Abstracts:Mechanical metamaterial beams (MMB) have been extensively studied given their potential functional applications in various areas, e.g. micro-electro-mechanical systems (MEMS), energy harvesting, and actuation. This study presents a novel class of graphene-reinforced MMB (GR-MMB) with arbitrarily periodic webbing. A size-dependent theoretical model is developed to predict and control the buckling response of the GR-MMB. The modified couple stress theory is expanded to include the effective material properties of microstructures. Clamped-clamped and simply supported GR-MMB with oval, hexagonal and cylindrical webbing patterns are showcased. Numerical simulations are conducted to validate the theoretical model and satisfactory agreements are obtained. Parametric studies are presented to unveil the effects of the graphene reinforcements and periodic design patterns on the buckling response of GR-MMB. The enhancement factor of the axial force between the GR-MMB and MMB, ψ, is studied with respect to the material ratio and geometric ratio. Density plots of the presented microstructures are provided to demonstrate the desired geometries that lead to the highest axial load and largest webbing diameter, i.e., lowest self-weight. The theoretical model presented in this study can be deployed to predict and tune the buckling response of GR-MMB with arbitrarily periodic webbing for different purposes.