Stress Analysis for Nano-Scale Elastic Materials : Elastic Contact Problems Considering Surface Stresses

It is known that intrinsic mechanical stress exists in a general free surface or interface, because of surface atomic structure changes relative to the bulk. We present an analysis of using the interrelationship between surface stresses, free surface and volume stress deduced in our previous paper. The surface stresses are closely related to the surface energy and surface geometry (mean curvature) of materials. In the present paper, an elastic contact problem in which an axisymmetric elastic body is pressed into an elastic half-region coated with a thin elastic film is analyzed using the three-dimensional theory of elasticity. In this analysis, the relevant dimensionless parameter, called the elastic capillary number, which is a function of surface energy, elastic modulus and the film thickness, is introduced. It is shown that the elastic modulus of the thin film apparently increases and the bulk stress also increases when the surface stresses are taken into account.