Buckling of multiwalled carbon nanotubes under axial compression and bending via a molecular mechanics model

Based on a molecular mechanics model, analytical solutions are obtained for the critical buckling strain of multiwalled carbon nanotubes (MWNT’s) under axial compression and bending. We show that only part of the outer layers buckles first while the remaining inner part remains stable in a very thick MWNT, which is quite different from the initial buckling mode of a relatively thin MWNT in which all individual tubes buckle simultaneously. Such a difference in the initial buckling modes results in quite different size effects on the critical buckling strain of thin and thick MWNT’s. For instance, inserting more inner individual tubes may increase the critical buckling strain of a thin MWNT, but cannot increase the critical buckling strain of a thick tube. The effects of tube size on the initial buckling wavelength are also examined, and it is shown that the initial buckling wavelength is weakly dependent on the thickness of the MWNT.

Figure 1

Critical buckling strain for axial compressed SWNT’s from different methods.

Figure 2

Normalized initial buckling amplitudes of MWNT’s versus index number of outermost tubes under (a) axial compression and (b) bending.

Figure 3

Critical buckling strain of solid MWNT’s versus number of tube walls (tube outer diameter) under (a) axial compression and (b) bending.

Figure 4

Thickness effects on the critical buckling strain of MWNT’s when the tube outer diameter is kept constant.

Figure 5

Thickness effects on the critical buckling strain of MWNT’s when the tube inner diameter is kept constant.

Figure 6

Thickness effects on the critical buckling strain of MWNT’s when the tube mean diameter is kept constant.

Figure 7

Correlation of the critical buckling strain of MWNT’s with arbitrary size.

Figure 8

Comparison of predictions from different approaches for the initial buckling wavelength of MWNT’s.