Improved beam theory for multilayer graphene nanoribbons with interlayer shear effect

The bending of multilayer graphene nanoribbons incorporating the effect of interlayer shear is analyzed in this Letter. An improved beam theory is adopted and extended in which the in-plane extension of each layer is also taken into account. The governing equations for bilayer and trilayer graphene nanoribbons subjected to bending are presented as illustrative examples. Exact solutions for cantilever multilayer graphene nanoribbons are derived. Compared with the molecular dynamics (MD) simulations, the present beam model predicts much better results than the previous beam model in which the in-plane extension is ignored. The current study provides a strong evidence to include the in-plane extension effect in the continuum modeling of multilayer graphene structures.