Frictionless contact of a rigid stamp with a semi-plane in the presence of surface elasticity in the Steigmann–Ogden form

Abstract

In this paper, the surface elasticity in the form proposed by Steigmann and Ogden is applied to study a plane problem of frictionless contact of a rigid stamp with an elastic upper semi-plane. The results of this work generalize the results for contact problems with Gurtin–Murdoch elasticity by including additional dependency on the curvature of the surface. The mechanical problem is reduced to a system of singular integro-differential equations, which is further regularized using the Fourier transform. The size dependency of the solutions of the problem is highlighted. It is observed that the curvature dependence of the surface energy is increasingly important at small scales. The numerical procedure of the solution of the system of singular integro-differential equations is presented, and numerical results are obtained for different values of the mechanical parameters.