Inscrição na biblioteca: Guest
Portal Digital Begell Biblioteca digital da Begell eBooks Diários Referências e Anais Coleções de pesquisa
International Journal for Uncertainty Quantification
Fator do impacto: 3.259 FI de cinco anos: 2.547 SJR: 0.417 SNIP: 0.8 CiteScore™: 1.52

ISSN Imprimir: 2152-5080
ISSN On-line: 2152-5099

Open Access

International Journal for Uncertainty Quantification

DOI: 10.1615/Int.J.UncertaintyQuantification.2014008153
pages 151-170

INFERENCE AND UNCERTAINTY PROPAGATION OF ATOMISTICALLY-INFORMED CONTINUUM CONSTITUTIVE LAWS, PART 1: BAYESIAN INFERENCE OF FIXED MODEL FORMS

Maher Salloum
Sandia National Laboratories, 7011 East Avenue, MS 9158, Livermore, California 94550, USA
Jeremy A. Templeton
Sandia National Laboratories, 7011 East Avenue, MS 9409, Livermore, California 94550, USA

RESUMO

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.


Articles with similar content:

INFERENCE AND UNCERTAINTY PROPAGATION OF ATOMISTICALLY INFORMED CONTINUUM CONSTITUTIVE LAWS, PART 2: GENERALIZED CONTINUUM MODELS BASED ON GAUSSIAN PROCESSES
International Journal for Uncertainty Quantification, Vol.4, 2014, issue 2
Jeremy A. Templeton, Maher Salloum
Generalized Mathematical Homogenization of Atomistic Media at Finite Temperatures
International Journal for Multiscale Computational Engineering, Vol.3, 2005, issue 4
Yuye Tang, Wen Chen, Jacob Fish
VARIABLE-SEPARATION BASED ITERATIVE ENSEMBLE SMOOTHER FOR BAYESIAN INVERSE PROBLEMS IN ANOMALOUS DIFFUSION REACTION MODELS
International Journal for Uncertainty Quantification, Vol.9, 2019, issue 3
Yuming Ba, Na Ou, Lijian Jiang
A Virtual Atom Cluster Approach to the Mechanics of Nanostructures
International Journal for Multiscale Computational Engineering, Vol.2, 2004, issue 2
Dong Qian, Rohit H. Gondhalekar
Computational Homogenization of Nonlinear Hydromechanical Coupling in Poroplasticity
International Journal for Multiscale Computational Engineering, Vol.4, 2006, issue 5-6
Fernando A. Rochinha, Marcio A. Murad, Jesus A. Luizar-Obregon