An Analysis of the Quasicontinuum Method

Details An Analysis of the Quasicontinuum Method An Analysis of the Quasicontinuum Method

2001-03-22

arxiv.org/abs/cond-mat/0103455v1

Physics

Condensed Matter

Materials Science

30 pages, 16 figures. To appear in Jornal of the Mechanics and Physics of Solids

Scientific paper

10.1016/S0022-5096(01)00034-5

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.

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