Mathematical modelling of dielectric properties of nanostructural composites using asymptotic homogenizing method

The paper presents a mathematical model for calculating effective dielectric properties of the composites modified by nanoinclusionson exposure to the external oscillating electrical field. The model is based on the asymptotic homogenizing method for differential equations of electrodynamics with rapidly oscillating coefficients. The local problem of electrodynamics on a composite periodicity cell is formulated. To solve the problem, the authors use the method of finite elements implemented in the SMCM software package developed in the Scientific Educational Center SIMPLEX at Bauman Moscow State Technical University. Both the CSIR storage schemes of discharged matrices and the method of biconjugate gradients are used. A settlement cycle of complex effective inductive capacity of a polymer composite with different carbon nanotube concentrations is performed. The authors consider the influence of nanotube cluster formations on generation of the nonmonotonous concentration dependence of the composite inductive capacity. The analysis of frequency dependence of dielectric loss tangent is carried out resulting in a good agreement with the experimental data.

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