A multiscale component mode synthesis approach for dynamic analysis of nanostructures

Lan, Jiebin; Li, G.

doi:10.1002/nme.4330

Cited by 4 publications

(2 citation statements)

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“…The goal of realizing predictive simulation rests upon development of constitutive relationships of sufficient accuracy with quantified uncertainty. An area where existing constitutive models have particular difficulty is nanoscience and engineering because macroscale relationships do not sufficiently resolve the physics at this small scale [1][2][3][4][5]. While continuum mechanics can be derived from molecular mechanics [6,7] in an average sense, well-known closures from classical mechanics are often inadequate for problems in nanoscience and nanoengineering where atomistic information becomes important.…”

Section: Introductionmentioning

confidence: 99%

Inference and Uncertainty Propagation of Atomistically-Informed Continuum Constitutive Laws, Part 1: Bayesian Inference of Fixed Model Forms

Salloum

Templeton

2014

Int. J. UncertaintyQuantification

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Uncertainty quantification techniques have the potential to play an important role in constructing constitutive relationships applicable to nanoscale physics. At these small scales, deviations from laws appropriate at the macroscale arise due to insufficient scale separation between the atomic and continuum length scales, as well as fluctuations due to thermal processes. In this work, we consider the problem of inferring the coefficients of an assumed constitutive model form using atomistic information and propagation of the associated uncertainty. A nanoscale heat transfer problem is taken as the model, and we use a polynomial chaos expansion to represent the thermal conductivity with a linear temperature dependence. A Bayesian inference method is developed to extract the coefficients in this expansion from molecular dynamics (MD) samples at prescribed temperatures. Importantly, the atomistic data are incompatible with the continuum model because of the finite probability of heat flowing in the opposite direction of the temperature gradient; we present a method to account for this in the model. The fidelity and uncertainty in these techniques are then examined. Validation is provided by comparing a continuum Fourier model against a larger all MD simulation representing the true solution.

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Section: Introductionmentioning

confidence: 99%

Inference and Uncertainty Propagation of Atomistically-Informed Continuum Constitutive Laws, Part 1: Bayesian Inference of Fixed Model Forms

Salloum

Templeton

2014

Int. J. UncertaintyQuantification

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“…Predictive simulation of engineering systems are often challenged by different phenomena operating over a broad range of length and times scales spreading from atomistic to continuum levels. Such phenomena are encountered for example in different engineering applications such as nanotechnology [25,78,54,104,112] and fluid dynamics [22,50,77,5,84,37]. The ubiquity of such dynamics is illustrated by the need to supply constitutive relationships in mathematical models of physical phenomena to compensate for the unresolved degrees of freedom.…”

Section: Solid-fluid Systemmentioning

confidence: 99%

Bridging the gap between atomistic phenomena and continuum behavior in electrochemical energy storage processes.

Davidson¹,

Griffiths²,

Lee³

et al. 2012

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One of the most significant impediments to advances in electrochemical energy storage lies in the gap between fundamental understanding of atomistic phenomena and our understanding of the impact of these phenomena on system performance at device scales. Atomistic models (DFT, MD, MC) provide insight into such phenomena along with a means of quantification, but such models are too computationally intensive to address device-scale behavior. Similarly, device-scale insight for design and optimization can be obtained through continuum models that are sufficiently fast, but these models account for only the simplest atomistic phenomena. There is thus a large gap between our ability to develop fundamental understanding and our ability to use this understanding to make rapid advances in energy storage technologies. The goal of this work is to help bridge this gap through an innovative synthesis of atomistic and continuum approaches in which atomistic phenomena are captured through fast reduced-order integral methods that can be imbedded into continuum-like models describing device-scale behavior.3 Acknowledgment

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Numerical–analytical model for transient dynamics of elastic-plastic plate under eccentric low-velocity impact

Jin

Yin

Wang

et al. 2019

Applied Mathematical Modelling

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A multiscale component mode synthesis approach for dynamic analysis of nanostructures

Cited by 4 publications

References 44 publications

Inference and Uncertainty Propagation of Atomistically-Informed Continuum Constitutive Laws, Part 1: Bayesian Inference of Fixed Model Forms

Inference and Uncertainty Propagation of Atomistically-Informed Continuum Constitutive Laws, Part 1: Bayesian Inference of Fixed Model Forms

Bridging the gap between atomistic phenomena and continuum behavior in electrochemical energy storage processes.

Numerical–analytical model for transient dynamics of elastic-plastic plate under eccentric low-velocity impact

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