Dispersion of elastic waves in random particulate composites

Abstract

Elastic wave propagation in a discrete random medium is studied to predict dynamic effective properties of composite materials containing spherical inclusions. A self-consistent method is proposed which is analogous to the well-known coherent potential approximation in alloy physics. Three conditions are derived that should be satisfied by two effective elastic moduli and effective density. The derived self-consistency conditions have the physical meaning that the scattering of a coherent wave by the constituents in the effective medium vanishes, on the average. The frequency-dependent effective wave speed and coherent attenuation can be obtained by solving the self-consistency conditions numerically. At the lowest resonance frequency, the phase speed increases rapidly and the attenuation reaches the maximum in the composites having a large density mismatch. The lowest resonance is caused mainly by the density mismatch between matrix and particles and higher resonances by the stiffness mismatch. The dispersion and attenuation of longitudinal and shear waves are affected by the lowest resonance much more than by higher ones. The lowest resonance frequency of particles in the effective medium is found to be higher than that of a single particle embedded in the matrix material of composites due to the stiffening effect. The results obtained from the present theory are shown to be in good agreement with previous experimental observations of Kinra et al. [Int. J. Solid Struct. 16, 301–312 (1980)]. Part of the calculated results are compared with those computed by the Waterman and Truell theory. The present theory is in better agreement with the experiments for the examples dealt with.

Effective medium theories for wave propagation in two-dimensional random inhomogeneous media

“…A quasistatic version for predicting mechanical properties of composites has been proposed by Berryman [1979;1980]. A dynamic generalization of this theory has been made for two and three-dimensional problems [Kim et al 1995;Kim 1996]. As shown in [Kim et al 1995], this theory was very successful in predicting the effective wave speed and attenuation in random particulate composites for wide ranges of frequency and volume fraction.…”

“…A dynamic generalization of this theory has been made for two and three-dimensional problems [Kim et al 1995;Kim 1996]. As shown in [Kim et al 1995], this theory was very successful in predicting the effective wave speed and attenuation in random particulate composites for wide ranges of frequency and volume fraction. A second variant is the dynamic extension [Sabina and Willis 1988;Bussink et al 1995;Kanaun and Levin 2003;Kanaun et al 2004] of the static self-consistent theories of [Budiansky 1965;Hill 1965].…”

“…One distinctive point in this theory is that multiple scattering is seen to occur in the effective medium [Kim et al 1995;Choy 1999]. In most effective medium type formulations, the single scattering approximation is adopted and thus the correlations between scatterers are neglected.…”

A comparative study on propagation of elastic waves in random particulate composites

“…Sabina and Willis demonstrated that the obtained self-consistency generate acceptable answers to determine effective dynamic properties just when wavelength of the elastic waves is at least four times that of radius of spherical inclusions. Kim et al (1995) presented an estimation of the effective dynamic properties and effective density which is similar to the coherent potential approximation in alloy physics. The obtained theoretical results are closer to the Kinra's experimental results as compared to Ying & Truell (1956) results.…”

Elastic wave propagation in nano-composites with random distribution of spherical inclusions

“…A thin layer with different elastic properties is considered as the interface of matrix and inclusion in this study. Kim et al (1995) presented an estimation of effective dynamic properties and effective density via a self-consistent method which is similar to the coherent potential approximation in alloy physics. These theoretical results have a better coincidence with the experimental observations of Kinra compared to Ying & Truell results.…”