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A priori error analysis of two force-based atomistic/continuum models of a periodic chain
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Makridakis , C. , Ortner, Christoph and Süli, Endre (2011) A priori error analysis of two force-based atomistic/continuum models of a periodic chain. Numerische Mathematik, Volume 119 (Number 1). pp. 83-121. doi:10.1007/s00211-011-0380-5 ISSN 0029-599X.
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Official URL: http://dx.doi.org/10.1007/s00211-011-0380-5
Abstract
The force-based quasicontinuum (QCF) approximation is a non-conservative atomistic/continuum hybrid model for the simulation of defects in crystals. We present an a priori error analysis of the QCF method, applied to a one-dimensional periodic chain, that is valid for an arbitrary interaction range, large deformations, and takes coarse-graining into account. Our main tool in this analysis is a new concept of atomistic stress. Moreover, we formulate a new atomistic/continuum coupling mechanism based on coupling stresses instead of forces and extend the a priori analysis to this new method. We show that the new method has several theoretical advantages over the original QCF method.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics T Technology > TA Engineering (General). Civil engineering (General) |
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Multiscale modeling, Crystalline polymers -- Defects -- Mathematical models, Continuum mechanics | ||||
Journal or Publication Title: | Numerische Mathematik | ||||
Publisher: | Springer | ||||
ISSN: | 0029-599X | ||||
Official Date: | 1 September 2011 | ||||
Dates: |
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Volume: | Volume 119 | ||||
Number: | Number 1 | ||||
Page Range: | pp. 83-121 | ||||
DOI: | 10.1007/s00211-011-0380-5 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access | ||||
Date of first compliant deposit: | 20 December 2015 | ||||
Date of first compliant Open Access: | 20 December 2015 | ||||
Funder: | Engineering and Physical Sciences Research Council (EPSRC), Seventh Framework Programme (European Commission) (FP7) |
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