The atomic-scale finite element method

Liu, B.; Huang, Yingsong; Jiang, Hanqing; Qu, S.; Hwang, Keh Chih

doi:10.1016/j.cma.2003.12.037

Cited by 254 publications

(169 citation statements)

References 26 publications

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“…These include the atomistic-based continuum theory [1][2][3] for the mechanical properties of CNTs, the Euler-Bernoulli beam theory [4][5][6] for the bending and the critical buckling load, elastic cylindrical shell models [6][7][8] for the axial compression buckling and torsional buckling, space truss/frame models 9,10 for the Young's and shear moduli and the equivalent wall thickness, and the finite element technique, [11][12][13] which links the conventional finite element method with the atomistic-based potential for the bending and axial compression of CNTs. The results that have been obtained from these continuum models show a good agreement with experimental results or molecular dynamics simulations of single-walled carbon nanotubes ͑SWNTs͒, which indicates that with the suitable modification, conventional continuum mechanics can obtain results that are as accurate as molecular-dynamics simulation, but that are much more efficient, especially for large-scale simulations.…”

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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Section: Introductionmentioning

confidence: 99%

Continuum model for the vibration of multilayered graphene sheets

2005

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“…The AFEM, as described by Liu et al (2004), is based on an energy approach. It requires an interatomic energy potential, U, describing local or non-local bonding forces of an atom interacting with a chosen set of other surrounding atoms.…”

Section: Atomic Scale Finite Element Methods Formulationmentioning

confidence: 99%

“…The computational cost in modelling nanomaterials is a fundamental challenge. In order to overcome this challenge, the Atomic-scale Finite Element Method (AFEM) was developed and applied for multiscale analysis of carbon nanotubes (CNTs) by Liu and his co-authors (Liu et al, 2004;Liu et al, 2005). Presently, the AFEM can model and analyze the mechanical behavior of many materials at the nanoscale (Malakouti, 2006;Tao et al, 2016;Damasceno et al, 2015).…”

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confidence: 99%

Mechanical Behavior of Nano Structures Using Atomic-Scale Finite Element Method (AFEM)

Damasceno

Mesquita

Rajapakse

2017

Lat. Am. j. solids struct.

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This work presents a detailed description of the formulation and implementation of the Atomistic Finite Element Method AFEM, exemplified in the analysis of one-and two-dimensional atomic domains governed by the Lennard Jones interatomic potential. The methodology to synthesize element stiffness matrices and load vectors, the potential energy modification of the atomistic finite elements (AFE) to account for boundary edge effects, the inclusion of boundary conditions is carefully described. The conceptual relation between the cut-off radius of interatomic potentials and the number of nodes in the AFE is addressed and exemplified for the 1D case. For the 1D case elements with 3, 5 and 7 nodes were addressed. The AFEM has been used to describe the mechanical behavior of one-dimensional atomic arrays as well as twodimensional lattices of atoms. The examples also included the analysis of pristine domains, as well as domains with missing atoms, defects, or vacancies. Results are compared with classical molecular dynamic simulations (MD) performed using a commercial package. The results have been very encouraging in terms of accuracy and in the computational effort necessary to execute both methodologies, AFEM and MD. The methodology can be expanded to model any domain described by an interatomic energy potential.

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“…In MDFEM, atoms and atomic displacements are considered as nodes and translational degrees of freedom (nodal displacements), respectively. Both first and second derivatives of system energy are used in the energy minimization computation, hence, it is faster than the standard conjugate gradient method which uses only the first order derivative of system energy as discussed by Liu, B., et al [27]. The stiffness matrices of these elements are established based upon interatomic potentials.…”

Section: Framework For Analysismentioning

confidence: 99%

“…Force field parameters are taken from the work by Sevik, C., et al [26] for B-N interactions. While DFT (Density Functional Theory) calculations and MD (Molecular Dynamics) simulations are time-consuming, MDFEMs (Molecular Dynamic Finite Element Methods), sometime known as atomic-scale finite element methods or atomistic finite element methods, have been developed to analyze nanostructured materials in a computationally efficient way [27,28]. To achieve the atomic positions of the BN-NT under specific boundary conditions, MDFEM is here adopted.…”

Section: Framework For Analysismentioning

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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The atomic-scale finite element method

Cited by 254 publications

References 26 publications

Continuum model for the vibration of multilayered graphene sheets

Continuum model for the vibration of multilayered graphene sheets

Mechanical Behavior of Nano Structures Using Atomic-Scale Finite Element Method (AFEM)

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

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