On the homogenization of orthotropic elastic composites by the strong-property-fluctuation theory

TL;DR

This paper extends the strong-property-fluctuation theory (SPFT) to orthotropic elastic composites, providing numerical insights into their effective properties and the influence of particle distribution and correlation length.

Contribution

The paper develops the elastodynamic SPFT for orthotropic composites and compares it with the Mori-Tanaka method, including second-order corrections for better accuracy.

Findings

Second-order SPFT improves stiffness tensor estimates.

Differences between SPFT and Mori-Tanaka grow with orthotropy.

Effective dissipation varies with correlation length.

Abstract

The strong-property-fluctuation theory (SPFT) provides a general framework for estimating the constitutive parameters of a homogenized composite material (HCM). We developed the elastodynamic SPFT for orthotropic HCMs, in order to undertake numerical studies. A specific choice of two-point covariance function - which characterizes the distributional statistics of the generally ellipsoidal particles that constitute the component materials - was implemented. Representative numerical examples revealed that the lowest-order SPFT estimate of the HCM stiffness tensor is qualitatively similar to the estimate provided by the Mori-Tanaka mean-field formalism, but the differences between the two estimates vary as the orthotropic nature of the HCM is accentuated. The second-order SPFT provides a correction to the lowest-order estimate of the HCM stiffness tensor and density. The correction, indicating effective dissipation due to scattering loss, increases as the HCM becomes less orthotropic but decreases as the correlation length becomes smaller.