Nonlocal plate model for nonlinear bending of bilayer graphene sheets subjected to transverse loads in thermal environments

This paper investigates the nonlinear bending behavior of a bilayer rectangular graphene sheet subjected to a transverse uniform load in thermal environments. The bilayer graphene sheet (BLGS) is modeled as a nonlocal double-layered plate which contains small scale effect and van der Waals interaction forces. The geometric nonlinearity in the von Kármán sense is adopted. The thermal effects are included and the material properties are assumed to be size-dependent and temperature-dependent, and are obtained from molecular dynamics (MD) simulations. The small scale parameter e0a is estimated by matching the deflections of graphene sheets observed from the MD simulation results with the numerical results obtained from the nonlocal plate model. The numerical results show that the stacking sequence has a moderate effect, whereas the temperature change as well as the aspect ratio has a significant effect on the nonlinear bending behavior of BLGSs. The results reveal that the small scale parameter reduces the static large deflections of BLGSs, and the small scale effect also plays an important role in the nonlinear bending of BLGSs.