Green's function method for dynamic contact calculations

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. Building on earlier methods that used elastic surface Green's functions to compute static substrate deformation, we present a numerically efficient dynamic Green's function technique to treat realistic, time-evolving, elastic solids. Our method solves substrate dynamics in reciprocal space and utilizes precomputed Green's functions that exactly reproduce elastic interactions without retaining the atomic degrees of freedom in the bulk. We invoke physical insights to determine the necessary number of explicit substrate layers required to capture the attenuation of subsurface waves as a function of surface wave vector. We observe that truncating substrate dynamics at depths that fall as a power of wave vector allows us to accurately model wave propagation without implementing arbitrary damping. The framework we have developed substantially accelerates molecular dynamics simulations of large elastic substrates. We apply the method to single asperity contact, impact, and sliding friction problems and present our preliminary findings.