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International Journal for Uncertainty Quantification

Published 6 issues per year

ISSN Print: 2152-5080

ISSN Online: 2152-5099

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INFERENCE AND UNCERTAINTY PROPAGATION OF ATOMISTICALLY INFORMED CONTINUUM CONSTITUTIVE LAWS, PART 2: GENERALIZED CONTINUUM MODELS BASED ON GAUSSIAN PROCESSES

Volume 4, Issue 2, 2014, pp. 171-184
DOI: 10.1615/Int.J.UncertaintyQuantification.2014008154
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ABSTRACT

Constitutive models in nanoscience and engineering often poorly represent the physics due to significant deviations in model form from their macroscale counterparts. In Part 1 of this study, this problem was explored by considering a continuum scale heat conduction constitutive law inferred directly from molecular dynamics (MD) simulations. In contrast, this work uses Bayesian inference based on the MD data to construct a Gaussian process emulator of the heat flux as a function of temperature and temperature gradient. No assumption of Fourier-like behavior is made, requiring alternative approaches to assess the well-posedness and accuracy of the emulator. Validation is provided by comparing continuum scale predictions using the emulator model against a larger all-MD simulation representing the true solution. The results show that a Gaussian process emulator of the heat conduction constitutive law produces an empirically unbiased prediction of the continuum scale temperature field for a variety of time scales, which was not observed when Fourier's law is assumed to hold. Finally, uncertainty is propagated in the continuum model and quantified in the temperature field so the impact of errors in the model on continuum quantities can be determined.

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  2. Barrett Christopher D., Carino Ricolindo L., The MEAM parameter calibration tool: an explicit methodology for hierarchical bridging between ab initio and atomistic scales, Integrating Materials and Manufacturing Innovation, 5, 1, 2016. Crossref

  3. Jones Reese E., Templeton Jeremy, Zimmerman Jonathan, Principles of Coarse-Graining and Coupling Using the Atom-to-Continuum Method, in Multiscale Materials Modeling for Nanomechanics, 245, 2016. Crossref

  4. Stephenson David, Kermode James R., Lockerby Duncan A., Accelerating multiscale modelling of fluids with on-the-fly Gaussian process regression, Microfluidics and Nanofluidics, 22, 12, 2018. Crossref

  5. Rizzi F., Khalil M., Jones R.E., Templeton J.A., Ostien J.T., Boyce B.L., Bayesian modeling of inconsistent plastic response due to material variability, Computer Methods in Applied Mechanics and Engineering, 353, 2019. Crossref

  6. Ricciardi Denielle E., Chkrebtii Oksana A., Niezgoda Stephen R., Uncertainty Quantification for Parameter Estimation and Response Prediction, Integrating Materials and Manufacturing Innovation, 8, 3, 2019. Crossref

  7. Rocha I.B.C.M., Kerfriden P., van der Meer F.P., On-the-fly construction of surrogate constitutive models for concurrent multiscale mechanical analysis through probabilistic machine learning, Journal of Computational Physics: X, 9, 2021. Crossref

  8. Kotha Shravan, Ozturk Deniz, Smarslok Benjamin, Ghosh Somnath, Uncertainty Quantified Parametrically Homogenized Constitutive Models for Microstructure-Integrated Structural Simulations, Integrating Materials and Manufacturing Innovation, 9, 4, 2020. Crossref

  9. Fish Jacob, Wagner Gregory J., Keten Sinan, Mesoscopic and multiscale modelling in materials, Nature Materials, 20, 6, 2021. Crossref

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