Abstract
A self‐consistent method of estimating effective macroscopic elastic constants for inhomogeneous materials with ellipsoidal inclusions has been formulated based on elastic‐wave scattering theory [J. G. Berryman, Appl. Phys. Lett. 35, 856 (1979)]. The self‐consistent effective medium is determined by requiring the scattered, long‐wavelength displacement field to vanish on the average. The resulting formulas are simpler to apply than previous self‐consistent scattering theories due to the reduction from tensor to vector equations. The results are compared to the rigorous Hashin‐Shtrikman bounds, Miller bounds, and Kuster‐Toksö estimates for the elastic module. For spherical inclusions, our formulas agree with statically derived self‐consistent moduli of Hill and Budiansky. For general ellipsoidal inclusions, our results always satisfy both the Hashin‐Shtrikman bounds and the more stringent Miller bounds. Furthermore, our theory reduces correctly to all known exact results in the appropriate limits. The theory is used to calculate velocity and attenuation of elastic waves in fluid‐saturated media.
Published Version
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