  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.
