2011/12/12 by Li, Xingjie Helen, Luskin, Mitchell, Ortner, Christoph
#65Z05 #70C20 #FOS: Mathematics #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.1112.2528
The development of consistent and stable quasicontinuum models for multi-dimensional crystalline solids remains a challenge. For example, proving stability of the force-based quasicontinuum (QCF) model remains an open problem. In 1D and 2D, we show that by blending atomistic and Cauchy--Born continuum forces (instead of a sharp transition as in the QCF method) one obtains positive-definite blended force-based quasicontinuum (B-QCF) models. We establish sharp conditions on the required blending width.