Abstract

In the analysis of neutral coated circular holes in an isotropic medium, it is well-known that neutrality to a general class of applied uniform fields can be realized only by the concentrically coated circle construction. It is of interest to examine to what degree eccentric circular coatings can be used to achieve effective or near-neutrality in the presence of a wider and more general class of applied fields. To this end, we consider the neutrality of a circular elastic inclusion bonded to its surrounding matrix through $N-\mathfrak{2}$ eccentric circular coatings ($N\ge \mathfrak{3}$) when the matrix is subjected to remote nonuniform antiplane shear stresses characterized by arbitrary polynomials of order $M\le N-\mathfrak{2}$. In our design, the first $N-M-\mathfrak{1}$ generalized polarization tensors associated with the $N$-phase structure vanish. Our results demonstrate conclusively that for arbitrary applied nonuniform fields, the stress disturbance in the matrix becomes negligible as $N$ becomes sufficiently large, indicating that the inclusion can be made “near-neutral” for a given $N$ and completely neutral as $N$ approaches infinity.

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Mathematical Subject Classification 2010

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