Modeling Axisymmetric Nanocontact Problems with Surface Effect and Friction

The axisymmetric nanocontact problem with surface effect and friction is modeled by an elastic theory based on surface energy density (C–Y theory). In the model, a non-classical boundary condition incorporating the surface effect is derived. With the methods of Love’s strain function and Hankel integral transformation, explicit integral-form solutions of the displacement and stress fields in the elastic half-space are obtained under the axisymmetric normal and tangential loadings. A dimensionless parameter, [Formula: see text], proportional to surface energy density of half-space [Formula: see text] and inversely proportional to the product of shear modulus [Formula: see text] and contact radius [Formula: see text], is introduced to characterize the surface effect. The results show that the surface effect reduces the radial and normal displacements, which makes the half-space stiffer. Besides, the surface effect also reduces the normal and shear stresses within the contact area. Due to the friction, the radial displacement and shear stress become larger, whereas the normal displacement and normal stresses become smaller. Such a fundamental model and corresponding results should be helpful to the deep understanding of the surface effect on nanocontact behavior.