An analysis of the quasicontinuum method
J. Knap J and M. Ortiz
Journal of the Mechanics and Physics of Solids, 49, 1899–1923 (2001).


The aim of this paper is to present a streamlined and fully three-dimensional
version of the quasicontinuum (QC) theory of Tadmor et al. (Philos. Mag. A 73
(1996) 1529; Langmuir 12 (1996) 4529) and to analyze its accuracy and
convergence characteristics. Specifically, we assess the effect of the
summation rules on accuracy; we determine the rate of convergence of the
method in the presence of strong singularities, such as point loads; and we
assess the effect of the refinement tolerance, which controls the rate at
which new nodes are inserted in the model, on the development of dislocation