Two-dimensional partial-slip contact analysis for a nano-flat punch accounting for surface effects

This work investigates a Cattaneo–Mindlin partial-slip contact model considering surface effects based on energy density theory, loaded by a two-dimensional rigid flat punch bonded to a homogeneous elastic half-space. A partial-slip contact model is established based on the Airy function and Chen–Yao theory. Using the Gauss-Chebyshev method and Goodman approximation, the numerical solutions are obtained under various contact conditions, including the surface-energy density, friction coefficient, and normal loadings, and are compared with different surface theories. Self-similarity of the flat-end punch has been proven by the change of normal loadings and tangential force manipulated by the friction coefficient. The surface traction associated with surface-energy density has also been clarified, which indicates surface effect may modify the stress and traction distributions in the response of partial-slip contact. An interesting phenomenon is that the Gurtin–Murdoch model may overvalue the surface effect compared with the Chen–Yao model for pure aluminum. The results of this study enhance the understanding of how residual surface energy influences the Cattaneo–Mindlin partial-slip contact response. These findings may provide a theoretical reference for the design of nanoscale contact systems and future studies on cyclic fretting damage considering surface effects.