Micromechanical modeling of viscoelastic voided composites in the low-frequency approximation

Journal of the Acoustical Society of America

Volumn 112, Issue 5 I, 2002, Pages 1937-1943

  Haberman, Michael R ^a   Berthelot, Yves H ^a   Jarzynski, J ^a   Cherkaoui, Mohammed ^b  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

^b UNIVERSITÉ DE LORRAINE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ANISOTROPY; COMPOSITE MICROMECHANICS; INCLUSIONS; VISCOELASTICITY;

VISCOELASTIC MATRICES;

ACOUSTICS;

ACOUSTICS; COMPOSITE;

ACOUSTICS;

ANISOTROPY; ARTICLE; COMPOSITE MATERIAL; MATHEMATICAL MODEL; MECHANICS; PRIORITY JOURNAL; SHEAR STRESS; SOUND TRANSMISSION; VISCOELASTICITY;

ANISOTROPY; ELASTICITY; MODELS, THEORETICAL; VISCOSITY;

EID: 0036840432     PISSN: 00014966     EISSN: None     Source Type: Journal    
DOI: 10.1121/1.1509424     Document Type: Article

References (38)

1. I. A. Chaban, "Self-consistent field approach to calculation of the effective parameters of microinhomogeneous media," Sov. Phys. Acoust. 10, 298-304 (1965).
2. G. T. Kuster and M. N. Toksoz, "Velocity and attenuation of seismic waves in two-phase media. I. Theoretical formulations, Geophysics 39, 587-606 (1974).
3. G. C. Gaunaurd and H. Überall, "Resonance theory of the effective properties of perforated solids," J. Acoust. Soc. Am. 71, 282-295 (1982).
4. P. C. Waterman and R. Truell, "Multiple scattering of waves," J. Math. Phys. 2, 513-537 (1961).
5. V. K. Varadan, Y. Ma, and V. V. Varadan, "A multiple scattering theory for elastic wave propagation in discrete random media," J. Acoust. Soc. Am. 77, 375-385 (1985).
6. K. P. Scharnhorst, "Comments on the applicability of the Kuster-Toksoz method to the derivation of the dynamic material parameters of inhomogeneous media," J. Acoust. Soc. Am. 82, 692-695 (1987).
7. F. Kerr, "The Scattering of a Plane Elastic Wave by Spherical Elastic Inclusions," Int. J. Eng. Sci. 30, 169-186 (1992).
8. A. N. Norris, "Scattering of elastic waves by spherical inclusions with applications to low frequency wave propagation in composites," Int. J. Eng. Sci. 24, 1271-1282 (1986).
9. A. M. Baird, F. H. Kerr, and D. J. Townend, "Wave propagation in a viscoelastic medium having fluid-filled microspheres," J. Acoust. Soc. Am. 105, 1527-1538 (1999).
10. B. E. Hornby, L. M. Schwartz, and J. A. Hudson, "Anisotropic effective modeling of the elastic properties of shales," Geophysics 59, 1570-1583 (1994).
11. M. Cherkaoui, H. Sabar, and M. Berveiller, "Micromechanical approach of the coated inclusion problem and applications to composite materials," J. Eng. Mater. Technol. 116, 274-278 (1994).
12. E. H. Kerner, "The elastic and thermo-elastic properties of composite media," Proc. Phys. Soc. London 69, 808-813 (1956).
13. R. Hill, "A self-consistent mechanics of composite materials," J. Mech. Phys. Solids 13, 213-222 (1965).
14. B. Budianski, "On the elastic properties of some heterogeneous media," J. Mech. Phys. Solids 13, 223-227 (1965).
15. R. M. Christensen, "A critical evaluation for a class of micromechanics models," J. Mech. Phys. Solids 38, 379-404 (1990).
16. R. M. Christensen and K. H. Lo, "Solutions for effective shear properties of three-phase sphere and cylinder models," J. Mech. Phys. Solids 27, 315-330 (1979).
17. J. G. Berryman, "Long-wavelength propagation in composite elastic media. II. Ellipsoidal inclusions," J. Acoust. Soc. Am. 68, 1820-1831 (1980).
18. S. K. Datta, "Diffraction of plane elastic waves by ellipsoidal inclusions," J. Acoust. Soc. Am. 61, 1432-1437 (1977).
19. J. E. Gubernatis, "Long-wave approximations for the scattering of elastic waves from flaws with applications to ellipsoidal voids and inclusions," J. Appl. Phys. 50, 4046-4058 (1979).
20. L. J. Walpole, "A coated inclusion in an elastic medium," Math. Proc. Cambridge Philos. Soc. 83, 495-506 (1978).
21. Y. Huang, K. X. Hu, X. Wei, and A. Chandra, "A generalized self-consistent mechanics method for composite materials with multiphase inclusions," J. Mech. Phys. Solids 42, 491-504 (1994).
22. E. J. Garboczi and J. G. Berryman, "Elastic moduli of a material containing composite inclusions: Effective medium theory and finite element computations," Mech. Mater. 33, 455-470 (2001).
23. J. G. Berryman, "Long-wavelength propagation in composite elastic media. I. Spherical inclusions," J. Acoust. Soc. Am. 68, 1809-1819 (1980).
24. Z. Hashin and S. Shtrikman, "A variational approach to the theory of the elastic behavior of multiphase materials," J. Mech. Phys. Solids 11, 127-140 (1963).
25. M. N. Miller, "Bounds for effective electrical, thermal, and magnetic properties of heterogeneous materials," J. Math. Phys. 10, 1988-2005 (1969).
26. L. V. Gibiansky and G. W. Milton, "On the effective viscoelastic moduli of two-phase media. I. Rigorous bounds on the complex bulk modulus," Proc. R. Soc. London, Ser. A 440, 163-188 (1993).
27. R. Hill, "Interfacial operators in the mechanics of composite media," J. Mech. Phys. Solids 31, 347-357 (1983).
28. J. D. Eshelby, "The Determination of the Elastic Field of an Ellipsoidal Inclusion, and Related Problems," in Proceedings of the Royal Society, A Vol. 241, 1957, pp. 376-396.
29. T. Mura, Micromechanics of Defects in Solids, 2nd Ed. (Kluwer Academic, 1987).
30. D. Lanhong, H. Zhuping, and W. Ren, An explicit expression of the effective moduli for composite materials filled with coated inclusions," Acta Mech. Sin. 14, 37-52 (1998).
31. J. S. Huang and L. J. Gibson, "Elastic moduli of a composite hollow spheres in a matrix," J. Mech. Phys. Solids 25, 55-75 (1993).
32. W. M. Madigosky, R. W. Harrison, and K. P. Scharnhorst, "Effect of air inclusions on absorption and velocity of sound in viscoelastic materials," Polym. Mater. Sci. Eng, 60, 489-496 (1989).
33. J. Jarzynski, "Mechanisms of Sound Attenuation in Materials," in Sound and Vibration Damping with Polymers, edited by R. D. Corsaro and L. H. Sperling (The American Chemical Society, Washington D.C., 1990), pp. 167-207.
34. S. Havriliak and S. Negami, "A complex plane analysis of α-dispersion in some polymer systems," J. Polym. Sci., Part C: Polym. Symp. 14, 99-117 (1966).
35. N. Lagakos, J. Jarzynski, J. H. Cole, and J. A. Bucaro, "Frequency and temperature dependence of elastic moduli polymers," J. Appl. Phys. 59, 4017-4031 (1986).
36. D. T. Blackstock, Fundamentals of Physical Acoustics (Wiley, New York, 2000), pp. 163-164.
37. Dynamic Mechanical Thermal Analyzer, Rheometrics Scientific, Inc.
38. J. D. Ferry, Viscoelastic Properties of Polymers (Wiley, New York, 1970), pp. 292-351.