Application of the integral equation method for electrodynamic parameters calculation of composites based on conducting fibres

Abstract

One of the most perspective directions in the field of composites development is the use of materials on the basis of dielectric matrices containing metal fibres inclusions with arbitrary configuration. These materials due to their advantages over similar ones, containing volumetric particles (small concentration of metal, small weight and high efficiency) are intensively used in practice. Production of such materials requires to elaborate the appropriate mathematical tool, that allow to carry out the modeling of a composite taking into account its micro- and macrostructure. The basic task is to determine effective electrodynamic parameters (EEP) of a composite by the geometry of a single inclusion, their electromagnetic properties and their distribution in a dielectric. In this case the decision is carried out in two steps. At the beginning, the scattering properties of inclusions are analyzed. Then, knowing a character of their distribution in a matrix, EEP are determined. The scattering properties of a particle are characterized by the polarizability factors (PF). The PF calculation is based on the numerical solution of Poklington's integral equation (IE) that describes the current distribution in thin-wire scatterers. The solution of IE is carried out by the collocation method with step basis function application. Since this IE is easily generalized for the case of impedance conductors, it enables to study the influence of particle conductivity on EEP of a composite.