Dynamic shell buckling behavior of multi-walled carbon nanotubes embedded in an elastic medium

This paper studies the dynamic shell buckling behavior of multi-walled carbon nanotubes(MWNTs) embedded in an elastic medium under step axial load based on continuum mechanics model.It is shown that,for occurrence of dynamic shell buckling of MWNTs or MWNTs embedded in an elastic medium,the buckling stress is higher than the critical buckling stress of the corresponding static shell buckling under otherwise identical conditions.Detailed results are demonstrated for dynamic shell buckling of individual double-walled carbon nanotubes(DWNTs) or DWNTs embedded in an elastic medium.A phenomenon is shown that DWNTs or embedded DWNTs in dynamic shell buckling are prone to axisymmetric buckling rather than non-axisymmetric buckling.Numerical results also indicate that the axial buckling form shifts from the lower buckling mode to the higher buckling mode with increasing buckling stress,but the buckling mode is invariable for a certain domain of buckling stress.Further,an approximate analytic formula is presented for the buckling stress and the associated buckling wavelength for dynamic axisymmetric buckling of embedded DWNTs.The effect of radii is also examined.