Modeling of a Curvilinear Planar Crack with a Curvature-Dependent Surface Tension
KAUST Grant NumberKUS-C1-016-04
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AbstractAn 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.
CitationZemlyanova AY, Walton JR (2012) Modeling of a Curvilinear Planar Crack with a Curvature-Dependent Surface Tension. SIAM Journal on Applied Mathematics 72: 1474–1492. Available: http://dx.doi.org/10.1137/110860100.
SponsorsReceived 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).