New optimal microstructures and restrictions on the attainable Hashin-Shtrikman bounds for multiphase composite materials

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We address the attainability of the Hashin-Shtrikman (HS) bounds for multiphase composite materials. We demonstrate that the HS bounds are not always attainable and give new restrictions on the attainable HS bounds in terms of the conductivities and volume fractions of the constituent phases. New optimal microstructures are also constructed to attain the HS bounds. Combined together, these results allow for precise characterization of the set of effective properties for a wide range of composite materials.

Original languageEnglish (US)
Pages (from-to)473-482
Number of pages10
JournalPhilosophical Magazine Letters
Issue number7
StatePublished - Jul 1 2011
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics


  • Hashin-Shtrikman bounds
  • composite materials
  • new optimal microstructures

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