539.3 Modeling nonlinear dielectric properties of composites based on the asymptotic homogenization method

Dimitrienko Y. I. (Bauman Moscow State Technical University), Gubareva E. A. (Bauman Moscow State Technical University), Zubarev K. M. (Bauman Moscow State Technical University)


doi: 10.18698/2309-3684-2020-2-2645

The paper is devoted to the development of a method for calculating the nonlinear dielectric properties of composites with a periodic structure. Methods for predicting of the nonlinear dielectric properties of composites play an important role in the design of dielectric materials with specified properties, in particular for heterogeneous ferroelectrics, which are widely used to create various devices and electrical devices, for example, to create memory storage devices for computers. A quasi-static problem of the distribution of an electric charge in an inhomogeneous polarizable medium with a periodic structure and nonlinear dielectric properties is considered. To solve this nonlinear problem, the asymptotic homogenization method proposed by N.S. Bakhvalov, E. Sanchez-Palencia, B.E. Pobedria. As a result, local nonlinear problems of electrostatics on the periodicity cell are formulated, an algorithm for calculating effective nonlinear constitutive relations for dielectric properties, and an averaged problem for a composite with effective properties are proposed. For the case of a composite with a layered structure, the solution of local problems is obtained, and effective defining relations for the nonlinear dielectric properties of the composite are constructed. It is shown that a laminated composite is a transversely isotropic nonlinear dielectric material if it is isotropic materials. A numerical example of calculating the nonlinear properties of a 2-layer composite based on barium titanate and ferroelectric ceramic varicond VK4 is considered. A model is proposed that describes the nonlinear dependence of the dielectric constant of these materials on the vector of the electric field strength. It is shown that the nonlinear dependence of the dielectric constant tensor of the composite on the strength vector differs significantly for the direction of the field in the plane of the layers and in the transverse direction. It is shown that the developed technique can serve as a basis for designing nonlinear dielectric composite materials with anisotropic properties.

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Димитриенко Ю.И., Губарева Е.А., Зубарев К.М. Моделирование нелинейных диэлектрических свойств композитов на основе метода асимптотической гомогенизации. Математическое моделирование и численные методы. 2020. № 2. с. 26–45

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