Comments on the applicability of the Kuster–Toksöz method to the derivation of the dynamic material parameters of inhomogeneous media

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Abstract
The Kuster–Toksöz method for predicting the quasistatic elastic properties of microinhomogeneous materials with low concentrations of inclusions and neglecting multiple scattering was extended by Gaunaurd and Überall to predict the dynamic effective material properties of bubbles in water, air-filled cavities in solids, and solid inclusions in solids. Excellent agreement with previously published theoretical results was obtained in the limiting cases of low concentrations of bubbles in water and air-filled cavities in rubbery solids. The purpose here is to present three areas of concern pertaining to the results of this theoretical treatment. These concerns apply to: (1) the numerical significance of a certain term (the X term) in the relationship derived by Gaunaurd and Überall, (2) the significance of multiple scattering; and (3) the existence of an anomalous wave amplification phenomenon predicted by their theory. It is believed that these areas of concern are of sufficient significance to warrant careful consideration by those who wish to apply the Gaunaurd and Überall relationships.

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