International Journal of Fracture

, Volume 179, Issue 1–2, pp 45–57 | Cite as

Modeling mixed-mode fracture propagation in isotropic elastic three dimensional solid

  • Chunfang MengEmail author
  • Frantz Maerten
  • David D. Pollard
Original Paper


A planar fracture when subjected to sufficient tensile and shear stresses will propagate off-plane, in what is known as mixed-mode propagation. Predicting the fracture path relies on an accurate calculation of the near-tip stress and an appropriate propagation criterion. The new criterion we present scales the propagation magnitude and direction with the near-tip tensile stress in the form of vectors that originate from the fracture tip-line. Boundary element method (BEM) models enable us to calculate the near-tip stress field of an arbitrary fracture. We use analytical Eshelby’s solution that evaluates near-tip stress of an ellipsoidal fracture to validate the BEM results. We feed the near-tip stress to the propagation criterion to determine the propagation vectors, and grow the BEM mesh by adding new tip-elements whose size and orientation are given by the propagation vectors. Then, we feed the new mesh back to the BEM to calculate the new near-tip stress. By running the BEM and the propagation criterion in a loop, we are able to model 3D fracture propagation.


Rock fracture Mixed-mode propagation BEM Eshelby’s solution Echelon shape 


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Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  • Chunfang Meng
    • 1
    Email author
  • Frantz Maerten
    • 2
  • David D. Pollard
    • 1
  1. 1.Department of Geological and Environmental SciencesStanford UniversityStanfordUSA
  2. 2.IGEOSS, SchlumbergerMontpelierFrance

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