On the use of continuum mechanics to estimate the properties of nanotubes

Govindjee, Sanjay; Sackman, Jerome L.

doi:10.1016/s0038-1098(98)00626-7

Cited by 282 publications

(116 citation statements)

References 4 publications

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“…Due to the aspect ratio and tube-like geometry of SWNT, many studies have been conducted concerning the buckling and bending response of nanotubes using both theoretical [12,15,[17][18][19][20] and experimental [21,22] approaches. In particular, Overney et al [17] conducted a computational study and calculated a bending parameter of a graphene sheet based on the vibrational modes of a nanotube.…”

Section: Bending Rigiditymentioning

confidence: 99%

“…Using the computationally obtained bending parameters, they calculated the Young's modulus and wall thickness of the shell. Govindjee and Sackman [19] theoretically investigated the validity of continuum mechanics at the nano-scale by examining the bending of multi-walled carbon nanotubes. They also assumed that the bending rigidity of each layer is proportional to the Young's modulus and moment of inertia.…”

Section: Bending Rigiditymentioning

confidence: 99%

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Equivalent-continuum modeling of nano-structured materials

Odegard

2002

Composites Science and Technology

581

302

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A method has been proposed for developing structure-property relationships of nano-structured materials. This method serves as a link between computational chemistry and solid mechanics by substituting discrete molecular structures with equivalent-continuum models. It has been shown that this substitution may be accomplished by equating the molecular potential energy of a nano-structured material with the strain energy of representative truss and continuum models. As important examples with direct application to the development and characterization of singlewalled carbon nanotubes and the design of nanotube-based structural devices, the modeling technique has been applied to two independent examples: the determination of the effectivecontinuum geometry and bending rigidity of a graphene sheet. A representative volume element of the chemical structure of graphene has been substituted with equivalent-truss and equivalentcontinuum models. As a result, an effective thickness of the continuum model has been determined. The determined effective thickness is significantly larger than the inter-planar spacing of graphite. The effective bending rigidity of the equivalent-continuum model of a graphene sheet was determined by equating the molecular potential energy of the molecular model of a graphene sheet subjected to cylindrical bending (to form a nanotube) with the strain energy of an equivalent-continuum plate subjected to cylindrical bending.

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Section: Bending Rigiditymentioning

confidence: 99%

Section: Bending Rigiditymentioning

confidence: 99%

Equivalent-continuum modeling of nano-structured materials

Odegard

2002

Composites Science and Technology

581

302

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“…We use Tersoff-Brenner potential for all the simulations on (10, 10) CNTs of different lengths at temperature of 300 K. Compression of CNTs (with and without polymer matrix) is simulated by prescribing end displacement (0.05 Å) at both the ends followed by equilibration (for 1000 steps). Figure 1 shows the compressive stress-displacement plot for (10, 10) nanotubes of different aspect ratios (10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22). Stress is calculated as the average of reaction force experienced by the fixed atoms over 100 time steps, divided by the cross sectional area (with thickness of 3.4 Å).…”

Section: Buckling Of Neat Carbon Nanotubesmentioning

confidence: 99%

“…Garg and Sinnott [20] have studied the compressive behavior of functionalized CNTs. There have been several other investigations on buckling of nanotubes using continuum beam or shell models [21,22,23]. Though this large volume of work concentrates on buckling of nanotubes by themselves, there have been relatively few studies on the compressive behavior of nanotubes when embedded in composites [15,18].…”

Section: Introductionmentioning

confidence: 99%

Role of atomic scale interfaces in the compressive behavior of carbon nanotubes in composites

Namilae

Chandra

2006

Composites Science and Technology

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“…These are atomistic model (Ball, 2001;Baughman et al, 2002), semi-continuum (Li and Chou, 2003) and continuum models (Govindjee and Sackman, 1999;He et al, 2005). However, both atomistic and semi-continuum models are computationally expensive and are unsuitable for analyzing large-scale systems.…”

Section: Introductionmentioning

confidence: 99%

Static analysis of nanoplates based on the nonlocal Kirchhoff and Mindlin plate theories using DQM

Kananipour

2014

Lat. Am. j. solids struct.

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In this study, static analysis of the two-dimensional rectangular nanoplates are investigated by the Differential Quadrature Method (DQM). Numerical solution procedures are proposed for deflection of an embedded nanoplate under distributed nanoparticles based on the DQM within the framework of Kirchhoff and Mindlin plate theories. The governing equations and the related boundary conditions are derived by using nonlocal elasticity theory. The difference between the two models is discussed and bending properties of the nanoplate are illustrated. Consequently, the DQM has been successfully applied to analyze nanoplates with discontinuous loading and various boundary conditions for solving Kirchhoff and Mindlin plates with small-scale effect, which are not solvable directly. The results show that the above mentioned effects play an important role on the static behavior of the nanoplates.

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On the use of continuum mechanics to estimate the properties of nanotubes

Cited by 282 publications

References 4 publications

Equivalent-continuum modeling of nano-structured materials

Equivalent-continuum modeling of nano-structured materials

Role of atomic scale interfaces in the compressive behavior of carbon nanotubes in composites

Static analysis of nanoplates based on the nonlocal Kirchhoff and Mindlin plate theories using DQM

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