Coupling of atomistic and continuum simulations using a bridging scale decomposition

We present a new method for coupling molecular dynamics (MD) and continuum mechanics simulations that is based on the projection of the MD solution onto the coarse scale shape functions. This projection, or “bridging scale”, represents that part of the solution that is obtainable by both solution methods. By subtracting the bridging scale from the total solution, we arrive at a coarse-fine decomposition that, by a proper choice of projection operator, decouples the kinetic energy of the two simulations. The resulting decomposition can be used in a finite-temperature simulation method in which MD is used only in a localized region, while the continuum simulation covers the entire domain, including the MD region to which it is coupled. One major advantage of this approach is that separate time step sizes can be used in the two simulations, so that the coarse scale time step is not limited to the time scale of the atomic vibrations present in the fine scale. Example problems are demonstrated on a 1D lattice, for which the method is shown to be accurate both for harmonic and anharmonic interatomic potentials.