A comparison of two methods for deriving bounds on the effective conductivity of composites

  • G. W. Milton
  • R. C. McPhedran
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 154)


An infinite set of bounds on the effective conductivity σe of a two-component composite has previously been derived using the analytic properties ofσc as a function of σ1 and σ2 (the conductivities of the components). We show that this same set of bounds can alternatively be derived from variational principles. The bounds incorporate information about the microstructure of the composite in addition to the volume fractions of the components.


Variational Principle Effective Conductivity Face Centered Cubic Body Center Cubic Simple Cubic 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Z. Hashin and S. Shtrikman, J. Appl. Phys. 33, 3125 (1962).Google Scholar
  2. 2.
    W. F. Brown, Trans. Soc. Rheol. 9, 357 (1965).Google Scholar
  3. 3.
    M. Beran, Nuovo Cimento 38, 771 (1965).Google Scholar
  4. 4.
    D. J. Bergman, Phys. Rep. 43, 377 (1978).Google Scholar
  5. 5.
    G. W. Milton, J. Appl. Phys., in press.Google Scholar
  6. 6.
    W. F. Brown, J. Chem. Phys. 23, 1514 (1955).Google Scholar
  7. 7.
    R. C. McPhedran and G. W. Milton, submitted to Appl. Phys.Google Scholar
  8. 8.
    O. Wiener, Abh. Math. Phys. Kl. Königl, Saechs. Ges. 32, 509 (1912).Google Scholar
  9. 9.
    N. Phan-Thien and G. W. Milton, submitted to Proc. Roy. Soc. Lond.Google Scholar
  10. 10.
    M. A. Elsayed, J. Math. Phys. 15, 2001 (1974).Google Scholar
  11. 11.
    D. J. Bergman, Phys. Rev. Lett. 44, 1285 (1980).Google Scholar
  12. 12.
    G. W. Milton, Appl. Phys. Lett. 37, 300 (1980).Google Scholar

Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • G. W. Milton
    • 1
  • R. C. McPhedran
    • 2
  1. 1.Laboratory of Atomic and Solid State Physics and Materials Science Center, Clark HallCornell UniversityIthacaUSA
  2. 2.Department of Theoretical PhysicsThe University of SydneySydneyAustralia

Personalised recommendations