Carbon-based bulk nanostructures are believed to entail certain advantages over their parent low-dimensional materials and are promising candidates for supercapacitors due to their unique properties such as extremely high specific surface area and high conductivity. Herein the mechanical and structural properties of four types of carbon nanopolymorph-based nanomaterials were calculated using molecular dynamics simulations. Bulk carbon nanostructures composed of structural units of bent graphene flakes, short carbon nanotubes, fullerenes and their mixture were considered. The effect of the loading scheme and temperature was studied and constitutive relationships describing the deformation of the materials were given. The simulation results revealed that the effect of the loading scheme significantly depends on the type of structural units, and was slightly affected by the temperature especially for high densities. The constitutive equations obtained in this work can be applied to describe the mechanical behavior of new bulk carbon nanostructures.