An Analysis of the Quasicontinuum Method
Materials Science
2009-11-07 v1
Abstract
The aim of this paper is to present a streamlined and fully three-dimensional version of the quasicontinuum (QC) theory of Tadmor et al. 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 microstructures.
Cite
@article{arxiv.cond-mat/0103455,
title = {An Analysis of the Quasicontinuum Method},
author = {J. Knap and M. Ortiz},
journal= {arXiv preprint arXiv:cond-mat/0103455},
year = {2009}
}
Comments
30 pages, 16 figures. To appear in Jornal of the Mechanics and Physics of Solids