Search

We present a method for deriving molecular dynamics boundary conditions for use in multiple scale simulations that can be applied at a planar boundary for any solid that has a periodically repeating crystal lattice. The method is based on a linearization in the vicinity of the boundary, and utilizes a Fourier and Laplace transforms in space and time to eliminate the degrees of freedom associated with atoms outside the boundary. This method is straightforward to implement numerically, and thus can be automated for a general crystal lattice. We show that this method reproduces the known kernel for a 1D linear chain, and apply the approach to obtain the damping kernel matrices for two real crystal lattices: the graphene and diamond structures of carbon. [Copyright &y& Elsevier]

We present a simple method for calculating a continuum temperature field directly from a molecular dynamics (MD) simulation. Using the idea of a projection matrix previously developed for use in the bridging scale, we derive a continuum temperature equation which only requires information that is readily available from MD simulations, namely the MD velocity, atomic masses and Boltzmann constant. As a result, the equation is valid for usage in any coupled finite element (FE)/MD simulation. In order to solve the temperature equation in the continuum where an MD solution is generally unavailable, a method is utilized in which the MD velocities are found at arbitrary coarse scale points by means of an evolution function. The evolution function is derived in closed form for a 1D lattice, and effectively describes the temporal and spatial evolution of the atomic lattice dynamics. It provides an accurate atomistic description of the kinetic energy dissipation in simulations, and its behavior depends solely on the atomic lattice geometry and the form of the MD potential. After validating the accuracy of the evolution function to calculate the MD variables in the coarse scale, two 1D examples are shown, and the temperature equation is shown to give good agreement to MD simulations. [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]