Effective medium theory for elastic composites

Bibliography

Beran, M. J. and J. Molyneux, 1966, Use of classical variational principles to determine bounds for the effective bulk modulus in heterogeneous media: Quarterly Journal of Applied Mathematics, 24, 107-118.

Berryman, J. G., 1979, Theory of elastic properties of composite materials: Applied Physics Letters, 35, 856-858.

----, 1980a, Long-wavelength propagation in composite elastic media. I. Spherical inclusions: Journal of the Acoustical Society of America, 68, 1809-1819.

----, 1980b, Long-wavelength propagation in composite elastic media. II. Ellipsoidal inclusions: Journal of the Acoustical Society of America, 68, 1820-1831.

----, 1995, Mixture theories for rock properties, in Ahrens, T. J., ed., Rock Physics and Phase Relations, 205-228, American Geophysical Union.

Boucher, S., 1974, On the effective moduli of isotropic two-phase elastic composites: Journal of Composite Materials, 8, 82-89.

Budiansky, B., 1965, On the elastic moduli of some heterogeneous materials: Journal of the Mechanics and Physics of Solids, 13, 223-227.

Elliott, R. J., J. A. Krumhansl, and P. L. Leath, 1974, The theory and properties of randomly disordered crystals and related physical systems: Reviews of Modern Physics, 46, 465-543.

Eshelby, J. D., 1957, The determination of the elastic field of an ellipsoidal inclusion, and related problems: Proceedings of the Royal Society of London A, 241, 376-396.

Gibianksy, L. V. and G. W. Milton, 1993, On effective viscoelastic moduli of two-phase media. I. Rigorous bounds on the complex bulk modulus in three dimensions: Proceedings of the Royal Society of London A, 241, 376-396.

Gibiansky, L. V., G. W. Milton, and J. G. Berryman, 1999, On effective viscoelastic moduli of two-phase media. III. Rigorous bounds on the complex shear modulus in two dimensions: Proceedings of the Royal Society of London A, 455, 2117-2149.

Gubernatis, J. E. and J. A. Krumhansl, 1975, Macroscopic engineering properties of polycrystalline materials: Elastic properties: Journal of Applied Physics, 46, 1875-1883.

Hashin, Z. and S. Shtrikman, 1961, Note on a variational approach to the theory of composite elastic materials: Journal of the Franklin Institute, 271, 336-341.

----, 1962, On some variational principles in anisotropic and nonhomogeneous elasticity: Journal of the Mechanics and Physics of Solids, 10, 335-342.

----, 1963, A variational approach to the theory of the elastic behaviour of multiphase materials: Journal of the Mechanics and Physics of Solids, 11, 127-140.

Hill, R., 1952, The elastic behaviour of a crystalline aggregate: Proceedings of the Physical Society of London A, 65, 349-354.

----, 1963, Elastic properties of reinforced solids: Some theoretical principles: Journal of the Mechanics and Physics of Solids, 11, 357-372.

----, 1965, A self-consistent mechanics of composite materials: Journal of the Mechanics and Physics of Solids, 13, 213-222.

Korringa, J., 1973, Theory of elastic constants of heterogeneous media: Journal of Mathematical Physics, 14, 509-513.

Korringa, J., R. J. S. Brown, D. D. Thompson, and R. J. Runge, 1979, Self-consistent imbedding and the ellipsoidal model for porous rocks: Journal of Geophysical Research, 84, 5591-5598.

Mal, A. K. and L. Knopoff, 1967, Elastic wave velocities in two-component systems: Journal of the Institute of Mathematics and Its Applications, 3, 376-387.

McCoy, J. J., 1970, On the displacement field in an elastic medium with random variation of material properties, in Eringen, A. C., ed., Recent Advances in Engineering Science, volume 5, 235-254, Gordon and Breach.

Miller, M. N., 1969a, Bounds for effective bulk modulus of heterogeneous materials: Journal of Mathematical Physics, 10, 2005-2013.

----, 1969b, Bounds for effective electrical, thermal, and magnetic properties of heterogeneous materials: Journal of Mathematical Physics, 10, 1988-2004.

Milton, G. W., 1981, Bounds on the electromagnetic, elastic, and other properties of two-component composites: Physical Review Letters, 46, 542-545.

Milton, G. W. and J. G. Berryman, 1997, On effective viscoelastic moduli of two-phase media. II. Rigorous bounds on the complex shear modulus in three dimensions: Proceedings of the Royal Society of London A, 453, 1849-1880.

Silnutzer, N. R., 1972, Effective constants of statistically homogeneous materials: PhD thesis, University of Pennsylvania.

(283pp).

Soven, P., 1967, Coherent-potential model of substitutional disordered alloys: Physical Review, 156, 809-813.

Velicky, B., S. Kirkpatrick, and H. Ehrenreich, 1968, Single-site approximations in the electronic theory of simple binary alloys: Physical Review, 175, 747-766.

Walpole, L. J., 1969, On the overall elastic moduli of composite materials: Journal of the Mechanics and Physics of Solids, 17, 235-251.

Watt, J. P., G. F. Davies, and R. J. O'Connell, 1976, Elastic properties of composite materials: Reviews of Geophysics and Space Physics, 14, 541-563.

Willis, J. R., 1977, Bounds and self-consistent estimates for the overall properties of anisotropic composites: Journal of the Mechanics and Physics of Solids, 25, 185-202.

----, 1981, Variational and related methods for the overall properties of composites, in Advances in Applied Mechanics, 1-78, Academic Press.

Wu, T. T., 1966, The effect of inclusion shape on the elastic moduli of a two-phase material: International Journal of Solids and Structures, 2, 1-8.

Zeller, R. and P. H. Dederichs, 1973, Elastic constants of polycrystals: Physica Status Solidi, B55, 831-842.