Mechanics of deformation of single- and multi-wall carbon nanotubes

Pantano, Antonio; Parks, David M.; Boyce, Mary C.

doi:10.1016/j.jmps.2003.08.004

Cited by 471 publications

(366 citation statements)

References 56 publications

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“…A special issue not explicitly included in MSM models (although the wall-curvature was included in the equations) is the preenergy, defined as the excess of strain energy from an infinite planar graphene sheet to the nanotube [17,32]. As has been shown [5,33,34,35], this preenergy is proportional to the curvature of the wall 1/R 2 (where R is the tube radius) leading to an stabilization effect into its cross-sectional area. In this paper, we introduce the preenergy as a system of initial strains which produces a 'prestressed state' previous to the action of any external loading.…”

Section: Introductionmentioning

confidence: 99%

A molecular structural mechanics model applied to the static behavior of single-walled carbon nanotubes: New general formulation

Merli

Lázaro

Monleón

et al. 2013

Computers & Structures

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ElsevierMerli Gisbert, R.; Lazaro, C.; Monleón Cremades, S.; Domingo Cabo, A. (2013). A molecular structural mechanics model applied to the static behavior of single-walled carbon nanotubes: New general formulation. Computers and Structures. 127:68-87. doi:10.1016/j.compstruc.2012.11.023 AbstractA new general formulation for the mechanical behavior of Single-Walled Carbon Nanotubes is presented. Carbon atoms are located at the nodes of an hexagonal honeycomb lattice wrapped into a cylinder. They are linked by covalent C − C bonds represented by a truss or spring element, and the three-body interaction among two neighboring covalent bonds is reproduced by a rotational spring. The main advantage of our approach is to allow general load conditions (and any chirality) with no need of specific formulation for each load case, in contrast with previous works [26], [27], [31]. Four load configurations are adopted: tension, compression, bending and torsion of cantivelered SWCNTs. Calculations with our own codes for both AMBER and Morse potential functions have been carried out, aimed to compare their final results. Initial positions of the atoms (nodes) into nanotube cylindrical geometry has been reproduced in great detail by means of a conformal mapping from the planar graphene sheet. Therefore, the effect of initial SWCNTs curvature has been introduced explicitly through a system of initial stresses (prestressed state) which contribute to maintain their circular cross-section. Numerical results and deformed shapes for nanotubes with several diameters and chiralities under each load case are used to obtain their mechanical parameters with the only objective of checking the present formulation with previous works [28], [30], [20], [24]. Also, the significance of the atomistic discrete simulations at the nano-scale size against other continuum models is underlined.

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Section: Introductionmentioning

confidence: 99%

A molecular structural mechanics model applied to the static behavior of single-walled carbon nanotubes: New general formulation

Merli

Lázaro

Monleón

et al. 2013

Computers & Structures

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“…Their simulations show that ultrahigh-frequency nanomechanical resonators can be achieved by using a MWNT. In addition, Pantano et al 23 carried out a finite element simulation on the bending and buckling of a MWNT, in which the interlayer vdW force was treated as a function of the interlayer distance by using the Lennard-Jones potential. More recently, the authors 24 of this paper derived two explicit formulas for the interlayer vdW force between two adjacent layers and any two layers of a MWNT.…”

Section: Introductionmentioning

confidence: 99%

Continuum model for the vibration of multilayered graphene sheets

2005

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The vibration analysis of multilayered graphene sheets ͑MLGSs͒ using a continuum model is reported in this paper. An explicit formula is derived to predict the van der Waals ͑vdW͒ interaction between any two sheets of a MLGS. Based on the derived formula, a continuum-plate model is developed for the vibration of MLGSs. Our investigation indicates that the lowest natural frequency ͑classical natural frequency͒ of a MLGS for a given combination of m and n is independent of the vdW interaction, but that all of the other higher natural frequencies ͑resonant frequencies͒ are significantly dependent on this interaction. The mode shapes that are associated with the natural frequencies are investigated for double-layered and ten-layered graphene sheets. We find that the vibration modes that are associated with the classical natural frequency of all the sheets are in the same direction and have the same amplitude, whereas the vibration modes of the sheets that are associated with the resonant frequencies are different due to the influence of the vdW interaction. Thus various resonance modes can be obtained by varying the number of layers of a MLGS.

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“…Fisher et al 24 developed a model which combines FEM results and micromechanical methods to predict the effective reinforcing modulus of a nanotube-reinforced polymer. Pantano et al 25 proposed an effective continuum/FE approach for modeling the structure and the deformation of single-and multiwalled CNTs. The simulation results of mechanical behavior of CNTs are in excellent agreement with MD results that are available in the literature.…”

Section: Introductionmentioning

confidence: 99%

Buckling of double-walled carbon nanotubes modeled by solid shell elements

Wang

Zhang

et al. 2006

Journal of Applied Physics

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A solid shell element model is proposed for the elastic bifurcation buckling analysis of double-walled carbon nanotubes ͑DWCNTs͒ under axial compression. The solid shell element allows for the effect of transverse shear deformation which becomes significant in a stocky DWCNT with relatively small radius-to-thickness ratio. The van der Waals ͑vdW͒ interaction between the adjacent walls is simulated by linear springs. Using this solid shell element model, the critical buckling strains of DWCNTs with various boundary conditions are obtained and compared with molecular dynamics results and those obtained by other existing shell and beam models. The results obtained show that the solid shell element is able to model DWCNTs rather well, with the appropriate choice of Young's modulus, tube thickness, and spring constant for modeling the vdW forces.

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Mechanics of deformation of single- and multi-wall carbon nanotubes

Cited by 471 publications

References 56 publications

A molecular structural mechanics model applied to the static behavior of single-walled carbon nanotubes: New general formulation

A molecular structural mechanics model applied to the static behavior of single-walled carbon nanotubes: New general formulation

Continuum model for the vibration of multilayered graphene sheets

Buckling of double-walled carbon nanotubes modeled by solid shell elements

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