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

TL;DR

This paper develops a strong-property-fluctuation theory (SPFT) for estimating the effective properties of orthorhombic piezoelectric composites, accounting for particle shape and distribution, and compares it with existing homogenization methods.

Contribution

The paper introduces a second-order SPFT approach for orthorhombic piezoelectric composites, incorporating particle shape and correlation effects, and demonstrates its improvements over traditional methods.

Findings

Second-order SPFT provides significant corrections to lowest-order estimates.

Differences between SPFT and Mori-Tanaka increase with particle eccentricity.

SPFT estimates reflect dissipative scattering losses.

Abstract

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.