▎ 摘　　要

Using first principle methods, we study the mechanical properties of monolayer and bilayer graphene with 50% and 100% coverage of hydrogen. We employ the vdW-DF, vdW-DF-C09(x), and vdW-DF2-C09(x) van der Waals functionals for the exchange correlation interactions that give significantly improved interlayer spacings and energies. We also use the PBE form for the generalized gradient corrected exchange correlation functional for comparison. We present a consistent theoretical framework for the in-plane layer modulus and the out-of-plane interlayer modulus and we calculate, for the first time, these properties for these systems. This gives a measure of the change of the strength properties when monolayer and bilayer graphene are hydrogenated. Moreover, comparing the relative performance of these functionals in describing hydrogenated bilayered graphenes, we also benchmark these functionals in how they calculate the properties of graphite. (C) 2013 AIP Publishing LLC.