Advanced nonlinear buckling analysis of a compressed single layer graphene sheet using the molecular mechanics method

Abstract

The standard molecular mechanics (MM) method with the DREIDING force field (see Mayo et al. The Journal of Physical Chemistry, 1990, 94: 8897–8909) and the molecular structural mechanics (MSM) method with Bernoulli–Euler beam elements are used to study the quasi-static nonlinear buckling and post-buckling behavior of a compressed nearly square single layer graphene sheet (SLGS) for different types of boundary conditions. The novelty of this study is the finding that well-calibrated parameter sets provide similar values of buckling forces/modes and similar post-buckling deformations for stable equilibrium configurations of SLGSs in simulations using the standard MM and MSM methods. In addition, the effect of accounting for non-bonded van der Waals (vdW) forces on the advanced post-buckling deformation modes of compressed SLGSs was studied for the first time. It is shown that the column-like post-buckling deformation modes of compressed SLGSs obtained without the inclusion of vdW interatomic forces are similar to the well-known ones for the planar Euler elastica, and the advanced post-buckling modes obtained with the inclusion of interatomic vdW forces are qualitatively different from the corresponding modes for the planar Euler elastica. In addition, the study shows the theoretical possibility of the existence of post-buckling out-of-plane equilibrium configurations whose stability is provided by attractive vdW forces.