General elasticity theory for graphene membranes based on molecular dynamics

Paper in proceeding, 2007

We have studied the mechanical properties of suspended graphene membranes using molecular dynamics (MD) and generalized continuum elasticity theory (GE) in order to develop and assess a continuum description for graphene. The MD simulations are based on a valence force field model which is used to determine the deformation and the elastic energy of the membrane (EMD) as a function of external forces. For the continuum description, we use the expression Econt = Estretching + Ebending for the elastic energy functional. The elastic parameters (tensile rigidity and Poisson ratio) entering Econt are determined by requiring that E cont = EMD for a set of deformations. Comparisons with the MD results show excellent agreement. We find that the elastic energy of a supported graphene sheets is typically dominated by the nonlinear stretching terms whereas a linear description is valid only for very small deflections. This implies that in some applications, i.e. NEMS, a linear description is of limited applicability.