A generalized quasinonlocal atomistic-to-continuum coupling method with finite-range interaction
X. H. Li and M. Luskin
IMA Journal of Numerical Analysis, 32, 377-393 (2012).

ABSTRACT
The accurate and efficient computation of the deformation of crystalline solids
requires the coupling of atomistic models near lattice defects such as cracks
and dislocations with coarse-grained models away from the defects.
Quasicontinuum methods utilize a strain energy density derived from the
Cauchy-Born rule for the coarse-grained model. Several quasicontinuum methods
have been proposed to couple the atomistic model with the Cauchy-Born strain
energy density. The quasinonlocal (QNL) coupling method is easy to implement and
achieves a reasonably accurate coupling for short-range interactions. In this
paper we give a new formulation of the QNL method in one space dimension that
allows its extension to arbitrary finite-range interactions. We also give an
analysis of the stability and accuracy of a linearization of our generalized QNL
method that holds for strains up to lattice instabilities.