A coupled atomistic/continuum model of defects in solids
L. E. Shilkrot and W. A. Curtin and R. E. Miller
Journal of the Mechanics and Physics of Solids, 50, 2085-2106 (2002).

ABSTRACT
A method is introduced for reducing the degrees of freedom in simulations of
mechanical behavior of materials without sacrificing important physics. The
method essentially combines the quasicontinuum (QC) method with continuum defect
models such as the discrete dislocation (DD) method. The QC formulation is used
to couple a fully atomistic region to a defect-free elastic continuum. Defects
existing in the elastic continuum region of the full problem of interest are
treated by the DD-like methods with special boundary conditions. The full
coupled problem is then solved by an Eshelby-like procedure involving
superposition of the QC and DD problems, and is appropriate in both 2d and 3d.
Special attention is given to dealing with dislocation defects. A procedure for
the "passing" of dislocation defects from the atomistic to the continuum
description in 2d problems is also presented. The overall 2d method with
dislocation defects is validated by comparing the predictions of the coupled
model to "exact" fully atomistic models for several equilibrium dislocation
geometries and a nanoindentation problem in aluminum, and excellent agreement is
obtained. The method proposed here should find application to a broad host of
problems associated with the multiscale modeling of atomistic, nano- and
micromechanical behavior of crystalline solids under mechanical loads.