A concurrent atomistic and continuum coupling method with applications to thermo‐mechanical problems

We present a novel method to couple molecular dynamics with finite elements at finite temperatures using spatial filters. The mismatch in the dispersion relations between continuum and atomistic models leads, at finite temperature, to unwanted mesh vibrations, which are illustrated using a standard least square coupling formulation. We propose the use of spatial filters with the least square minimization to selectively damp the unwanted mesh vibrations. Then, we extend the idea of selective damping of wavelength modes to couple atomistic and continuum models at finite temperatures. The restitution force from the generalized Langevin equation is modified to perform a two‐way thermal coupling between the two models. Three different numerical examples are shown to validate the proposed coupling formulation in two‐dimensional space. Finally, the method is applied to a high‐speed impact simulation. Copyright © 2013 John Wiley & Sons, Ltd.