Relationship between local buckling and atomic elastic stiffness in multi-walled carbon nanotubes under compression and bending deformations

Abstract

This paper discusses unified criteria for the local buckling of multi-walled carbon nanotubes in both compression and bending deformations from a standpoint of atomic simulations. Defective and non-defective five-walled carbon nanotubes are subjected to compression and bending deformation by the molecular dynamics method using the adaptive intermolecular reactive empirical bond order potential. The atomic elastic stiffness of each atom, Bijα, is then evaluated during the deformations to discuss the onset of local buckling. The Bijα corresponds to the second-order derivatives of the atomic energy, i.e., the gradient of the local stress–strain surfaces in six-dimensional strain space. If Bijα has a negative eigenvalue, a local unstable path will exist in the direction of the strain. Under compression, the smallest eigenvalues, λ(1)α, of the Bijα for all atoms changes to a negative value long before buckling occurs, while the second-smallest eigenvalues, λ(2)α, of the Bijα of some atoms change to a negative value just prior to buckling. Under bending deformation, the change in the positivity of λ(2)α corresponds to a rippling deformation on the side of compressive bending stresses. A variation in the location of defects in the carbon nanotubes affects the peak stresses under compression and the peak moments under a bending deformation. However, for all models, local buckling occurs from the dense region of atoms whose λ(2)α<0 in some outer layers. This suggests that the atomic elastic stiffness is capable of acting as an evaluation criterion for local buckling in multi-walled carbon nanotubes.