Vol. 3, No. 2, 2015

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Neutrality of eccentrically coated elastic inclusions

Xu Wang and Peter Schiavone

Vol. 3 (2015), No. 2, 163–175

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 2 eccentric circular coatings (N 3) when the matrix is subjected to remote nonuniform antiplane shear stresses characterized by arbitrary polynomials of order M N 2. In our design, the first N M 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.

neutral inclusion, remote nonuniform loading, multiple coating, Apollonius circles, generalized polarization tensor
Mathematical Subject Classification 2010
Primary: 74B05
Secondary: 74M25
Received: 1 November 2013
Revised: 13 February 2014
Accepted: 21 April 2014
Published: 16 May 2015

Communicated by Francesco dell'Isola
Xu Wang
School of Mechanical and Power Engineering
East China University of Science and Technology
130 Meilong Road
Shanghai, 200237
Peter Schiavone
Department of Mechanical Engineering
University of Alberta
4-9 Mechanical Engineering Building
Edmonton, Alberta
Canada T6G 2G8