Although graphene sheets have 2D symmetry, carbon nanotubes by geometry have different properties in axial and radial directions. It has been single walled carbon nanotubes pdf that CNTs are very strong in the axial direction.
Since carbon nanotubes have a low density for a solid of 1. Although the strength of individual CNT shells is extremely high, weak shear interactions between adjacent shells and tubes lead to significant reduction in the effective strength of multi-walled carbon nanotubes and carbon nanotube bundles down to only a few GPa. 17 GPa for double-walled carbon nanotube bundles. CNTs are not nearly as strong under compression.
On the other hand, there was evidence that in the radial direction they are rather soft. Young’s modulus of on the order of several GPa showed that CNTs are in fact very soft in the radial direction. Radial direction elasticity of CNTs is important especially for carbon nanotube composites where the embedded tubes are subjected to large deformation in the transverse direction under the applied load on the composite structure. In this way, mechanical characterization is more accurate.