Journal of Elasticity

, Volume 97, Issue 2, pp 173–188 | Cite as

Proof of the Strong Eshelby Conjecture for Plane and Anti-plane Anisotropic Inclusion Problems

  • Bai-Xiang Xu
  • Ying-Tao Zhao
  • Dietmar Gross
  • Min-Zhong Wang


Based on the Stroh formalism for anisotropic elasticity and the complex variable function method, we prove in this paper that the strong Eshelby conjecture holds for simply-connected anisotropic inclusion problems under plane or anti-plane deformation. The interfaces can be either perfect or dislocation-like. For these inclusion problems, if the induced stress field inside the inclusion is uniform for a single uniform eigenstrain, the inclusion is of the elliptic shape. Thanks to the generality of the proof method, we obtain also alternative proofs of the strong Eshelby conjecture for isotropic inclusion problems, which are given in the Appendix.


Eshelby inclusion problem Eshelby conjecture Anisotropic inclusion problems Dislocation-like interface 

Mathematics Subject Classification (2000)



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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  • Bai-Xiang Xu
    • 1
  • Ying-Tao Zhao
    • 2
  • Dietmar Gross
    • 3
  • Min-Zhong Wang
    • 1
  1. 1.State Key Laboratory for Turbulence and Complex Systems and Department of Mechanics and Aerospace Engineering, College of EngineeringPeking UniversityBeijingPeople’s Republic of China
  2. 2.Department of Applied MechanicsBeijing Institute of TechnologyBeijingPeople’s Republic of China
  3. 3.Division of Solid Mechanics, Department of Civil Engineering & GeodesyTU DarmstadtDarmstadtGermany

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