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A nonlinear structural mechanics based approach for modeling the structure and the deformation of single-wall and multiwall carbon nanotubes (CNTs) is presented. Individual tubes are modeled using shell finite elements, where a specific pairing of elastic properties and mechanical thickness of the tube wall is identified to enable successful modeling with shell theory. The effects of van der Waals forces are simulated with special interaction elements. This new CNT modeling approach is verified by comparison with molecular dynamics simulations and high-resolution micrographs available in the literature. The mechanics of wrinkling of multiwall CNTs are studied, demonstrating the role of the multiwalled shell structure and interwall van der Waals interactions in governing buckling and postbuckling behavior.

A recently developed procedure for modeling the deformation of single and multi-wall carbon nanotubes [13,14] is applied to nanotube buckling and post-buckling under axial compression. Critical features of the model, which is grounded in elastic shell theory, include identification of (a) an appropriate elastic modulus and thickness pair matching both the wall stretching and bending resistances of the single atomic layer nanotube walls, and (b) a sufficiently stiff interwall van der Waals potential to preserve interwall spacing in locally buckled MWNTs, as is experimentally observed. The first issue is illustrated by parametric buckling studies on a SWNT and comparisons to a corresponding MD simulation from the literature; results clearly indicating the inadequacy of arbitrarily assigning the shell thickness to be the equilibrium spacing of graphite planes. Details of the evolution of local buckling patterns in a nine-walled CNT are interpreted based on a complex interplay of local shell buckling and evolving interwall pressure distributions. The transition in local buckling wavelengths observed with increasing post-buckling deformation is driven by the lower energy of a longer-wavelength, multiwall deformation pattern, compared to the shorter initial wavelength set by local buckling in the outermost shell. This transition, however, is contingent on adopting a van der Waals interaction sufficiently stiff to preserve interlayer spacing in the post-buckled configuration.

The peak stress method (PSM) is an engineering, finite element (FE)‐oriented method to rapidly estimate the notch stress intensity factors by using the singular linear elastic peak stresses calculated from coarse FE analyses. The average element size adopted to generate the mesh pattern can be chosen arbitrarily within a given range. Originally, the PSM has been calibrated under pure mode I and pure mode II loadings by means of Ansys FE software. In the present contribution, a round robin between 10 Italian universities has been carried out to calibrate the PSM with 7 different commercial FE codes. To this aim, several two‐dimensional mode I and mode II problems have been analysed independently by the participants. The obtained results have been used to calibrate the PSM for given stress analysis conditions in (i) FE software, (ii) element type and element formulation, (iii) mesh pattern, and (iv) criteria for stress extrapolation and principal stress analysis at FE nodes.

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Carbon nanotube (CNT) fibres, especially if perfect in terms of their purity and alignment,\ud are extremely anisotropic. With their high axial strength but ready slippage between the\ud CNTs, there is utmost difficulty in transferring uniformly any applied force. Finite element\ud analysis is used to predict the stress distribution in CNT fibres loaded by grips attached to\ud their surface, along with the resulting tensile stress–strain curves. This study demonstrates\ud that, in accordance with St Venant’s principle, very considerable length-to-diameter ratios\ud (103) are required before the stress becomes uniform across the fibre, even at low strains.\ud It is proposed that lack of perfect orientation and presence of carbonaceous material\ud between bundles greatly enhances the stress transfer, thus increasing the load the fibre\ud can carry before failing by shear. It is suggested that a very high strength batch of fibres previously\ud observed experimentally had an unusually high concentration of internal particles,\ud meaning that the pressure exerted by the grips would assist stress transfer between the\ud layers. We conclude that the strength of CNT fibres depends on the specific testing geometries\ud and that imperfections, whether by virtue of less-than-perfect orientation or of\ud embedded impurities, can act as major positive contributors to the observed strength