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.
- Tribology Division
Analytical Solution for the Stress Field of Eshelby’s Inclusion of Polygonal Shape
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Jin, X, Keer, LM, & Wang, Q. "Analytical Solution for the Stress Field of Eshelby’s Inclusion of Polygonal Shape." Proceedings of the ASME/STLE 2009 International Joint Tribology Conference. ASME/STLE 2009 International Joint Tribology Conference. Memphis, Tennessee, USA. October 19–21, 2009. pp. 487-489. ASME. https://doi.org/10.1115/IJTC2009-15211
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