  Graphene-based papers attract particular interests recently owing to their
outstanding properties, the key of which is their layer-by-layer hierarchical
structures similar to the biomaterials such as bone, teeth and nacre, combining
intralayer strong sp2 bonds and interlayer crosslinks for efficient load
transfer. Here we firstly study the mechanical properties of various interlayer
and intralayer crosslinks via first-principles calculations and then perform
continuum model analysis for the overall mechanical properties of
graphene-based papers. We find that there is a characteristic length scale
l_{0}, defined as \Sqrt{Dh_{0}/4G}, where D is the stiffness of the graphene
sheet, h_{0} and G are the height of interlayer crosslink and shear modulus
respectively. When the size of the graphene sheets exceeds 3l_{0}, the
tension-shear (TS) chain model that are widely used for nanocomposites fails to
predict the overall mechanical properties of the graphene-based papers. Instead
we proposed here a deformable tension-shear (DTS) model by considering the
elastic deformation of the graphene sheets, also the interlayer and intralayer
crosslinks. The DTS is then applied to predict the mechanics of graphene-based
paper materials under tensile loading. According to the results we thus obtain,
optimal design strategies are provided for designing graphene papers with
ultrahigh stiffness, strength and toughness.
