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Thermal Response Variability of Random Polycrystalline Microstructures

Published online by Cambridge University Press:  20 August 2015

Bin Wen ,
Zheng Li  and
Nicholas Zabaras
Bin Wen
Affiliation:
Materials Process Design and Control Laboratory, Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853-3801, USA
Zheng Li
Affiliation:
Materials Process Design and Control Laboratory, Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853-3801, USA State Key Laboratory of Structural Analysis for Industrial Equipment, Faculty of Vehicle Engineering and Mechanics, Dalian University of Technology, Dalian 116024, China
Nicholas Zabaras*
Affiliation:
Materials Process Design and Control Laboratory, Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853-3801, USA
*
*Corresponding author.Email:[email protected]
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Abstract

A data-driven model reduction strategy is presented for the representation of random polycrystal microstructures. Given a set of microstructure snapshots that satisfy certain statistical constraints such as given low-order moments of the grain size distribution, using a non-linear manifold learning approach, we identify the intrinsic low-dimensionality of the microstructure manifold. In addition to grain size, a linear dimensionality reduction technique (Karhunun-Loéve Expansion) is used to reduce the texture representation. The space of viable microstructures is mapped to a low-dimensional region thus facilitating the analysis and design of polycrystal microstructures. This methodology allows us to sample microstructure features in the reduced-order space thus making it a highly efficient, low-dimensional surrogate for representing microstructures (grain size and texture). We demonstrate the model reduction approach by computing the variability of homogenized thermal properties using sparse grid collocation in the reduced-order space that describes the grain size and orientation variability.

Keywords

52B1065D1868U0568U07Non-linear model reductionpolycrystalline microstructurehomogenizationmicrostructure reconstructionstochastic analysisKarhunun-Loéve Expansionmultiscale modelingheat conduction
Type
Research Article
Information
Communications in Computational Physics , Volume 10 , Issue 3 , September 2011 , pp. 607 - 634
Copyright
Copyright © Global Science Press Limited 2011

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