Modeling of a Curvilinear Planar Crack with a Curvature-Dependent Surface Tension

A. Y. Zemlyanova, J. R. Walton

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


An approach to modeling fracture incorporating interfacial mechanics is applied to the example of a curvilinear plane strain crack. The classical Neumann boundary condition is augmented with curvature-dependent surface tension. It is shown that the considered model eliminates the integrable crack-tip stress and strain singularities of order 1/2 present in the classical linear fracture mechanics solutions, and also leads to the sharp crack opening that is consistent with empirical observations. Unlike for the case of a straight crack, for a general curvilinear crack some components of the stresses and the derivatives of the displacements may still possess weaker singularities of a logarithmic type. Generalizations of the present study that lead to complete removal of all crack-tip singularities, including logarithmic, are the subject of a future paper. © 2012 Society for Industrial and Applied Mathematics.
Original languageEnglish (US)
Pages (from-to)1474-1492
Number of pages19
JournalSIAM Journal on Applied Mathematics
Issue number5
StatePublished - Jan 2012
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-C1-016-04
Acknowledgements: Received by the editors December 22, 2011; accepted for publication (in revised form) June 25, 2012; published electronically September 27, 2012. This work was supported by award KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.


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