Dielectric responses of graded composites having generalized gradation profiles |
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Authors: | Wei En-Bo Gu Guo-Qing and Yu Kin-Wah |
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Institution: | Institute of Oceanology, Chinese Academy of Sciences, Qingdao 266071, China; School of Information Science and Technology, East China Normal University, Shanghai 200062, China; Department of Physics, The Chinese University of Hong Kong, Hong Kong, China |
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Abstract: | 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, $\varepsilon _i (r)=c(b+
r)^k\e^{\beta r}$ where $r$ is the radial variable of the cylindrical
inclusions and
$c$, $b$, $k$ and $\beta $ 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 $\varepsilon_\i (r)=c\e^{\beta r}$, the general power
law profile $\varepsilon_\i (r)=c(b+r)^k$ and the profile $\varepsilon_\i
(r)=cr^k\e^{\beta r}$, 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. |
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Keywords: | generalized profiles graded composite effective response |
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