메뉴 건너뛰기




Volumn 455, Issue 1982, 1999, Pages 543-566

Effective constitutive properties of a disordered elastic solid medium via the strong-fluctuation approach

Author keywords

Composite materials; Disordered media; Homogenization theory; Renormalization; Strong fluctuation theory

Indexed keywords


EID: 33746415791     PISSN: 13645021     EISSN: None     Source Type: Journal    
DOI: 10.1098/rspa.1999.0323     Document Type: Article
Times cited : (12)

References (56)
  • 1
    • 0021787831 scopus 로고
    • The propagation of clastic waves through a textured granular material
    • Atthey, D. R. 1985 The propagation of clastic waves through a textured granular material. Int. J. Engng. Sei. 23, 937-951.
    • (1985) Int. J. Engng. Sei. , vol.23 , pp. 937-951
    • Atthey, D.R.1
  • 3
    • 33746434841 scopus 로고
    • Elastic wave propagation in polycrystalline media: A causal response
    • Beltzer, A. I. & Brauner, N. 1985 Elastic wave propagation in polycrystalline media: a causal response. Appl. Phys. Lett. 47, 1054-1055.
    • (1985) Appl. Phys. Lett. , vol.47 , pp. 1054-1055
    • Beltzer, A.I.1    Brauner, N.2
  • 5
    • 0347154014 scopus 로고
    • Effective dielectric constant in the calculation of the second field moments in a randomly inhomogeneous medium
    • (In Russian.)
    • Brekhovskikh, V. L. 1985 Effective dielectric constant in the calculation of the second field moments in a randomly inhomogeneous medium. Zh. Eksp. Teor. Fiz. 89, 2013-2020. (In Russian.)
    • (1985) Zh. Eksp. Teor. Fiz. , vol.89 , pp. 2013-2020
    • Brekhovskikh, V.L.1
  • 6
    • 8344236638 scopus 로고
    • On the elastic moduli of some heterogeneous materials
    • Budiansky, B. 1965 On the elastic moduli of some heterogeneous materials. J. Alech. Phys. Solids 13, 223-227.
    • (1965) J. Alech. Phys. Solids , vol.13 , pp. 223-227
    • Budiansky, B.1
  • 8
    • 85020799622 scopus 로고
    • On the determination of relationship between mean stress and strain tensors in structurally inhomogeneous elastic media
    • (In Russian.)
    • Chigarev, A. V. 1980 On the determination of relationship between mean stress and strain tensors in structurally inhomogeneous elastic media. Prikladn. Matem. Mekh. 44, 550-556. (In Russian.)
    • (1980) Prikladn. Matem. Mekh. , vol.44 , pp. 550-556
    • Chigarev, A.V.1
  • 9
    • 0542442402 scopus 로고
    • Wave propagation in a random medium. the correlation group method
    • (In Russian.)
    • Finkelberg, V. M. 1967 Wave propagation in a random medium. The correlation group method. Zh. Eksp. Tear. Fiz. 53, 401-416. (In Russian.)
    • (1967) Zh. Eksp. Tear. Fiz. , vol.53 , pp. 401-416
    • Finkelberg, V.M.1
  • 10
    • 33645020054 scopus 로고
    • The multiple scattering of waves
    • Foldy, L. L. 1945 The multiple scattering of waves. Phys. Rev. 67, 107-119.
    • (1945) Phys. Rev. , vol.67 , pp. 107-119
    • Foldy, L.L.1
  • 11
    • 0019681268 scopus 로고
    • A simple formula for calculating the bounds and the self-consistent value of the shear modulus of a polycrystalline aggregate of cubic crystals
    • Gairola, B. K. D. & Kröner, E. 1981 A simple formula for calculating the bounds and the self-consistent value of the shear modulus of a polycrystalline aggregate of cubic crystals. Int. J. Engng. Sei. 19, 865-869.
    • (1981) Int. J. Engng. Sei. , vol.19 , pp. 865-869
    • Gairola, B.K.D.1    Kröner, E.2
  • 13
    • 0020816026 scopus 로고
    • Analysis of composite materials-a survey
    • Hashin, Z. 1983 Analysis of composite materials-a survey. J. Appl. Mech. 50, 481-505.
    • (1983) J. Appl. Mech. , vol.50 , pp. 481-505
    • Hashin, Z.1
  • 14
    • 27744489677 scopus 로고
    • On some variational principles in anisotropic and nonhomogeneous elasticity
    • Hashin, Z. & Shtrikman, S. 1962 On some variational principles in anisotropic and nonhomogeneous elasticity. J. Mech. Phys. Solids 10, 335-342.
    • (1962) J. Mech. Phys. Solids , vol.10 , pp. 335-342
    • Hashin, Z.1    Shtrikman, S.2
  • 15
    • 6544226089 scopus 로고
    • Elastic properties of reinforced solids: Some theoretical principles
    • Hill, R. 1963 Elastic properties of reinforced solids: some theoretical principles. J. Mech. Phys. Solids 11, 357-372.
    • (1963) J. Mech. Phys. Solids , vol.11 , pp. 357-372
    • Hill, R.1
  • 16
    • 11644304284 scopus 로고
    • A self-consistent mechanics of composite materials
    • Hill, R. 1965 A self-consistent mechanics of composite materials. J. Mech. Phys. Solids 13, 213-222.
    • (1965) J. Mech. Phys. Solids , vol.13 , pp. 213-222
    • Hill, R.1
  • 17
    • 0002531324 scopus 로고
    • Bounds for effective elastic moduli of disordered materials
    • Kröner, E. 1977 Bounds for effective elastic moduli of disordered materials. J. Mech. Phys. Solids 25, 137-155.
    • (1977) J. Mech. Phys. Solids , vol.25 , pp. 137-155
    • Kroner, E.1
  • 18
    • 33746416524 scopus 로고
    • Effective elastic parameters of inhomogeneous media
    • (In Russian.)
    • Kudinov, V. A., Moizhes, B. Ya. & O-Gym-Dien, V. 1975 Effective elastic parameters of inhomogeneous media. Zh. Tekhn. Fiz. 45, 759-765. (In Russian.)
    • (1975) Zh. Tekhn. Fiz. , vol.45 , pp. 759-765
    • Kudinov, V.A.1    Ya, M.B.2    O-Gym-Dien, V.3
  • 19
    • 15644366767 scopus 로고
    • Multiple scattering of waves. II. the effective field in dense systems
    • Lax, M. 1952 Multiple scattering of waves. II. The effective field in dense systems. Rev. Mod. Phys. 85, 621-629.
    • (1952) Rev. Mod. Phys. , vol.85 , pp. 621-629
    • Lax, M.1
  • 21
    • 0000001906 scopus 로고
    • On the theory of ultrasonic wave propagation in polycrystals
    • (In Russian.)
    • Lifshitz, I. M. & Parkhomovski, G. D. 1950 On the theory of ultrasonic wave propagation in polycrystals. Zh. Eksp. Tear. Fiz. 20, 175-184. (In Russian.)
    • (1950) Zh. Eksp. Tear. Fiz. , vol.20 , pp. 175-184
    • Lifshitz, I.M.1    Parkhomovski, G.D.2
  • 22
    • 0000631771 scopus 로고
    • On the theory of elastic properties of polycrystals
    • (In Russian.)
    • Lifshitz, I. M. & Rosenzveig, L. N. 1946 On the theory of elastic properties of polycrystals. Zh. Eksp. Tear. Fiz. 16, 967-980. (In Russian.)
    • (1946) Zh. Eksp. Tear. Fiz. , vol.16 , pp. 967-980
    • Lifshitz, I.M.1    Rosenzveig, L.N.2
  • 23
    • 33750419948 scopus 로고
    • Correction to the article 'On the elastic properties of polycrystals.' Zh
    • (In Russian.)
    • Lifshitz, I. M. & Rosenzveig, L. N. 1951 Correction to the article 'On the elastic properties of polycrystals.' Zh. Eksp. Tear. Fiz. 21, 1184. (In Russian.)
    • (1951) Eksp. Tear. Fiz. , vol.21 , pp. 1184
    • Lifshitz, I.M.1    Rosenzveig, L.N.2
  • 24
    • 0028463093 scopus 로고
    • Random medium model approach to scattering from a random collection of discrete scatterers
    • Lin, H. H., Veysoglu, M. E., Yueh, S. H., Shin, R. T. & Kong, J. A. 1994 Random medium model approach to scattering from a random collection of discrete scatterers. J. Electromagn. Waves Appl. 8, 801-817.
    • (1994) J. Electromagn. Waves Appl. , vol.8 , pp. 801-817
    • Lin, H.H.1    Veysoglu, M.E.2    Yueh, S.H.3    Shin, R.T.4    Kong, J.A.5
  • 26
    • 0000354366 scopus 로고
    • Strong-property-fluctuation theory for homogenizing chiral particulate composites
    • Michel, B. & Lakhtakia, A. 1995 Strong-property-fluctuation theory for homogenizing chiral particulate composites. Phys. Rev. E 51, 5701-5707.
    • (1995) Phys. Rev. E , vol.51 , pp. 5701-5707
    • Michel, B.1    Lakhtakia, A.2
  • 27
    • 0030171897 scopus 로고    scopus 로고
    • On the application of the strong property fluctuation theory for homogenizing chiral-in-chiral composites
    • Michel, B. & Lakhtakia, A. 1996 On the application of the strong property fluctuation theory for homogenizing chiral-in-chiral composites. J. Phys. D 29, 1431-1440.
    • (1996) J. Phys. D , vol.29 , pp. 1431-1440
    • Michel, B.1    Lakhtakia, A.2
  • 28
    • 33746449912 scopus 로고
    • Self-consistent T-matrix solution for the effective elastic properties of perfectly disordered polycrystals
    • Middya, T. R., Basu, A. N. & Sengupta, S. 1985 Self-consistent T-matrix solution for the effective elastic properties of perfectly disordered polycrystals. J. Appl. Phys. 58, 1809-1813.
    • (1985) J. Appl. Phys. , vol.58 , pp. 1809-1813
    • Middya, T.R.1    Basu, A.N.2    Sengupta, S.3
  • 29
    • 0022035002 scopus 로고
    • A differential scheme for the effective moduli of composites
    • Norris, A. N. 1985 A differential scheme for the effective moduli of composites. Mech. Mater. 4, 1-16.
    • (1985) Mech. Mater. , vol.4 , pp. 1-16
    • Norris, A.N.1
  • 30
    • 0021519792 scopus 로고
    • On the nonlocal aspects of acoustic waves incident on the boundary of a half-space
    • Nowinski, J. L. 1984 On the nonlocal aspects of acoustic waves incident on the boundary of a half-space. J. Acoust. Soc. Am. 76, 1543-1548.
    • (1984) J. Acoust. Soc. Am. , vol.76 , pp. 1543-1548
    • Nowinski, J.L.1
  • 31
    • 0028400615 scopus 로고
    • On the Extended Maxwell-Garnett and the Extended Bruggeman approaches for dielectric-in-dielectric composites
    • Prinkey, M. T., Lakhtakia, A. & Shanker, B. 1994 On the Extended Maxwell-Garnett and the Extended Bruggeman approaches for dielectric-in-dielectric composites. Optik 96, 25-30.
    • (1994) Optik , vol.96 , pp. 25-30
    • Prinkey, M.T.1    Lakhtakia, A.2    Shanker, B.3
  • 32
    • 84956078977 scopus 로고
    • Berechnung der Fliessgrenze von Mischkristallen auf Grund der Plastizitätsbe-dingung für Einkristalle
    • Reuss, A. 1929 Berechnung der Fliessgrenze von Mischkristallen auf Grund der Plastizitätsbe-dingung für Einkristalle. Z. Angew. Math. Mech. 9, 49-58.
    • (1929) Z. Angew. Math. Mech. , vol.9 , pp. 49-58
    • Reuss, A.1
  • 34
    • 0042284659 scopus 로고
    • Radiation and propagation of electromagnetic waves in randomly inhomogeneous media
    • (In Russian.)
    • Ryzhov, Y. A. & Tamoikin, V. V. 1970 Radiation and propagation of electromagnetic waves in randomly inhomogeneous media. Izv. Vyssh. Uchebn. Zaved. Radiofizika 13, 356-387. (In Russian.)
    • (1970) Izv. Vyssh. Uchebn. Zaved. Radiofizika , vol.13 , pp. 356-387
    • Ryzhov, Y.A.1    Tamoikin, V.V.2
  • 35
    • 0024000336 scopus 로고
    • A simple self-consistent analysis of wave propagation in particulate composites
    • Sabina, F. J. & Willis, J. R. 1988 A simple self-consistent analysis of wave propagation in particulate composites. Wave Motion 10, 127-142.
    • (1988) Wave Motion , vol.10 , pp. 127-142
    • Sabina, F.J.1    Willis, J.R.2
  • 37
    • 0027681725 scopus 로고
    • Extended Maxwell-Garnett model for chiral-in-chiral composites
    • Shanker, B. & Lakhtakia, A. 1993 Extended Maxwell-Garnett model for chiral-in-chiral composites. J. Phys. D 26, 1746-1758.
    • (1993) J. Phys. D , vol.26 , pp. 1746-1758
    • Shanker, B.1    Lakhtakia, A.2
  • 40
    • 0020848450 scopus 로고
    • The bilocal approximation for the electric field in strong fluctuation theory
    • Stogryn, A. 1983 The bilocal approximation for the electric field in strong fluctuation theory. IEEE Trans. Antennas Propag. AP31, 985-986.
    • (1983) IEEE Trans. Antennas Propag. AP , vol.31 , pp. 985-986
    • Stogryn, A.1
  • 41
    • 0025460932 scopus 로고
    • Strong fluctuation theory equations for electric field second moments in anisotropic media
    • Stogryn, A. 1990 Strong fluctuation theory equations for electric field second moments in anisotropic media. IEEE Thins. Antennas Propagat. 38, 1099-1101.
    • (1990) IEEE Thins. Antennas Propagat. , vol.38 , pp. 1099-1101
    • Stogryn, A.1
  • 42
    • 0020014771 scopus 로고
    • Variational estimates for dispersion and attenuation of waves in random composites
    • Talbot, D. R. S. &: Willis, J. R. 1982a Variational estimates for dispersion and attenuation of waves in random composites. I. General theory. Int. J. Solids Structures 18, 673-683.
    • (1982) I. General Theory. Int. J. Solids Structures , vol.18 , pp. 673-683
    • Talbot, D.R.S.1    Willis, J.R.2
  • 43
    • 0020007948 scopus 로고
    • Variational estimates for dispersion and attenuation of waves in random composites. II. Isotropie composites
    • Talbot, D. R. S. & Willis, J. R. 1982& Variational estimates for dispersion and attenuation of waves in random composites. II. Isotropie composites. Int. J. Solids Structures 18, 685-698.
    • (1982) Int. J. Solids Structures , vol.18 , pp. 685-698
    • Talbot, D.R.S.1    Willis, J.R.2
  • 44
    • 0020879965 scopus 로고
    • Variational estimates for dispersion and attenuation of waves in random composites. III. Fibre-reinforced materials
    • Talbot, D. R. S. & Willis, J. R. 1982c Variational estimates for dispersion and attenuation of waves in random composites. III. Fibre-reinforced materials. Int. J. Solids Structures 18, 793-811.
    • (1982) Int. J. Solids Structures , vol.18 , pp. 793-811
    • Talbot, D.R.S.1    Willis, J.R.2
  • 45
    • 33747862408 scopus 로고
    • Random heterogeneous media: Microstructure and improved bounds on effective properties
    • Torquato, S. 1991 Random heterogeneous media: microstructure and improved bounds on effective properties. Appl. Mech. Rev. 44, 37-76.
    • (1991) Appl. Mech. Rev. , vol.44 , pp. 37-76
    • Torquato, S.1
  • 46
    • 0019612950 scopus 로고
    • Multiple scattering of acoustic waves by random distributions of discrete scatterers with the use of quasicrystalline-coherent potential approximation
    • Tsang, L. & Kong, J. A. 1981a Multiple scattering of acoustic waves by random distributions of discrete scatterers with the use of quasicrystalline-coherent potential approximation. J. Appl. Phys. 52, 5448-5458.
    • (1981) J. Appl. Phys. , vol.52 , pp. 5448-5458
    • Tsang, L.1    Kong, J.A.2
  • 47
    • 0019567783 scopus 로고    scopus 로고
    • 19816 Scattering of electromagnetic waves from random media with strong permittivity fluctuations
    • Tsang, L. and Kong, J. A. 19816 Scattering of electromagnetic waves from random media with strong permittivity fluctuations. Radio Sei. 16, 303-320.
    • Radio Sei. , vol.16 , pp. 303-320
    • Tsang, L.1    Kong, J.A.2
  • 48
    • 0024878930 scopus 로고
    • Scattering and attenuation of elastic waves in random media
    • Varadan, V: K., Ma, Y. & Varadan, V. V. 1989 Scattering and attenuation of elastic waves in random media. Pure Appl. Geophys. 131, 577-603.
    • (1989) Pure Appl. Geophys. , vol.131 , pp. 577-603
    • Varadan, V.K.1    Ma, Y.2    Varadan, V.V.3
  • 50
    • 0000794966 scopus 로고
    • Three-dimensional time-harmonic elastodynamic Green's functions for anisotropic solids
    • Wang, C.-Y. & Achenbach, J. D. 1995 Three-dimensional time-harmonic elastodynamic Green's functions for anisotropic solids. Proc. R. Soc. Land. A 449, 441-458.
    • (1995) Proc. R. Soc. Land. a , vol.449 , pp. 441-458
    • Wang, C.-Y.1    Achenbach, J.D.2
  • 51
    • 0019265450 scopus 로고
    • A polarization approach to the scattering of elastic waves. I. Scattering by a single inclusion
    • Willis, J. R. 1980a A polarization approach to the scattering of elastic waves. I. Scattering by a single inclusion. J. Mech. Phys. Solids 28, 287-305.
    • (1980) J. Mech. Phys. Solids , vol.28 , pp. 287-305
    • Willis, J.R.1
  • 52
    • 0019262819 scopus 로고
    • A polarization approach-to the scattering of elastic waves. II. Multiple scattering from inclusions
    • Willis, J. R. 1980& A polarization approach-to the scattering of elastic waves. II. Multiple scattering from inclusions. J. Mech. Phys. Solids 28, 307-327.
    • (1980) J. Mech. Phys. Solids , vol.28 , pp. 307-327
    • Willis, J.R.1
  • 53
    • 0019697033 scopus 로고
    • Variational and related methods for the overall properties of composites
    • (ed. C. S. Jeh), New York: Academic.
    • Willis, J. R. 1981 Variational and related methods for the overall properties of composites. In Advances in applied mechanics (ed. C. S. Jeh), vol. 21, pp. 1-79. New York: Academic.
    • (1981) Advances in Applied Mechanics , vol.21 , pp. 1-79
    • Willis, J.R.1
  • 54
    • 0001463780 scopus 로고
    • Strong-fluctuation theory for a mean electromagnetic field in a statistically homogeneous random medium with arbitrary anisotropy of electrical and statistical properties
    • Zhuck, N. P. 1994 Strong-fluctuation theory for a mean electromagnetic field in a statistically homogeneous random medium with arbitrary anisotropy of electrical and statistical properties. Phys. Rev. B 50, 15636-15645.
    • (1994) Phys. Rev. B , vol.50 , pp. 15636-15645
    • Zhuck, N.P.1
  • 55
    • 33744678119 scopus 로고
    • Effective parameters of a statistically homogeneous fluid with strong density and compressibility fluctuations
    • Zhuck, N. P. 1995 Effective parameters of a statistically homogeneous fluid with strong density and compressibility fluctuations. Phys. Rev. B 52, 919-926.
    • (1995) Phys. Rev. B , vol.52 , pp. 919-926
    • Zhuck, N.P.1
  • 56
    • 0030053732 scopus 로고    scopus 로고
    • Strong fluctuation theory for a mean acoustic field in a random fluid medium with statistically anisotropic perturbations
    • Zhuck, N. P. 1996 Strong fluctuation theory for a mean acoustic field in a random fluid medium with statistically anisotropic perturbations. J. Acoust. Soc. Am. 99, 46-54.
    • (1996) J. Acoust. Soc. Am. , vol.99 , pp. 46-54
    • Zhuck, N.P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.