We develop a technique for simulation of the mechanics of micron-scale solid systems: coarse-grained molecular dynamics (CGMD). It captures the important atomistic effects without the computational cost of conventional molecular dynamics (MD). The CGMD equations of motion are derived directly from finite temperature MD through a statistical coarse graining procedure, so they agree with MD as the mesh size is reduced to the atomic scale. This allows a seamless coupling of length scales. The use of efficient CGMD in peripheral regions extends atomistic simulation to much larger systems than amenable to MD alone.

Coarse-grained molecular dynamics (CGMD) is a technique developed as a concurrent multiscale model that couples conventional molecular dynamics (MD) to a more coarse-grained description of the periphery. The coarse-grained regions are modeled on a mesh in a formulation that generalizes conventional finite element modeling (FEM) of continuum elasticity. CGMD is derived solely from the MD model, however, and has no continuum parameters. As a result, it provides a coupling that is smooth and provides control of errors that arise at the coupling between the atomistic and coarse-grained regions. In this paper, we elaborate on the formulation of CGMD, describing in detail how CGMD is applied to anharmonic solids and finite-temperature simulations. As tests of CGMD, we present in detail the calculation of the phonon spectra for solid argon and tantalum in three dimensions, demonstrating how CGMD provides a better description of the elastic waves than that provided by FEM. We also present elastic wave scattering calculations that show the elastic wave scattering is more benign in CGMD than FEM. We also discuss the dependence of scattering on the properties of the mesh. We introduce a rigid approximation to CGMD that eliminates internal relaxation, similar to the quasicontinuum technique, and compare it to the full CGMD.

We report the results of first-principles density functional theory calculations of the Young’s modulus and other mechanical properties of hydrogen-passivated Si⟨001⟩ nanowires. The nanowires are taken to have predominantly {100} surfaces, with small {110} facets according to the Wulff shape. The Young’s modulus, the equilibrium length, and the constrained residual stress of a series of prismatic beams of differing sizes are found to have size dependences that scale like the surface area to volume ratio for all but the smallest beam. The results are compared with a continuum model and the results of classical atomistic calculations based on an empirical potential. We attribute the size dependence to specific physical structures and interactions. In particular, the hydrogen interactions on the surface and the charge density variations within the beam are quantified and used both to parametrize the continuum model and to account for the discrepancies between the two models and the first-principles results.