Based on the surface elasticity theory, we examined the effects of surface stresses on nanosized contact problems. The Fourier integral transform method is adopted to derive the general solution for the contact problem under pressure. As two examples, the deformations induced, respectively, by a uniform distributed pressure and a concentrated force are analyzed in detail. The results indicate some interesting characteristics in contact mechanics, which are distinctly different from those in classical elasticity theory. Both the contact normal stress and the deformation gradient on the deformed surface vary smoothly across the loading boundary as a result of surface stress. In addition, the indent depth and the maximum normal contact stress depend strongly on the surface stress for nanoindentation.

The diffractions of plane compressional waves (P-wave) and shear waves (SV-wave) by a cylindrical nano-inclusion are investigated in this paper. To account for the surface/interface effect at nanoscale, the surface/interface elasticity theory is adopted in the analysis. Using the displacement potential method, we obtain the solutions for the elastic fields induced by incident P- and SV-waves near a cylindrical nano-inclusion. The results show that surface/interface has a significant effect on the diffractions of elastic waves as the radius of the inclusion shrinks to nanoscale. For incident waves with different frequencies, the effects of interfacial properties on the dynamic stress concentration around the nano-inclusion are discussed in detail.

In the present paper, the multiple diffraction of plane harmonic compressional waves (P-wave) by two nanosized circular cylindrical holes embedded in an elastic solid is investigated. The surface elasticity theory is adopted to account for the effect of surface energy at nanoscales. It is found that when the radii of holes reduce to nanometers, surface energy significantly affects the diffraction of elastic waves. The dynamic stresses around the holes under incident waves of different frequencies are examined to display the influence of surface energy and the interaction between holes in the multiple scattering phenomena.

In the present letter, we studied the surface buckling of a bending beam using the surface elasticity theory, and the corresponding buckling wave number was obtained analytically. It is found that surfaces with positive surface elastic modulus may buckle under compression, while surfaces with negative surface elastic modulus are possible to wrinkle irrespective of the sign of surface strain. By this method, various surface buckling phenomena happened in thin films or carbon nanotubes can be elucidated.

In this paper, an incremental equivalent contact model is developed for elastic-perfectly plastic solids with rough surfaces. The contact of rough surface is modeled by the accumulation of circular contacts with varying radius, which is estimated from the geometrical contact area and the number of contact patches. For three typical rough surfaces with various mechanical properties, the present model gives accurate predictions of the load-area relation, which are verified by direct finite element simulations. An approximately linear load-area relation is observed for elastic-plastic contact up to a large contact fraction of 15%, and the influence of yield stress is addressed.