Determination of the overall moduli in second order incompressible elasticity

Ali Imam, George C. Johnson, Mauro Ferrari

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


The problem of finding the overall second order elastic moduli for a biphase material is considered. The material consists of an incompressible isotropic matrix containing a dilute concentration of spherical inhomogeneities which are also incompressible and isotropic. To evaluate the effective moduli, the second order elastic field of a single inhomogeneity in an infinite matrix under homogeneous displacement boundary conditions is determined. This elastic field is assumed to approximate that of the composite with a dilute concentration of the second phase. No interaction between the particles is considered. Subsequently, through the equality of the strain energies of the inhomogeneous material and an equivalent homogeneous material, explicit expressions for the overall elastic constants are obtained.

Original languageEnglish (US)
Pages (from-to)1087-1104
Number of pages18
JournalJournal of the Mechanics and Physics of Solids
Issue number7
StatePublished - Jul 1995

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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