AxisymmetricDislocationandDislocationDipole(DD.PDFVIP

Axisymmetric Dislocation and Dislocation Dipole (DD) Singularities in an Elastic Half- Space Authors: Elizaveta Gordeliy and Emmanuel Detournay (corr. author, detou001@) University of Minnesota, USA Last Modification: June 2011 Available at /97344 This notebook provides expressions for ring dislocation and ring dislocation dipole solutions and for the involved generalized Lipshitz-Hankel integrals. The notebook includes an example of computation of the dis- placement field around a cone DD element in an infinite space. To access a Mathematica notebook containing expressions for the ring dislocation solutions relevant to a cylindrical discontinuity surface, suitable for evalua- tion along a cylindrical cut, visit /97344. Reference: [1] E. Gordeliy and E. Detournay. Displacement Discontinuity Method for Modeling Axisymmetric Cracks in an Elastic Half-Space. International Journal of Solids and Structures (2011), doi:10.1016/j.ijsolstr.2011.05.009. This work was supported by the National Science Foundation under Grant No. 0600058. This work is licensed under the Creative Commons Attribution - NonCommercial - ShareAlike 3.0 License (CC BY - NC - SA 3.0). To view a copy of this license, visit Influence Functions ü Generalised Lipshitz-Hankel integrals (independent of cut orientation) 2 r1ê2 k @r_ , z_ D := IH1 + r L2 + z2 M1ê2 2 2 1ê2 H1 - r L + z k1 @r_ , z_ D := H1 + r L2 + z2 4 r h @r_ D := ; H1 + r L2 1 -1ê2 2 P000 @r_ , z_ D := k @r , z D r EllipticK Ak @r , z D E p