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• Compressive properties of 3D graphene are studied by theory and MD simulations. • The unified constitutive relations of three kinds of 3D graphene are derived. • Compressive deformation mechanisms of three kinds of 3D graphene are discussed. • The configuration-property relationships of 3D graphene are elucidated. • Energy absorption capacities of three kinds of 3D graphene are analyzed. Combining molecular dynamics (MD) simulations and continuum modeling, the uniaxial in-plane compressive properties of honeycomb three-dimensional (h3D), triangle-like 3D (t3D) and non-equilateral hexagon 3D (nh3D) graphene are investigated to elucidate configuration-property relationships, and the constitutive relations of three kinds of 3D graphene are derived to evaluate the compressive mechanical properties. Based on theoretical and MD simulation results, it is found that the compressive stress-strain responses of 3D graphene can be divided into five stages. The compressive mechanical properties and deformation mechanisms of each stage are different. When 3D graphene is compressed, graphene sidewalls undergo rotations, bending and buckling deformations, collapses. Because graphene sidewalls of h3D graphene are prone to undergo buckling deformations, there is large locking strain in h3D graphene. For t3D and nh3D graphene, their high plateau stress is attributed to unique configurations. Moreover, we also find that with increasing graphene sidewall width, Young's modulus and plateau stress of 3D graphene gradually decrease. In addition to the above investigations, the energy absorption mechanisms and compression-unloading stress-strain curves of 3D graphene are also studied. It is found that there are extraordinary compression-recovery properties and energy absorption capacities in 3D graphene. Finally, the selection criteria of 3D graphene are proposed. [Display omitted] [ABSTRACT FROM AUTHOR]

Two-dimensional (2D) graphene possesses a variety of excellent properties. It is worth using 2D graphene as building block to construct novel three-dimensional (3D) graphene which "inherits" superb performance of 2D graphene. Combining theoretical calculations and finite element method (FEM) based on molecular structural mechanics, the effects of graphene sidewall width, junction structure, in-plane domain size and in-plane overall shape on the elastic properties of zigzag honeycomb 3D graphene and three types of triangle-like 3D graphene are investigated, and the analytical expressions for Young's modulus of triangle-like 3D graphene are derived. The results of FEM are consistent with those of theoretical method. It is found that as graphene sidewall width increases, in-plane/out-of-plane Young's moduli of the above-mentioned 3D graphene first decrease and then tend to stabilize. For the armchair and zigzag triangle-like 3D graphene (sidewall width remains unchanged) with rectangular in-plane overall shape, the Young's modulus will vary with in-plane domain size. These results show that the elastic properties of 3D graphene are strongly dependent on structural size. In addition, junction structure has little influence on the elastic properties of 3D graphene. • A novel triangle-like 3D graphene containing sp3-sp3 carbon bond is constructed. • The size-dependent Young's modulus of triangle-like 3D graphene is investigated. • Analytical expressions of Young's modulus of triangle-like 3D graphene are derived. • The influencing factors for elastic properties of 3D graphene are studied by FEM. [ABSTRACT FROM AUTHOR]