  In this study, we have comprehensively investigated the scaling law for
elastic properties of three-dimensional honeycomb-like graphenes (3D-graphenes)
using hybrid neural network potential based molecular dynamics simulations and
theoretical analyses. The elastic constants as functions of honeycomb hole
size, denoted by the graphene wall length $L$, were provided. All five
independent elastic constants in the large $L$ limit are proportional to
$L^{-1}$. The associated coefficients are combinations of two-dimensional
graphene's elastic constants. High-order terms including $L^{-2}$ and $L^{-3}$
emerge for finite $L$ values. They have three origins, the distorted areas
close to the joint lines of 3D-graphenes, the variation of solid angles between
graphene plates, and the bending distortion of graphene plates. Significantly,
the chirality becomes essential with the decreasing of $L$, because the joint
line structures are different between the armchair and zigzag type
3D-graphenes. Our findings provide insights into the elastic properties of
graphene-based superstructures and can be used for further studies on
graphene-based materials.
