An Iterative Effective Medium Approximation for Wave Dispersion and Attenuation Predictions in Particulate Composites

Abstract

This work deals with the dispersion and attenuation of elastic waves propagating in a random particlereinforced composite. A new iterative effective medium approximation based on the single scattering consideration, for the quantitative estimation of wave dispersion and attenuation is proposed. The iterations are carried out via the classical dispersion relation of Foldy while the convergence of the iterative procedure is accomplished through a self-consistent condition proposed by Kim et al. [6]. The methodology is quite general and it works for any type of particles. The single scattering problem is solved numerically by means of an advanced boundary element code. Numerical results concerning the frequency dependent behaviour of the wave velocity and attenuation coefficient for three particular types of composites are presented. The results obtained are compared to those taken either experimentally or numerically by other investigators.

Wave propagation in cementitious material containing artificial distributed damage

“…It is difficult to provide a general explanation for wave propagation in inhomogeneous media because each scattering problem is unique. The wave field depends on the mechanical properties of the matrix and the scatterers, the scatterers' shape, size, volume fraction as well as, their distribution in three-dimensional space and the propagating wavelength [28].…”

An iterative effective medium approximation (IEMA) for wave dispersion and attenuation predictions in particulate composites, suspensions and emulsions

“…The self-consistent or effective medium theories appear in the literature with different versions and procedures depending on the type of suspensions they applied. Thus, for particulate composites one can mention the self-consistent models of Talbot and Willis, 31 Sabina and Willis 32 and Devaney, 33 the effective medium approximations of Kerr 34 and Kanaun et al, 35 the dynamic self-consistent effective medium approximations of Berryman, 36 Kim et al 37 and Tsinopoulos et al 38 and the incremental self-consistent approach of Anson and Chivers 11 and Biwa et al 39 For liquid suspensions, one can mention the effective medium approaches of Anson and Chivers, 40 Hemar et al, 41 Cowan et al, 42 McClements et al 43 and Hipp et al 44,45 and the coupled-phase models of Harker et al, 46 Atkinson and Kytomaa 47 and Evans and Attenborough. 48 Comparisons with experimental results have shown that the self-consistent models are those which are able to predict satisfactory the behavior of a wave pulse propagating within a dense distribution of particle-scatterers.…”

“…However, scattering occurs due to the interaction of the incident wave with the randomly distributed particles. Thus, considering inclusions and matrix as scatterers the surfaces of which have opposite unit normal vector, the self-consistent hypothesis of Kim et al 37 seems to be quite reasonable Later, Tsinopoulos et al 38 proposed an iterative effective medium approximation ͑IEMA͒ combining effectively the self-consistent model of Kim et al 37 and the simple multiple scattering theory of Foldy. 1 In their work, the evaluation of the wave speed and attenuation coefficient was accomplished through a practical and simple iterative procedure avoiding thus the solution of complex nonlinear systems of equations such those required in the approximation of Kim et al Moreover, comparing the estimations provided by the two methods, IEMA appears to be more efficient and accurate in cases of highly concentrated elastic mixtures.…”

“…Here, the IEMA of Tsinopoulos et al 38 is properly modified and improved in order to predict well wave dispersion and attenuation in particulate composites, particle suspensions and emulsions. Our aim in the current work is twofold: first to develop a single theoretical model that predicts well wave dispersion and attenuation for all types of suspensions and second to provide an iterative computational scheme that for the case of spherical particles is simple and easily implemented.…”

Phase velocity and attenuation predictions of waves in cancellous bone using an iterative effective medium approximation

“…To this end, an iterative effective medium approximation (IEMA) has been introduced in [1,15], which predicts wave dispersion and attenuation in non-homogeneous materials that include particles with volume concentrations as high as V 50%. This version of IEMA combines the self-consistent model of Kim et al [12] with the quasicrystalline approximation of Waterman and Truell [8].…”