View : 107 Download: 0

Inclusion pairs satisfying eshelby's uniformity property

Title
Inclusion pairs satisfying eshelby's uniformity property
Authors
Kang H.Eunjoo K.I.M.Milton G.W.
Ewha Authors
김은주
Issue Date
2008
Journal Title
SIAM Journal on Applied Mathematics
ISSN
0036-1399JCR Link
Citation
vol. 69, no. 2, pp. 577 - 595
Indexed
SCI; SCIE; SCOPUS WOS scopus
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 Pólya and Szegö 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. © 2008 Society for Industrial and Applied Mathematics.
DOI
10.1137/070691358
Appears in Collections:
연구기관 > 수리과학연구소 > Journal papers
Files in This Item:
There are no files associated with this item.
Export
RIS (EndNote)
XLS (Excel)
XML


qrcode

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.

BROWSE