Abstract of the paper ``Long-wavelength propagation in composite elastic media II.
Ellipsoidal inclusions''
A self-consistent method of estimating effective macroscopic elastic constants for
inhomogeneous materials with ellipsoidal inclusions is formulated using
elastic-wave scattering theory. The method is a generalization of the method
for spherical inclusions presented in the first part of this series.
The results are compared to the Kuster-Toksoz estimates for the elastic
moduli and to the rigorous Hashin-Shtrikman bounds and Miller bounds.
For general ellipsoidal inclusions, our self-consistent estimates satisfy
both the Hashin-Shtrikman bounds and the more stringent Miller bounds, whereas
the Kuster-Toksoz estimates for nonspherical inclusions do not satisfy even the
Hashin-Shtrikman bounds in general. Our self-consistency conditions for the cases of
needle and disk inclusions differ from those of Wu, Walpole, and Boucher.
Since our results are in better agreement with the rigorous bounds, it is concluded
that our results are to be preferred. The method is also briefly compared to
other self-consistent scattering theory approaches. The theory is used to
calculate velocity and attenuation of elastic waves in fluid-saturated media
with oblate and prolate spheroidal inclusions.
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