The rise of straintronics—the possibility of fine-tuning the electronic properties of nanosystems by applying strain to them—has enhanced the interest in characterizing the mechanical properties of these systems when they are subjected to tensile (or compressive), shear and torsion strains. Four parameters are customarily used to describe the mechanical behavior of a macroscopic solid within the elastic regime: Young’s and shear moduli, the torsion constant and Poisson’s ratio. There are some relations among these quantities valid for elastic continuous isotropic systems that are being used for 2D nanocrystals without taking into account the non-continuous anisotropic nature of these systems. We present in this work computational results on the mechanical properties of six small quasi-square (aspect ratio between 0.9 and 1.1) graphene nanocrystals using the PM7 semiempirical method. We use the results obtained to test the validity of two relations derived for macroscopic homogeneous isotropic systems and sometimes applied to 2D systems. We show they are not suitable for these nanostructures and pinpoint the origin of some discrepancies in the elastic properties and effective thicknesses reported in the literature. In an attempt to recover one of these formulas, we introduce an effective torsional thickness for graphene analogous to the effective bending thickness found in the literature. Our results could be useful for fitting interatomic potentials in molecular mechanics or molecular dynamics models for finite carbon nanostructures, especially near their edges and for twisted systems.
