  Cross-sectional area and volume become difficult to define as material
dimensions approach the atomic scale. This limits the transferability of
macroscopic concepts such as Young's modulus. We propose a new volume
definition where the enclosed nanosheet or nanotube average electron density
matches that of the parent layered bulk material. We calculate the Young's
moduli for various nanosheets (including graphene, BN and MoS2) and nanotubes.
Further implications of this new volume definition such as a Fermi level
dependent Young's modulus and out-of-plane Poisson's ratio are shown.
