Discrete and homogenized mechanical models for single walled carbon nanotubes

Abstract

In this paper, we propose two mechanical models for the single walled carbon nanotubes: (a) a discrete mechanical model at the nanoscale level based on replacing the atomic structure by a discrete lattice of elastic bars and (b) a homogenized continuous mechanical model based on atomistic experimental results on the stretching and angular variations of carbon atomic bonds. Two different interatomic mechanical models (linear and exponential) for the stretching–compression behavior of the carbon–carbon atomic bond have been used. The numerical results show that the homogenized asymptotic model is a good approximation of the full discrete model. The former has the advantage of requiring very little computational resources whereas the latter requires a huge computational cost hence limiting its application to structures with a small number of atoms and atomic bonds. Moreover, the obtained results show that the axial Young’s modulus is almost insensitive to the radius and the chirality but it is very sensitive to the choice of the interatomic mechanical models and their corresponding elastic constants. The linear interatomic model seems to be invalid when used for large deformation of the nanotubes, i.e. it is valid only for small displacements. On the other hand, and most importantly, the stress–strain curves obtained from the homogenized model using the exponential interatomic potential show that the nanotube type determines completely its mechanical characteristics. For instance, the tensile strength and elongation at break are the largest in the case of the armchair nanotubes and the smallest in the case of the zigzag nanotubes.