This paper studies the dynamic buckling behavior of multi-walled carbon nanotubes （MWNTs） subjected to step axial loading. A buckling condition is derived, and numerical results are presented for MWNTs under fixed boundary conditions. It is shown that the critical buckling load of MWNTs is of multi-branches and decreases as the time elongates. The associated buckling modes for different layers of MWNTs can be either in-phase or out of phase, which is related to the branch that the critical buckling load belongs to. For MWNTs with the same innermost tube radius, the critical buckling load is decreased when increasing the layers.
The dynamics equation for each individual atom is established directly around the equilibrium state of the system of N atoms based on the inter-atomic potential energy of EAM model.Using the theory of lattice dynamics and periodical boundary condition,the 3N×3N stiffness matrix in eigen equations of vibration frequencies for a parallelepiped crystal is reduced to a 3n×3n matrix of eigen equations of vibration frequencies for a unit lattice.The constitutive relation of the crystal at finite temperature is extracted based on the quantum-mechanical principle.The thermodynamic properties and the stress-strain relationships of crystal Cu with large plastic deformation at different temperatures are calculated,the calculation results agree well with experimental data.
By solving the total energy equation, we obtain the formula of exchange-correlation functional for the first time. This functional is usually determined by fitting experimental data or the numerical results of models. In the uniform electron gas limit, our exchangecorrelation functional can exactly reproduce the results of Perdew-Zunger parameterization from the jellium model. By making use of a particular solution, our exchange-correlation functional could take into accotmt the case of non-uniform electron density, and its validity can be confirmed through comparisons of the band structure, equilibrium lattice constant, and bulk modulus of aluminum and silicon. The absence of mechanical prescriptions for the systematic improvement of exchange-correlation functional hinders further development of density-functional theory （DFT）, and the formula of exchange-correlation functional given in this study might provide a new perspective to help DFT out of this awkward situation.
In the present research,the measurement fluctuations of mechanical properties in nanowires (NWs) are investigated by using the molecular dynamics simulation.The large numbers of simulations are performed to study the yield behaviors of the NWs.The results have shown that the yield behavior of the smaller diameter NW is more sensitive to the presence of vacancies,and the dispersion of the measured mechanical properties for the small scale NW is larger than that for the large scale NW.Present results have also shown that vacancies escape from the bulk to the free surfaces as a result of high stress applied at the small scale systems similar to the dislocation starvation phenomenon observed in the compression test of nano-pillars,and dislocation nucleation induced by surface defect occurs after the vacancy reaches free surface leading to lower yield strength.Moreover,the strong surface vacancy interactions at the nanoscale level are also investigated.
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.
