Perturbation analysis for an imperfect interface crack problem using weight function techniques

A. Vellender*, G. Mishuris, A. Piccolroaz

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Citations (SciVal)


We analyse a problem of anti-plane shear in a bi-material plane containing a semi-infinite crack situated on a soft imperfect interface. The plane also contains a small thin inclusion (for instance an ellipse with high eccentricity) whose influence on the propagation of the main crack we investigate. An important element of our approach is the derivation of a new weight function (a special solution to a homogeneous boundary value problem) in the imperfect interface setting. The weight function is derived using Fourier transform and Wiener-Hopf techniques and allows us to obtain an expression for an important constant of (which may be used in a fracture criterion) that describes the leading order of tractions near the crack sigma((0))(0) for the unperturbed problem. We present computations that demonstrate how sigma((0))(0) varies depending on the extent of interface imperfection and contrast in material stiffness. We then perform perturbation analysis to derive an expression for the change in the leading order of tractions near the tip of the main crack induced by the presence of the small defect, whose sign can be interpreted as the inclusion's presence having an amplifying or shielding effect on the propagation of the main crack. (C) 2013 Elsevier Ltd. All rights reserved.

Original languageEnglish
Pages (from-to)4098-4107
Number of pages10
JournalInternational Journal of Solids and Structures
Issue number24
Early online date25 Aug 2013
Publication statusPublished - Nov 2013


  • Imperfect interface
  • Crack
  • Weight function
  • Perturbation
  • Inclusion
  • Fracture criterion


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