Abstract
The effective property has been investigated theoretically in graded elliptical cylindrical composites consisting of inhomogeneous graded elliptical cylinders and an isotropic matrix under external uniform electric field. As a theoretical model, the dielectric gradient profile in the elliptical cylinder is modeled by a power-law function of short semi-axis variable parameter ( ξ 2 - 1 ) in the elliptical cylindrical coordinates, namely ε i ( ξ ) = c k ( ξ 2 - 1 ) k , where c k and k are the parameters, and ξ is the long semi-axis space variable in an elliptical cylindrical inclusion region. In the dilute limit, the local analytical potentials in inclusion and matrix regions are derived exactly by means of the hyper-geometric function, and the formulas are given for estimating the effective dielectric responses under the external field along x ^ - and y ^ -directions, respectively. Furthermore, we have demonstrated that our effective response formulas can be reduced to the well-known results of homogeneous isotropic elliptical cylindrical composites if we take the limit k → 0 in graded elliptical cylindrical composites.
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