REFERENCES

• Avellaneda, M., 1987, Iterated homogenization, differential effective medium theory and applications: Commun.Pure Appl.Math 40, 527-554.
• Benveniste, Y., 1987, A new approach to the application of Mori-Tanaka's theory in composite materials: Mech.Mat. 6, 147-157.
• Berge, P. A., Berryman, J. G. & Bonner, B. P., 1993, Influence of microstructure on rock elastic properties: Geophys.Res. Letters 20, 2619-2622., J. G., 1980a, Long-wavelength propagation in composite elastic media I. Spherical inclusions: J. Acoust.Soc.Am. 68, 1809-1819., J. G., 1980b, Long-wavelength propagation in composite elastic media II. Ellipsoidal inclusions: J. Acoust.Soc.Am. 68, 1820-1831.
• Berryman, J. G., 1995, Mixture theories for rock properties: in Rock Physics and Phase Relations, edited by T. J. Ahrens, AGU, Washington, DC, pp.205-228.
• Berryman, J. G., 1999, Origin of Gassmann's equations: Geophysics 64, 1627-1629.
• Biot, M. A., 1941, General theory of three-dimensional consolidation: J. Appl.Phys. 12, 155-164.
• Biot, M. A. & Willis, D. G., 1957, The elastic coefficients of the theory of consolidation: J. App.Mech. 24, 594-601.
• Bruggeman, D. A. G., 1935, Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen: Ann.Physik. (Leipzig) 24, 636-679.
• Budiansky, B., 1965, On the elastic moduli of some heterogeneous materials: J. Mech.Phys.Solids 13, 223-227.
• Budiansky, B. & O'Connell, R. J., 1976, Elastic moduli of a cracked solid: Int.J. Solids Struct. 12, 81-97.
• Cleary, M. P, Chen, I.-W., & Lee, S.-M., 1980, Self-consistent techniques for heterogeneous media: ASCE J. Eng.Mech. 106, 861-887.
• Dunn, M. L., & Ledbetter, H., 1995, Poisson's ratio of porous amd microcracked solids: Theory and application to oxide superconductors: J. Mater.Res. 10, 2715-2722.
• Eshelby, J. D., 1957, The determination of the elastic field of an ellipsoidal inclusion, and related problems: Proc.Roy.Soc.London A 241, 376-396.
• Gassmann, F., 1951, Über die elastizität poröser medien: Veirteljahrsschrift der Naturforschenden Gesellschaft in Zürich 96, 1-23.
• Goertz, D., & Knight, R., 1998, Elastic wave velocities during evaporative drying: Geophysics 63, 171-183.
• Hashin, Z., 1988, The differential scheme and its application to cracked materials: J. Mech.Phys.Solids 36, 719-734.
• Hashin, Z., & Shtrikman, S., 1961, Note on a variational approach to the theory of composite elastic materials: J. Franklin Inst. 271, 336-341.
• Hashin, Z. & Shtrikman, S., 1962, A variational approach to the theory of elastic behaviour of polycrystals: J. Mech.Phys.Solids 10, 343-352.
• Henyey, F. S., & Pomphrey, N., 1982, Self-consistent elastic moduli of a cracked solid: Geophys.Res.Lett. 9, 903-906.
• Hildebrand, F. B., 1956, Introduction to Numerical Analysis, Dover, New York, pp.285-297.
• Hill, R., 1965, A self-consistent mechanics of composite materials: J. Mech.Phys.Solids 13, 213-222.
• Hudson, J. A., 1981, Wave speeds and attenuation of elastic waves in material containing cracks: Geophys.J. R. Astron.Soc. 64, 133-150.
• Hudson, J. A., 1986, A higher order approximation to the wave propagation constants for a cracked solid: Geophys.J. R. Astron.Soc. 87, 265-274.
• Hudson, J. A., 1990, Overall elastic properties of isotropic materials with arbitrary distribution of circular cracks: Geophys.J. Int. 102, 465-469.
• Kachanov, M., 1992, Effective elastic properties of cracked solids: Critical review of some basic concepts: Appl.Mech.Rev. 45, 304-335.
• Kushch, V. I. & Sangani, A. S., 2000, Stress intensity factor and effective stiffness of a solid containing aligned penny-shaped cracks: Int.J. Solids Struct. 37, 6555-6570.
• Laws, N. & Dvorak, G. J., 1987, The effect of fiber breaks and aligned penny-shaped cracks on the stiffness and energy release rates in unidirectional composites: Int.J. Solids Struct. 23, 1269-1283.
• Mavko, G. & Jizba, D., 1991, Estimating grain-scale fluid effects on velocity dispersion in rocks: Geophysics 56, 1940-1949.
• Mavko, G., Mukerji, T. & Dvorkin, J., 1998, The Rock Physics Handbook: Tools for Seismic Analysis in Porous Media, Cambridge University Press, Cambridge, pp.307-309.
• Nemat-Nasser, S. & Hori, M., 1993, Micromechanics: Overall Properties of Heterogeneous Materials, North-Holland, Amsterdam, pp.427-431.
• Nemat-Nasser, S., Yu, N. & Hori, M., 1993, Solids with periodically distributed cracks: Int.J. Solids Struct. 30, 2071-2095.
• Norris, A. N., 1985, A differential scheme for the effective moduli of composites: Mech.Mater. 4, 1-16.
• O'Connell, R. J. & Budiansky, B., 1974, Seismic velocities in dry and saturated cracked solids: J. Geophys.Res. 79, 4626-4627.
• O'Connell, R. J. & Budiansky, B., 1977, Viscoelastic properties of fluid-saturated cracked solids: J. Geophys.Res. 82, 5719-5735.
• Reuss, A., 1929, Berechung der Fliessgrenze von Mischkristallen: Z. Angew.Math.Mech. 9, 55.
• Sayers, C. M. & Kachanov, M., 1991, A simple technique for finding effective elastic constants of cracked solids for arbitrary crack orientation statistics: Int.J. Solids Struct. 27, 671-680.
• Skempton, A. W., 1954, The pore-pressure coefficients A and B: Geotechnique 4, 143-147.
• Smyshlyaev, V. P., Willis, J. R. & Sabina, F. J., 1993, Self-consistent analysis of waves in a matrix-inclusion composite. 3. A matrix containing cracks: J. Mech.Phys.Solids 41, 1809-1824.
• Voigt, W., 1928, Lehrbuch der Kristallphysik, Teubner, Leipzig, p.962.
• Walsh, J. B., 1969, New analysis of attenuation in partially melted rock: J. Geophys.Res. 74, 4333-4337.
• Walsh, J. B., 1980, Static deformation of rock: ASCE J. Engng.Mech. 106, 1005-1019.
• Willis, J. R., 1980, A polarization approach to the scattering of elastic waves. Part II: Multiple scattering from inclusions: J. Mech.Phys.Solids 28, 307-327.
• Wu, T. T., 1966, The effect of inclusion shape on the elastic moduli of a two-phase material: Int.J. Solids Struct. 2, 1-8 (1966).
• Zimmerman, R. D., 1985, The effect of microcracks on the elastic moduli of brittle materials: J. Mater.Sci.Lett. 4, 1457-1460.
• Zimmerman, R. D., 1994, Behavior of the Poisson ratio of a two-phase composite material in the high-concentration limit: Appl.Mech.Rev. 47, S38-S44.