Limit transitions in plane homogenization problems for two-phase dielectric composites with extreme material properties of one phase

Abstract

The plane problem of calculating the effective dielectric constant of two-phase composite consisting of main material with one circular inclusion is considered. To solve the homogenization problem, the method of effective moduli with the support of the energy balance between the composite and the homogeneous comparison medium was used. In the solution obtained, the passage to the limit was made for the case of an inclusion with zero dielectric constant and for the case of a conductive inclusion. The limiting solutions are compared with the solutions of homogenization problems for a medium with a hollow and for a medium with a conducting inclusion boundary.