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Macroscopic fracture parameters are investigated on 2D graphene systems containing atomic-scale cracks. In the discrete atomistic simulations the interatomic forces are described by the Tersoff-Brenner potential. Two methods to calculate the elastic energy release rates in atomic systems, the global energy method and the local force method, are developed. The values of energy release rates of several graphene systems in symmetric (mode I) and antisymmetric (mode II) small deformation are obtained from atomistic simulations and then compared with the results obtained through homogenized material properties based on linear elastic fracture mechanics. The results show good agreement between discrete atomistic and continuum mechanics modeling for fracture. Meanwhile, atomic stress fields in front of crack tips are investigated through molecular mechanics simulation by applying remote K-field deformation. The atomic stress distributions match very well with those of linear elastic solutions. These establish connections of fracture parameters between microscopic and macroscopic description of fracture in covalently bonded solids.
Jin et al. (Fri,) studied this question.