Volume 10, Issue 3
Thermal Response Variability of Random Polycrystalline Microstructures

Bin Wen, Zheng Li & Nicholas Zabaras

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

Published online: 2011-10

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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.

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@Article{CiCP-10-607, author = {}, title = {Thermal Response Variability of Random Polycrystalline Microstructures}, journal = {Communications in Computational Physics}, year = {2011}, volume = {10}, number = {3}, pages = {607--634}, 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.200510.061210a}, url = {http://global-sci.org/intro/article_detail/cicp/7454.html} }
TY - JOUR T1 - Thermal Response Variability of Random Polycrystalline Microstructures JO - Communications in Computational Physics VL - 3 SP - 607 EP - 634 PY - 2011 DA - 2011/10 SN - 10 DO - http://dor.org/10.4208/cicp.200510.061210a UR - https://global-sci.org/intro/article_detail/cicp/7454.html KW - AB -

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.

Bin Wen, Zheng Li & Nicholas Zabaras. (2020). Thermal Response Variability of Random Polycrystalline Microstructures. Communications in Computational Physics. 10 (3). 607-634. doi:10.4208/cicp.200510.061210a
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