Concurrent coupling of length scales: Methodology and application

Broughton, Jeremy Q.; Abraham, Farid F.; Bernstein, Noam; Kaxiras, Efthimios

doi:10.1103/physrevb.60.2391

Cited by 565 publications

(409 citation statements)

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“…Our QCDFT method provides a useful framework for multiscale modeling of metallic materials because it does not require the existence of localized covalent bonds for computing the coupling energy as all other multiscale methods do. [3][4][5][6] Furthermore, this approach is completely general and versatile: it can be applied to diverse materials problems, such as dislocations, cracks, surfaces, and grain boundaries. Finally, the automatic adaption feature of the QCDFT method allows the DFT and/or EAM region to move and change in response to the current deformation state, when for example, defects are being nucleated in an otherwise perfect region.…”

Section: ͕͑F͖͒ ͑1͒mentioning

confidence: 99%

“…In contrast to sequential approaches, concurrent simulations are still relatively new and only a few models have been developed to date. [1][2][3][4][5][6] A successful concurrent multiscale method is the quasicontinuum ͑QC͒ method originally proposed by Tadmor et al 2 The idea underlying this method is that atomistic processes of interest often occur in very small spatial domains while the vast majority of atoms in the material behave according to well-established continuum theories. To exploit this fact, the QC method retains atomic resolution only where necessary and grades out to a continuum finite element description elsewhere.…”

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From electrons to finite elements: A concurrent multiscale approach for metals

2006

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We present a multiscale modeling approach that concurrently couples quantum-mechanical, classical atomistic, and continuum mechanical simulations in a unified fashion for metals. This approach is particularly useful for systems where chemical interactions in a small region can affect the macroscopic properties of a material. We discuss how the coupling across different scales can be accomplished efficiently, and we apply the method to multiscale simulations of an edge dislocation in aluminum in the absence and presence of H impurities. DOI: 10.1103/PhysRevB.73.024108 PACS number͑s͒: 71.15.Mb, 62.20.Mk, 71.15.Dx Some of the most fascinating problems in all fields of science involve multiple spatial and/or temporal scales: processes that occur at a certain scale govern the behavior of the system across several ͑usually larger͒ scales. In the context of materials science, the ultimate microscopic constituents of materials are ions and valence electrons; interactions among them at the atomic level determine the behavior of the material at the macroscopic scale, the latter being the scale of interest for technological applications. Conceptually, two categories of multiscale simulations can be envisioned, sequential, consisting of passing information across scales, and concurrent, consisting of seamless coupling of scales. 1 The majority of multiscale simulations that are currently in use are sequential ones, which are effective in systems where the different scales are weakly coupled. For systems whose behavior at each scale depends strongly on what happens at the other scales, concurrent approaches are usually required. In contrast to sequential approaches, concurrent simulations are still relatively new and only a few models have been developed to date. [1][2][3][4][5][6] A successful concurrent multiscale method is the quasicontinuum ͑QC͒ method originally proposed by Tadmor et al. 2 The idea underlying this method is that atomistic processes of interest often occur in very small spatial domains while the vast majority of atoms in the material behave according to well-established continuum theories. To exploit this fact, the QC method retains atomic resolution only where necessary and grades out to a continuum finite element description elsewhere. The original formulation of QC was limited to classical potentials for describing interactions between atoms. Since many materials properties depend explicitly on the behavior of electrons, such as bond breaking/ forming at crack tips or defect cores, chemical reactions with impurities, and surface reactions and reconstructions, it is desirable to incorporate appropriate quantum mechanical descriptions into the QC formalism. In this paper, we extend the original QC approach so that it can be directly coupled with quantum mechanical calculations based on density functional theory ͑DFT͒ for metallic systems. We refer to the new approach as QCDFT.The goal of the QC method is to model an atomistic system without explicitly treating every atom in the problem. 2,7 This is ...

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Section: ͕͑F͖͒ ͑1͒mentioning

confidence: 99%

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From electrons to finite elements: A concurrent multiscale approach for metals

2006

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“…In order to remove rotational rigid body motions and also to ensure uniform distribution of the traction on the boundaries of the matrix and the inclusion, the locations of points B and D are prescribed using semi-Dirichlet boundary conditions and updated iteratively until no spurious force develops. We should, however, highlight that the prescribed displacements at point [1,0] in y-direction for the inclusion and the matrix are, in general, not identical.…”

Section: -12 / Vol 68 September 2016mentioning

confidence: 99%

“…Recall that the positions of points A and B on the material configuration are arbitrary. A simple concrete case is to assign point A to [0,0] and point B to [1,0], as illustrated in Fig. 8.…”

Section: Constant Traction Boundarymentioning

confidence: 99%

“…Multiscale models are traditionally categorized into the homogenization method, where the length scales of micro-and macroproblems are sufficiently separate, and the concurrent method, see, e.g., Refs. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20], which considers strong coupling between the scales. 2 This contribution details on the former one.…”

Section: Introductionmentioning

confidence: 99%

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Aspects of Computational Homogenization at Finite Deformations: A Unifying Review From Reuss' to Voigt's Bound

Saeb

Steinmann

Javili

2016

Applied Mechanics Reviews

190

138

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The objective of this contribution is to present a unifying review on strain-driven computational homogenization at finite strains, thereby elaborating on computational aspects of the finite element method. The underlying assumption of computational homogenization is separation of length scales, and hence, computing the material response at the macroscopic scale from averaging the microscopic behavior. In doing so, the energetic equivalence between the two scales, the Hill-Mandel condition, is guaranteed via imposing proper boundary conditions such as linear displacement, periodic displacement and antiperiodic traction, and constant traction boundary conditions. Focus is given on the finite element implementation of these boundary conditions and their influence on the overall response of the material. Computational frameworks for all canonical boundary conditions are briefly formulated in order to demonstrate similarities and differences among the various boundary conditions. Furthermore, we detail on the computational aspects of the classical Reuss' and Voigt's bounds and their extensions to finite strains. A concise and clear formulation for computing the macroscopic tangent necessary for FE 2 calculations is presented. The performances of the proposed schemes are illustrated via a series of two-and three-dimensional numerical examples. The numerical examples provide enough details to serve as benchmarks.

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Multiscale Computational Characterization

Stan

2012

Characterization of Materials

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To understand, predict, and control matter and energy at the electronic, atomic, molecular, microstructural, and continuum levels, scientists need to investigate materials at a combination of length and time scales that are characteristic to relevant physical and chemical phenomena. As a consequence, experimental, theoretical, and computational methods must cover a wide range of space and time scales, starting with the nucleus and the electronic structure of individual or clustered atoms (Å), to nano/microstructural features, all the way to continuum properties of the sample (cm). Along the time scale, the investigation domain ranges from excitations (ps) to nucleation of new phases (ns), all the way to diffusion (minutes, hours) and aging characteristic times (months, years). The article briefly reviews the major theoretical and computational methods used in multiscale characterization of materials, including atomistic (DFT, MD, AIMD, kMC), mesoscale (PF, DD, DDD), and continuum (FEM, FDM, FVM, CALPHAD) methods. Method coupling schemes are also discussed, from sequential to loose and tight concurrent coupling and ending with hybrid coupling methods. The multiscale characterization methodology is illustrated with results of simulations phenomena in Li‐ion and UO 2 materials. The chapter ends with a discussion of challenges and opportunities in the multiscale characterization of materials.

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Concurrent coupling of length scales: Methodology and application

Cited by 565 publications

References 24 publications

From electrons to finite elements: A concurrent multiscale approach for metals

From electrons to finite elements: A concurrent multiscale approach for metals

Aspects of Computational Homogenization at Finite Deformations: A Unifying Review From Reuss' to Voigt's Bound

Multiscale Computational Characterization

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