On atomistic-to-continuum couplings without ghost forces in three dimensions

In this paper we construct energy based numerical methods free of ghost forces in three dimen- sional lattices arising in crystalline materials. The analysis hinges on establishing a connection of the coupled system to conforming finite elements. Key ingredients are: (i) a new representation of discrete derivatives related to long range interactions of atoms as volume integrals of gradients of piecewise linear functions over bond volumes, and (ii) the construction of an underlying globally continuous function representing the coupled modeling method

Coupling atomistic and continuum hydrodynamics through a mesoscopic model: application to liquid water

We have conducted a triple-scale simulation of liquid water by concurrently coupling atomistic, mesoscopic, and continuum models of the liquid. The presented triple-scale hydrodynamic solver for molecular liquids enables the insertion of large molecules into the atomistic domain through a mesoscopic region. We show that the triple-scale scheme is robust against the details of the mesoscopic model owing to the conservation of linear momentum by the adaptive resolution forces. Our multiscale approach is designed for molecular simulations of open domains with relatively large molecules, either in the grand canonical ensemble or under non-equilibrium conditions.Comment: triple-scale simulation, molecular dynamics, continuum, wate

The role of the patch test in 2D atomistic-to-continuum coupling methods

For a general class of atomistic-to-continuum coupling methods, coupling multi-body interatomic potentials with a P1-finite element discretisation of Cauchy--Born nonlinear elasticity, this paper adresses the question whether patch test consistency (or, absence of ghost forces) implies a first-order error estimate. In two dimensions it is shown that this is indeed true under the following additional technical assumptions: (i) an energy consistency condition, (ii) locality of the interface correction, (iii) volumetric scaling of the interface correction, and (iv) connectedness of the atomistic region. The extent to which these assumptions are necessary is discussed in detail.Comment: Version 2: correction of some minor mistakes, added discussion of multiple connected atomistic region, minor improvements of styl

Multiscale modeling of rapid granular flow with a hybrid discrete-continuum method

Both discrete and continuum models have been widely used to study rapid granular flow, discrete model is accurate but computationally expensive, whereas continuum model is computationally efficient but its accuracy is doubtful in many situations. Here we propose a hybrid discrete-continuum method to profit from the merits but discard the drawbacks of both discrete and continuum models. Continuum model is used in the regions where it is valid and discrete model is used in the regions where continuum description fails, they are coupled via dynamical exchange of parameters in the overlap regions. Simulation of granular channel flow demonstrates that the proposed hybrid discrete-continuum method is nearly as accurate as discrete model, with much less computational cost

Elasticity effects on the stability of growing films

It is shown how the combination of atomic deposition and nonlinear diffusion may lead, below a critical temperature, to the growth of nonuniform layers on a substrate. The dynamics of such a system is of the Cahn-Hilliard type, supplemented by reaction terms representing adsorption-desorption processes. The instability of uniform layers leads to the formation of nanostructures which correspond to regular spatial variations of substrate coverage. Since coverage inhomogeneities generate internal stresses, the coupling between coverage evolution and film elasticity fields is also considered, for film thickness below the critical thickness for misfit dislocation nucleation. It is shown that this coupling is destabilizing and favors nanostructure formation. It also favors square planforms which could compete, and even dominate over the haxagonal or stripe nanostructures induced by coverage dynamics alon

A Laplacian-based algorithm for non-isothermal atomistic-continuum hybrid simulation of micro and nano-flows

We propose a new hybrid algorithm for incompressible micro and nanoflows that applies to non-isothermal steady-state flows and does not require the calculation of the Irving–Kirkwood stress tensor or heat flux vector. The method is validated by simulating the flow in a channel under the effect of a gravity-like force with bounding walls at two different temperatures and velocities. The model shows very accurate results compared to benchmark full MD simulations. In the temperature results, in particular, the contribution of viscous dissipation is correctly evaluated