A comparison of stochastic and effective medium approaches to the backscattered signal from a porous layer in a solid matrix

Abstract

This paper reports a study of the backscattering behavior of a solid layer containing randomly spaced spherical cavities in the long wavelength limit. The motivation for the work arises from a need to model the responses of porous composite materials in ultrasonic NDE procedures. A comparison is made between models based on a summation over discrete scatterers, which show interesting emergent properties, and an integral formulation based on an ensemble average, and with a simple slab effective medium approximation. The similarities and differences between these three models are demonstrated. A simple quantitative criterion is established which sets the maximum frequency at which ensemble average or equivalent homogeneous medium models can represent echo signal generation in a porous layer for given interpore spacing, or equivalently, given pore size and concentration.

Simulation of incoherent and coherent backscattered wave fields from cavities in a solid matrix

“…1, bottom half), whose properties are derived from the Foldy ensemble-averaged wavenumber. The work extends that reported in the previous paper 7 by investigating the effects of cavity radius, concentration, and frequency to establish the validity criteria for effective medium properties applied to single scatterer configurations. Fuller details of the models were given in the previous paper 7 and are only summarized here.…”

“…Analytical expressions for the coefficients in the long wavelength limit were given in an earlier paper. 7 FIG. 1.…”

“…Many different schemes exist for the derivation of these effective properties, including models termed effective medium models, self-consistent models, multiple scattering models, ensemble-average models, and homogenization schemes. A broad selection of such studies was reviewed in a previous paper; 7 papers by Kanaun and Levin, 8 Kim, 5 and Parnell et al 6 also include useful reviews of this literature. The field is still an active one, despite its long history, and although many works are based on elastostatic analyses 9,10 rather than on wave propagation, new variants on effective medium models are published frequently.…”

Numerical and analytical investigation of the influence of porosity on the frequency response of GLARE composite

“…For a particular volume fraction φ of cavities the complex wave number K of the effective medium [7], [8] is given as:…”

“…In the applied effective-medium model a complex wave number is used to match the response of a homogenous medium to the frequency-dependent response of a random distribution of cavities, calculated from the scattering from a single cavity [7], [8], [9]. As well as effective-medium models, also numerical simulation can be used to study wave-propagation problems in inhomogeneous media, such as periodic structures [10] or random media [11].…”