Atomistic simulations of J-integral in 2D graphene nanosystems

The J-integral is investigated in discrete atomic systems using molecular mechanics simulations. A method of calculating J-integral in specified atomic domains is developed. Two cases, a semi-infinite crack in an infinite domain under the remote K-field deformation and a finite crack length in a finite geometry under the tensile and shear deformation prescribed on the boundary, are studied in the two-dimensional graphene sheets and the values of J-integral are obtained under small-strain deformation. The comparison with energy release rates in Mode I and Mode 11 based on continuum theory of linear elastic fracture mechanics show good agreements. Meanwhile, the nonlinear strain and stress relation of a 2D graphene sheet is evaluated and is fitted with a power law curve. With necessary modifications on the Tersoff-Brenner potential, the critical values of J-integral of 2D graphene systems, which denoted as J(c), are eventually obtained. The results are then compared with those from the relevant references.