New method to generate three-point bounds on effective properties of composites: Application to viscoelasticity

L. V. Gibiansky, Salvatore Torquato

Research output: Contribution to journalArticle

15 Scopus citations

Abstract

The general goal of this paper is to develop a new approach for bounding the effective moduli (e.g. elastic moduli, conductivity, or thermal expansion coefficients) of composite materials. Specifically, this paper aims to: (1) formulate a procedure that combines the translation method and the Beran procedure into one powerful method that has the advantages of both approaches; and (2) apply the new method to study effective properties of viscoelastic composites. The new method enables one to get the most restrictive three-point geometrical-parameter bounds. In particular, we obtain new three-point bounds on the complex bulk modulus of an isotropic viscoelastic composite. The new bounds are given by the outermost of several circular arcs in the complex bulk modulus plane. They take into account three-point statistical information and thus are much more restrictive than previously known two-point bounds.

Original languageEnglish (US)
Pages (from-to)749-783
Number of pages35
JournalJournal of the Mechanics and Physics of Solids
Volume46
Issue number4
DOIs
StatePublished - Jan 1 1998

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

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