H. Moshrefzadeh-Sani - School of Mechanical Engineering, Iran University of Science and Technology, Narmak, Tehran 16846, Iran
B. Saboori - School of Mechanical Engineering, Iran University of Science and Technology, Narmak, Tehran 16846, Iran
M. Alizadeh - School of Mechanical Engineering, Iran University of Science and Technology, Narmak, Tehran 16846, Iran

In this paper, a continuum model is proposed so that a Stone-Wales (SW) defected carbon nanotube(CNT) is replaced by an initial circumferential crack in a continuum cylindrical shell. For this purpose,the critical energy release rate and then the fracture toughness of a defected CNT are calculated usingthe results of an existing atomistic-based continuum finite element simulation. Finally, the equivalentcrack length is obtained from the fracture toughness. The proposed model can be applicable tovariouskinds of continuum-based simulations of nano-structures like nano-composites and nano-probes wherethe fracture resistance studies become important. It is concluded for a case study that the armchair (12,12) CNT containing a SW defect could be replaced with a continuum cylindrical shell with acircumferential crack length of 0.83 nm. Furthermore, the damage variable is discussed to achieve amethod for estimating the effective Young's modulus of defected nanotubes with numerous defectssubjected to the progressive damage. This estimation method is evaluated by the atomistic based FEsimulation of a double defected CNT.

NanotubeContinuum ModelRacture ToughnessEnergy Release RateDamage