An ordinary state-based peridynamic model for the fracture of zigzag graphene sheets

This study develops an ordinary state-based peridynamic coarse-graining (OSPD-CG) model for the investigation of fracture in single-layer graphene sheets (SLGS), in which the peridynamic (PD) parameters are derived through combining the PD model and molecular dynamics (MD) simulations from the fully atomistic system via energy conservation. The fracture failure of pre-cracked SLGS under uniaxial tension is studied using the proposed PD model. And the PD simulation results agree well with those from MD simulations, including the stress-strain relations, the crack propagation patterns and the average crack propagation velocities. The interaction effect between cracks located at the centre and the edge on the crack propagation of the pre-cracked SLGS is discussed in detail. This work shows that the proposed PD model is much more efficient than the MD simulations and, thus, indicates that the PD-based method is applicable to study larger nanoscale systems.

Modelling of Granular Fracture in Polycrystalline Materials Using Ordinary State-Based Peridynamics

An ordinary state-based peridynamic formulation is developed to analyse cubic polycrystalline materials for the first time in the literature. This new approach has the advantage that no constraint condition is imposed on material constants as opposed to bond-based peridynamic theory. The formulation is validated by first considering static analyses and comparing the displacement fields obtained from the finite element method and ordinary state-based peridynamics. Then, dynamic analysis is performed to investigate the effect of grain boundary strength, crystal size, and discretization size on fracture behaviour and fracture morphology.