| Issue |
ESAIM: M2AN
Volume 52, Number 2, March–April 2018
|
|
|---|---|---|
| Page(s) | 729 - 749 | |
| DOI | https://doi.org/10.1051/m2an/2017057 | |
| Published online | 19 July 2018 | |
Cauchy–Born strain energy density for coupled incommensurate elastic chains
* Corresponding author: luskin@umn.edu
Received:
15
March
2016
Accepted:
9
November
2017
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.
Mathematics Subject Classification: 65Z05 / 70C20 / 74E15 / 70G75
Key words: Two-dimensional materials / heterostructures / incommensurability / Cauchy–Born
© EDP Sciences, SMAI 2018
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