The homogenization of orthorhombic piezoelectric composites by the strong–property–fluctuation theory

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.