THE HEMISPHERICAL NANOPIT AT THE PLANE BOUNDARY OF AN ELASTIC HALF-SPACE SUBJECTED TO STATICALLY EQUIVALENT SHEAR TRACTIONS

The elastic deformation of a semi-infinite substrate containing a nanosized hemispherical pit on its plane boundary crucially relies on the mechanical response of the pit surface. In this paper, we develop a micromechanical model that couples Gurtin and Murdoch's model of surface mechanics with the classical theory of elasticity, and we explicitly evaluate the stress concentration, displacement and stress distribution resulting from a family of statically equivalent shear tractions applied on the pit surface. We found that two intrinsic dimensionless parameters, both constructed from the characteristic length and material properties, govern the highly localized elastic field. Both the magnitude and sign of these parameters are of great importance. Negative values tend to increase stress concentrations, whereas positive ones have the opposite effect. We further highlight the consequences of our analysis by comparing a number of shear tractions that correspond to the same torque. The comparison provides the means of evaluating the degree of difference in elastic fields in the immediate vicinity of statically equivalent force distributions.