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A priori error analysis of two force-based atomistic/continuum models of a periodic chain
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Makridakis, Charalambos, Ortner, Christoph and Süli, Endre. (2011) A priori error analysis of two force-based atomistic/continuum models of a periodic chain. Numerische Mathematik, Vol.119 (No.1). pp. 83-121. 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 |
|---|---|
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Faculty of Science > Mathematics |
| Journal or Publication Title: | Numerische Mathematik |
| Publisher: | Springer |
| ISSN: | 0029-599X |
| Date: | September 2011 |
| Volume: | Vol.119 |
| Number: | No.1 |
| Page Range: | pp. 83-121 |
| Identification Number: | 10.1007/s00211-011-0380-5 |
| Status: | Peer Reviewed |
| Publication Status: | Published |
| Access rights to Published version: | Restricted or Subscription Access |
| URI: | http://wrap.warwick.ac.uk/id/eprint/43923 |
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