In-plane force fields and elastic properties of graphene

Abstract

Bond stretching and angle bending force fields, appropriate to describe in-plane properties of graphene sheets, are derived using first principles' methods. The obtained force fields are fitted by analytical anharmonic potential energy functions, providing efficient means of calculations in molecular mechanics simulations. Using both molecular dynamics simulations and first principles' methods, numerical results regarding the mechanical behavior of graphene monolayers under various loads, like uniaxial tension in different directions or hydrostatic tension, are presented and compared. Graphene's response in shear stress is also investigated using molecular dynamics, where a noticeable asymmetric mechanical behavior is found. Stress-strain curves and elastic constants, such as, Young modulus, Poisson's ratio, bulk modulus, and shear modulus, are calculated. Our results are compared with available experimental estimates, as well as, with corresponding theoretical calculations. Finally, the effects of the anharmonicity of the extracted bond stretching and angle bending potentials on the mechanical properties of graphene are discussed.