Numerical validation of a concurrent atomistic-continuum multiscale method and its application to the buckling analysis of carbon nanotubes

Hollerer, Stefan

doi:10.1016/j.cma.2013.11.014

Cited by 17 publications

(2 citation statements)

References 38 publications

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“…As noted in the previous section, an inner displacement describing the rearrangement within the representative cell has to be considered. This is actually very important for the overall model because numerical experiments in [26] have shown that the material behavior is much too stiff if the inner relaxation is not performed. The global strain measures C and K are independent of the inner relaxation, and consequently, the inner relaxation can be performed on the constitutive level, apart from the global minimization.…”

Section: Inner Relaxationmentioning

confidence: 99%

A general approximation of the exponential Cauchy–Born hypothesis to model arbitrarily shaped shell‐like nanostructures within continuum mechanics

Findeisen

Wackerfuß

2015

Numerical Meth Engineering

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In this paper, a continuum membrane theory and its subsequent finite element approximation for the description of arbitrary shell-like nanostructures such as graphene-based nanostructures is presented. This is carried out by applying a multiscale approach where the continuum membrane is linked to the underlying atomistic lattice. This linkage is performed by the exponential generalization of the Cauchy-Born hypothesis, because the classical Cauchy-Born hypothesis is restricted to three-dimensional bulk structures and is thus not applicable to shell-like structures. However, the approximations of the exponential Cauchy-Born hypothesis published so far are limited to structures with a planar reference configuration. In this paper, we present an extended approximation, which does not require the reference configuration to be planar and is thus applicable to arbitrarily shaped shell-like nanostructures. A detailed elaboration of the related finite element implementation with important computational aspects is presented. Finally, the accuracy of the proposed method and its implementation is verified with several numerical examples.A GENERAL APPROXIMATION OF THE EXPONENTIAL CAUCHY-BORN HYPOTHESIS 749 introduced by Arroyo and Belytschko and applying the exponential Cauchy-Born hypothesis, but in contrast to the implementations presented in the literature (applying the simplification for planar reference configurations) [14,17], an approximation of the inverse exponential map is used as well. By doing this, the new method is no longer restricted to planar reference configurations, and the aforementioned initial transformation step is no longer required. The new finite membrane element developed in this work accounts for both the material nonlinearities (in terms of a nonlinear constitutive equation) and the geometrical nonlinearities (in terms of a geometrically exact formulation). The main idea of this work has already been presented by the current authors in [18]. Now, we present a detailed derivation of the method and a thorough analysis of its capabilities.The paper is organized as follows. In the beginning (Section 2), the essential basics of continuum mechanics and differential geometry are reviewed in view of a clear definition of the used terms and concepts. The basic idea of homogenization of atomistic structures in terms of the standard Cauchy-Born hypothesis for space-filling crystals is introduced in Section 3 and its limitation for the application to shell-like nanostructures is discussed subsequently. The different extensions of the classical Cauchy-Born hypothesis for the analysis of shell-like nanostructures, namely, the higher-order Cauchy-Born hypothesis introduced by Sunyk and Steinmann [19] and the exponential Cauchy-Born hypothesis introduced by Arroyo and Belytschko [14], are discussed. Section 4 investigates the approximation of the exponential Cauchy-Born hypothesis. The simplified approximation of the exponential Cauchy-Born hypothesis introduced by Arroyo and Belytschko [15] is summarized, and, ...

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Section: Inner Relaxationmentioning

confidence: 99%

A general approximation of the exponential Cauchy–Born hypothesis to model arbitrarily shaped shell‐like nanostructures within continuum mechanics

Findeisen

Wackerfuß

2015

Numerical Meth Engineering

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“…So far, theoretical studies of the buckling behavior under bending of BN-NTs seem still unexplored. It should be noted that the buckling behavior of CNTs under bending has been investigated by continuum methods, atomistic simulations and multi-scale approach [23,24]. In this paper, the buckling behavior of (15, 0) zigzag BN nanotubes under bending is studied through molecular dynamics finite element method with Tersoff potential.…”

Section: Introductionmentioning

confidence: 99%

The Buckling Behavior of Boron Nitride Nanotubes under Bending: An Atomistic Study

Nguyen¹

2017

JESE-A

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Abstract:In this paper, the buckling behavior of zigzag BN (Boron Nitride) nanotubes under bending is studied through molecular dynamics finite element method with Tersoff potential. The tube with namely (15, 0) BN zigzag tube is investigated. The critical bending buckling angle, moment and curvature are studied and examined with respect to the tube length-diameter ratios from 5 to 30. Effects of a SW (Stone-Wales) defect in the middle tube on the bending behavior are also discussed. The results show that the tube length affects significantly the bending behavior of these tubes. All tubes exhibit brittle fracture under bending. The buckling takes place at the middle in the compressive side of these tubes. These results are important information on the buckling behaviors of pristine and Stone-Wales BN nanotubes, which will be useful for their future applications.

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Atomistic Simulation of Boron Nitride Nanotubes Under Bending

Nguyen-Van

Nguyen-Danh

Le-Minh

2018

Proceedings of the International Conference on Advances in Computational Mechanics 2017

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Numerical validation of a concurrent atomistic-continuum multiscale method and its application to the buckling analysis of carbon nanotubes

Cited by 17 publications

References 38 publications

A general approximation of the exponential Cauchy–Born hypothesis to model arbitrarily shaped shell‐like nanostructures within continuum mechanics

A general approximation of the exponential Cauchy–Born hypothesis to model arbitrarily shaped shell‐like nanostructures within continuum mechanics

The Buckling Behavior of Boron Nitride Nanotubes under Bending: An Atomistic Study

Atomistic Simulation of Boron Nitride Nanotubes Under Bending

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