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

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.