A hybrid continuum and molecular mechanics model for the axial buckling of chiral single-walled carbon nanotubes

•Development of a hybrid continuum-atomistic model to study the axial buckling of chiral SWCNTs.•Establishing the variational form of nonlocal Flügge-type buckling equations within the framework of calculus of variation.•Applying the RayleighRitz analytical procedure to treat different boundary conditions.•Extracting analytical formulas for chirality- and size-dependant properties of SWCNTs based on MM in conjunction with DFT.•Calibration of appropriate nonlocal small scale factors using molecular dynamics results generated.

The purpose of this study is to describe the axial buckling behavior of chiral single-walled carbon nanotubes (SWCNTs) using a combined continuum-atomistic approach. To this end, the nonlocal Flugge shell theory is implemented into which the nonlocal elasticity of Eringen incorporated. Molecular mechanics is used in conjunction with density functional theory (DFT) to precisely extract the effective in-plane and bending stiffnesses and Poisson's ratio used in the developed nonlocal Flugge shell model. The Rayleigh-Ritz procedure is employed to analytically solve the problem in the context of calculus of variation. The results generated from the present hybrid model are compared with those from molecular dynamics simulations as a benchmark of good accuracy and excellent agreement is achieved. The influences of small scale factor, commonly used boundary conditions and chirality on the critical buckling load are fully explored. It is indicated that the importance of the small length scale is affected by the type of boundary conditions considered.

Graphical abstractA hybrid continuum-atomistic model is developed to study the axial buckling behavior of chiral single-walled carbon nanotubes.Figure optionsDownload full-size imageDownload as PowerPoint slide