A chirality-dependent peridynamic model for the fracture analysis of graphene sheets

Abstract

Based on the bond-based peridynamic (BPD) method, a chirality-dependent peridynamic (CDPD) model is proposed for the fracture analysis of single layer graphene sheets (SLGS). The peridynamic (PD) parameters in the CDPD model are derived by analyzing the stress-strain relations of SLGS at atomic scale, and thus the CDPD model can provide a multiscale insight into the fracture analysis of SLGS with considering the effect of chirality. In order to increase the efficiency of CDPD simulations of large atomic-scale systems, a special coarse-grain (CG) technique is employed by considering the chiral structure of SLGS in the CDPD simulations. The effect of grid type, grid orientation and grid spacing on the numerical convergence is investigated. The proposed CDPD model is validated by comparing with the available molecular dynamics (MD) results, and the comparisons demonstrate the importance of considering the atomistic structure of SLGS when PD theory is applied in the fracture analysis because the chirality dominates the propagating directions of cracks. The crack propagations in SLGS with various chiralities are studied using the CDPD model. The numerical results indicate that the fracture of SLGS is significantly dependent on the chirality. Especially, examples of large-sized SLGS (750 nm × 750 nm) with about 20 million atoms in the corresponding fully atomistic systems demonstrate the applicability and effectiveness of the proposed CDPD model in the simulation of microscale structures of SLGS without loss of chiral features. To study such large systems is almost impractical for the fully atomistic simulation. This study also provides a significant insight for extending the PD model to the studies on chirality-related materials at microscale.