On the molecular mechanics of single layer graphene sheets

The molecular structural mechanics (MSM) method is developed by applying beam elements to model bonded interactions between carbon atoms in the atomic lattices of single-layer graphene sheets (SLGSs). The novelty of the approach developed in this paper lies in the accurate adjustment of the geometric and material parameters of Bernoulli-Euler beam elements to simulate reference mechanical moduli (2D Young's modulus, Poisson's ratio, and bending rigidity modulus) of graphene. The MSM method with an advanced geometric and material parameter set of Bernoulli-Euler beam elements is implemented by means of the commercial MSC.Marc finite element (FE) code. We also employ the standard molecular mechanics (MM) method using the DREIDING force field (see Mayo et al. The Journal of Physical Chemistry, 1990, 94: 8897-8909). We implemented this force field in the homemade PIONER FE code using a modified parameter set which reproduces the mechanical moduli of graphene reasonably well. Computer simulations show that the free vibration frequencies and modes of SLGSs obtained using the standard MM and MSM methods converge. However, the buckling forces of compressed SLGSs obtained by the two methods provide acceptable convergence only for the lowest values of the critical forces.