SURFACE ELASTICITY EFFECTS IN PIN-HOLE CONTACT WITH RADIAL CLEARANCE

This work investigates the frictionless contact of a loaded rigid circular pin inserted with radial clearance into a circular hole in an infinite isotropic elastic plane, with the hole boundary described by surface elasticity theory. The problem is motivated by small-scale mechanical systems and by surface-treated pin joints, where the near-surface region may have mechanical properties that differ from those of the bulk material. The elastic field in the plane is represented by the Michell solution in cylindrical coordinates, while the hole boundary is endowed with surface elastic properties according to the Gurtin–Murdoch model. The resulting surface stress modifies the classical traction boundary conditions through curvature-dependent and surface-gradient terms. By imposing the unilateral frictionless contact conditions, the problem is reduced to a system of dual trigonometric series equations, which are transformed into an infinite system of linear algebraic equations and solved numerically by truncation. The analysis focuses on the influence of surface elasticity on the contact semi-angle, contact pressure distribution, and hoop stress at the hole rim. Comparisons with the classical solution show how surface elastic parameters can modify the contact pressure transmitted through the pin–hole interface and smooth the hoop stress concentration around the hole. The results are then supported by verifying that the M-integral remains invariant along arbitrary circular contours enclosing the hole. The formulation provides an extension of classical pin-loaded hole theory to cases where surface effects, surface treatments, or small geometric length scales are mechanically significant.