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Multi-scale modeling of elastic response of three-dimensional voxel-based microstructure datasets using novel DFT-based knowledge systems / Giacomo Landi in Acta materialia, Vol. 58 N° 7 (Avril 2010) 

Public ISBD [article]  in Acta materialia > Vol. 58 N° 7 (Avril 2010) . - pp. 2716–2725 Titre : Multi-scale modeling of elastic response of three-dimensional voxel-based microstructure datasets using novel DFT-based knowledge systems Type de document : texte imprimé Auteurs : Giacomo Landi, Auteur ; Stephen R. Niezgoda, Auteur ; Surya R. Kalidindi, Auteur Année de publication : 2011 Article en page(s) : pp. 2716–2725 Note générale : Métallurgie Langues : Anglais (eng) Mots-clés : Microstructure  Elastic  response  Multi-scale  modeling  Discrete  Fourier  transforms Résumé : In this paper, we present a novel approach for predicting the elastic fields in three-dimensional voxel-based microstructure datasets subjected to uniform periodic boundary conditions. This new formalism has its theoretical roots in the statistical continuum theories developed originally by Kroner. However, in the approach described by Kroner the terms in the series were established by selecting a reference medium and numerically evaluating a complex series of nested convolution integrals. This approach is largely hampered by the principal value problem and exhibits high sensitivity to the properties of the selected reference medium. In the present work, we have recast the same series expressions into much more computationally efficient representations using discrete Fourier transforms (DFTs). The main advantage of the new DFT-based framework is that it allows easy calibration of Kroner’s expansions to results from finite element methods, thereby overcoming all of the main obstacles associated with the principal value problem and the need to select a reference medium. Consequently, the DFT-based approach presented here produces much more accurate predictions. In this paper the new mathematical formalism is first presented in a generalized framework, and its viability is then demonstrated for a selected class of two phase composites. DEWEY : 669 ISSN : 1359-6454 En ligne : http://www.sciencedirect.com/science/article/pii/S1359645410000108 [article] Multi-scale modeling of elastic response of three-dimensional voxel-based microstructure datasets using novel DFT-based knowledge systems [texte imprimé] / Giacomo Landi, Auteur ; Stephen R. Niezgoda, Auteur ; Surya R. Kalidindi, Auteur . - 2011 . - pp. 2716–2725. Métallurgie Langues : Anglais (eng) in Acta materialia > Vol. 58 N° 7 (Avril 2010) . - pp. 2716–2725 Mots-clés : Microstructure  Elastic  response  Multi-scale  modeling  Discrete  Fourier  transforms Résumé : In this paper, we present a novel approach for predicting the elastic fields in three-dimensional voxel-based microstructure datasets subjected to uniform periodic boundary conditions. This new formalism has its theoretical roots in the statistical continuum theories developed originally by Kroner. However, in the approach described by Kroner the terms in the series were established by selecting a reference medium and numerically evaluating a complex series of nested convolution integrals. This approach is largely hampered by the principal value problem and exhibits high sensitivity to the properties of the selected reference medium. In the present work, we have recast the same series expressions into much more computationally efficient representations using discrete Fourier transforms (DFTs). The main advantage of the new DFT-based framework is that it allows easy calibration of Kroner’s expansions to results from finite element methods, thereby overcoming all of the main obstacles associated with the principal value problem and the need to select a reference medium. Consequently, the DFT-based approach presented here produces much more accurate predictions. In this paper the new mathematical formalism is first presented in a generalized framework, and its viability is then demonstrated for a selected class of two phase composites. DEWEY : 669 ISSN : 1359-6454 En ligne : http://www.sciencedirect.com/science/article/pii/S1359645410000108