Evaluation of Dielectric Permittivity of Composite with Dispersed Inclusions

The article discusses the sequential estimation of dielectric permittivity of a composite with dispersed inclusions. The estimation process starts with using the variational formulation of the electrostatics problem for isotropic continuous medium and it finishes by applying the theory of blenders. The variational approach allows both performing two-sided estimates of the true value of dielectric permittivity for a composite and finding the maximum possible error of the value, which corresponds to the half-sum of the calculated estimates. The proposed mathematical model of the representative element of the composite structure causes the computational correspondence, which coincides with the formulae for magnetic permittivity and thermal conductivity of heterogeneous bodies, to an accuracy of notations. This fact can be considered as an explicit confirmation of the model adequacy. The presented estimates allow predicting effective values of the dielectric permittivity of heterogeneous materials including the composites with tailored matrix electric properties and dispersed inclusions, which can be used as nanostructure elements.

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