Effects of surface tension on axisymmetric Hertzian contact problem

Surface tension plays an important role in micro/nanosized contact problems. Based on the solution of a point force acting on a half plane with surface tension, we consider the axisymmetric contact between a rigid sphere and an elastic half space. It is found that when the contact radius is comparable with the ratio of surface tension to elastic modulus, surface tension significantly affects the pressure distribution on the contact region. Compared to the classical Hertzian contact solution, the existence of surface tension decreases the displacements on the half plane and yields continuous slopes of normal stress and displacements across the contact fringe. In addition, the present model predicts the increase of hardness as the radius of indenter decreasing. This study is helpful to characterize and measure the mechanical properties of soft materials or biomaterials through micro-indentation.