Skip to main content
Log in

Linear and nonlinear dielectric properties of particulate composites at finite concentration

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

An analytical method was proposed to calculate effective linear and nonlinear dielectric properties for particulate composites. The method is based on an approximate solution of two-particle interaction problem, and it can be applied to relatively high volume concentration of particles (up to 50%). Nonlinear dielectric property was also examined by means of secant method. It is found that for low applied electric filed the proposed method is close to Stroud and Hui’s method and for high applied electric filed it is close to Yu’s method.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Garnett J C M. Colors in metal glasses and in metallic films[J]. Trans Royal Soc London, 1904, 203:385–420.

    MATH  Google Scholar 

  2. Garnett J C M. Colors in metal glasses, in metallic films, and in metallic solutions-II[J]. Trans Royal Soc London, 1906, 205:237–288.

    Google Scholar 

  3. Bruggeman V D A G. Betechnung vershiedener physikalischer konstanten von heterogenen substanzen[J]. Annalen der Physik, 1935, 24:636–664.

    Google Scholar 

  4. Doyle W T, Jacobs I S. Effective cluster model of dielectric enhancement in metal-insulator composites[J]. Physical Review B, 1990, 42(15):9319–9327.

    Article  Google Scholar 

  5. Torquato S. Effective electrical conductivity of two-phase disordered composite media[J]. Journal of Applied Physics, 1985, 58(10):3790–3797.

    Article  Google Scholar 

  6. Kanaun S K. Dielectric properties of matrix composite materials with high volume concentrations of inclusions (effective field approach)[J]. International Journal of Engineering Science, 2003, 41(12):1287–1312.

    Article  MathSciNet  Google Scholar 

  7. Stroud D, Hui P M. Nonlinear susceptibilities of granular matter[J]. Physical Review B, 1988, 37(15):8719–8724.

    Article  Google Scholar 

  8. Yu K W, Hui P M, Stroud D. Effective dielectric response of nonlinear composites[J]. Physical Review B, 1993, 47(21):14150–14156.

    Article  Google Scholar 

  9. Pellegrini Y P. Field distributions and effective-medium approximation for weakly nonlinear media[J]. Physical Review B, 2000, 61(14):9365–9372.

    Article  Google Scholar 

  10. Zhou Xiaoming, Hu Gengkai. Prediction of effective nonlinear susceptibility of composites[J]. Acta Materiae compositae Sinica, 2005, 21(6):149–154 (in Chinese).

    Google Scholar 

  11. Qiu Y P, Weng G J. A theory of plasticity for porous materials and particle-reinforced composites[J]. Journal of Applied Mechanics, 1992, 59(2):261–268.

    MATH  Google Scholar 

  12. Hu G K. A method of plasticity for general aligned spheroidal voids or fiber reinforced composites[J]. International Journal of Plasticity, 1996, 12(4):439–449.

    Article  MATH  Google Scholar 

  13. Chew W C. Waves and Fields in Inhomogeneous Media[M]. Van Nostrand Reinhold, New York, 1990.

    Google Scholar 

  14. Ju J W, Chen T M. Effective elastic moduli of two-phase composites containing randomly dispersed spherical inhomogeneities[J]. Acta Mechanics, 1994, 103(1/4):123–144.

    Article  MATH  MathSciNet  Google Scholar 

  15. Batchelor G K, Green J T. The determination of the bulk stress in a suspension of spherical particles to order c 2[J]. Journal of Fluid Mechanics, 1972, 56(3):401–427.

    Article  MATH  Google Scholar 

  16. Willis J R, Acton J R. The overall elastic moduli of a dilute suspension of spheres[J]. Quart J Mech Appl Math, 1976, 29(2):163–177.

    MATH  Google Scholar 

  17. Chen H S, Acrivos A. The effective elastic moduli of composite materials containing spherical inclusions at non-dilute concentrations[J]. International Journal of Solids and Structures, 1978, 14(5):349–364.

    Article  MATH  Google Scholar 

  18. Percus J K, Yevick G J. Analysis of classical statistical mechanics by means of collective coordinates[J]. Physical Review, 1958, 110(1):1–13.

    Article  MATH  MathSciNet  Google Scholar 

  19. Ponte Castaneda P. The effective mechanical properties of nonlinear isotropic composite[J]. Journal of the Mechanics and Physics of Solids, 1991, 39(1):45–71.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Hu Geng-kai  (胡更开).

Additional information

Contributed by HU Geng-kai

Project supported by the National Natural Science Foundation of China (No.10325210)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhou, Xm., Hu, Gk. Linear and nonlinear dielectric properties of particulate composites at finite concentration. Appl Math Mech 27, 1021–1030 (2006). https://doi.org/10.1007/s10483-006-0802-1

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10483-006-0802-1

Key words

Chinese Library Classification

2000 Mathematics Subject Classification

Navigation