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

En-Bo Wei, Y. M. Poon
2005 Journal of Applied Physics  
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 i ͑r͒ = c͑b + r͒ k ͑where r is the radius of the cylindrical inclusions and c , b and k are parameters͒. Analytical solutions for the local electrical potentials are derived in terms of hypergeometric functions and the effective dielectric response of the graded
more » ... onse of the graded composites is predicted in the dilute limit. Moreover, for a simple power-law dielectric profile i ͑r͒ = cr k and a linear dielectric profile i ͑r͒ = c͑b + r͒, 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, i ͑r͒ = c͑b + r͒ k e ␤r . to 158.132.161.9. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissions ⌽ h ͑r,͒ = − ͑r + a 2 Br −1 ͒E 0 cos͑͒, ͑12͒ 014104-2 E.-B. Wei and Y. M. Poon J. Appl. Phys. 98, 014104 ͑2005͒
doi:10.1063/1.1947388 fatcat:hwwqcrfhhvcazaisajjvnbwjdq