  The presence of defects such as vacancies in solids has prominent effects on
their mechanical properties. It not only modifies the stiffness and strength of
materials, but also changes their morphologies. The latter effect is extremely
significant for low- dimensional materials such as graphene. We show in this
work that graphene swells while point defects such as vacancies are created at
finite concentrations. The distorted geometry resulted from this areal
expansion, in combination with the in-plane softening effect, predicts an
unusual defect concentration dependence of stiffness measured for supported
graphene membrane in nanoindentation tests, which explains the defect- induced
stiffening phenomenon reported recently. The mechanism is elucidated through an
analytical membrane model as well as numerical simulations at atomistic and
continuum levels. In addition to elucidate the counter-intuitive observations
in experiments and computer simulations, our findings also highlight the role
of defect- modulated morphology engineering that can be quite effective in
designing nanoscale material and structural applications.
