Eshelby Tensor of a Polygonal Inclusion and its Special Properties |
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Authors: | Mishio Kawashita Hideaki Nozaki |
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Institution: | (1) Department of Mathematics, Graduate School of Science, Hiroshima University, Higashi-Hiroshima 739-8526, Japan;(2) Faculty of Education, Ibaraki University, Mito, Ibaraki 310-8512, Japan |
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Abstract: | Nozaki and Taya (ASME J. Appl. Mech. 64 (1997) 495–502) analyzed the elastic field in a convex polygonal inclusion in an infinite body. By numerical analysis, they
found that, when the shape of the inclusion is a regular polygon, “the strain at the center of inclusion” and “the strain
energy per unit volume of inclusion” have strange and remarkable properties: these values are the same as those of a circular
inclusion and are invariant for inclusion's orientation if the shape of the inclusion is not a square. In this paper, we first derive a simple, exact expression of the Eshelby tensor for an arbitrary polygonal inclusion. Using
the expression, we then show a mathematical explanation why these special properties appear.
This revised version was published online in July 2006 with corrections to the Cover Date. |
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Keywords: | polygonal inclusion eigenstrain Eshelby tensor strain strain energy regular polygon |
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