A molecular dynamics-continuum concurrent multiscale model for quasi-static nanoscale contact problems

Analyzing contact performances between two surfaces plays a key role in studying friction, wear, and lubrication in tribological systems. Advancements of micro/nano-electromechanical system (MEMS/NEMS) and nanotechnology in recent years demand the developments of multiscale contact mechanics. By using multiscale methods, calculation domains which consider local mechanical behaviors with nanoscale characteristics could be simulated by atomistic methods, and other domains can still use conventional methods for larger lengths and time scales in order to save computational costs or achieve high-performance calculations for larger scale systems. A molecular dynamics-continuum concurrent multiscale model for quasi-static nanoscale contacts is presented, which can both implement equilibrium of the energy field and force field in different scale domains. In molecular dynamics simulations, since the speed of the approaching probe is very small in comparison with the longitudinal sound speed, which is usually in the order of 10 ³ m/s, the results of the contact process can be treated approximately as the quasi-static case in nature. For continuum simulations, the Cauchy-Born rule is employed to evaluate the nonlinear constitutive relationship of the coarse scale. By using the present multiscale model, simulations of nanoscale adhesive contacts between a cylinder and a substrate are implemented. The results show that the boundary conditions are effective for the contact problems. Furthermore, 2-D adhesive contacts of rough surfaces are investigated. Some behaviors of the nanoscale contact processes are discussed, and differences between the multiscale model and the pure molecular dynamics simulation are revealed.