Continuum contact model for friction between graphene sheets that accounts for surface anisotropy and curvature

Understanding the interaction mechanics between graphene layers and coaxial carbon nanotubes (CNTs) is essential for modeling graphene and CNT-based nanoelectromechanical systems. This work proposes a new continuum contact model to study interlayer interactions between curved graphene sheets. The continuum model is calibrated and validated using molecular dynamics (MD) simulations. These are carried out employing the reactive empirical bond order (REBO)$+$Lennard-Jones (LJ) potential to model the interactions within a sheet, while the LJ, Kolmogorov-Crespi (KC), and Lebedeva potentials are used to model the interactions between sheets. The continuum contact model is formulated for separation distances greater than 0.29 nm, when sliding contact becomes nondissipative and can be described by a potential. In this regime, sheet deformations are sufficiently small and do not affect the sheet interactions substantially. This allows to treat the master contact surface as rigid, thus simplifying the contact formulation greatly. The model calibration is conducted systematically for a sequence of different stackings using existing and newly proposed ansatz functions. The calibrated continuum model is then implemented in a curvilinear finite-element (FE) shell formulation to investigate the pull-out and twisting interactions between coaxial CNTs. The resisting pull-out forces and torques depend strongly on the chirality of the considered CNTs. The absolute differences between FE and MD results are very small and can be attributed to model assumptions and loading conditions.