Analytical solution for the stress field of Eshelby's inclusion of polygonal shape

Xiaoqing Jin*, Leon M. Keer, Qian Wang

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Scopus citations

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.

Original languageEnglish (US)
Title of host publicationProceedings of the ASME/STLE International Joint Tribology Conference 2009, IJTC2009
Pages487-489
Number of pages3
DOIs
StatePublished - Jun 24 2010
Event2009 ASME/STLE International Joint Tribology Conference, IJTC2009 - Memphis, TN, United States
Duration: Oct 19 2009Oct 21 2009

Publication series

NameProceedings of the ASME/STLE International Joint Tribology Conference 2009, IJTC2009

Other

Other2009 ASME/STLE International Joint Tribology Conference, IJTC2009
CountryUnited States
CityMemphis, TN
Period10/19/0910/21/09

ASJC Scopus subject areas

  • Colloid and Surface Chemistry
  • Fluid Flow and Transfer Processes
  • Surfaces and Interfaces

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