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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. [Copyright &y& Elsevier]

Abstract: Inspired by the pioneering work of Professor T.J.R. Hughes on the variational multi-scale method, this document summarizes recent developments in multiple-scale modeling using a newly developed technique called the bridging scale. The bridging scale consists of a two-scale decomposition in which the coarse scale is simulated using continuum methods, while the fine scale is simulated using atomistic approaches. The bridging scale offers unique advantages in that the coarse and fine scales evolve on separate time scales, while the high frequency waves emitted from the fine scale are eliminated using lattice impedance techniques. Recent advances in extending the bridging scale to quantum mechanical/continuum coupling are briefly described. The method capabilities are demonstrated via quasistatic nanotube bending, dynamic crack propagation and dynamic shear banding. [Copyright &y& Elsevier]