Spring boundary model for a partially closed crack

The spring boundary conditions have been widely employed to describe the acoustic properties of rough surfaces in partial contact. Central to this model is the role of the interfacial stiffness. Recently, a singular stiffness model has been proposed to remove inconsistencies which arise when these boundary conditions are used to describe the acoustic response of partially closed cracks with a position-independent and finite stiffness. Here, an alternative solution to this problem is discussed which is based on the micromechanics of rough surfaces in contact. For cracks that are partially closed, it prescribes a finite crack stiffness that varies along the crack faces and, rather than diverging, becomes null within a small but finite neighborhood of the crack tip. The conditions under which the local stiffness of a non-planar crack can be evaluated are also reviewed.