A continuum‐to‐atomistic bridging domain method for composite lattices

Xu, Mingkun; Gracie, Robert; Belytschko, Ted

doi:10.1002/nme.2745

Cited by 26 publications

(14 citation statements)

References 39 publications

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“…Promising approaches based on a concurrent coupling of a fine-scale model in the regions where fracture/dislocations occur with homogenized models elsewhere were presented. [64][65][66][67] Alternative methods propose to reduce the computational expense through algebraic model reduction. [68][69][70][71] Ultimately, these approaches aim at permitting to study structures of engineering relevance at an affordable computational cost.…”

Section: Mechanical Models Of Graphenementioning

confidence: 99%

Defect Engineering of 2d Monatomic-Layer Materials

et al. 2013

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Atomic-thick monolayer two-dimensional materials present advantageous properties compared to their bulk counterparts. The properties and behavior of these monolayers can be modified by introducing defects, namely defect engineering. In this paper, we review a group of common two-dimensional crystals, including graphene, graphyne, graphdiyne, graphn-yne, silicene, germanene, hexagonal boron nitride monolayers and MoS 2 monolayers, focusing on the effect of the defect engineering on these two-dimensional monolayer materials. Defect engineering leads to the discovery of potentially exotic properties that make the field of two-dimensional crystals fertile for future investigations and emerging technological applications with precisely tailored properties.

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Section: Mechanical Models Of Graphenementioning

confidence: 99%

Defect Engineering of 2d Monatomic-Layer Materials

et al. 2013

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“…[25,9,26,2,24,32,21]), and the corresponding coupled methods for crystalline materials (cf. [39,7,23,10,8,4,3,5,6,15,14,36,17,16,27,30,18,19,20,35,28,37,38,43,44,1,22,34,35,42,41]). …”

Section: Introductionmentioning

confidence: 99%

Finite Element Analysis of Cauchy–Born Approximations to Atomistic Models

Makridakis

Süli

2012

Arch Rational Mech Anal

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ABSTRACT. This paper is devoted to a new finite element consistency analysis of Cauchy-Born approximations to atomistic models of crystalline materials in two and three space dimensions. Through this approach new "atomistic Cauchy-Born" models are introduced and analyzed. These intermediate models can be seen as first level atomistic/quasicontinuum approximations in the sense that they involve only short-range interactions. The analysis and the models developed herein are expected to be useful in the design of coupled atomistic/continuum methods in more than one dimension. Taking full advantage of the symmetries of the atomistic lattice we show that the consistency error of the models considered both in energies and in dual W 1,p type norms is O(ε 2 ), where ε denotes the interatomic distance in the lattice.

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“…In composite lattices, the secondary lattice atoms should still remain free of BDM constraints to allow internal relaxation, as mentioned earlier. However, we maintain the conventional averaging weighting scheme described earlier instead of adopting the scheme developed in , which is limited in its applicability to nearest‐neighbor interactions. We accomplish the same equilibrium effect by applying forces asymmetrically, that is, between atoms existing on the primary and secondary sublattices, the force applied is

{\overset{f}{falsemml-overline}}_{α} MathClass-rel= ({, \begin{matrix} falsenonefalsearray \\ arrayleft w MathClass-open(X_{α}, X_{β} MathClass-close) f_{α} & arrayleft α \in primary lattice \\ arrayleft f_{α} & arrayleft α \in secondary lattice \end{matrix}) MathClass-punc.

…”

Section: Methodsmentioning

confidence: 99%

“…The difficulties of suppressing spurious wave reflection at the interfaces are addressed by Xu and Belytschko [11]. Additionally, the BDM has been extended for coupling with composite lattices such as graphene [12], which can be complicated for interface coupling methods. Similar approaches include the bridging scales method [13][14][15].The traditional multiscale methods described earlier are ineffective when applied to moving, branching, or expanding defects.…”

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Adaptive atomistic‐to‐continuum modeling of propagating defects

Moseley

Oswald

Belytschko

2012

Numerical Meth Engineering

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SUMMARY An adaptive atomistic‐to‐continuum method is presented for modeling the propagation of material defects. This method extends the bridging domain method to allow the atomic domain to dynamically conform to the evolving defect regions during a simulation, without introducing spurious oscillations and without requiring mesh refinement. The atomic domain expands as defects approach the bridging domain method coupling domain by fine graining nearby finite elements into equivalent atomistic subdomains. Additional algorithms coarse grain portions of the atomic domain to the continuum scale, reducing the degrees of freedom, when the atomic displacements in a subdomain can be approximated by FEM or extended FEM elements to within a certain homogeneity tolerance. The extended FEM approximations are created by fitting the broken inter‐atomic bonds of fractured surfaces and dislocation slip planes. Because atomic degrees of freedom are maintained only where needed for each timestep, the solution retains the advantages of multiscale modeling, with a reduced computational cost compared with other multiscale methods. Copyright © 2012 John Wiley & Sons, Ltd.

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A continuum‐to‐atomistic bridging domain method for composite lattices

Cited by 26 publications

References 39 publications

Defect Engineering of 2d Monatomic-Layer Materials

Defect Engineering of 2d Monatomic-Layer Materials

Finite Element Analysis of Cauchy–Born Approximations to Atomistic Models

Adaptive atomistic‐to‐continuum modeling of propagating defects

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