Dielectric response of graded composites having general power-law-graded cylindrical inclusions

Abstract

The dielectric response of graded composites having general power-law-graded cylindrical inclusions under a uniform applied electric field is investigated. The dielectric profile of the cylindrical inclusions is modeled by the equation εᵢ(r)=c(b+r)ᵏ(where r is the radius of the cylindrical inclusions and c, b and k are parameters). Analytical solutions for the local electrical potentials are derived in terms of hypergeometric functions and the effective dielectric response of the graded composites is predicted in the dilute limit. Moreover, for a simple power-law dielectric profile εᵢ(r)=crᵏ and a linear dielectric profile εᵢ(r)=c(b+r), analytical expressions of the electrical potentials and the effective dielectric response are derived exactly from our results by taking the limits b→0 and k→1, respectively. For a higher concentration of inclusions, the effective dielectric response is estimated by an effective-medium approximation. In addition, we have discussed the effective response of graded cylindrical composites with a more complex dielectric profile of inclusion, εᵢ(r)=c(b+r)ᵏeᵝʳ.