Dielectric responses of graded composites having generalized gradation profiles

摘要

Under an external uniform electric field, the dielectric response of graded cylindrical composites having generalized dielectric profile inclusions is investigated. The generalized dielectric profile of graded cylindrical inclusion is expressed in the form,εi(γ) = c(b +γ)κeβγ where γ is the radial variable of the cylindrical inclusions and c,b,κand β are parameters. The local potential solution of generalized dielectric profile graded composites is derived by means of the power series method and the effective dielectric response is predicted in the dilute limit.Moreover,from the result of generalized profile, the analytical solutions of local potentials and the effective responses of graded composites having three cases of dielectric profiles,I.e.,the exponential profile εi(γ) = ceβγ, the general power law protile εi(γ) = c (b +γ)κ and the profileεi (γ) = cγκeβγ, are sorted out,respectively.In the dilute limit,our exact results are used to test the validity of differential effective dipole approximation (DEDA) for estimating the effective response of graded cylindrical composites,and it is shown that the DEDA is in excellent agreement with the exact result.