Commun. Comput. Phys., 10 (2011), pp. 607-634.


Thermal Response Variability of Random Polycrystalline Microstructures

Bin Wen 1, Zheng Li 2, Nicholas Zabaras 1*

1 Materials Process Design and Control Laboratory, Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853-3801, USA.
2 Materials Process Design and Control Laboratory, Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853-3801, USA; and State Key Laboratory of Structural Analysis for Industrial Equipment, Faculty of Vehicle Engineering and Mechanics, Dalian University of Technology, Dalian 116024, China.

Received 20 May 2010; Accepted (in revised version) 6 December 2010
Available online 1 June 2011
doi:10.4208/cicp.200510.061210a

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-Loeve 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.

AMS subject classifications: 52B10, 65D18, 68U05, 68U07

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Key words: Non-linear model reduction, polycrystalline microstructure, homogenization, microstructure reconstruction, stochastic analysis, Karhunun-Loeve Expansion, multiscale modeling, heat conduction.

*Corresponding author.
Email: zabaras@cornell.edu (N. Zabaras)
 

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