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International Journal for Multiscale Computational Engineering

Impact factor: 1.103

ISSN Print: 1543-1649
ISSN Online: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.2011002388
pages 51-64


C. Makridakis
Department of Applied Mathematics, University of Crete, 71409 Heraklion-Crete, Institute of Applied and Computational Mathematics, FORTH, 71110 Heraklion-Crete
Christoph Ortner
University of Oxford
E. Suli
Mathematical Institute, 24-29 S. Giles', Oxford OX1 3LB, United Kingdom


The force-based quasicontinuum (QCF) approximation isthe principle that lies behind the most commonly usedatomistic/continuum hybrid models for crystalline solids. Recentanalyses have shown some potential pitfalls of the QCF method, particularly the lack of positive definiteness of the linearized QCF operator and the lack of uniform stability as the number ofatoms tends to infinity. We derive a weak variational representation of the QCF operator and identify the origin ofthese difficulties as the lack of an interface condition on thestresses. This leads us to propose an improved variant of the QCF method that can be understood as a coupling mechanism based onstresses rather than forces.


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