TY - GEN

T1 - Analytical solution for the stress field of Eshelby's inclusion of polygonal shape

AU - Jin, Xiaoqing

AU - Keer, Leon M.

AU - Wang, Qian

PY - 2010/6/24

Y1 - 2010/6/24

N2 - 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.

AB - 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.

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U2 - 10.1115/IJTC2009-15211

DO - 10.1115/IJTC2009-15211

M3 - Conference contribution

AN - SCOPUS:77953707581

SN - 9780791848951

T3 - Proceedings of the ASME/STLE International Joint Tribology Conference 2009, IJTC2009

SP - 487

EP - 489

BT - Proceedings of the ASME/STLE International Joint Tribology Conference 2009, IJTC2009

T2 - 2009 ASME/STLE International Joint Tribology Conference, IJTC2009

Y2 - 19 October 2009 through 21 October 2009

ER -