Fundamental deflection behavior of an infinite two-dimensional graphene lattice subjected to a transverse point force has been analyzed using lattice statics and the continuum Green's functions. An analytic expression has been derived for the lattice statics Green's function of graphene in the deflection mode. It is shown that its asymptotic limit corresponds to the elastically stable Kirchhoff plate and, unlike normal solids, not the Green's function for the two-dimensional Christoffel nist-equations. This correspondence shows the stability of the graphene lattice against transverse deflections and is necessary for relating the mechanical parameters of graphene at macroscales to the interatomic potential. Using the Tersoff-Brenner potential, the flexural rigidity of graphene is calculated to be 0.797 eV. A lattice cell model is developed to calculate the multiscale Green's function by imposing the fundamental solution of a plate as the boundary condition. Transverse deflection is calculated for a clamped graphene lattice subjected to uniform pressure, which agrees with the continuum model results for a Kirchhoff plate.
Applied Physics Letters
Christoffel equations, continuum Green's function, flexural rigidity of plate, Kirchhoff plate, lattice statics Green's function