Wave propagation in graphene sheets with nonlocal elastic theory via finite element formulation

A nonlocal elastic plate model that accounts for the scale effects is first developed for wave propagations in graphene sheets. Moreover, a finite element model developed from the weak-form of the elastic plate model is reported to fulfill a comprehensive wave study in the sheets and realize an application of the sheets as gas sensors. The applicability of the finite element model is verified by molecular dynamics simulations. The studies show that the nonlocal finite element plate model is indispensable in predicting graphene phonon dispersion relations, especially at wavelengths less than 1 nm, when the small-scale effect becomes dominant. Moreover, the nonlocal parameter e0a, a key parameter in the nonlocal model, is calibrated through the verification process. The dependence of the small-scale effect and the width of sheets on the dispersion relation is also investigated, and simulation results show that the phase velocity decreases to an asymptotic value with the width of sheets reaches a sufficiently large size. As an application of the investigation, the potential of graphene sheets as nano-sensors for noble gas atoms is explored by defining and examining an index based on the phase velocity shifts in a graphene sheet attached by gas atoms.