As
defects play a pivotal role in the mechanical properties of
graphene, much research has been underway to understand their specific
effects. However, the determination of mechanical properties of defective
graphene such as strength and ductility remains challenging, due to
the indeterminacy of local stress distributions, potentially released
out-of-plane behavior, and multidefect interactions that are involved
when subject to external loads. To cast light on the above complexities,
in this paper, stress field characteristics of defective graphene
are studied via molecular dynamics simulations, which are shown to
be strongly dependent on defect geometries. To detail this influence,
defect geometries are decoupled into defect size and shape, where
the former determines the area shielded from increasing stress and
consequently produces low-stress regions, while the latter determines
local stress concentration and governs stress distribution along the
defect rim. Additionally, it is shown that the nonuniformity of the
stress field can potentially release the out-of-plane degree of freedom
and therefore induce spatial patterns. To understand the effects of
multiple defects in graphene sheets, an analytical strategy of defect
grouping is proposed. The obtained understanding of the defect-affected
stress distribution is utilized to rationally optimize the collective
mechanical properties of defective graphene sheets. We show that even
though the mechanical properties of defective graphene sheets vary
with different defect geometry, the proportionality of ultimate strength
and failure strain is in general preserved. Finally, the relative
significance of the system parameters is discussed. This paper systematically
discusses the influence of defects on the stress field and collective
mechanical properties of graphene, which solidifies the defect-engineering
based tuning approach of the mechanics of graphene as well as other
two-dimensional materials.