A priori error analysis of two force-based atomistic/continuum models of a periodic chain
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 0029-599XFull text not available from this repository.
Official URL: http://dx.doi.org/10.1007/s00211-011-0380-5
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|
|Official Date:||September 2011|
|Page Range:||pp. 83-121|
|Access rights to Published version:||Restricted or Subscription Access|
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