Molecular-Dynamics Analysis of Nanoindentation of Graphene Nanomeshes: Implications for 2D Mechanical Metamaterials

We report results of a comprehensive computational study of the mechanical response to nanoindentation of graphene nanomeshes (GNMs) or nanoporous graphene, namely, single-layer graphene sheets with periodic arrangements of nanopores, based on molecular-dynamics simulations of nanoindentation tests according to a reliable interatomic bond-order potential. We find the GNMs' response to indentation to be nonlinearly elastic until fracture initiation, with elastic properties that depend strongly on the GNM porosity but are not sensitive to pore edge passivation, which, however, influences the GNM failure mechanism past fracture initiation. Increasing GNM porosity leads to a monotonic decrease of the 2D elastic modulus of the GNMs, and the modulus-porosity dependence follows a quadratic scaling law. The maximum stress reached at the GNM breaking point is high throughout the porosity range examined, even at very high porosity. The maximum deflection of the indented GNMs at their breaking point exhibits a minimum at porosities below 20%; beyond this critical porosity, the maximum deflection increases monotonically with increasing porosity and can reach values comparable to half of the indented sample radius at high porosities. Such high deformability is interpreted on the basis of the C-C bond length and stress distribution over the GNM at its breaking point. Moreover, our analysis reveals an inelastic, dissipative necking mechanism of GNM failure at high porosities that further enhances the excellent deformability of the GNMs. Our findings highlight the potential of graphene nanomeshes as 2D mechanical metamaterials whose mechanical response can be tuned by proper tailoring of their structural features.