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Title: Dielectric response of graded composites having general power-law-graded cylindrical inclusions
Authors: Wei, EB
Poon, YM
Keywords: Dielectric materials
Composite materials
Issue Date: 1-Jul-2005
Publisher: American Institute of Physics
Source: Journal of applied physics, 1 July 2005, v. 98, no. 1, 014104, p. 1-5 How to cite?
Journal: Journal of applied physics 
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.
ISSN: 0021-8979 (print)
1089-7550 (online)
DOI: 10.1063/1.1947388
Rights: © 2005 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in E. B. Wei & Y. M. Poon, J. Appl. Phys. 98, 014104 (2005) and may be found at
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