Atomistic FE modelling of the monotonic and hysteretic out-of-plane behaviour of graphene

This paper presents an investigation on the out-of-plane behaviour of graphene when cyclically loaded in-plane. Using an atomistic finite element approach, previous developed and validated by the authors, the stress-strain behaviour of graphene is evaluated under different cyclic loading tests (uniaxial, biaxial, shear). To simulate the bonds between carbon-carbon (C–C) atoms, beam elements are used, with their stiffness being described by the Morse potential associated to an elastoplastic law. Monotonic and hysteretic tests are performed and a comparison with the in-plane behaviour results, recently obtained, is accomplished. The instabilities of graphene, that occur in compression, are discussed and the buckling stresses are compared with those calculated from simple analytical formulae. The graphene failure modes obtained are also analysed. Finally, some concluding remarks are drawn about the main differences between the monotonic and hysteretic behaviour, as well as the in-plane and out-of-plane ones.