A differential approach to microstructure-dependent bounds for multiphase heterogeneous media

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We present a new method of deriving microstructure-dependent bounds on the effective properties of general heterogeneous media. The microstructure is specified by the average Eshelby tensors. In the small contrast limit, we introduce and calculate the expansion coefficient tensors. We then show that the effective tensor satisfies a differential inequality with the initial condition given by the expansion coefficient tensors in the small contrast limit. Using the comparison theorem, we obtain rigorous bounds on the effective tensors of multiphase composites. These new bounds, taking into account the average Eshelby tensors for homogeneous problems, are much tighter than the microstructure-independent Hashin-Shtrikman bounds. Also, these bounds are applicable to non-well-ordered composites and multifunctional composites. We anticipate that this new approach will be useful for the modeling and optimal design of multiphase multifunctional composites.

Original languageEnglish (US)
Pages (from-to)1245-1266
Number of pages22
JournalActa Mechanica
Issue number4-5
StatePublished - Apr 2014

All Science Journal Classification (ASJC) codes

  • Computational Mechanics
  • Mechanical Engineering


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