Critique of two explicit schemes for estimating elastic properties of multiphase composites

Mechanics of Materials

Volumn 22, Issue 2, 1996, Pages 149-164

  Berryman, James G ^a   Berge, Patricia A ^a  

^a LAWRENCE LIVERMORE NATIONAL LABORATORY   (United States)

Author keywords

Composite materials; Effective medium theories; Kuster Toks z method; Mechanical properties of composites; Mori Tanaka method; Realizability

Indexed keywords

APPROXIMATION THEORY; CALCULATIONS; ELASTICITY; ESTIMATION; MECHANICAL PROPERTIES;

EXPLICIT SCHEMES; KUSTER-TOKSOZ METHOD; MORI-TANAKA METHOD; MULTIPHASE COMPOSITES; REALIZABILITY;

COMPOSITE MATERIALS;

EID: 0030084076     PISSN: 01676636     EISSN: None     Source Type: Journal    
DOI: 10.1016/0167-6636(95)00035-6     Document Type: Article

References (47)

1. Avellaneda, M. (1987), Iterated homogenization, differential effective medium theory and applications, Commun. Pure Appl. Math. 40, 527-554.
2. Benveniste, Y. (1987), A new approach to the application of Mori-Tanaka's theory in composite materials, Mech. Mater. 6, 147-157.
3. Berge, P.A., G.J. Fryer and R.H. Wilkens (1992), Velocity-porosity relationships in the upper oceanic crust: Theoretical considerations, J. Geophys. Res. 97, 15239-15254.
4. Berge, P.A., J.G. Berryman and B.P. Bonner (1993), Influence of microstructure on rock elastic properties, Geophys. Res. Lett. 20, 2619-2622.
5. Berge, P.A., B.P. Bonner and J.G. Berryman (1995), Ultrasonic velocity-porosity relationships for sandstone analogs made from fused glass beads, Geophysics 60, 108-119.
6. Berryman, J.G. (1980), Long-wavelength propagation in composite elastic media, II. Ellipsoidal inclusions, J. Acoust. Soc. Am. 68, 1820-1831.
7. Berryman, J.G. (1992), Single-scattering approximations for coefficients in Biot's equations of poroelasticity, J. Acoust. Soc. Am. 91, 551-571.
8. Berryman, J.G. (1994), Role of porosity in estimates of composite elastic constants, Trans. ASME J. Energy Resources Technol. 116, 87-96.
9. Berryman, J.G. and P.A. Berge (1993), Rock elastic properties: Dependence on microstructure, in: C.S. Cheng and J.W. Ju, eds., Homogenization and Constitutive Modeling for Heterogeneous Materials, AMSE, New York, pp. 1-13.
10. Budiansky, B. (1965), On the elastic moduli of some heterogeneous materials, J. Mech. Phys. Solids 13, 223-227.
11. Cheng, C.H.A. (1978), Seismic Velocities in Porous Rocks: Direct and Inverse Problems, Ph.D. thesis, MIT, Cambridge, MA.
12. Cheng, C.H. and M.N. Toksöz (1979), Inversion of seismic velocities for the pore aspect ratio spectrum of a rock, J. Geophys. Res. 84, 7533-7543.
13. Christensen, R.M. (1990), A critical evaluation for a class of micromechanics models, J. Mech. Phys. Solids 38, 379-404.
14. Cleary, M.P., L.-W. Chen and S.-M. Lee (1980), Self-consistent techniques for heterogeneous media, ASCE J. Eng. Mech. 106, 861-887.
15. Dvorak, G.J. and Y. Benveniste (1992), On transformation strains and uniform fields in multiphase elastic media, Proc. R. Soc. London A 437, 291-310.
16. Eshelby, J.D. (1957), The determination of the elastic field of an ellipsoidal inclusion and related problems, Proc. Roy. Soc. London Ser. A 241, 376-396.
17. Fate, W.A. (1975), High temperature elastic moduli of polycrystalline silicon nitride, J. Appl. Phys. 46, 2375-2377.
18. Ferrari, M. (1991), Asymmetry and the high concentration limit of the Mori-Tanaka effective medium theory, Mech. Mater. 11, 251-256.
19. Ferrari, M. and M. Filipponi (1991), Appraisal of current homogenizing techniques for the elastic response of porous and reinforced glass, J. Am. Ceramic Soc. 74, 229-231.
20. 4 matrix composites with SiC whisker reinforcement, in: S.K. Das, C.P. Bollard and F. Marikar, eds., High Performance Composites for the 1990's, The Minerals, Metals and Materials Society, Warrendale, PA, pp. 365-370.
21. 4 matrix composites with SiC whisker reinforcement, J. Am. Ceramics Soc. 75, 908-914.
22. Gubernatis, J.E. and J.A. Krumhansl (1975), Macroscopic engineering properties of polycrystalline materials: Elastic properties, J. Appl. Phys. 46, 1875-1883.
23. Hashin, Z. and S. Shtrikman (1963), A variational approach to the elastic behavior of multiphase materials, J. Mech. Phys. Solids 11, 127-140.
24. Hill, R. (1963), Elastic properties of reinforced solids: Some theoretical principles, J. Mech. Phys. Solids 11, 357-372.
25. Hill, R. (1965), A self-consistent mechanics of composite materials, J. Mech. Phys. Solids 13, 213-222.
26. Hori, M. and S. Nemat-Nasser (1993), Double-inclusion model and overall moduli of multi-phase composites, Mech. Mater. 14, 189-206.
27. Ju, J.W. and T.M. Chen (1994a), Micromechanics and effective moduli of elastic composites containing randomly dispersed ellipsoidal inhomogeneities, Acta Mechanica 103, 103-121.
28. Ju, J.W. and T.M. Chen (1994b), Effective elastic moduli of two-phase composites containing randomly dispersed spherical inhomogeneities, Acta Mechanica 103, 123-144.
29. Korringa, J., R.J.S. Brown, D.D. Thompson and R.J. Runge (1979), Self-consistent imbedding and the ellipsoidal model for porous rocks, J. Geophys. Res. 84, 5591-5598.
30. Kuster, G.T. and M.N. Toksöz (1974), Velocity and attenuation of seismic waves in two-phase media: I. Theoretical formulation, Geophysics 39, 587-606.
31. Milton, G.W. (1985), The coherent potential approximation is a realizable effective medium theory, Commun. Math. Phys. 99, 463-500.
32. Mori, T. and K. Tanaka (1973), Average stress in matrix and average elastic energy of materials with misfitting inclusions, Acta Metal. 21, 571-574.
33. Nemat-Nasser, S. and M. Hori (1993), Micromechanics: Overall Properties of Heterogeneous Materials, North-Holland, Amsterdam, pp. 345-357.
34. Nemat-Nasser, S., N. Yu and M. Hori (1993), Bounds and estimates of overall moduli of composites with periodic microstructure, Mech. Mater. 15, 163-181.
35. Norris, A.N. (1985), A differential scheme for the effective moduli of composites, Mech. Mater. 4, 1-16.
36. Norris, A.N. (1989), An examination of the Mori-Tanaka effective medium approximation for multiphase composites, ASME J. App. Mech. 56, 83-88.
37. Toksöz, M.N., C.H. Cheng and A. Timur (1976), Velocities of seismic waves in porous rocks, Geophysics 41, 621-645.
38. Walpole, L.J. (1969), On the overall elastic moduli of composite materials, J. Mech. Phys. Solids 17, 235-251.
39. Walsh, J.B. (1969), New analysis of attenuation in partially melted rock, J. Geophys. Res. 74, 4333-4337.
40. Walsh, J.B., W.F. Brace and A.W. England (1965), Effect of porosity on compressibility of glass, J. Am. Ceramic Soc. 48, 605-608.
41. Weng, G.J. (1984), Some elastic properties of reinforced solids, with special reference to isotropic ones containing spherical inclusions, Int. J. Eng. Sci. 22, 845-856.
42. Weng, G.J. (1990), The theoretical connection between Mori-Tanaka's theory and the Hashin-Shtrikman bounds, Int. J. Eng. Sci. 28, 1111-1120.
43. Wilkens, R.H., G.J. Fryer and J. Karsten (1991), Evolution of porosity and seismic structure of upper oceanic crust: Importance of aspect ratios, J. Geophys. Res. 96, 17981-17995.
44. Willis, J.R. (1977), Bounds and self-consistent estimates for the overall properties of anisotropic composites, J. Mech. Phys. Solids 25, 185-202.
45. Wu, T.T. (1966), The effect of inclusion shape on elastic moduli of a two-phase material, Internat. J. Solids Structures 2, 1-8.
46. Zimmerman, R.W. (1991a), Elastic moduli of a solid containing spherical inclusions, Mech. Mater. 21, 17-24.
47. Zimmerman, R.W. (1991b), Compressibility of Sandstones, Elsevier, Amsterdam, Chapter 11.