  We study the atomistic-to-continuum limit for a model of a quasi-static crack
evolution driven by time-dependent boundary conditions. We consider a
two-dimensional atomic mass spring system whose interactions are modeled by
classical interaction potentials, supplemented by a suitable irreversibility
condition accounting for the breaking of atmoic bonding. In a simultaneous
limit of vanishing interatomic distance and discretized time step, we identify
a continuum model of quasi-static crack growth in brittle fracture featuring an
irreversibility condition, a global stability, and an energy balance. The proof
of global stability relies on a careful adaptation of the jump-transfer
argument by Francfort and Larsen to the atomistic setting.
