On bounding the effective conductivity of isotropic composite materials

  • Khanh Le Chau
  • Pham Duc Chinh
Original Papers

Abstract

In this paper inequalities for the effective conductivity of isotropic composite materials are derived. These inequalities depend on several coefficients characterizing the microstructure of composites. The obtained coefficients can be exactly calculated for models of a two-component aggregate of multisized, coated ellipsoidal inclusions, packed to fill all space. As a result, new bounds for effective conductivity, considerably narrower than those of Hashin-Shtrikman, are established for such models of composite materials.

Keywords

Microstructure Composite Material Mathematical Method Effective Conductivity Ellipsoidal Inclusion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    Berdichevski, V. L.,Variational principles of mechanics of continuum media. M.: Nauka 1983.Google Scholar
  2. [2]
    Hashin, Z. and Shtrikman, S.,A variational approach to the theory of the effective magnetic permeability of multiphase materials. J. Appl. Phys.,33, 3125–3131 (1962).Google Scholar
  3. [3]
    Lurie, K. A. and Cherkaev, A. V.,Exact estimates of conductivity of composites formed by two isotropically conducting media taken in prescribed proportion. Proc. Roy. Soc. Edinburgh99A, 71–87 (1984).Google Scholar
  4. [4]
    Tartar, L.,Estimations fines des coéfficients homogènéisés. In Ennio DeGiorgi's Colloquium (edited by P. Kree). Research Notes in Mathematics125, Pitman Press, London 1985.Google Scholar
  5. [5]
    Milton, G. W. and Kohn, R. V.,Variational bounds on the effective moduli of anisotropic composites. J. Mech. Phys. Solids36, 597–629 (1988).Google Scholar
  6. [6]
    Beran, M. J.,Use of the variational approach to determine bounds for the effective permeability in random media. Nuovo Cim.38, 771–795 (1965).Google Scholar
  7. [7]
    Miller, M. N.,Bounds on the effective electrical, thermal and magnetic properties of heterogeneous materials. J. Math. Phys.10, 1988–2004 (1969).Google Scholar
  8. [8]
    Bergman, D. J.,The dielectric constant of a composite material—a problem in classical physics. Phys. Lett. C: Phys. Rep.43, 377–407 (1978).Google Scholar
  9. [9]
    Berryman, J. G. and Milton, G. W.,Microgeometry of random composites and porous media. J. Phys.21D, 87–94 (1988).Google Scholar
  10. [10]
    Kellogg, O. D.,Foundations of Potential Theory. Springer, Berlin 1967.Google Scholar

Copyright information

© Birkhäuser Verlag 1991

Authors and Affiliations

  • Khanh Le Chau
    • 1
  • Pham Duc Chinh
    • 1
  1. 1.Institute of MechanicsHanoiVietnam

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