A computational investigation of applicability of nonlinear fracture mechanics in nano-scale fracture of graphene

One of the main concerns for large-scale applications of graphene is unwanted fracture due to its low fracture toughness, close to that of an ideally brittle solid. However, graphene fracture properties and criteria have not been fully understood yet and the related understanding at the continuum-mechanics level is mostly limited to the linear elastic fracture mechanics (LEFM) investigations. In this paper, the applicability of nonlinear fracture mechanics (NLFM) to describe the fracture behavior of graphene is investigated through modeling the graphene sheets, including a center crack along the armchair and zigzag directions under mode I and mode II loading. A hyperelastic high-order continuum description is developed to be used in the nonlinear finite element simulations at the continuum level, by expanding the elastic strain energy in terms of the Lagrangian strains up to the seventh-order terms. The proposed continuum model is parameterized using the molecular dynamics (MD) simulation results to accurately reproduce the nonlinear mechanical behavior of graphene in uniaxial strain, equi-biaxial strain, and simple shear deformations. Finally, the applicability of NLFM, compared to LEFM, is investigated for graphene fracture through the continuum mechanics and MD fracture simulations. (C) 2001 Elsevier Science. All rights reserved