Quasicontinuum analysis of defects in solids

Tadmor, Ellad B.; Ortiz, Michael; Phillips, Rob

doi:10.1080/01418619608243000

Cited by 1,330 publications

(992 citation statements)

References 19 publications

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“…89,90 Moreover, simulations show that some solute atoms (dopants) can provide additional strengthening for grain boundary related deformation processes and nanocrystalline materials, in general. 29,92 Furthermore, the development of tools and algorithms that extend both the length and time scales of molecular dynamics [93][94][95] as well as the ability to characterize and visualize atomistic results [96][97][98][99][100] can aid in using molecular dynamics as a tool for insight into nanocrystalline materials design and behavior. While these simulations can give atomistic details of the nature of these solute atoms in thermal stability and deformation, there have been a limited number of atomistic studies of binary and higher-order alloys compared to the large amount of literature devoted to pure nanocrystalline copper, in part due to the limited number of appropriate interatomic potentials.…”

Section: Modeling and Simulation Approachesmentioning

confidence: 99%

“Bulk” Nanocrystalline Metals: Review of the Current State of the Art and Future Opportunities for Copper and Copper Alloys

Tschopp

Murdoch

Kecskes

et al. 2014

JOM

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It is a new beginning for innovative fundamental and applied science in nanocrystalline materials. Many of the processing and consolidation challenges that have haunted nanocrystalline materials are now more fully understood, opening the doors for bulk nanocrystalline materials and parts to be produced. While challenges remain, recent advances in experimental, computational, and theoretical capability have allowed for bulk specimens that have heretofore been pursued only on a limited basis. This article discusses the methodology for synthesis and consolidation of bulk nanocrystalline materials using mechanical alloying, the alloy development and synthesis process for stabilizing these materials at elevated temperatures, and the physical and mechanical properties of nanocrystalline materials with a focus throughout on nanocrystalline copper and a nanocrystalline Cu-Ta system, consolidated via equal channel angular extrusion, with properties rivaling that of nanocrystalline pure Ta. Moreover, modeling and simulation approaches as well as experimental results for grain growth, grain boundary processes, and deformation mechanisms in nanocrystalline copper are briefly reviewed and discussed. Integrating experiments and computational materials science for synthesizing bulk nanocrystalline materials can bring about the next generation of ultrahigh strength materials for defense and energy applications.

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Section: Modeling and Simulation Approachesmentioning

confidence: 99%

“Bulk” Nanocrystalline Metals: Review of the Current State of the Art and Future Opportunities for Copper and Copper Alloys

Tschopp

Murdoch

Kecskes

et al. 2014

JOM

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“…Several different methods (quasicontinuum [54], bridging scale method [55], bridging domain [56], etc.) have been proposed to extend the length and time scale of molecular simulations.…”

Section: Calculation Of Local Stress In Molecular Modelsmentioning

confidence: 99%

Applicability of Continuum Fracture Mechanics in Atomistic Systems

Cheng

Sun

2011

Volume 8: Mechanics of Solids, Structures and Fluids; Vibration, Acoustics and Wave Propagation

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Stress intensity factor is one of the most significant fracture parameters in linear elastic fracture mechanics (LEFM). Due to its simplicity, many researchers directly employed this concept to explain their results from molecular simulation. However, stress intensity factor defines the amplitude of the singular stress, which is the product of continuum elasticity. Under atomistic systems without the stress singularity, the concept of stress intensity factor must be examined. In addition, the difficulty of studying the stress intensity factor in atomistic systems may be traced back to the ambiguous definition of the local atomistic stress. In this study, the definition of the local virial stress is adopted. Subsequently, through the consideration of K-dominance, the approximated stress intensity factor based on the atomistic stress can be projected within a reasonable region. Moreover, the influence of cutting interatomic bonds to create traction free crack surfaces and the critical stress intensity factor is also discussed.

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“…We also remark that Methods of types I, III, and IV do not satisfy Newton's third law over the blend region, and so these methods do not lead to a symmetric formulation. We also contrast AtC blending with the quasicontinuum method [39]. In a local quasicontinuum method, the Cauchy-Born hypothesis [10] is used to eliminate degrees of freedom in a particle model, lessening the computational complexity.…”

Section: Summary and Comparison Of Force-based Atc Blending Methodsmentioning

confidence: 99%

“…It is important to note that using (6.20) to eliminate atomistic degrees of freedom from Ω b does not delete any of the atomistic force balance equations in Ω b from the AtC blending method (6.14), as is done in the quasicontinuum method [39]. Instead, using (6.20) …”

Section: Remark 63mentioning

confidence: 99%

“…The main challenge is the synthesis of the two distinct models in a manner that minimizes, or altogether eliminates, undesirable artifacts such as ghost forces, unphysical solutions let alone supporting mathematical analysis. Notable AtC coupling methods include the quasicontinuum method [39], the bridging scale decomposition [41], and [24] where atomistic and continuum models are overlapped (see the latter two references, and those mentioned above for numerous citations to the literature). The numerical analysis of AtC methods has lagged in comparison to the number of methods proposed; see the recent papers [2,3,17,31,26,27] for analyses of the quasicontinuum method.…”

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confidence: 99%

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Blending Methods for Coupling Atomistic and Continuum Models

Bochev¹,

Lehoucq²,

Parks³

et al. 2009

Multiscale Methods

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In this paper we review recent developments in blending methods for atomisticto-continuum (AtC) coupling in material statics problems. Such methods tie together atomistic and continuum models by using a bridge domain that connects the two models. There are several reasons why AtC coupling methods (of which blending methods are a subset) are important and have been subject to an increased interest in the recent years. Despite tremendous increases in computational power, fully atomistic simulations on an entire model domain remain computationally infeasible for many applications of interest. As a result, attention has focused on hybrid schemes where in all regions with well-behaved solutions, the atomistic (microscopic) model is replaced by a (macroscopic) continuum model enabling a more efficient computational scheme (see [14,29,9] for general information). The main challenge is the synthesis of the two distinct models in a manner that minimizes, or altogether eliminates, undesirable artifacts such as ghost forces, unphysical solutions let alone supporting mathematical analysis. Notable AtC coupling methods include the quasicontinuum method [39], the bridging scale decomposition [41], and [24] where atomistic and continuum models are overlapped (see the latter two references, and those mentioned above for numerous citations to the literature). The numerical analysis of AtC methods has lagged in comparison to the number of methods proposed; see the recent papers [2,3,17,31,26,27] for analyses of the quasicontinuum method.Blending methods couple atomistic/continuum modes via a dedicated blending, or bridge, region inserted between the atomistic and continuum subdomains. The atomistic and continuum models are tied together by using a suitable "continuity" condition (or balance law) for the atomistic and continuum positions or displacements in this region. A complicating factor is that the atomistic and (classical) continuum elastic models rely on nonlocal and local models of force interaction, respectively. In the (classical) elastic context, the "local force" is that exerted on a body by contact forces occurring on the surface (of the body). In contrast, in the atomistic model, forces are summed from atoms separated by a finite distance. The incompatibility arising from coupling local and nonlocal force models is intrinsic. The goal of our paper is threefold. First, we review how blending approaches attempt to ameliorate the various negative effects by relying on an interface between the two models. Second, we discuss the beginnings of a JFISH: "CHAP06" -2009/6/4 -17:33 -PAGE 166 -#2 166Blending methods for coupling atomistic and continuum models numerical analysis by discussing consistency of the resulting numerical schemes. Third, we suggest how the intrinsic limitation associated with coupling nonlocal and local mechanical theories may be avoided by replacing the classical elastic theory with a nonlocal elastic theory.The use of a bridge domain in blending methods bears a resemblance to conventional overlapping...

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Quasicontinuum analysis of defects in solids

Cited by 1,330 publications

References 19 publications

“Bulk” Nanocrystalline Metals: Review of the Current State of the Art and Future Opportunities for Copper and Copper Alloys

“Bulk” Nanocrystalline Metals: Review of the Current State of the Art and Future Opportunities for Copper and Copper Alloys

Applicability of Continuum Fracture Mechanics in Atomistic Systems

Blending Methods for Coupling Atomistic and Continuum Models

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