  Various fields such as mechanical engineering, materials science, etc., have
seen a widespread use of linear elastic fracture mechanics (LEFM) at the
continuum scale. LEFM is also routinely applied to the atomic scale. However,
its applicability at this scale remains less well studied, with most studies
focusing on non-linear elastic effects. Using a harmonic (snapping spring)
nearest-neighbor potential which provides the closest match to LEFM on a
discrete lattice, we show that the discrete nature of an atomic lattice leads
to deviations from the LEFM displacement field during energy minimization. We
propose that these deviations can be ascribed to geometrical nonlinearities
since the material does not have a nonlinear elastic response prior to bond
breaking. We demonstrate that crack advance and the critical stress intensity
factor in an incremental loading scenario is governed by the collectively
loaded region, and can not be determined analytically from the properties (max.
elongation, max. sustained force, etc.) of the stressed crack tip bond alone.
