V. B. Shenoy, R. Miller, E. B. Tadmor, D. Rodney, R. Phillips and M. Ortiz
Journal of the Mechanics and Physics of Solids, 47, 611–642 (1999).
Mixed atomistic and continuum methods offer the possibility of carrying out
simulations of material properties at both larger length scales and longer
times than direct atomistic calculations. The quasicontinuum method links
atomistic and continuum models through the device of the finite element
method which permits a reduction of the full set of atomistic degrees of
freedom. The present paper gives a full description of the quasicontinuum
method, with special reference to the ways in which the method may be used
to model crystals with more than a single grain. The formulation is validated
in terms of a series of calculations on grain boundary structure and
energetics. The method is then illustrated in terms of the motion of a stepped
twin boundary where a critical stress for the boundary motion is calculated
and nanoindentation into a solid containing a subsurface grain boundary to
study the interaction of dislocations with grain boundaries.