International Journal of Fracture

, Volume 211, Issue 1–2, pp 149–162 | Cite as

Calculation of T-stress for cracks in two-dimensional anisotropic elastic media by boundary integral equation method

  • Han D. Tran
  • Mark E. Mear
Original Paper


A numerical procedure is proposed to compute the T-stress for two-dimensional cracks in general anisotropic elastic media. T-stress is determined from the sum of crack-face displacements which are computed via an integral equation of the boundary data. To smooth out the data in order to perform accurately numerical differentiation, the sum of crack-face displacement is established in a weak-form integral equation in which the integration domain is simply the crack-tip element. This weak-form integral equation is then solved numerically using standard Galerkin approximation to obtain the nodal values of the sum of crack-face displacements. The procedure is incorporated in a weakly-singular symmetric Galerkin boundary element method in which all integral equations for the traction and displacement on the boundary of the domain and on the crack faces include (at most) weakly-singular kernels. To examine the accuracy and efficiency of the developed method, various numerical examples for cracks in infinite and finite domains are treated. It is shown that highly accurate results are obtained using relatively coarse meshes.


T-stress SGBEM Crack Anisotropic Weakly singular 


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© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Computational EngineeringVietnamese-German UniversityBinh DuongVietnam
  2. 2.Department of Aerospace Engineering and Engineering MechanicsThe University of Texas at AustinAustinUSA

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