The Research On Nano-Contact Problems With Surface Effects

Contact mechanics mainly study the stress and strain generated by the interaction of two objects under external loads. With the development of micro/nanotechnology in recent years, the prefect macro-contact mechanic is faced with many new challenges in the basic theory and research methods. The nano-materials show some special properties from the conventional materials as their small size and high surface-to-volume ratio. However, since there is no intrinsic length scale involved in the constitutive laws of the classical elastic theory, it is unable to predict the size-dependent behavior of nano-materials. When the characteristic size of solid is reduced to nano-scale, the remarkable effects of the size and the surface on the behaviors of contact mechanic can not be ignored. In frame of surface elasticity, the nano-contact problems with effects of surface are studied, the main researches are listed as follows:(1) The nano-contact problem applied with the triangle distribution pressure. The general solution for the contact problem under the triangle distribution pressure is derived by using Fourier integral transformation. The results show that:due to the existence of surface tension, the normal stress and the deformation gradient on the deformed surface change smoothly across the loading boundary; and the maximum normal stress and the indent depth show a significant dependence on the surface stress.(2) The frictionless nano-contact problem between a rigid flat cylindrical punch and an elastic half space. By using the Gauss-Chebyshev quadrature formula, the approximate numerical solutions are obtained. The results show that, the surface tension significantly affects the pressure distribution on the contact region. Compared to the classical contact solution, the existence of surface tension decreases the displacements of the half plane and yields continuous slopes of normal stress and displacements across the contact fringe.