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Analytical Solution for the Stress Field of Eshelby’s Inclusion of Polygonal Shape

[+] Author Affiliations
Xiaoqing Jin, Leon M. Keer, Qian Wang

Northwestern University, Evanston, IL

Paper No. IJTC2009-15211, pp. 487-489; 3 pages
doi:10.1115/IJTC2009-15211
From:
  • ASME/STLE 2009 International Joint Tribology Conference
  • ASME/STLE 2009 International Joint Tribology Conference
  • Memphis, Tennessee, USA, October 19–21, 2009
  • Conference Sponsors: Tribology Division
  • ISBN: 978-0-7918-4895-1 | eISBN: 978-0-7918-3862-4
  • Copyright © 2009 by ASME

abstract

Recently, we developed a closed-form solution to the stress field due to a point eigenstrain in an elastic full plane. This solution can be employed as a Green’s function to compute the stress field caused by an arbitrary-shaped Eshelby’s inclusion subjected to any distributed eigenstrain. In this study, analytical expressions are derived when uniform eigenstrain is distributed in a planar inclusion bounded by line elements. Here it is demonstrated that both the interior and exterior stress fields of a polygonal inclusion subjected to uniform eigenstrain can be represented in a unified expression, which consists of only elementary functions. Singular stress components are identified at all the vertices of the polygon. These distinctive properties contrast to the well-known Eshelby’s solution for an elliptical inclusion, where the interior stress field is uniform but the formulae for the exterior field are remarkably complicated. The elementary solution of a polygonal inclusion has valuable application in the numerical implementation of the equivalent inclusion method.

Copyright © 2009 by ASME
Topics: Stress , Shapes

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