The Research On Two-dimensional Nano-contact Problem With Surface Effects

Contact mechanics is a subject studying the laws between local stress and strain distribution induced by the contact of two objects. And contact mechanics have extensive application in industrial production, and they can also be extended to the micro-and nano-technological realm, with the incessant development of nanoscience and nanotechno logy.Owing to the increased ratio of surface/interface to bulk volume at nanoscales, the mechanical performances of nanomaterials and nano-devices are clearly distinct from those macroscopic counterparts, such as size-dependent phenomena and thermal elasticity etc. In the conventional elastic theory, there is no an intrinsic length involved in the constitutive laws, thereby the theoretical predictions predictions are of size-independent. The surface elasticity, in which surface/interface energy is incorporated, shows a good agreement with atomic simulations and can illuminate some mechanical characteristics at nanoscales. In our thesis, we research on two-dimensional frictionless nano-contact problem with surface/interface effects by using Fourier integral transform, which is based on the surface of elasticity. Two major parts are:(1) Research on tangential triangle distribution force with surface effects. Using Fourier integral transform, we obtain the fundamental solutions of stress and displacement applied distribution force. The results reveal that, when the surface effects is considered, the contact normal stress and surface displacement change smoothly across the loading boundary. This results are different from those in the classical elasticity.(2) Research on two-dimensional nano-contact problem of a rigid flat indenter with sharp square corner indenting on an elastic half plane with surface effects. It is found that surface tension significantly alters the pressure distribution in the contact region and the contact width. In addition, Considering the surface tension, the singularity of normal stress disappeares gradually when the width of indenter reduce to nanosize.