Year: 2011
Communications in Computational Physics, Vol. 10 (2011), Iss. 3 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.200510.061210a
Communications in Computational Physics, Vol. 10 (2011), Iss. 3 : pp. 607–634
Published online: 2011-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 28