Finite element analysis of Cauchy-Born approximations to atomistic models

Makridakis, Charalambos and Süli, Endre (2013) Finite element analysis of Cauchy-Born approximations to atomistic models. Archive for Rational Mechanics and Analysis, 207 (3). pp. 813-843. ISSN 0003-9527

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Abstract

This paper is devoted to a new finite element consistency analysis of Cauchy–Born approximations to atomistic models of crystalline materials in two and three space dimensions. Through this approach new “atomistic Cauchy–Born” models are introduced and analyzed. These intermediate models can be seen as first level atomistic/quasicontinuum approximations in the sense that they involve only short-range interactions. The analysis and the models developed herein are expected to be useful in the design of coupled atomistic/continuum methods in more than one dimension. Taking full advantage of the symmetries of the atomistic lattice, we show that the consistency error of the models considered both in energies and in dual W 1,p type norms is O(ε2) , where ε denotes the interatomic distance in the lattice.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QA Mathematics > QA0297 Numerical analysis
Depositing User: Richard Chambers
Date Deposited: 21 May 2013 09:52
Last Modified: 21 May 2013 09:52
URI: http://sro.sussex.ac.uk/id/eprint/44781
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