Cauchy-Born strain energy density for coupled incommensurate elastic chains

Paul Cazeaux, Mitchell Luskin

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)729-749
Number of pages21
JournalESAIM: Mathematical Modelling and Numerical Analysis
Issue number2
StatePublished - Mar 1 2018

Bibliographical note

Funding Information:
Acknowledgements. This work was supported in part by ARO MURI Award W911NF-14-1-0247. Mitchell Luskin was also supported in part by the Radcliffe Institute for Advanced Study at Harvard University. The authors would like to thank Ilia Novikov and Ellad Tadmor for sharing their work on continuum models for 2D layered materials [22].

Publisher Copyright:
© 2016 Sociedad Matemática Mexicana.


  • Cauchy-Born
  • Heterostructures
  • Incommensurability
  • Two-dimensional materials


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