Axially compressed buckling of pressured multiwall carbon nanotubes

Axisymmetric compressive buckling of multi-walled carbon nanotubes under different boundary conditions

“…In this paper, as that used by Ru [7,8] and Wang et al [11,12], a linearized analysis is adopted to model the effect of van der Waals forces between intertube, i.e., the pressure p k(k+1) due to buckling can be described by…”

“…It is seen from Eq. (4) that, for axisymmetric compressive buckling of MWNTs, it is only necessary to know the values of the effective bending stiffness D k and the inplane stiffness Eh k , where k = 1, 2, · · · , N. Here, we take [6,12,23].…”

“…Figures 6 and 7 show, respectively, the critical buckling load versus inner/innermost radius for axisymmetric compressive buckling of DWNTs and five-layer MWNTs subjected to simply supported boundary condition, with a comparison to the corresponding critical buckling load for axial compressive buckling calculated from the model presented in Ref. [12]. It can be seen that, for both DWNTs and five-layer MWNTs, the critical buckling load for axial compressive buckling and the one for axisymmetric compressive buckling are very close to each other, and have the same trend of variation versus the inner/innermost radius.…”

“…In their results, it was indicated that, in some mechanical properties of CNTs from measurements, one needs to be particularly cautious in using classical results obtained from the linear elasticity. Wang et al [11,12] studied elastic buckling of individual MWNTs under external radial pressure and axially compressed buckling of pressured MWNTs using a multiple-shell model. Their results showed that the predicted critical pressure and the predicted increment of critical axial stress due to an internal radial pressure using continuum mechanics model were in reasonably good agreement with the experiment results [13] and the results for filled CNTs by molecular dynamics simulations [14], respectively.…”

“…For MWNTs, the van der Waals interaction pressures (per unit area) between the k-th tube and the (k + 1)-th tube are equal and opposite. Thus, the (inward) pressure exerted on the k-th tube due to the (k + 1)-th tube, p k(k+1) , and the similar (inward) pressure exerted on the (k + 1)-th tube due to the k-th tube, p (k+1)k , can be related by [11,12] …”