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

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Macroscopic Properties of Disordered Media

Part of the book series: Lecture Notes in Physics ((LNP,volume 154))

Abstract

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.

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Author information

Authors and Affiliations

  1. Laboratory of Atomic and Solid State Physics and Materials Science Center, Clark Hall, Cornell University, 14853, Ithaca, NY, USA

    G. W. Milton

  2. Department of Theoretical Physics, The University of Sydney, 2006, Sydney, N.S.W., Australia

    R. C. McPhedran

Authors
  1. G. W. Milton
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  2. R. C. McPhedran
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Editor information

R. Burridge S. Childress G. Papanicolaou

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© 1982 Springer-Verlag

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Milton, G.W., McPhedran, R.C. (1982). A comparison of two methods for deriving bounds on the effective conductivity of composites. In: Burridge, R., Childress, S., Papanicolaou, G. (eds) Macroscopic Properties of Disordered Media. Lecture Notes in Physics, vol 154. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-11202-2_13

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  • DOI: https://doi.org/10.1007/3-540-11202-2_13

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11202-0

  • Online ISBN: 978-3-540-39031-2

  • eBook Packages: Springer Book Archive

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