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Effective elastic parameters of random composites
1.A. J. Devaney, J. Math. Phys (in press);
1.A. J. Devaney, H. Levine, and T. Plona, J. Acoust. Soc. Am. 67, S44 (1980).
2.B. L. Gyorffy, Phys. Rev. B 1, 3290 (1970).
3.G. T. Kuster and M. N. Toksöz, Geophysics 39, 587 (1974).
3.See also M. N. Toksöz and C. H. Cheng, Arabian J. Sci. Eng. (Special Issue), 109 (1978).
4.G. T. Kuster and M. N. Toksöz, Geophysics 39, 607 (1974).
5.B. Budiansky, J. Mech. Phys. Solids 13, 223 (1965).
6.R. Hill, J. Mech. Phys. Solids 13, 213 (1965).
7.For example, these theories predict that the shear modulus of a concentration of solid spheres in a nonviscous fluid matrix is the same as a concentration of nonviscous liquid spheres in a solid matrix.
8.J. G. Berryman, Appl. Phys. Lett. 35, 856 (1979).
9.R. J. Elliott, J. A. Krumhansl, and P. L. Leath, Rev. Mod. Phys. 46, 465 (1974).
10.J. E. Gubernatis, E. Domany, and J. A. Krumhansl, J. Appl. Phys. 48, 2804 (1977).
11.J. E. Gubernatis, J. A. Krumhansl, and R. M. Thomson, J. Appl. Phys. 50, 3338 (1979). In order for the Rayleigh approximation to be valid the wavelengths of the elastic field both within the effective medium and within the scatterer must be significantly larger than the circumference of the spherical inclusion.
12.Here, we assume that and are positive, real quantities so that the effective medium is nonabsorbing.
13.The equivalence of the two theories in the weak scattering limit is illustrated by the fact that Eqs. (8) give almost identical fits to experimental velocity data examined by Kuster and Toksöz (Ref. 4) as that provided by the Kuster‐Toksöz model (10).
14.T. Plona, Appl. Phys. Lett. 36, 259 (1980).
15.The elastic constants K and μ defined in Eq. (3) are negative for the composite system studied in Ref. 14. This means that the wavelengths within the scatterer are zero, thus resulting in a violation of the Rayleigh approximation (see Ref. 11).
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