Rupture of graphene sheets with randomly distributed defects.

We use atomistic simulation (molecular mechanics and molecular dynamics) to investigate failure of graphene sheets containing randomly distributed vacancies. We investigate the dependency of the failure stress on defect concentration and sheet size and show that our findings are consistent with the Duxbury-Leath-Beale (DLB) theory of mechanical or electric breakdown in random media. The corresponding distribution of failure stresses falls into the Gumbel, rather than the Weibull class of extremal statistics. By comparing molecular mechanics and zero-temperature molecular dynamics simulations we establish the role of kinetic energy in crack propagation and its impact on crack patterns emerging before sheet rupture. [ABSTRACT FROM AUTHOR]