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Stress-based atomistic/continuum coupling : a new variant of the quasicontinuum approximation
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Makridakis, C., Ortner, Christoph and Süli, Endre (2012) Stress-based atomistic/continuum coupling : a new variant of the quasicontinuum approximation. International Journal for Multiscale Computational Engineering, Volume 10 (Number 1). pp. 51-64. doi:10.1615/IntJMultCompEng.2011002388 ISSN 1543-1649.
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Official URL: http://dx.doi.org/10.1615/IntJMultCompEng.20110023...
Abstract
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.
Item Type: | Journal Article | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | International Journal for Multiscale Computational Engineering | ||||
Publisher: | Begell House, Inc. | ||||
ISSN: | 1543-1649 | ||||
Official Date: | 2012 | ||||
Dates: |
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Volume: | Volume 10 | ||||
Number: | Number 1 | ||||
Page Range: | pp. 51-64 | ||||
DOI: | 10.1615/IntJMultCompEng.2011002388 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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