Qiang Lu and Rui Huang

Department of Aerospace Engineering and Engineering mechanics, University of Texas, Austin,
TX 78712, USA

Abstract: The unique lattice structure and properties of graphene has drawn tremendous interests recently.
By combining continuum and atomistic approaches, this paper investigates the mechanical
properties of single-atomic-layer graphene sheets. A theoretical framework of nonlinear
continuum mechanics is developed for graphene under both in-plane and bending deformation.
Atomistic simulations are carried out to deduce the effective mechanical properties. It is found
that graphene becomes highly nonlinear and anisotropic under finite-strain uniaxial stretch, and
coupling between stretch and shear occurs except for stretching in the zigzag and armchair
directions. The theoretical strength (fracture strain and fracture stress) of perfect graphene lattice
also varies with the chiral direction of uniaxial stretch. By rolling graphene sheets into
cylindrical tubes of various radii, the bending modulus of graphene is obtained. Buckling of
graphene ribbons under uniaxial compression is simulated and the critical strain for the onset of
buckling is compared to a linear buckling analysis.

This work has been submitted for review, and the manuscript is attached.

Update on September 7, 2009: This manuscript has been published as: Q. Lu and R. Huang, Nonlinear mechanics of single-atomic-layer
graphene sheets. Int. J. Applied Mechanics 1, 443-467 (2009).