Effective-medium theory for weakly nonlinear composites

X. C. Zeng, D. J. Bergman, P. M. Hui, D. Stroud

Research output: Contribution to journalArticle

253 Citations (Scopus)

Abstract

We propose an approximate general method for calculating the effective dielectric function of a random composite in which there is a weakly nonlinear relation between electric displacement and electric field of the form D=E+|E|2E, where and are position dependent. In a two-phase composite, to first order in the nonlinear coefficients 1 and 2, the effective nonlinear dielectric susceptibility is found to be e=i=1,2(ipi)(ei)0|ei|0, where e(0) is the effective dielectric constant in the linear limit (i=0,i=1,2) and i and pi are the dielectric function and volume fraction of the ith component. The approximation is applied to a calculation of e in the Maxwell-Garnett approximation (MGA) and the effective-medium approximation. For low concentrations of nonlinear inclusions in a linear host medium, our MGA reduces to the results of Stroud and Hui. An exact calculation of e is carried out for the Hashin-Shtrikman microgeometry and compared to our MG approximation.

Original languageEnglish (US)
Pages (from-to)10970-10973
Number of pages4
JournalPhysical Review B
Volume38
Issue number15
DOIs
StatePublished - Jan 1 1988

Fingerprint

composite materials
Composite materials
approximation
Volume fraction
Permittivity
Electric fields
low concentrations
inclusions
permittivity
magnetic permeability
electric fields
coefficients

ASJC Scopus subject areas

  • Condensed Matter Physics

Cite this

Effective-medium theory for weakly nonlinear composites. / Zeng, X. C.; Bergman, D. J.; Hui, P. M.; Stroud, D.

In: Physical Review B, Vol. 38, No. 15, 01.01.1988, p. 10970-10973.

Research output: Contribution to journalArticle

Zeng, XC, Bergman, DJ, Hui, PM & Stroud, D 1988, 'Effective-medium theory for weakly nonlinear composites', Physical Review B, vol. 38, no. 15, pp. 10970-10973. https://doi.org/10.1103/PhysRevB.38.10970
Zeng, X. C. ; Bergman, D. J. ; Hui, P. M. ; Stroud, D. / Effective-medium theory for weakly nonlinear composites. In: Physical Review B. 1988 ; Vol. 38, No. 15. pp. 10970-10973.
@article{b7baba3e88b74ba3940dfba2ec3efc1d,
title = "Effective-medium theory for weakly nonlinear composites",
abstract = "We propose an approximate general method for calculating the effective dielectric function of a random composite in which there is a weakly nonlinear relation between electric displacement and electric field of the form D=E+|E|2E, where and are position dependent. In a two-phase composite, to first order in the nonlinear coefficients 1 and 2, the effective nonlinear dielectric susceptibility is found to be e=i=1,2(ipi)(ei)0|ei|0, where e(0) is the effective dielectric constant in the linear limit (i=0,i=1,2) and i and pi are the dielectric function and volume fraction of the ith component. The approximation is applied to a calculation of e in the Maxwell-Garnett approximation (MGA) and the effective-medium approximation. For low concentrations of nonlinear inclusions in a linear host medium, our MGA reduces to the results of Stroud and Hui. An exact calculation of e is carried out for the Hashin-Shtrikman microgeometry and compared to our MG approximation.",
author = "Zeng, {X. C.} and Bergman, {D. J.} and Hui, {P. M.} and D. Stroud",
year = "1988",
month = "1",
day = "1",
doi = "10.1103/PhysRevB.38.10970",
language = "English (US)",
volume = "38",
pages = "10970--10973",
journal = "Physical Review B-Condensed Matter",
issn = "0163-1829",
publisher = "American Institute of Physics",
number = "15",

}

TY - JOUR

T1 - Effective-medium theory for weakly nonlinear composites

AU - Zeng, X. C.

AU - Bergman, D. J.

AU - Hui, P. M.

AU - Stroud, D.

PY - 1988/1/1

Y1 - 1988/1/1

N2 - We propose an approximate general method for calculating the effective dielectric function of a random composite in which there is a weakly nonlinear relation between electric displacement and electric field of the form D=E+|E|2E, where and are position dependent. In a two-phase composite, to first order in the nonlinear coefficients 1 and 2, the effective nonlinear dielectric susceptibility is found to be e=i=1,2(ipi)(ei)0|ei|0, where e(0) is the effective dielectric constant in the linear limit (i=0,i=1,2) and i and pi are the dielectric function and volume fraction of the ith component. The approximation is applied to a calculation of e in the Maxwell-Garnett approximation (MGA) and the effective-medium approximation. For low concentrations of nonlinear inclusions in a linear host medium, our MGA reduces to the results of Stroud and Hui. An exact calculation of e is carried out for the Hashin-Shtrikman microgeometry and compared to our MG approximation.

AB - We propose an approximate general method for calculating the effective dielectric function of a random composite in which there is a weakly nonlinear relation between electric displacement and electric field of the form D=E+|E|2E, where and are position dependent. In a two-phase composite, to first order in the nonlinear coefficients 1 and 2, the effective nonlinear dielectric susceptibility is found to be e=i=1,2(ipi)(ei)0|ei|0, where e(0) is the effective dielectric constant in the linear limit (i=0,i=1,2) and i and pi are the dielectric function and volume fraction of the ith component. The approximation is applied to a calculation of e in the Maxwell-Garnett approximation (MGA) and the effective-medium approximation. For low concentrations of nonlinear inclusions in a linear host medium, our MGA reduces to the results of Stroud and Hui. An exact calculation of e is carried out for the Hashin-Shtrikman microgeometry and compared to our MG approximation.

UR - http://www.scopus.com/inward/record.url?scp=0000642325&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000642325&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.38.10970

DO - 10.1103/PhysRevB.38.10970

M3 - Article

AN - SCOPUS:0000642325

VL - 38

SP - 10970

EP - 10973

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 0163-1829

IS - 15

ER -