A closed-form solution for the Eshelby Tensor and the elastic field outside an Elliptic Cylindrical Inclusion

Xiaoqing Jin*, Leon M. Keer, Qian Wang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

33 Scopus citations


From the analytical formulation developed by Ju and Sun [1999, "A Novel Formulation for the Exterior-Point Eshelby's Tensor of an Ellipsoidal Inclusion," ASME Trans. J. Appl. Mech., 66, pp. 570-574], it is seen that the exterior point Eshelby tensor for an ellipsoid inclusion possesses a minor symmetry. The solution to an elliptic cylindrical inclusion may be obtained as a special case of Ju and Sun's solution. It is noted that the closed-form expression for the exterior-point Eshelby tensor by Kim and Lee [2010, "Closed Form Solution of the Exterior-Point Eshelby Tensor for an Elliptic Cylindrical Inclusion," ASME Trans. J. Appl. Mech., 77, p. 024503] violates the minor symmetry. Due to the importance of the solution in micromechanics-based analysis and plane-elasticity-related problems, in this work, the explicit analytical solution is rederived. Furthermore, the exterior-point Eshelby tensor is used to derive the explicit closed-form solution for the elastic field outside the inclusion, as well as to quantify the elastic field discontinuity across the interface. A benchmark problem is used to demonstrate a valuable application of the present solution in implementing the equivalent inclusion method.

Original languageEnglish (US)
Article number031009
JournalJournal of Applied Mechanics, Transactions ASME
Issue number3
StatePublished - Feb 25 2011


  • exterior field
  • exterior-point Eshelby tensor
  • inclusion
  • micromechanics

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

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