The recent fabrication of weakly interacting incommensurate two-dimensional layer stacks (A. Geim and I. Grigorieva, Nature 499 (2013) 419–425) requires an extension of the classical notion of the Cauchy–Born strain energy density since these atomistic systems are typically not periodic. In this paper, we rigorously formulate and analyze a Cauchy–Born strain energy density for weakly interacting incommensurate one-dimensional lattices (chains) as a large body limit and we give error estimates for its approximation by finite samples as well as the popular supercell method.
Accepté le :
DOI : 10.1051/m2an/2017057
Mots clés : Two-dimensional materials, heterostructures, incommensurability, Cauchy–Born
@article{M2AN_2018__52_2_729_0,
author = {Cazeaux, Paul and Luskin, Mitchell},
title = {Cauchy{\textendash}Born strain energy density for coupled incommensurate elastic chains},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {729--749},
publisher = {EDP-Sciences},
volume = {52},
number = {2},
year = {2018},
doi = {10.1051/m2an/2017057},
zbl = {1416.74011},
mrnumber = {3834441},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2017057/}
}
TY - JOUR AU - Cazeaux, Paul AU - Luskin, Mitchell TI - Cauchy–Born strain energy density for coupled incommensurate elastic chains JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2018 SP - 729 EP - 749 VL - 52 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2017057/ DO - 10.1051/m2an/2017057 LA - en ID - M2AN_2018__52_2_729_0 ER -
%0 Journal Article %A Cazeaux, Paul %A Luskin, Mitchell %T Cauchy–Born strain energy density for coupled incommensurate elastic chains %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2018 %P 729-749 %V 52 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2017057/ %R 10.1051/m2an/2017057 %G en %F M2AN_2018__52_2_729_0
Cazeaux, Paul; Luskin, Mitchell. Cauchy–Born strain energy density for coupled incommensurate elastic chains. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 52 (2018) no. 2, pp. 729-749. doi : 10.1051/m2an/2017057. http://www.numdam.org/articles/10.1051/m2an/2017057/
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