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Finite element analysis of Cauchy-Born approximations to atomistic models

journal contribution
posted on 2023-06-08, 14:58 authored by Charalambos MakridakisCharalambos Makridakis, Endre Süli
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(e2) , where e denotes the interatomic distance in the lattice.

History

Publication status

  • Published

Journal

Archive for Rational Mechanics and Analysis

ISSN

0003-9527

Publisher

Springer Verlag

Issue

3

Volume

207

Page range

813-843

Department affiliated with

  • Mathematics Publications

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2013-05-21

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