Determination of random material properties of graphene sheets with different types of defects

This paper presents a computational procedure for the determination of the stochastic material properties of graphene with different types and density of defects. The lattice of graphene is modeled using the molecular structural mechanics (MSM) approach, which is a continuum based nanoscale modeling technique, where the C-C covalent bonds are replaced by energetically equivalent beam elements. Random fields describing the spatial variation of the anisotropic elasticity tensor of defective graphene sheets are determined using the moving window method and Monte Carlo (MC) simulation. Three types of randomly dispersed defects are examined, namely Stone-Wales (SW), single vacancy (SV) and double vacancy (DV). The effect of window size, defect type and density on the random elastic properties of graphene sheets of area 100×100nm2 is investigated. The computed results reveal that vacancy defects can reduce the axial stiffness of graphene by approximately 60% with respect to that of pristine graphene, whereas the effect of SW defects is less significant. The computed random elasticity tensors can be assigned to equivalent continuum stochastic finite elements used in the framework of continuum modeling of graphene structures.