A pod/pgd reduction approach for an efficient parameterization of data-driven material microstructure models
Liang Xia1,2
, Balaji Raghavan1, Piotr Breitkopf1, Weihong Zhang2
1Laboratoire Roberval, UMR 7337 UTC-CNRS, UTC, Compiègne, France.
2Engineering Simulation and Aerospace Computing (ESAC), NPU, Xi’an, China.
DOI:
https://doi.org/10.7494/cmms.2013.2.0433
Abstract:
The general idea here is to produce a high quality representation of the indicator function of different phases of the material while adequately scaling with the storage requirements for high resolution Digital Material Representation (DMR). To this end, we propose a three-stage reduction algorithm combining Proper Orthogonal Decomposition (POD) and Proper Generalized Decomposition (PGD)- first, each snapshot pixel/voxel matrix is decomposed into a linear combination of tensor products of 1D basis vectors. Next a common basis is determined for the entire set of microstructure snapshots. Finally, the analysis of the dimensionality of the resulting nonlinear space yields the minimal set of parameters needed in order to represent the microstructure with sufficient precision. We showcase this approach by constructing a low-dimensional model of a two-phase composite microstructure.
Cite as:
Xia, L., Raghavan, B., Breitkopf, P., & Zhang, W. (2013). A pod/pgd reduction approach for an efficient parameterization of data-driven material microstructure models. Computer Methods in Materials Science, 13(2), 219 – 225. https://doi.org/10.7494/cmms.2013.2.0433
Article (PDF):
Keywords:
Parameterization of microstructure, Homogenization, Voxel approaches, Storage costs, Material uncertainties
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