### 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 language | English (US) |
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Pages (from-to) | 10970-10973 |

Number of pages | 4 |

Journal | Physical Review B |

Volume | 38 |

Issue number | 15 |

DOIs | |

State | Published - Jan 1 1988 |

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### ASJC Scopus subject areas

- Condensed Matter Physics

### Cite this

*Physical Review B*,

*38*(15), 10970-10973. https://doi.org/10.1103/PhysRevB.38.10970

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

Research output: Contribution to journal › Article

*Physical Review B*, vol. 38, no. 15, pp. 10970-10973. https://doi.org/10.1103/PhysRevB.38.10970

}

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 -