### 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 - 1988 |

### ASJC Scopus subject areas

- Condensed Matter Physics

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## Cite this

*Physical Review B*,

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