▎ 摘　　要

The unique mechanical, physical, and chemical properties of carbon nanotubes and graphene project them as seemless and stand alone materials with performances much better than other metallic and nonmetallic materials in wide variety of applications. Due to their perfect hexagonal lattice structural configuration, electrons can be transmitted without resistance, heat can be conducted even better than in diamond, and loads are carried out and transferred more efficient than in high strength steels. However, carbon nanotubes and graphene sheets are not free of structural defects, which are basically induced during their processing and purification stages. Owing to the fact that defects exist in different configurations and they can considerably influence the performance and properties of carbon nanotubes and graphene, they are not always undesirable. Therefore, with increased interests in functionalization of carbon nanotubes and graphene, detailed studies and investigations regarding the effects of such vacancy defects, due to the absence of carbon atoms from the lattice structure, on their properties warrants a detailed investigation. Nevertheless, the advantages and disadvantages of the presence of vacancy defects strongly depend on their applications. In this work, an attempt is made to numerically model and analyze the effects of vacancy defects of carbon nanotubes and graphene sheets on their effective mechanical properties. The effects of these defects in different configurations of carbon nanotubes and graphene sheets are (i.e., armchair, chiral, and zig-zag, depending on the direction of applied load) reported. A detailed finite element analysis has been performed to predict their axial mechanical properties.