Markevich

In this paper, the authors presented a mathematical model for calculating effective dielectric characteristics of complex structured composite materials influenced by an external alternating electric field. An asymptotic investigation of electro-dynamic differential equations with fast oscillating coefficients was carried out. A local electro-dynamic problem on the composite’s “periodicity cell” was formulated. An effective complex permittivity of composite materials with various volume fractions of the fine-dispersed ferroelectric ceramic inclusions was calculated by the finite element method and the biconjugate gradient stabilized method. The authors analyzed frequency dependence of dielectric characteristics and dielectric loss tangent of composite ceramics. The obtained results are good congruous to experimental data.

In this paper, the authors consider calculation of effective dielectric parameters of composite materials with complex three-dimensional armoring. The method of asymptotic averaging of periodic structures is used for averaging of long-term quasi-static electric fields in composites with dielectric components. Series of local electrostatic tasks were formulated with the use of periodicity cells; electrostatic variational problems were also formulated. To solve spatial local problems for composite materials with three-dimensional complex armoring, the finite element numerical method was used. In this article, the authors proposed an algorithm for computation of effective tensor of dielectric permeability of three-dimensional armored composite materials. Test computations were carried out in order to obtain distribution of the local electric field, effective dielectric characteristics of three-dimensional orthogonal armored composite materials with different inclusion volume fractions.