material
distributions, the SPFT estimates of the HCM constitutive parameters were
expressed in terms of numerically--tractable two--dimensional integrals.
Representative numerical calculations revealed that: (i) the lowest--order SPFT
estimates are qualitatively similar to those provided by the corresponding
Mori--Tanaka homogenization formalism, but differences between the two
estimates become more pronounced as the component particles become more
eccentric in shape; and (ii) the second--order SPFT estimate provides a
significant correction to the lowest--order estimate, which reflects
dissipative losses due to scattering.
