A POD/PGD reduction approach for an efficient reparameterization of data-driven material microstructure models
Résumé
The general idea here is to produce a high quality representa tion of the indicator function of different phases of the material while adequately scaling with the storage require ments for high resolution Digital Material Representation (DMR). To this end, we pr opose a three-stage reduction algorithm comb ining Proper Orthogonal Decomposition (POD) and Proper Generalized Decomposition (PGD)- first, each snapshot pixel/voxel matrix is decomposed into a linear com- bination 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 sp ace 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