Double-layer graphene nanoribbons promise potential application in nanoelectromechanical systems and optoelectronic devices, and knowledge about mechanical stability is a crucial parameter to flourish the application of these materials at the next generation of nanodevices. In this paper, molecular mechanics is utilized to investigate nonlinear buckling behavior, critical buckling stress, and lateral deflection of double-layered graphene nanoribbons under various configurations of stacking mode and chirality. The implicit arc-length iterative method (modified Riks method) with Ramm’s algorithm is utilized to analyze the nonlinear structural stability problem. The covalent bonds are modeled using three-dimensional beam elements in which elastic moduli are calculated based on molecular structural mechanics technique, and the interlayer van der Waals (vdW) interactions are modeled with nonlinear truss elements. An analytical expression for Young’s modulus of nonlinear truss elements is derived based on the Lennard–Jones potential function and implemented in numerical simulation with a UMAT subroutine based on FORTRAN code to capture the nonlinearity of the vdW interactions during the buckling analysis. The results indicate that the highest critical buckling stress and the minimum lateral deflection occur for armchair and zigzag chirality, both with AB stacking mode, respectively. Moreover, the critical buckling stress is found to be directly dependent on the mode shape number regardless of in-phase or anti-phase deflection direction of layers. Lateral deflection exhibits a similar trend with mode shape in anti-phase mode; however, it is decreasing by increasing mode shape number in in-phase mode.

    Abstract
    1 Introduction
    2 Covalent bonds
        2.1 Simulation of the covalent bond
        2.2 Verification of the covalent bond modeling
    3 Van der Waals interaction
        3.1 Simulation of the VdW interactions
        3.2 Verification of the VdW interactions’ modeling
    4 FE modeling
    5 Results and discussion
        5.1 In-phase and anti-phase critical buckling stresses
        5.2 Mode shapes and geometrical instability analysis
    6 Conclusion
    References

• Mohammad Sadegh Namnabat(Department of Mechanical Engineering, Isfahan University of Technology, Department of Mechanical Engineering, College of Engineering, University of Tehran)
• Amin Barzegar(Department of Mechanical Engineering, College of Engineering, University of Tehran)
• Emilio Barchiesi(International Research Center M&MoCS, Università degli Studi dell’Aquila)
• Mahdi Javanbakht(Department of Mechanical Engineering, Isfahan University of Technology)