A POD/PGD reduction approach for an efficient reparameterization of data-driven material microstructure models (original) (raw)
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The first part of this research describes an attempt to develop a formulation to obtain 3D approximate solutions for the heat conduction problem in highly heterogeneous materials, by a sequence of one-dimensional FEM problems generated by the Proper Generalized Decomposition (PGD) technique. Here only the steady state problem is considered. Along the PGD iterations, the separation of variables is done between the all three space coordinates, instead of the time as it is usual in PGD applications. In this way, it is sought to obtain, iteratively, an accurate a-posteriori approximation of the complex oscillation of the temperature, with a reduced number of modes. The method involves an iterative sequence of global solutions, even in a linear problem. However, previous experiences in the literature shows that the number of iterations and modes is small, and the total computational cost involved is generally smaller than the cost of the single 3D analysis by 3D solid finite elements mod...
Computational Materials Science, 2014
3D reconstructions of heterogeneous microstructures are important for assessing material properties using advanced simulation techniques such as finite element analysis (FEA). Nevertheless, for many materials systems like polymer nanocomposites, only 2D microstructural images are available even with the state-of-the-art imaging techniques. This paper proposes a new descriptor-based methodology for reconstructing 3D particle-based heterogeneous microstructures based on 2D images. The proposed methodology characterizes a 2D microstructural morphology using a small set of microstructure descriptors covering features including material composition, dispersion status, and phase geometry, and then reconstructs statistically equivalent microstructures in a 3D space based on the 3D descriptors derived from 2D characterization and a few reasonable assumptions. Our approach is the most useful when the direct 3D microstructure analysis, such as 3D tomography, is not available due to either high cost or difficulties in sample preparations. Other practical features of descriptor-based characterization include low dimensionality, which enables optimal parametric design of microstructures, as well as physically meaningful mapping of processing related material parameters. In reconstruction, the proposed algorithm is capable to generate large size 3D structures at a low computational cost. Furthermore, since the algorithm is stochastic, it can be used to construct both Representative Volume Element (RVE) and Statistical Volume Element (SVE) for FEA studies. We demonstrate the proposed methodology by characterizing and reconstructing polymer nanocomposites.
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