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The elastic response of a circular single graphene sheet with a diameter of 65.32
A under a transverse central load is studied using molecular dynamics (MD),
closed-form elasticity solution (EL), and finite element method (FEM). Results
showed that the mismatch in deformation profiles between MD calculations and
continuum mechanics methods is about 8~9% at a central deflection of one graphene
layer thickness. The mismatch reduces to less than 5% when the central
deflection increased to a 10-layer thickness. The mismatch rooted from
mechanics: MD predicts predominant bond stretching mode while continuum mechanics
predict a bending to stretching transition process under increasing deflection.
Results suggest that continuum mechanics can yield predictions close to molecular
mechanics under large deformation for certain loading configurations when modes
of deformation are similar.
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