Molecular-Dynamics Simulations on Nanoindentation of Graphene-Diamond Composite Superstructures in Interlayer-Bonded Twisted Bilayer Graphene: Implications for Mechanical Metamaterials

We report results of a systematic computational analysis of the mechanical and structural response to indentation loading of nanodiamond superstructures in interlayer-bonded twisted bilayer graphene (IB-TBG), which are formed by patterned hydrogenation of commensurate graphene bilayers. The analysis is based on molecular-dynamics simulations of nanoindentation of IB-TBG nanodiamond superstructures over a broad range of concentration of sp3-hybridized interlayer-bonded C atoms (fsp3), which provides a metric of nanodiamond content in these 2D graphene-diamond nanocomposite materials. We find that superstructures characterized by a fsp3 below a critical level of ∼4.1% exhibit a strongly nonlinear inelastic response to indentation up to the onset of fracture, which is driven by a nondissipative and nonrecoverable inelastic deformation mechanism that is responsible for inducing a stiffening effect, as well as large hysteresis loops in indentation loading/unloading cycles. Detailed structural characterization reveals that this inelastic mechanism is mediated by the relative twisting between the top and bottom layers of the nanodiamond clusters in the central region (directly below the indenter tip) of the indented superstructure. In addition, we find that these nanodiamond superstructures are characterized by a high elastic modulus and high deformability, as measured by the maximum vertical deflection at the breaking point, and that both the deformability and the elastic modulus of such superstructures are relatively insensitive to their interlayer bond density. The strength of the superstructures decreases monotonically with increasing fsp3 but remains very high even at high values of nanodiamond fraction. Finally, we characterize in detail the structural evolution of the indented superstructures past their fracture initiation, and elucidate the effects of structural and indentation parameters on their structural response. In general, we find that these IB-TBG nanodiamond superstructures exhibit remarkable resistance to indentation loading and establish them further as 2D mechanical metamaterials.