An atomistic-based continuum approach for calculation of elastic properties of single-layered graphene sheet

Abstract

The elastic deformation of a single-layer nanostructured graphene sheet is investigated using an atomistic-based continuum approach. This is achieved by equating the stored energy in a representative unit cell for a graphene sheet at atomistic scale to the strain energy of an equivalent continuum medium under prescribed boundary conditions. Proper displacement-controlled (essential) boundary conditions which generate a uniform strain field in the unit cell model are applied to calculate directly one elastic modulus at a time. Three atomistic finite element models are adopted with an assumption that the force interaction among carbon atoms can be modeled by either spring-like or beam elements. Thus, elastic moduli for graphene structure are determined based on the proposed modeling approach. Then, effective Young's modulus and Poisson's ratio are extracted from the set of calculated elastic moduli.Results of Young's modulus obtained by employing the different atomistic models show a good agreement with the published theoretical and numerical predictions. However, Poisson's ratio exhibits sensitivity to the considered atomistic model. This observation is supported by a significant variation in estimates as can be found in the literature. Furthermore, isotropic behavior of in-plane graphene sheets was validated based on current modeling.