An Adhesive Contact Problem for a Semi-plane with a Surface Elasticity in the Steigmann-Ogden Form

Abstract

The main goal of the present paper is to study a two-dimensional problem of adhesive contact of a rigid stamp with an elastic upper semi-plane. Surface elasticity in the Steigmann-Ogden form acts on the free boundary of the semi-plane. The mechanical problem is solved using integral representations of the stresses and the displacements. The resulting system of singular integro-differential equations is regularized using Fourier transform method. The numerical procedure of the solution of the system of singular integro-differential equations is presented, and the numerical results are obtained for different values of the mechanical parameters. The size-dependency of the solutions of the problem is studied. It can be seen that taking into account curvature-dependency of the surface energy is increasingly important at the very small scales (characteristic length of the contact interval is under $20~\mbox{nm}$ ).