Effective stiffness tensor of composite media: II. Applications to isotropic dispersions

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Accurate approximate relations for the effective elastic moduli of two- and three-dimensional isotropic dispersions are obtained by truncating, after third-order terms, an exact series expansion for the effective stiffness tensor of d-dimensional two-phase composites (obtained in the first paper) that perturbs about certain optimal dispersions. Our third-order approximations of the effective bulk modulus Ke and shear modulus Ge are compared to benchmark data, rigorous bounds and popular self-consistent approximations for a variety of macroscopically isotropic dispersions in both two and three dimensions, for a wide range of phase moduli and volume fractions. Generally, for the cases considered, the third-order approximations are in very good agreement with benchmark data, always lie within rigorous bounds, and are superior to popular self-consistent approximations.

Original languageEnglish (US)
Pages (from-to)1411-1440
Number of pages30
JournalJournal of the Mechanics and Physics of Solids
Issue number8
StatePublished - Aug 1 1998

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


  • Elastic material
  • Microstructures
  • Particulate reinforced material


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