Anna Zemlyanova, azem@math.ksu.edu
Curvature-dependent surface tension in modelling of fracture
A new model of fracture mechanics which takes into account interfacial effects due to a curvature-dependent
surface tension will be considered. This model is based on a physically valid assumption that the behavior of
molecules near a surface of a material is significantly different from those in the bulk and depends on the local
curvature of the material surface. The theory will be presented through several examples: a curvilinear
non-interface and interface crack, and contact problems for a rigid stamp indentation into an elastic half-plane.
It will be shown that the incorporation of surface effects on the crack boundary eliminates the power and
oscillating singularities at the crack tips which are predicted by linear elastic fracture mechanics. The
mechanical problems will be reduced to the systems of singular integro-differential equations. The
regularization and numerical solution of these systems will be addressed and numerical examples will be
presented. Potential direction for future research and connections with experimental results will be discussed.