On Maxwells concept of equivalent inhomogeneity: When do the interactions matter?

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The concept of Maxwells equivalent inhomogeneity is re-evaluated in the context of the effective elastic properties of unidirectional multi-phase composite materials with the fibers of circular cross-section. The following key questions are addressed in this paper. Is the concept of equivalent inhomogeneity valid only for the materials with low volume fractions, as originally suggested by Maxwell? When do the interactions among the fibers matter? Could Maxwells concept be generalized to allow for accurate estimates of the effective properties? The approach advocated in the paper provides an unique opportunity to study, in the framework of one model, the effects of the interactions among fibers on the effective transversely isotropic elastic properties of multi-phase composite materials.

Original languageEnglish (US)
Pages (from-to)391-417
Number of pages27
JournalJournal of the Mechanics and Physics of Solids
Issue number3
StatePublished - Mar 2012


  • Elastic properties
  • Maxwell approximation formula
  • Multi-phase fiber-reinforced composites

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