Bulk properties of composite media. I. Simplification of bounds on the shear modulus of suspensions of impenetrable spheres

Asok K. Sen, F. Lado, S. Torquato

Research output: Contribution to journalArticle

4 Scopus citations

Abstract

We study third-order upper and lower bounds on the shear modulus of a model composite made up of equisized, impenetrable spherical inclusions randomly distributed throughout a matrix phase. We determine greatly simplified expressions for the two key multidimensional cluster integrals (involving the three-point distribution function for one of the phases) arising in these bounds. These expressions are obtained by expanding the orientation-dependent terms in the integrand in spherical harmonics and employing the orthogonality property of this basis set. The resulting simplified integrals are in a form that makes them much easier to compute. The approach described here is quite general in the sense that it has application in cases where the spheres are permeable to one another (models of consolidated media such as sandstones and sintered materials) and to the determination of other bulk properties, such as the bulk modulus, thermal/electrical conductivity, and fluid permeability.

Original languageEnglish (US)
Pages (from-to)3503-3513
Number of pages11
JournalJournal of Applied Physics
Volume62
Issue number9
DOIs
StatePublished - Dec 1 1987
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

Fingerprint Dive into the research topics of 'Bulk properties of composite media. I. Simplification of bounds on the shear modulus of suspensions of impenetrable spheres'. Together they form a unique fingerprint.

  • Cite this