Displacement discontinuity method for modeling axisymmetric cracks in an elastic half-space

Elizaveta Gordeliy, Emmanuel M Detournay

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This paper describes a displacement discontinuity method for modeling axisymmetric cracks in an elastic half-space or full space. The formulation is based on hypersingular integral equations that relate displacement jumps and tractions along the crack. The integral kernels, which represent stress influence functions for ring dislocation dipoles, are derived from available axisymmetric dislocation solutions. The crack is discretized into constant-strength displacement discontinuity elements, where each element represents a slice of a cone. The influence integrals are evaluated using a combination of numerical integration and a recursive procedure that allows for explicit integration of hyper- and Cauchy singularities. The accuracy of the solution at the crack tip is ensured by adding corrective stresses across the tip element. The method is validated by a comparison with analytical and numerical reference solutions.

Original languageEnglish (US)
Pages (from-to)2614-2629
Number of pages16
JournalInternational Journal of Solids and Structures
Issue number19
StatePublished - Sep 15 2011

Bibliographical note

Funding Information:
The authors wish to thank Dr. J.A.L. Napier (University of the Witwatersrand and CSIR, South Africa) and Dr. R. Piccinin (University of Minnesota, USA) for their help with verifying the numerical results of Axi-DDM. The authors gratefully acknowledge support from the National Science Foundation under Grant No. 0600058 . Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.


  • Axisymmetric crack
  • Displacement discontinuity method
  • Ring dislocation
  • Ring dislocation dipole


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