Development of a 4-node finite element for the computation of nano-structured materials

Nasdala, Lutz; Ernst, Gerald

doi:10.1016/j.commatsci.2004.09.047

Cited by 54 publications

(22 citation statements)

References 12 publications

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“…Here, as is analytically described in [12], the springs have some advantages over beam elements in regard to accurate C-C bond simulation, i.e., they allow straightforward input of physical constants provided by molecular theory, and furthermore, they do not violate the molecular theory rule that the bonds must always remain straight. A comprehensive discussion on this topic can be found in [22]. The solution of the eigenvalue problem reveals numerous natural frequencies and corresponding mode shapes.…”

Section: Resultsmentioning

confidence: 99%

An efficient numerical model for vibration analysis of single-walled carbon nanotubes

2008

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This paper presents a linear spring-based element formulation for computation of vibrational characteristics of single-walled carbon nanotubes (CNTs). Three-dimensional nanoscale elements and corresponding elemental equations are developed for the numerical treatment of the dynamic behaviour of single-walled CNTs, including appropriate stiffness and mass characteristics. The atomistic microstructure of nanotubes is used to assemble the elemental equations and construct the dynamic equilibrium equation. The developed elements simulate the relative translations and rotations between atoms as well as the mass of the atoms. In this way, molecular mechanics theory can be applied directly because the atomic bonds are modelled by using exclusively physical variables such as bond stretching. The modelling is regenerative and can provide simulations for different geometric characteristics of the nanotubes. Numerical results are presented that illustrates new natural frequencies and mode shapes, going beyond the usual ones for various nanotubes under different support conditions and defects. Comparisons with corresponding numerical predictions from the literature, where they are possible, show very good agreement.

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Section: Resultsmentioning

confidence: 99%

An efficient numerical model for vibration analysis of single-walled carbon nanotubes

2008

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“…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 [43][44][45][46][47]. In MDFEM, atoms and atomic displacements are considered as nodes and translational degrees of freedom (nodal displacements), respectively.…”

Section: Numerical Proceduresmentioning

confidence: 99%

The role of defects in the tensile properties of silicene

Nguyen

2014

Appl. Phys. A

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Effects of vacancies and Stone-Wales defects on the mechanical properties of silicene are investigated through molecular dynamic finite element method with Tersoff potential. Young's modulus, Poisson's ratio and uniaxial tensile stress-strain curves are considered in the armchair and zigzag directions. It is found that pristine and lowly defective silicene sheets exhibit almost the same elastic nature up to fracture points. However, a single defect weakens significantly the silicene sheet, resulting in a considerable reduction in the fracture strength. One 2-atom vacancy in the sheet's center reduces 18-20 % in fracture stress and 33-35 % in fracture strain. The weakening effects of Stone-Wales defects vary with the tensile direction and the orientation of these defects.

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“…The residuum vector and the stiffness matrix of the finite element are explicitly stated as well. The finite elements presented in [17,19] take into account all possible interactions between the element nodes, thus yielding a fully occupied symmetric element stiffness matrix. The finite element presented in [8] considers the mutual interaction between the reference and neighboring atoms, yielding a sparse symmetric element stiffness matrix.…”

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confidence: 99%

Molecular mechanics in the context of the finite element method

Wackerfuß

2008

Numerical Meth Engineering

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SUMMARYIn molecular mechanics, the formalism of the finite element method can be exploited in order to analyze the behavior of atomic structures in a computationally efficient way. Based on the atom-related consideration of the atomic interactions, a direct correlation between the type of the underlying interatomic potential and the design of the related finite element is established. Each type of potential is represented by a specific finite element. A general formulation that unifies the various finite elements is proposed. Arbitrary diagonal-and cross-terms dependent on bond length, valence angle, dihedral angle, improper dihedral angle and inversion angle can also be considered. The finite elements are formulated in a geometrically exact setting; the related formulas are stated in detail. The mesh generation can be performed using wellknown procedures typically used in molecular dynamics. Although adjacent elements overlap, a double counting of the element contributions (as a result of the assembly process) cannot occur a priori. As a consequence, the assembly process can be performed efficiently line by line. The presented formulation can easily be implemented in standard finite element codes; thus, already existing features (e.g. equation solver, visualization of the numerical results) can be employed. The formulation is applied to various interatomic potentials that are frequently used to describe the mechanical behavior of carbon nanotubes. The effectiveness and robustness of this method are demonstrated by means of several numerical examples.

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Development of a 4-node finite element for the computation of nano-structured materials

Cited by 54 publications

References 12 publications

An efficient numerical model for vibration analysis of single-walled carbon nanotubes

An efficient numerical model for vibration analysis of single-walled carbon nanotubes

The role of defects in the tensile properties of silicene

Molecular mechanics in the context of the finite element method

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