2011/12/22 by Anna Y. Zemlyanova, A. Y. Zemlyanova, Zemlyanova, A. Y. +3 · 3 citations
Engineering · Mathematics · #74B20 #74G70 #74R10 #Analysis of PDEs (math.AP) #FOS: Mathematics #Fatigue and fracture mechanics #Numerical methods in engineering #Rock Mechanics and Modeling #math.AP #msc:74B20 #msc:74G70 #msc:74R10
paper · pdf · doi:10.48550/arxiv.1112.5235
18 pages, 9 figures
openalex publication_date 2011/12/22 · arxiv created 2012/06/15 · arxiv updated 2012/06/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
IAn 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.