Random heterogeneous media: Hicrosttucture and improwed bounds on effective properties

Research output: Contribution to journalArticle

514 Scopus citations

Abstract

The purpose of the present article is to review recent advances made in the determination and calculation of improved bounds on the effective properties of random heterogeneous media that depend upon the microstructure via n-point correlation functions. New breakthroughs made in the quantitative characterization of the microstructure of heterogeneous materials are also reviewed. The following four different effective properties shall be studied: (i) effective conductivity tensor (which includes, by mathematical analogy, the dielectric constant, magnetic permeability, and diffusion coefficient); (ii) effective stiffness tensor; (iii) diffusioncontrolled trapping constant; and (iv) fluid permeability tensor. It shall be demonstrated that improved upper and lower bounds can provide a relatively sharp estimate of the effective property even when the bounds diverge from one another. Although this article reviews stateof- the-art advances in the field, an attempt will be made to elucidate methods and principles for the nonexpert.

Original languageEnglish (US)
Pages (from-to)37-76
Number of pages40
JournalApplied Mechanics Reviews
Volume44
Issue number2
DOIs
StatePublished - Feb 1991
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mechanical Engineering

Fingerprint Dive into the research topics of 'Random heterogeneous media: Hicrosttucture and improwed bounds on effective properties'. Together they form a unique fingerprint.

  • Cite this