Abstract

For interpreting results of an indentation test on a single-layer graphene sheet (SLGS), it is frequently modeled as an elastic, isotropic, and homogeneous membrane. With a small thickness (similar to 10(-10) m) as compared to a characteristic length (similar to 10(-6) m) of specimens used in experiments, the non-dimensional von-Karman factor (vKf similar to 10(8)) for a SLGS predicts negligible flexural rigidity (D similar to 10(-19) Nm). Since the membrane undergoes large deformations under a small force, a direct relationship between the resulting force-displacement curves and elasticities of the graphene sheet is still elusive. Here we compare predicted load-displacement curves for nanoindentation of a SLGS by using a full non-linear theory with St. Venant-Kirchhoff material, and the Foppl-von Karman nonlinear equations with a Hookean material. The nonlinear governing equations in each formulation are numerically integrated by the shooting method. Even though the radial variations of the membrane deflections computed with the two theories differ by at most 1.5%, the stresses, the declination angles, the curvatures and the strain energy densities may reach differences as high as 6.4%, 7.4%, 70% and 25%, respectively. These differences are significant enough to reexamine using the FvK derived solutions to find elastic constants from the test data.