  We investigate the stability of circular monolayer graphene subjected to a
radial load using non-equilibrium molecular dynamics simulations. When
monolayer graphene is radially stressed, after some small circular strain
($\sim 0.4%$) it buckles and bends into a new bowl like shape. Young's modulus
is calculated from the linear relation between stress and strain before the
buckling threshold, which is in agreement with experimental results. The
prediction of elasticity theory for the buckling threshold of a radially
stressed plate is presented and its results are compared to the one of our
atomistic simulation. Jarzynski equality is used to estimate the difference
between the free energy of the non-compressed states and the buckled states.
From a calculation of the free energy we obtain the optimum radius for which
the system feels the minimum boundary stress.
