Internal lattice relaxation of single-layer graphene under in-plane deformation

• Published in: Journal of the mechanics and physics of solids Vol. 56; no. 4; pp. 1609 - 1623
• Main Authors: Zhou, Jun, Huang, Rui
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.04.2008
• Subjects: Carbon nanotube; Elastic modulus; Graphene; Molecular dynamics; Carbon nanotube; Molecular dynamics; Elastic modulus; Graphene
• ISSN: 0022-5096
• DOI: 10.1016/j.jmps.2007.07.013

For noncentrosymmetric crystals, internal lattice relaxation must be considered for theoretical predictions of elastic properties. This paper develops a molecular dynamics approach for determination of the internal relaxation displacement in a single-layer graphene sheet under macroscopically homogeneous in-plane deformation. Based on an analytical interatomic potential, a generally nonlinear relationship between the internal relaxation displacement and the applied macroscopic strain is obtained explicitly from molecular dynamics simulations with a rhombic unit cell under finite deformation. A linear relationship is derived for relatively small strains, which can be conveniently incorporated into a continuum description of the elastic behavior of graphene. It is found that the internal relaxation has a strong effect on theoretical elastic moduli of graphene. In addition, the relationship between elastic properties for graphene and carbon nanotubes is discussed.