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JGB thanks Gareth Block, Mark Kachanov, Ernest L. Majer, and
Joseph P. Morris for helpful discussions and comments on the manuscript.
REFERENCES
-
Avellaneda, M., 1987, Iterated homogenization, differential effective
medium theory and applications: Commun.Pure Appl.Math.,
40, 527-554.
-
Bazant, Z. P, and Planas, J., 1998, Fracture and Size Effect in
Concrete and Other Quasibrittle Materials: CRC Press, Boca Raton,
Louisiana, pp.560-563.
- Benveniste, Y., 1987, A new approach to the application
of Mori-Tanaka's theory in composite materials: Mech.Mater.,
6, 147-157.
-
Berryman, J. G., 1980, Long-wavelength propagation in composite elastic
media II. Ellipsoidal inclusions: J. Acoust.Soc.Am.,
68, 1820-1831.
-
Berryman, J. G., 2004a, Bounds on elastic constants for random
polycrystals of laminates: J. Appl.Phys., 96, 4281-4287.
-
Berryman, J. G., 2004b, Poroelastic shear modulus dependence on
pore-fluid properties arising in a model of thin isotropic layers:
Geophys.J. Int.,127, 415-425.
-
Berryman, J. G., 2005, Bounds and self-consistent estimates for
elastic constants of random polycrystals with hexagonal, trigonal,
and tetragonal symmetries:
J. Mech.Phys.Solids, 53, 2141-2173.
-
Berryman, J. G., and Berge, P. A., 1996, Critique of explicit schemes for
estimating elastic properties of multiphase composites:
Mech.Materials, 22, 149-164.
-
Berryman, J. G., Pride, S. R., and Wang, H. F., 2002,
A differential scheme for elastic properties of rocks with dry or
saturated cracks: Geophys.J. Int., 151 (2), 597-611.
-
Bruner, W. M., 1976, Comment on ``Seismic velocities in dry and cracked solids'' by
R. J. O'Connell and B. Budiansky: J. Geophys. Res., 81, 2573-2576.
-
Budiansky, B., and O'Connell, R. J., 1976, Elastic moduli of a cracked solid:
Int.J. Solids Struc., 12, 81-97.
-
Grechka, V., 2005, Penny-shaped fractures revisited:
Stud.Geophys.Geod., 49, 365-381.
-
Grechka, V., and Kachanov, M., 2006a, Effective elasticity of fractured
rocks: The Leading Edge, 25, 152-155.
-
Grechka, V., and Kachanov, M., 2006b, Effective elasticity of rocks with
closely spaced and intersecting cracks: Geophysics, 71, D85.
-
Grechka, V., and Kachanov, M., 2006c, Seismic characterization of multiple fracture sets:
Does orthotropy suffice?: Geophysics, 71, D93.
-
Hashin, Z., and Shtrikman, S., 1962a, On some variational principles in
anisotropic and nonhomogeneous elasticity: J. Mech.Phys.Solids,
10, 335-342.
-
Hashin, Z., and Shtrikman, S., 1962b, A variational approach to the theory
of the elastic behaviour of polycrystals: J. Mech.Phys.Solids,
10, 343-352.
-
Hashin, Z., and Shtrikman, S., 1963, A variational approach to the theory
of the elastic behaviour of multiphase materials:
J. Mech.Phys.Solids, 11, 127-140.
-
Henyey, F. S., and Pomphrey, N., 1982, Self-consistent elastic moduli
of a cracked solid: Geophys.Res.Lett., 9 (8), 903-906.
-
Hill, R., 1952, The elastic behaviour of crystalline aggregate:
Proc.Phys.Soc.London A65, 349-354.
-
Huet, C., 1990, Application of variational concepts to size effects
in elastic heterogeneous bodies: J. Mech.Phys.Solids, 38,
813-841.
-
Kachanov, M., 1980, Continuum model of medium with cracks:
ASCE J. Engineering Mech., 106, 1039-1051.
-
Kachanov, M., and Sevostianov, I., 2005, On quantitative characterization
of microstructures and effective properties:
Int. J. Solids and Structures, 42, 309-336.
-
Kuster, G. T., and Toksöz, M. N., 1974, Velocity and attenuation of seismic
wave in two-phase media: Part I.Theoretical Formulations & Part II. Experimental results: Geophysics, 39, 587-618.
-
Mavko, G. M., and Nur, A., 1978, The effect of nonelliptical cracks on the
compressibility of rocks: J. Geophys.Res., 83, 4459-4468.
-
Milton, G. W., 1985, The coherent potential approximation is a
realizable effective medium theory: Commun.Math.Phys.,
99, 463-500.
-
Milton, G. W., 2002, The Theory of Composites:
Cambridge University Press, Cambridge, UK, pp.487-490.
- Norris, A. N., 1985, A differential scheme for the
effective moduli of composites: Mech.Mater. 4, 1-6.
-
O'Connell, R. J., and Budiansky, B., 1974, Seismic velocities in dry
and saturated cracked solids: J. Geophys.Res., 79,
5412-5426.
-
Olson, T., and Avellaneda, M., 1992, Effective dielectric and elastic
constants of piezoelectric polycrystals: J. Appl.Phys.,
71, 4455-4464.
-
Peselnick, L., and Meister, R., 1965, Variational method of determining
effective moduli of polycrystals: (A) Hexagonal symmetry,
(B) trigonal symmetry:
J. Appl.Phys., 36, 2879-2884.
-
Reuss, A., 1929, Berechung der Fleissgrenze von Mischkristallen:
Z. Angew.Math.Mech., 9, 55.
-
Sayers, C. M., and Kachanov, M., 1991, A simple technica for finding
effective elastic constants of cracked solids for arbitrary crack
orientation statistics: Int. J. Solids Struct., 27, 671-680.
-
Voigt, W., 1928, Lehrbuch der Kristallphysik: Teubner, p.962.
-
Watt, J. P., 1979, Hashin-Shtrikman bounds on the effective elastic moduli of
polycrystals with orthorhombic symmetry:
J. Appl.Phys., 50, 6290-6295.
-
Watt, J. P., and Peselnick, L., 1980, Clarification of the Hashin-Shtrikman
bounds on the effective elastic moduli of polycrystals with hexagonal,
trigonal, and tetragonal symmetries:
J. Appl.Phys., 51, 1525-1531.
-
Willis, J.R., 1977, Bounds and self-consistent estimates for the overall
properties of anisotropic composites:
J. Mech.Phys.Solids, 25, 185-202.
-
Willis, J. R., 1981, Variational and related methods for the overall
properties of composites: in Advances in Applied Mechanics,
Vol.21, edited by C.-S. Yih, Academic Press, New York, pp.1-78.
-
Zimmerman, R. W., 1984, The elastic moduli of a solid with spherical pores:
New self-consistent method: Int.J. Rock Mech. Mining Sci., 21,
339-343.
-
Zimmerman, R. W., 1991, Compressibility of Sandstones,
Elsevier, Amsterdam.
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Up: Berryman and Grechka: Random
Previous: DISCUSSION AND CONCLUSIONS
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1/16/2007