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After a brief review of atomistic theories of defect dynamics in solids, a summary of Slepyan's first computation of dynamic fracture in a lattice is presented. Some of the main extensions and clarifi- cations of the original physical picture are then summarized. Many molecular dynamics simulations of fracture would benefit if Slepyan's work were better known. This article is part of the theme issue 'Modelling of dynamic phenomena and localization in structured media (part 1)'. [ABSTRACT FROM AUTHOR]

We examine the fracture mechanics of tearing graphene. We present a molecular dynamics simulation of the propagation of cracks in clamped, free-standing graphene as a function of the out-of-plane force. The geometry is motivated by experimental configurations that expose graphene sheets to out-of-plane forces, such as back-gate voltage. We establish the geometry and basic energetics of failure and obtain approximate analytical expressions for critical crack lengths and forces. We also propose a method to obtain graphene's toughness. We observe that the cracks' path and the edge structure produced are dependent on the initial crack length. This work may help avoid the tearing of graphene sheets and aid the production of samples with specific edge structures. [ABSTRACT FROM AUTHOR]