Prediction of fracture toughness and crack propagation of graphene via coupling of boundary element and nonlinear beam element

A new approach of multi-scale simulation via coupling of boundary element and finite element is proposed to predict fracture toughness and crack propagation of a single layer graphene sheet. In this simulation a molecular dynamics-based nonlinear beam element is developed for the atomistic model near the crack tip, whereas a special two-dimensional boundary element is employed for the continuum model in the remaining field of the cracked specimen. The material and section properties required in the nonlinear beam element are estimated through the equivalence between the potential energy of molecular dynamics and the elastic strain energy of continuum mechanics. With the estimated properties of beam element, the material properties of boundary element are further estimated by applying loads on the specimen of graphene, which is formed by a hexagonal lattice of carbon atoms. Coupling the nonlinear beam elements by boundary elements with the local-global concept of multi-scale modeling, a vast of computational time can be saved. The accuracy of near tip stresses obtained in our simulation remedies the inaccuracy of linear elastic fracture mechanics, and can be used for the prediction of atomic bond-breaking, which leads to crack propagation. The associated critical load can then be applied in the continuum model for the cracked specimen to predict mode I and mode II fracture toughness of graphene. The obtained values are then verified by the published results measured or predicted by the other methods. By varying the size of cracks and orientation of applied loads, several interesting phenomena have been observed and discussed in this paper.