О предельных переходах в пространственных задачах гомогенизации двухкомпонентных диэлектрических композитов с экстремальными модулями одной из фаз

Abstract

The spatial problem of calculating the effective permittivity of two-component composite, consisting of a base material filling a spherical layer and one spherical inclusion, is considered. The homogenization problem is solved by effective moduli method with calculation of the energy characteristics in the composite medium and in its individual phases. In the obtained solution, the limit transitions are made for two extreme cases: pores or inclusions with zero dielectric constant and conductive inclusions with infinitely high dielectric constant. The solutions of these problems are compared with the solutions of homogenization problems for a medium with void and for a medium with conductive inclusion boundary. In problems with one basic material, the properties of inclusions were taken into account only by the corresponding boundary conditions on the interface. It is shown that calculations of the effective permittivity by energy criterion give correct results in all the cases considered, while the calculations by the average permittivity for a composite with a conductive inclusion boundary may be erroneous.