The elastic modulus of single-wall carbon nanotubes: a continuum analysis incorporating interatomic potentials

Zhang, P.; Huang, Yonggang; Geubelle, Philippe H.; Klein, Patrick A.; Hwang, Keh Chih

doi:10.1016/s0020-7683(02)00186-5

Cited by 378 publications

(224 citation statements)

References 61 publications

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“…16,17,26 The in-plane moduli of graphene can be treated following standard methods of crystal elasticity; other results have been recently reported. 37 Here, the precise expressions in terms of the functional form of the potential are provided, as well as a discussion of how to interpret them. The proposed theory also furnishes expressions for the flexural stiffness.…”

Section: A In-plane Modulimentioning

confidence: 99%

Finite crystal elasticity of carbon nanotubes based on the exponential Cauchy-Born rule

2004

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A finite deformation continuum theory is derived from interatomic potentials for the analysis of the mechanics of carbon nanotubes. This nonlinear elastic theory is based on an extension of the Cauchy-Born rule called the exponential Cauchy-Born rule. The continuum object replacing the graphene sheet is a surface without thickness. The method systematically addresses both the characterization of the small strain elasticity of nanotubes and the simulation at large strains. Elastic moduli are explicitly expressed in terms of the functional form of the interatomic potential. The expression for the flexural stiffness of graphene sheets, which cannot be obtained from standard crystal elasticity, is derived. We also show that simulations with the continuum model combined with the finite element method agree very well with zero temperature atomistic calculations involving severe deformations.Peer ReviewedPostprint (published version

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Section: A In-plane Modulimentioning

confidence: 99%

Finite crystal elasticity of carbon nanotubes based on the exponential Cauchy-Born rule

2004

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“…From Equation (10) and Equation (12), the bond length in terms of Green-Lagrange strain tensor is given by Equation (14) and Equation (15) [50],…”

Section: Atomic Structurementioning

confidence: 99%

“…The second Piola-Kirchhoff stress tensor, T, is given by Equation (50) [50], and can be converted to Cauchy stress tensor using Equation (60) [143] [144], where J is the Jacobian of the deformation. The constitutive response of nanocomposites is dependent on the ratio of element volume (VEL) to NRVE volume (VNRVE) as in Equation (61) [45].…”

Section: Constitutive Responsementioning

confidence: 99%

Modeling and Simulation of Graphene Based Polymer Nanocomposites: Advances in the Last Decade

Atif¹,

Inam²

2016

Graphene

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Modeling and simulation allow methodical variation of material properties beyond the capacity of experimental methods. The polymers are one of the most commonly used matrices of choice for composites and have found applications in numerous fields. The stiff and fragile structure of monolithic polymers leads to the innate cracks to cause fracture and therefore the engineering applications of monolithic polymers, requiring robust damage tolerance and high fracture toughness, are not ubiquitous. In addition, when "many-parts" cling together to form polymers, a labyrinth of molecules results, which does not offer to electrons and phonons a smooth and continuous passageway. Therefore, the monolithic polymers are bad conductors of heat and electricity. However, it is well established that when polymers are embedded with suitable entities especially nano-fillers, such as metallic oxides, clays, carbon nanotubes, and other carbonaceous materials, their performance is propitiously improved. Among various additives, graphene has recently been employed as nano-filler to enhance mechanical, thermal, electrical, and functional properties of polymers. In this review, advances in the modeling and simulation of grapheme based polymer nanocomposites will be discussed in terms of graphene structure, topographical features, interfacial interactions, dispersion state, aspect ratio, weight fraction, and trade-off between variables and overall performance.

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“…Through the years, it has been shown that continuum mechanics can be used to characterize precisely the mechanical behavior of structures even at the nano-scale. A good example may be the mechanics study of nanotubes (Zhang et al, 2002;Qian et al, 2002), which was possibly initiated by Yakobson et al (1996) who employed a continuum shell model and explained successfully the buckling behavior of nanotubes subjected to axial strain. Wong et al (1997) proposed an experimental setup to examine the elastic properties of nanostructures, the principle of which is based on a continuum beam model.…”

Section: Mechanics Gets Closer To Quantum Mechanicsmentioning

confidence: 99%

The renaissance of continuum mechanics

Chen

2014

J. Zheijang Univ.-Sci.

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Continuum mechanics, just as the name implies, deals with the mechanics problems of all continua, whose physical (or mechanical) properties are assumed to vary continuously in the spaces they occupy. Continuum mechanics may be seen as the symbol of modern mechanics, which differs greatly from current physics, the two often being mixed up by people and even scientists. In this short paper, I will first try to give an illustration on the differences between (modern) mechanics and physics, in my personal view, and then focus on some important current research activities in continuum mechanics, attempting to identify its path to the near future. We can see that continuum mechanics, while having a dominating impact on engineering design in the 20th century, also plays a pivotal role in modern science, and is much closer to physics, chemistry, biology, etc. than ever before.

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The elastic modulus of single-wall carbon nanotubes: a continuum analysis incorporating interatomic potentials

Cited by 378 publications

References 61 publications

Finite crystal elasticity of carbon nanotubes based on the exponential Cauchy-Born rule

Finite crystal elasticity of carbon nanotubes based on the exponential Cauchy-Born rule

Modeling and Simulation of Graphene Based Polymer Nanocomposites: Advances in the Last Decade

The renaissance of continuum mechanics

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