Geodesic
Cauchy–Born strain energy density for coupled incommensurate elastic chains
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 52 (2018) no. 2, pp. 729-749

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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.

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DOI : 10.1051/m2an/2017057
Classification : 65Z05, 70C20, 74E15, 70G75
Keywords: Two-dimensional materials, heterostructures, incommensurability, Cauchy–Born 
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     title = {Cauchy{\textendash}Born strain energy density for coupled incommensurate elastic chains},
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     pages = {729--749},
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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

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