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Special properties of Eshelby tensor for a regular polygonal inclusion

Special properties of Eshelby tensor for a regular polygonal inclusion Abstract When studying the regular polygonal inclusion in 1997, Nozaki and Taya discovered numerically some remarkable properties of Eshelby tensor: Eshelby tensor at the center and the averaged Eshelby tensor over the inclusion domain are equal to that of a circular inclusion and independent of the orientation of the inclusion. Then Kawashita and Nozaki justified the properties mathematically. In the present paper, some other properties of a regular polygonal inclusion are discovered. We find that for an N-fold regular polygonal inclusion except for a square, the arithmetic mean of Eshelby tensors at N rotational symmetrical points in the inclusion is also equal to the Eshelby tensor for a circular inclusion and independent of the orientation of the inclusion. Furthermore, in two corollaries, we point out that Eshelby tensor at the center, the averaged Eshelby tensor over the inclusion domain, and the line integral average of Eshelby tensors along any concentric circle of the inclusion are all identical with the arithmetic mean. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png "Acta Mechanica Sinica" Springer Journals

Special properties of Eshelby tensor for a regular polygonal inclusion

"Acta Mechanica Sinica" , Volume 21 (3): 5 – Jun 1, 2005

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References (11)

Publisher
Springer Journals
Copyright
2005 Springer-Verlag Berlin Heidelberg
ISSN
0567-7718
eISSN
1614-3116
DOI
10.1007/s10409-005-0034-x
Publisher site
See Article on Publisher Site

Abstract

Abstract When studying the regular polygonal inclusion in 1997, Nozaki and Taya discovered numerically some remarkable properties of Eshelby tensor: Eshelby tensor at the center and the averaged Eshelby tensor over the inclusion domain are equal to that of a circular inclusion and independent of the orientation of the inclusion. Then Kawashita and Nozaki justified the properties mathematically. In the present paper, some other properties of a regular polygonal inclusion are discovered. We find that for an N-fold regular polygonal inclusion except for a square, the arithmetic mean of Eshelby tensors at N rotational symmetrical points in the inclusion is also equal to the Eshelby tensor for a circular inclusion and independent of the orientation of the inclusion. Furthermore, in two corollaries, we point out that Eshelby tensor at the center, the averaged Eshelby tensor over the inclusion domain, and the line integral average of Eshelby tensors along any concentric circle of the inclusion are all identical with the arithmetic mean.

Journal

"Acta Mechanica Sinica"Springer Journals

Published: Jun 1, 2005

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