Modeling nonlinear dielectric properties of laminated composites

Abstract

sThe article is devoted to the development of a method for predicting the nonlinear dielectric properties of layered composites with complex dependences of the dielectric constant on the electric field strength, which consider the effects of a sharp increase and subsequent decrease in the dielectric constant with increasing field strength. The method is based on the use of the theory of asymptotic averaging proposed by N.S. Bakhvalov, E. Sanchez-Palencia, in relation to the nonlinear problem of electrostatics in a layered medium. As a result of applying this method, local nonlinear problems of electrostatics on a periodicity cell are formulated, and an algorithm for calculating effective nonlinear dielectric constants is proposed. It is shown that a layered composite is a transversely isotropic nonlinear dielectric material if its layers are 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. Calculations have shown that the developed method for calculating the nonlinear-dielectric ratios of composites is quite effective and makes it possible to predict the dielectric properties of composites at various values of the electric field strength, including the regions where the dielectric permittivities of the layer materials are saturated. The developed technique can serve as a basis for designing new nonlinear dielectric composite materials with unusual properties.