Dependence of elastic properties of materials on their porosity: Review of models

Journal of Porous Media

Volumn 9, Issue 4, 2006, Pages 335-355

  Kaczmarek, Mariusz ^a   Goueygou, Marc ^b  

^a KAZIMIERZ WIELKI UNIVERSITY   (Poland)

^b ECOLE CENTRALE DE LILLE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ELASTIC MODULI; ISOTOPES; MATHEMATICAL MODELS; MATRIX ALGEBRA; POROSITY;

DRY ISOTROPIC POROUS MATERIALS; ELASTIC PROPERTIES; QUANTITATIVE PREDICTIONS; SOLID MATRIX;

POROUS MATERIALS;

EID: 33751252809     PISSN: 1091028X     EISSN: None     Source Type: Journal    
DOI: 10.1615/JPorMedia.v9.i4.50     Document Type: Article

References (67)

1. Aboudi, J., Mechanics of Composite Materials, Elsevier, Amsterdam, 1991.
2. Aboudi, J., Micromechanical analysis of composites by the method of cells-update, Appl. Mech. Rev., vol. 49, pp. S83-S91, 1996.
3. Benveniste, Y., A new approach to the application of Mori-Tanaka's theory in composite materials, Mech. Mater., vol. 6, pp. 147-157, 1987.
4. Berge, P. A., Bonner, B. P., and Berryman, J. G., Ultrasonic velocity-porosity relationships for sandstone analogs made from fused glass beads, Geophysics, vol. 60, pp. 108-119, 1995.
5. Berryman, J. G., Long-wavelength propagation in composite elastic media, J. Acoust. Soc. Am., vol. 68, pp. 1809-1831, 1980.
6. Berryman, J. G., Role of porosity in estimates of composite elastic constants, J. Energy Res. Tech., vol. 116, pp. 87-96, 1994.
7. Berryman, J. G., and Berge, P. A., Rock elastic properties: dependence on microstructure, in: Homogenization and Constitutive Modeling for Heterogeneous Materials, Chang, C. S. and Ju, J. W., eds., ASME, New York, AMD, vol. 166, pp. 1-13, 1993.
8. Berryman, J. G., and Berge, P. A., Critique of two explicit schemes for estimating elastic properties of multiphase composites, Mech. Mater., vol. 22, pp. 149-164, 1995.
9. Biot, M. A., General theory of three-dimensional consolidation, J. Appl. Phys., vol. 12, pp. 155-164, 1941.
10. Biot, M. A., Theory of elastic waves in a fluid-saturated porous solid, J. Acoust. Soc. Am., vol. 28, pp. 168-191, 1956.
11. Biot, M. A., and Willis, D. G., The elastic coefficients of the theory of consolidation, J. Appl. Mech., vol. 24, pp. 594-601, 1957.
12. Bourbie, T., Coussy, O., and Zinszner, B., Acoustics of Porous Media, Gulf Publishing, Houston, 1987.
13. Budiansky, B., On the elastic moduli of some heterogeneous materials, J. Mech. Phys. Solids, vol. 13, pp. 223-227, 1965.
14. Chang, L.-S., Chuang, W. J., and Wei, W. J., Characterization of alumina ceramics by ultrasonic testing, Mater. Characteriz., vol. 45, pp. 221-226, 2000.
15. Chapman, A. M., and Higdon, J. J. L., Effective elastic properties for a periodic bicontinuous porous medium, J. Mech. Phys. Solids, vol. 42, no. 2, pp. 283-305, 1994.
16. Chen, Q., and Nur, A., Critical concentration models for porous materials, in: Advances in Porous Media, vol. 2, Corapcioglu, M. Y., ed., Elsevier, New York, pp. 169-308, 1994.
17. Christensen, R. M., A critical evaluation for a class of micromechanics models, J. Mech. Phys. Solids, vol. 38, pp. 379-404, 1990.
18. Cleary, M. P., Chen, I.-W., and Lee, S.-M., Self-consistent techniques for heterogeneous media, ASCE J. Eng. Mech., vol. 106, pp. 861-887, 1980.
19. Dean, E. A., Elastic moduli of porous sintered materials as modeled by a variable-aspect-ratio self-consistent oblatespheroidal-inclusion theory, J. Am. Ceram. Soc., vol. 66, pp. 847-854, 1983.
20. Dean, E. A., and Lopez, J. A., Empirical dependence of elastic moduli on porosity for ceramic materials, J. Am. Ceram. Soc., vol. 66, pp. 366-870, 1983.
21. Dunn M. L. and Ledbetter H., Poisson's ratio of porous and microcracked solids: Theory and application to oxide superconductors, J. Mater. Res., vol. 10, pp. 2715-2722, 1995.
22. Eshelby, J. D., The determination of the elastic field of an ellipsoidal inclusion, and related problems, Proc. Roy. Soc. London A, vol. 241, pp. 376-396, 1957.
23. Fan, Q., Takatsubo, J., and Yamamoto S., Quantitative characterization of advanced porous ceramics based on a probabilistic theory of ultrasonic wave propagation, J. Appl. Phys., vol. 86, pp. 4023-4028, 1999.
24. Grffiths, T. J., and Ghanizadeh, A., Determination of elastic constants for porous sintered iron powder compacts, Powder Metall., vol. 29, pp. 129-133, 1986.
25. Gueguen, Y., Chelidze, T., and Le Ravalec, M., Microstructures, percolation thresholds, and rock physical properties, Tectonophysics, vol. 279, pp. 23-35, 1997.
26. Hashin, Z., Analysis of composite materials - A survey, J. Appl. Mech., vol. 105, pp. 481-505, 1983.
27. Hasselman, D. P. H., On the porosity dependence of the elastic moduli of polycrystalline refractory materials, J. Am. Ceram. Soc., vol. 45, pp. 452-453, 1962.
28. Herakovich, C. T., and Baxter, S. C., Influence of pore geometry on effective response of porous media, J. Mater. Sci., vol. 34, pp. 1595-1609, 1999.
29. Ji, S., Generalized means as an approach for predicting Young's moduli of multiphase materials, Mater. Sci. Eng., vol. A366, pp. 195-201, 2004.
30. Ji, S., Wang, Q., Xia, B., and Marcotte, D., Mechanical properties of multiphase materials and rocks: phenomenological approach using generalized means, J. Struct. Geol., vol. 26, pp. 1377-1390, 2004.
31. Knudsen, F. P., Dependence of mechanical strength of brittle polycrystalline specimens on porosity and grain size, J. Am. Ceram. Soc., vol. 42, pp. 376-387, 1959.
32. Knudsen, F. P., Effect of porosity on Young modulus of alumina, J. Am. Ceram. Soc., vol. 45, pp. 94-95, 1962.
33. Kupkova, M., Porosity dependence of material elastic moduli, J. Mater. Sci., vol. 28, pp. 5265-5268, 1993.
34. Kuster, G. T., and Toksöz, M. N., Velocity and attenuation of seismic waves in two-phase media: part I. Theoretical formulations, Geophysics, vol. 39, pp. 587-606, 1974.
35. Kolodziej, J. A., and Kaczmarek, M., Motion equations of the dynamic theory of consolidation from the point of view of the theory of transient pipe flows, Transport Porous Media, vol. 8, pp. 227-241, 1992.
36. Mackenzie, J. K., The elastic constants of a solid containing spherical holes, Proc. Phys. Soc. London B, vol. 63, pp. 2-11, 1950.
37. Martin, R. B., and Haynes, R. R., Confirmation of theoretical relation between stiffness and porosity in ceramics, J. Am. Ceram. Soc., vol. 54, pp. 410-411, 1971.
38. Martin, L. P., Dadon, D., and Rosen, M., Evaluation of ultrasonically determined elasticity-porosity relations in zinc oxide, J. Am. Ceram. Soc., vol. 79, pp. 1281-1289, 1996.
39. Mavko, G., Mukerrji, T., and Dvorkin, J., The Rock Physics Handbook. Tools for Seismic Analysis in Porous Media, Cambridge University Press, Cambridge, England, 1998.
40. Mindess, S., Relationships between strength and micro structure for cement-based materials: An overview, in: Very High Strength Cement-Based Materials, Young, J. F., ed., Mat. Res. Soc. Symp. Proc, vol. 42, pp. 53-68, 1985.
41. Mukhopadhyay, A. K., and Phani, K. K., Young's modulus-porosity relations: an analysis based on a minimum contact area model, J. Mater. Sci., vol. 33, pp. 69-72, 1998.
42. Nielsen, E. N., Predicting the Properties of Mixtures: Mixture Rules in Science and Engineering, Marcel Decker, New York, 1978.
43. Nielsen, L. F., Elastic properties of two-phase materials, Mater. Sci. Eng., vol. 52, pp. 39-62, 1982.
44. Nolen-Hoeksema, R. C., Modulus-porosity relations, Gassmann's equations, and the low-frequency elastic-wave response ta fluids, Geophysics, vol. 65, pp. 1355-1363, 2000.
45. Paley, M., and Aboudi, J., Micromechanical analysis of composites by the generalized cells model, Mech. Mater., vol. 14, pp. 127-139, 1992.
46. Panakkal, J. P., Willems, H., and Arnold, W., Nondestructive evaluation of elastic parameters of sintered iron powder compacts, J. Mater. Sci., vol. 25, pp. 1397-1402, 1990.
47. Phani, K. K., Niyogi, S. K., Mitra, A. K., and Roychaudhury, M., Strength and elastic modulus of a porous brittle solid: an acousto-ultrasonic study, J. Mater. Sci., vol. 21, pp. 4335-4341, 1986.
48. Ramakrishnan, N., and Arunachalam, V. S., Effective elastic moduli of porous solids, J. Mater. Sci., vol. 25, pp. 3930-3037, 1990.
49. Ramakrishnan, N., and Arunachalam, V. S., Effective elastic moduli of porous ceramic materials, J. Am. Ceram. Soc., vol. 76, pp. 2745-2752, 1993.
50. Rice, R. W., Evaluating porosity parameters for porosity-property relations, J. Am. Ceram. Soc., vol. 76, pp. 1081-1808, 1993.
51. Rice, R. W., Comparison of physical property-porosity behaviour with minimum solid area models, J. Mater. Sci., vol. 31, pp. 1509-1528, 1996.
52. Roberts, A. P, and Garboczi, E. J., Elastic properties of model porous ceramics, J. Am. Ceram. Soc., vol. 83, pp. 3041-3048, 2000.
53. Roberts, A. P, and Garboczi, E. J., Computation of the linear elastic properties of random porous materials with a wide variety of microstructures, Proc. Roy. Soc. London A, vol. 458, pp. 1033-1054, 2002.
54. Rossi, R. C., Prediction of the elastic moduli of composites, J. Am. Ceram. Soc., vol. 51, pp. 433-439, 1968.
55. Sanchez-Palencia, E., Non-Homogeneous Media and Vibration Theory, Lecture Notes in Physics 127, Springer-Verlag, Berlin, 1980.
56. Sihn, S., and Roy, A. K., Modeling and prediction of bulk properties of open-cell carbon foam, J. Mech. Phys. Solids, vol. 52, pp. 167-191, 2004.
57. Soroka, I. P., and Sereda J., Interrelation of hardeness modulus of elasticity and porosity in various gypsum systems, J. Am. Ceram. Soc., vol. 51, pp. 337-338, 1968.
58. Spriggs, R. M., Expression for effect of porosity on elastic modulus of polycrystalline refractory materials, particularly aluminum oxide, J. Am. Ceram. Soc., vol. 44, pp. 628-629, 1961.
59. Spriggs, R. M., Brissette, L. A., and Vasilos, T., Effect of porosity on elastic and shear moduli of polycrystalline magnesium oxide, J. Am. Ceram. Soc., vol. 45, p. 400, 1962.
60. Wang, J. C., Young's modulus of porous materials, J. Mater. Sci., vol. 19, pp. 801-808, 1984.
61. Watt, J. P., Davies, G. E. R., and O'Connell, J., The elastic properties of composite materials, Rev. Geophys. Space Phys., vol. 14, pp. 541-563, 1976.
62. Williams, J. L., Ultrasonic wave propagation in cancellous and cortical bone: Prediction of some experimental results by Biot's theory, J. Acoust. Soc. Am., vol. 91, pp. 1106-1114, 1992.
63. Wu, T. T., The effect of inclusion shape on the elastic moduli of a tw-phase material, Int. J. Solids Struct., vol. 2, pp. 1-8, 1966.
64. Yaman, I. O., Hearn, N., Aktan, H. M., Active and non-active porosity in concrete, Mater. Struct., vol. 35, pp. 102-116, 2002.
65. Yeheskel, O., and Tevet, O., A new assessment method for the bulk modulus and the Poisson's ratio of porous ceramics, J. Testing Eval., vol. 28, pp. 189-198, 2000.
66. Zhao, Y. H., Tandon, G. P., and Weng, G. J., Elastic moduli for a class of porous materials, Acta Mechanica, vol. 76, pp. 105-130, 1989.
67. Zimmerman, R. W., Elastic moduli of a solid containing spherical inclusions, Mech. Mater., vol. 12, pp. 17-24, 1991.