Euler elastica as a Γ-Limit of discrete bending energies of one-dimensional chains of atoms

2016/04/26 by Malena I. Español, Espanol, Malena I., Dmitry Golovaty +3
Engineering · Materials Science · #Carbon Nanotubes in Composites #Composite Material Mechanics #Elasticity and Material Modeling #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · pdf · doi:10.48550/arxiv.1604.07879

openalex publication_date 2016/04/26 · openalex created_date 2022/09/30 · openalex updated_date 2026/07/28

Abstract

This work is motivated by discrete-to-continuum modeling of the mechanics of a graphene sheet, which is a single-atom thick macromolecule of carbon atoms covalently bonded to form a hexagonal lattice. The strong covalent bonding makes the sheet essentially inextensible and gives the sheet a resistance to bending. We study a one-dimensional atomistic model that describes the cross-section of a graphene sheet as a collection of rigid links connected by torsional springs. Γ-convergence is used to rigorously justify an upscaling procedure for the discrete bending energy of the atomistic model. Our result establishes that as the bond length in the atomistic model goes to 0, the bending energies Γ-converge to Euler's elastica.

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