Compressibility and shear compliance of spheroidal pores: Exact derivation via the Eshelby tensor, and asymptotic expressions in limiting cases

International Journal of Solids and Structures

Volumn 48, Issue 5, 2011, Pages 680-686

  David, E C ^a   Zimmerman, R W ^a  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

Crack; Elasticity; Eshelby's tensor; Isotropic; Pore aspect ratio; Pore compliance; Porous media

Indexed keywords

ESHELBY'S TENSOR; ISOTROPIC; PORE ASPECT RATIO; PORE COMPLIANCE; POROUS MEDIA;

ASYMPTOTIC ANALYSIS; COMPRESSIBILITY; CRACKS; ELASTIC MODULI; ELASTICITY; NEEDLES; POROUS MATERIALS; TENSORS;

ASPECT RATIO;

EID: 78651398234     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijsolstr.2010.11.001     Document Type: Article

References (22)

1. Y. Benveniste A new approach to the application of mori-tanaka's theory in composite materials Mech. Mater. 6 1987 147 157 (Pubitemid 18530321)
2. J.G. Berryman Long-wavelength propagation in composite elastic media II. Ellipsoidal inclusions J. Acoust. Soc. Am. 68 1980 1820 1831 (Pubitemid 11459107)
3. B. Budiansky, and R. O'Connell Elastic moduli of a cracked solid Int. J. Solids Struct. 12 1976 81 97
4. C.H. Cheng, and M.N. Toksoz Inversion of seismic velocities for the pore aspect ratio spectrum of a rock J. Geophys. Res. 84 1979 7533 7543
5. M.L. Dunn, and H. Ledbetter Poisson's ratio of porous and microcracked solids: Theory and application to oxyde superconductors J. Mater. Res. 10 1995 2715 2722
6. R.H. Edwards Stress concentrations around spheroidal inclusions and cavities J. Appl. Mech. 18 1951 19 27
7. J.D. Eshelby The determination of the elastic field of an ellipsoidal inclusion, and related problems Proc. Roy. Soc. London A 241 1957 376 396
8. A. Giraud, D. Hoxha, D. Do, and V. Magnenet Effect of pore shape on effective porothermoelastic properties of isotropic rocks Int. J. Solids Struct. 45 2008 1 23 (Pubitemid 351635592)
9. Z. Hashin, and S. Shtrikman Note on a variational approach to the theory of composite elastic materials J. Franklin Inst. 271 1961 336 341
10. M. Kachanov, and I. Sevostianov On quantitative characterization of microstructures and effective properties Int. J. Solids Struct. 42 2005 309 336
11. M. Kachanov, B. Shafiro, and I. Tsukrov Handbook of Elasticity Solutions 2003 Kluwer Dordrecht
12. G.T. Kuster, and M.N. Toksoz Velocity and attenuation of seismic waves in two-phase media: Part I. Theoretical formulations Geophysics 39 1974 587 606
13. M. LeRavalec, and Y. Gueguen High- and low-frequency elastic moduli for a saturated porous/cracked rock - differential self-consistent and poroelastic theories Geophysics 61 1996 1080 1094 (Pubitemid 27159244)
14. J.K. MacKenzie The elastic constants of a solid containing spherical holes Proc. Roy. Soc. London B 63 1950 2 11
15. M. Markov, V. Levine, A. Mousatov, and E. Kazatchenko Elastic properties of double-porosity rocks using the differential effective medium model Geophys. Prospect. 53 2005 733 754 (Pubitemid 41710829)
16. G. Mavko, T. Mukerji, and J. Dvorkin The Rock Physics Handbook 1998 Cambridge University Press Cambridge
17. I. Sevostianov, and M. Kachanov Connections between elastic and conductive properties of heterogeneous materials Adv. Appl. Mech. 42 2008 69 252
18. B. Shafiro, and M. Kachanov Materials with fluid-filled pores of various shapes: effective elastic properties and fluid pressure polarization Int. J. Solids Struct. 34 1997 3517 3540 (Pubitemid 27516962)
19. J.B. Walsh The effect of cracks on the compressibility of rocks J. Geophys. Res. 70 1965 381 389
20. T.T. Wu The effect of inclusion shape on the elastic moduli of a two-phase material Int. J. Solids Struct. 2 1966 1 8
21. R.W. Zimmerman Compressibility of an isolated spheroidal cavity in an isotropic elastic medium J. Appl. Mech. 52 1985 606 608
22. R.W. Zimmerman Compressibility of sandstones 1991 Elsevier Amsterdam