INCLUSION PAIRS SATISFYING ESHELBY'S UNIFORMITY PROPERTY

Title
INCLUSION PAIRS SATISFYING ESHELBY'S UNIFORMITY PROPERTY
Authors
Kang, H.; Kim, E.; Milton, G.W.
Keywords
Eshelby's conjecture, Polya-Szego conjecture, Weierstrass zeta function
Issue Date
2008
Publisher
SIAM PUBLICATIONS
Abstract
Eshelby conjectured that if for a given uniform loading the field inside an inclusion is uniform, then the inclusion must be an ellipse or an ellipsoid. This conjecture has been proved to be true in two and three dimensions provided that the inclusion is simply connected. In this paper we provide an alternative proof of Cherepanov's result that an inclusion with two components can be constructed inside which the field is uniform for any given uniform loading for two-dimensional conductivity or for antiplane elasticity. For planar elasticity, we show that the field inside the inclusion pair is uniform for certain loadings and not for others. We also show that the polarization tensor associated with the inclusion pair lies on the lower Hashin-Shtrikman bound, and hence the conjecture of Polya and Szego is not true among nonsimply connected inclusions. As a consequence, we construct a simply connected inclusion, which is nothing close to an ellipse, but in which the field is almost uniform.
URI
http://dspace.inha.ac.kr/handle/10505/1969
ISSN
0036-1399
Appears in Collections:
College of Natural Science(자연과학대학) > Mathematics (수학) > Journal Papers, Reports(수학 논문, 보고서)
Files in This Item:
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