On the local and non-local plate models of single layer graphene

Abstract

In the application of continuum plate theories for modeling the mechanics of single layer graphene, significant inconsistencies exist in the literature on how to deal with the discrepancy between the continuum assumptions and discrete nature of the graphene lattice, whether using the classical plate theories or the more recent non-local elasticity based plate models. Physically vague properties such as graphene thickness and non-local parameter are often used as fitting parameters for calibrating the numerical results against those obtained from atomistic models or experimental data. However, very often a set of parameters that work well for a particular case can lead to large errors in other cases. This work attempts to answer the following question: can the mechanical behavior of single layer graphene sheets be described accurately and consistently using a continuum plate model? By using the results from atomic lattice mechanics calculations as reference for error analysis, we demonstrate that, when the sources of error in the classical plate model are properly identified, mechanics of single layer graphene can be accurately described by a modified non-local plate model with an interatomic potential based constitutive relation and a corrected boundary configuration.