TY - JOUR

T1 - Computational uncertainty analysis in multiresolution materials via stochastic constitutive theory

AU - Steven Greene, M.

AU - Liu, Yu

AU - Chen, Wei

AU - Liu, Wing Kam

N1 - Funding Information:
Steven Greene is supported by a Graduate Research Fellowship from the National Science Foundation and extends his gratitude to the NSF. The grant support from National Science Foundation ( CMMI-0928320 ) is also greatly acknowledged. The views expressed are those of the authors and do not necessarily reflect the views of the sponsors.

PY - 2011/1/1

Y1 - 2011/1/1

N2 - A stochastic constitutive theory is proposed in this work to propagate microstructure uncertainties in computational multiscale continuum models to bulk multiresolution material behavior. Ubiquitous fine resolution uncertainty sources influencing prediction of material properties based on their structures are categorized in detail, and this research transmits these uncertainties to coarser material resolutions by introducing a stochastic constitutive theory deduced from volume element simulations. To implement the stochastic upscaling process, two advanced uncertainty quantification methods are examined: statistical copula functions and random process polynomial chaos expansion. Both methods confront the mathematical difficulty in randomizing constitutive laws by capturing the marked correlation among constitutive parameters seen in complex materials, thus the results proffer a more accurate probabilistic estimation of constitutive material behavior. The contribution of this work is twofold: uncertainty is propagated from heterogeneous material "structure" to material "property" via the stochastic constitutive theory, and rigorous, data-driven mathematics are formalized to represent complicated dependence structures in multivariate statistical distributions. To the authors' knowledge, this is the first work in multiresolution mechanics that presents an approach to computationally derive correlation functions from numerical experiments, as opposed, for instance, to assuming one a priori. The method put forth in this research, though quite general, is applied to a mathematical example and plastic, high strength steel alloy for demonstration. Results include stochastic constitutive curve confidence intervals for the material stress-strain response and qualitative comparisons of the two stochastic methods detailed herein.

AB - A stochastic constitutive theory is proposed in this work to propagate microstructure uncertainties in computational multiscale continuum models to bulk multiresolution material behavior. Ubiquitous fine resolution uncertainty sources influencing prediction of material properties based on their structures are categorized in detail, and this research transmits these uncertainties to coarser material resolutions by introducing a stochastic constitutive theory deduced from volume element simulations. To implement the stochastic upscaling process, two advanced uncertainty quantification methods are examined: statistical copula functions and random process polynomial chaos expansion. Both methods confront the mathematical difficulty in randomizing constitutive laws by capturing the marked correlation among constitutive parameters seen in complex materials, thus the results proffer a more accurate probabilistic estimation of constitutive material behavior. The contribution of this work is twofold: uncertainty is propagated from heterogeneous material "structure" to material "property" via the stochastic constitutive theory, and rigorous, data-driven mathematics are formalized to represent complicated dependence structures in multivariate statistical distributions. To the authors' knowledge, this is the first work in multiresolution mechanics that presents an approach to computationally derive correlation functions from numerical experiments, as opposed, for instance, to assuming one a priori. The method put forth in this research, though quite general, is applied to a mathematical example and plastic, high strength steel alloy for demonstration. Results include stochastic constitutive curve confidence intervals for the material stress-strain response and qualitative comparisons of the two stochastic methods detailed herein.

KW - Copula

KW - Microstructure

KW - Polynomial chaos

KW - Stochastic constitutive theory

KW - Stochastic upscaling

KW - Uncertainty

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U2 - 10.1016/j.cma.2010.08.013

DO - 10.1016/j.cma.2010.08.013

M3 - Article

AN - SCOPUS:78649630054

VL - 200

SP - 309

EP - 325

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

SN - 0374-2830

IS - 1-4

ER -