Coupling Atomistic and Continuum Finite Element Models: Multi-Scale Simulations of Nanotribological Contacts of Nanometer Scale Coatings

Abstract

Summary When thesizeofaphysicalsystemissmallerthanitscharacteristicdimensions, the macroscopic viewpoint may not be applicable. In addition, experiments at micro/nanometer scale are difficult and the analysis of nano-experimental data is far from simple. Thisismostly duetothelack ofeffective modelsthat are ableto study the structural characteristics and mechanics behaviorof themicro/nanometer physical systems. Atomic simulation simulation has been used extensively in the investigation of nanoscale phenomena. However, the size limit of atomic simulation is far short to reach the macroscale because of the limitation in computer capacity. Therefore, the atomic simulation alone cannot predict the properties and responses of macroscopic/microscopic materials directly from their nano-structures. On the other hand, the conventional continuum based finite element method (FEM) are not applicable to nanoscale components because they are developed for macro/microscale problems. The macro/microscale behaviors of the materials are incorporated in the conventional continuum FEM via the constitutive models of solids, which are usually determined from macroscopic experiments. These constitutivemodels represent the collective behavior of many atoms, and cannot accurately predict the response of discrete atoms. Since the atomistic and continuum simulations have difficulties to investigate the material behavior at micro- and nano- scales, respectively, recently developed multiscale simulation approaches have emerged as a viable means to study materials and systems across different length scales [1-7]. Such multiscale approaches utilize the atomic simulation and the finite element method for the atomistic and continuum descriptions, respectively. The basic idea is to combine the atomistic simulation methods which capture the nanoscale physics laws with the continuum FEM which represents the collective behavior of atoms but significantly reduces the degrees of freedom [8-12]. Tribology is the science and technology of interacting surfaces in relative motion. It is of immense economic importance [13-15]. Tribology has found wide acceptance in both science and engineering. The study of rolling element bearings, seals, gears, cams, viscous dampers, human joints, and magnetic storage devices, are some of the applications in which tribology is currently used. Tribology is also