A differential scheme for the effective moduli of composites

Research output: Contribution to journalArticlepeer-review

547 Scopus citations


A differential scheme to compute the effective moduli of composites is presented. The method is based on the idea of realizability, i.e. the composite is constructed explicitly from an initial material through a series of incremental additions. The construction process is uniquely specified by parametrizing the volume fractions of the included phases. The properties of the final composite depend upon the construction path taken and not just on the final volume fractions. Assuming the grain shapes are ellipsoidal, a system of ordinary differential equations for the moduli is obtained which is integrated along the path. The present method includes as special cases of paths or endpoints the differential scheme of Roscoe-Boucher and the self-consistent scheme of Kroner-Hill, respectively. The method includes a realization of the Hashin-Shtrikman bounds for a two-phase composite with K(1 2- K2)(μ1 - μ2) {slanted equal to or greater-than} 0. For example, the upper bounds are achieved by imbedding disks of the stiffer material in a matrix of the more compliant material.

Original languageEnglish (US)
Pages (from-to)1-16
Number of pages16
JournalMechanics of Materials
Issue number1
StatePublished - Mar 1985
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Materials Science(all)
  • Instrumentation
  • Mechanics of Materials

Fingerprint Dive into the research topics of 'A differential scheme for the effective moduli of composites'. Together they form a unique fingerprint.

Cite this