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International Journal for Multiscale Computational Engineering
STRESS-BASED ATOMISTIC/CONTINUUM COUPLING: A NEW VARIANT OF THE QUASICONTINUUM APPROXIMATION
Department of Applied Mathematics, University of Crete, 71409 Heraklion-Crete, Institute of Applied and Computational Mathematics, FORTH, 71110 Heraklion-Crete
University of Oxford
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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