A Green’s Function Method for Solving Dynamical Contact Problems*

Resolving atomic scale details while capturing long-range elastic deformation is the principal difficulty when solving contact mechanics problems with computer simulations. Fully atomistic simulations must consider large blocks of atoms to support long wavelength deformation modes, meaning that most atoms are far removed from the region of interest. We have developed a numerically efficient dynamic Green’s function technique to remedy the inability of simulations to treat realistic, time-evolving, elastic solids. Our method utilizes pre-computed Green’s functions that exactly reproduce elastic interactions without retaining the atomic degrees of freedom in the bulk. We invoke physical insights about the attenuation of subsurface waves as a power of wavevector to limit the number of crystalline layers required to accurately model wave propagation, without implementing arbitrary damping. We apply the method to single asperity sliding to study the velocity dependence of friction and present our preliminary findings. This geometry is typical of friction force and atomic force microscopy, and our results are suitable for comparison to experimental work in the field, where a detailed atomistic description of dynamics is lacking.