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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]

A three-dimensional molecular dynamics (MD) simulation is performed to study the stress generation mechanisms in carbon thin films grown by ion-beam deposition. The relationship between the kinetic energy of incident ions and the steady-state film stress is established. Examination of the atomic stress and film microstructures reveals that the grown films contain a significant fraction of vacancies, contradicting the presumption of the subplantation model. By taking into account both interstitials and vacancies, an analytical model is developed, in which the formation of the compressive stress is attributed to competing mechanisms between generation and recovery of the defects. This model can satisfactorily explain the numerical observation in which compressive stress prevails in films in the presence of vacancies. The present study provides useful insights into tailoring residual stress to control thin film curvature in microelectromechanical systems (MEMS) by ion-beam machining. [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]