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Abstract:
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Polycrystalline materials consist of single-crystal grains packed into a space-filling complex. Mechanical performance of the bulk material depends on many properties including morphological distribution of grains (volume, aspect ratio, preferred alignment), crystalline lattice type, orientation distribution, loading dynamics, and many other details.
Physical simulation tools can calculate stress and strain tensor fields in polycrystalline volumes at the micro scale but predictions of bulk performance properties, and especially their failure mechanisms, has been an elusive grand challenge. We relate our recent forays into this domain by describing three spatial prediction problems in statistical terms, detailing modeling results, and describing some lessons learned in fitting statistical models to complex 3D mesh data sets from finite element simulations. Techniques used range from Gauss-Markov random fields, to data reduction and multiple regression.
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