Geometrical distortion leads to Griffith strength reduction in graphene membranes

Geometrical distortion plays an important role in modulating the mechanical responses of low-dimensional materials. Upon a structural transition from planar to non-planar conformations, the elastic energy stored in a membrane will be redistributed in between the stretching and bending modes of deformation. In this work, we present a molecular simulation based study that demonstrates remarkable reduction in the Griffith strength of graphene with the presence of out-of-plane distortion. The reduction is much more significant in mode II crack where the wrinkles are delocalized compared to the results for mode I crack where localized buckles are activated. Atomistic stress analysis and theoretical models based on the linear elastic fracture mechanics explain this strength reduction as a consequence of the out-of-plane distortion that releases in-plane elastic deformation, and predict the mechanical resistance of crack-containing graphene membranes. These findings are important for using graphene, and in general two-dimensional materials, as structural or functional membrane components where the non-planar distortion in unavoidable.