Multiscale modelling of fracture in graphene sheets

Abstract

Most of the continuum scale processes, such as fracture, plasticity, etc., trace their origin to atomistic scale phenomena. To gain deeper insights into these processes, one needs to understand the behaviour of materials through the lens of multiscale methods. In this manuscript, we study the problem of fracture crack propagation in graphene sheets through a sequential multiscaling technique. The continuum-mechanical smoothed particle hydrodynamics (SPH) is coupled with the atomistic scale molecular dynamics (MD) simulations through proper constitutive modelling — the non-linear material properties and the mechanical equation of state which serve as the inputs to the SPH model are evaluated directly from the MD simulations. Such handshaking ensures that the continuum-scale SPH model is able to faithfully reproduce the atomistic scale stress–strain behaviour until failure. Using a pre-notched continuum scale graphene sheet, we show that the mode-I stress intensity factor obtained from our SPH model agrees well with the published literature. We subsequently study crack propagation in pre-notched graphene sheets, where the influence of the orientation of the notch is evaluated. Lastly, we take the case of a continuum-scale graphene sheet having randomly oriented cracks and identify the changes in the stress–strain behaviour vis-à-vis a pristine graphene sheet.