Nonlocal elasticity theory for graphene modeling and simulation: prospects and challenges

Liew, K. M.; Zhang, Yang; Zhang, L. W.

doi:10.1515/jmmm-2016-0159

Cited by 23 publications

(7 citation statements)

References 86 publications

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“…From the results and previous discussion, it is found that the microscale effect is not apparent for structures with dimensions in the order of microns, while it can be noticeable in nanoscale dimensions which is consistent with the observations of Wang and Liew [70]. Also, when the stress at the source of a nanoscale heating problem is determined, the non-local behavior is a key factor which cannot be ignored [16,[48][49][50]. According to this new non-local theory, we must define a new classification for all materials in accordance with the elastic non-Fig.…”

Section: The Effect Of Non-local Parametersupporting

confidence: 87%

“…The non-local continuum theory expressed by Koutsoumaris et al [48], either in integral or differential forms, is commonly utilized for describing the size dependency in micro-and nanoscale structures. Liew et al [49] literary studied the recent works related to the application of non-local elasticity theory for modeling and simulation of graphene sheets. Rajneesh et al [50] conducted a temporary study on the phase-lagged non-local thermoelastic thick micro-stretches.…”

Section: Introductionmentioning

confidence: 99%

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Computational analysis of an infinite magneto-thermoelastic solid periodically dispersed with varying heat flow based on non-local Moore–Gibson–Thompson approach

Abouelregal

Sedighi

Shirazi

et al. 2021

Continuum Mech. Thermodyn.

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In this investigation, a computational analysis is conducted to study a magneto-thermoelastic problem for an isotropic perfectly conducting half-space medium. The medium is subjected to a periodic heat flow in the presence of a continuous longitude magnetic field. Based on Moore–Gibson–Thompson equation, a new generalized model has been investigated to address the considered problem. The introduced model can be formulated by combining the Green–Naghdi Type III and Lord–Shulman models. Eringen’s non-local theory has also been applied to demonstrate the effect of thermoelastic materials which depends on small scale. Some special cases as well as previous thermoelasticity models are deduced from the presented approach. In the domain of the Laplace transform, the system of equations is expressed and the problem is solved using state space method. The converted physical expressions are numerically reversed by Zakian’s computational algorithm. The analysis indicates the significant influence on field variables of non-local modulus and magnetic field with larger values. Moreover, with the established literature, the numerical results are satisfactorily examined.

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Section: The Effect Of Non-local Parametersupporting

confidence: 87%

Section: Introductionmentioning

confidence: 99%

Computational analysis of an infinite magneto-thermoelastic solid periodically dispersed with varying heat flow based on non-local Moore–Gibson–Thompson approach

Abouelregal

Sedighi

Shirazi

et al. 2021

Continuum Mech. Thermodyn.

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show abstract

“…Equation (16) indicates that the local amplitude can be corrected for the nonlocal residual with the incorporation of ( ) as a nonlocal residual-based fictitious force. By introducing = / as a nonlocal residual-based correction factor, equation ( 16) can be rewritten in the form:…”

Section: Static Bending Of Nonlocal Euler-bernoulli Beamsmentioning

confidence: 99%

“…integral nonlocal theory, was used to investigate the dispersions of plane waves [9], stress concentrations near a crack tip [4], plasticity and damage of materials [10], softening plasticity [11], mechanics of nonlocal bars [12], and mechanics of nonlocal beams [13]. As for the differential nonlocal theory which depends on a differential operator, an uncountable list of studies were conducted; examples include [14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Correction of local elasticity for nonlocal residuals: application to Euler–Bernoulli beams

Shaat

2018

Meccanica

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Complications exist when solving the field equation in the nonlocal field. This has been attributed to the complexity of deriving explicit forms of the nonlocal boundary conditions. Thus, the paradoxes in the existing solutions of the nonlocal field equation have been revealed in recent studies.In the present study, a new methodology is proposed to easily determine the elastic nonlocal fields from their local counterparts without solving the field equation. This methodology depends on the iterativenonlocal residual approach in which the sum of the nonlocal fields is treaded as a residual field. Thus, in this study the corrections of the local-linear elastic fields for the nonlocal residuals in materials are presented. These corrections are formed based on the general nonlocal theory. In the context of the general nonlocal theory, two distinct nonlocal parameters are introduced to form the constitutive equations of isotropic-linear elastic continua. In this study, it is demonstrated that the general nonlocal theory outperforms Eringen's nonlocal theory in accounting for the impacts of the material's Poisson's ratio on its mechanics. To demonstrate the effectiveness of the proposed approach, the corrections of the local static bending, vibration, and buckling characteristics of Euler-Bernoulli beams are derived. Via these corrections, bending, vibration, and buckling behaviors of simple-supported nonlocal Euler-Bernoulli beams are determined without solving the beam's equation of motion.

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“…That graphene could be modeled in the framework of the non-local elasticity has been conjectured in the literature several times. A review of recent research studies on this matter can be found in [20]. Unlike classical continuum models, within the framework of non-local elasticity it is assumed that the stress at a reference point in a body depends not only on the strains at that point, but also on strains at all other points of the body.…”

Section: Introductionmentioning

confidence: 99%

A REBO-potential-based model for graphene bending by $Γ$-convergence

Davini,

Favata,

Paroni

2017

Preprint

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An atomistic to continuum model for a graphene sheet undergoing bending is presented. Under the assumption that the atomic interactions are governed by a harmonic approximation of the 2nd-generation Brenner REBO (reactive empirical bond-order) potential, involving first, second and third nearest neighbors of any given atom, we determine the variational limit of the energy functionals. It turns out that the Γ-limit depends on the linearized mean and Gaussian curvatures. If some specific contributions in the atomic interaction are neglected, the variational limit is non-local.

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Nonlocal elasticity theory for graphene modeling and simulation: prospects and challenges

Cited by 23 publications

References 86 publications

Computational analysis of an infinite magneto-thermoelastic solid periodically dispersed with varying heat flow based on non-local Moore–Gibson–Thompson approach

Computational analysis of an infinite magneto-thermoelastic solid periodically dispersed with varying heat flow based on non-local Moore–Gibson–Thompson approach

Correction of local elasticity for nonlocal residuals: application to Euler–Bernoulli beams

A REBO-potential-based model for graphene bending by $Γ$-convergence

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