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

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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.