Atomistic–continuum coupled model for nonlinear analysis of single layer graphene sheets

• Atomistic–continuum coupled model based on Cauchy–Born rule and Tersoff–Brenner potential is employed for nonlinear flexural response of single layer graphene sheet.
• The effect of material nonlinearity through interatomic potential is softening which increases with the decrease in the size of graphene sheet.
• The response with the inclusion of both material and geometric nonlinearities is hardening type.
• The Kirchhoff plate theory predicts smaller deflection as compared to multiscale model at higher loads specifically for large size graphene sheets.

In this paper, atomistic–continuum coupled model for nonlinear flexural response of single layer graphene sheet is presented considering von-Karman geometric nonlinearity and material nonlinearity due to atomic interactions. The strain energy density function at continuum level is established by coupling the deformation at continuum level to that of at atomic level through Cauchy–Born rule. Strain and curvature dependent tangent in-plane extensional, bending–extension coupling, bending stiffness matrices are derived from strain energy density function constructed through Tersoff–Brenner potential. The finite element method is used to discretize the graphene sheet at continuum level and nonlinear bending response with and without material nonlinearity is studied. The present results are also compared with Kirchhoff plate model and significant differences at higher load are observed. The effects of other parameters like number of atoms in the graphene sheet, boundary conditions on the central/maximum deflection of graphene sheet are investigated. It is also brought out that the occurrence of bond length exceeding cutoff distance initiates at corners for CFCC, CFCF, SFSS, SFSF graphene sheets and near center for SSSS and CCCC graphene sheets.