FFT‐based homogenization using a reduced set of frequencies and a clustered microstructure

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Abstract: To capture the material behavior of composite microstructures, Moulinec and Suquet [5] proposed a homogenization scheme making use of fast Fourier transforms (FFT) and fixed‐point iterations. To reduce the computational effort of this spectral method, Kochmann et al. [3] introduced a model order reduction technique, which is based on using a fixed reduced set of frequencies for the computations in Fourier space. Within the current work, we improved the accuracy of the approach by use of a geometrically adapted set of frequencies, see [1]. Since the constitutive relations are still evaluated in real space, the technique is most beneficial for a linear material behavior. Considering nonlinear material behavior, most of the computing time is related to solving the constitutive relations. Therefore, the total speed‐up is lower. To achieve a further reduction of the computational effort for a nonlinear material behavior, the earlier proposed model order reduction technique is coupled with a clustering analysis [4]. The whole microstructure is thus divided into clusters, which show a similar material behavior. Within these clusters, the micromechanical fields are assumed to be constant which leads to a significant reduction of computational costs compared to the highly resolved solution.

Location: Deutsche Nationalbibliothek Frankfurt am Main

Extent: Online-Ressource

Language: Englisch

Bibliographic citation: FFT‐based homogenization using a reduced set of frequencies and a clustered microstructure ; volume:21 ; number:1 ; year:2021 ; extent:2
Proceedings in applied mathematics and mechanics ; 21, Heft 1 (2021) (gesamt 2)

Creator: Waimann, Johanna
Gierden, Christian
Schmidt, Annika
Svendsen, Bob
Reese, Stefanie

DOI: 10.1002/pamm.202100241

URN: urn:nbn:de:101:1-2021121514142985949254

Rights: Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.

Last update: 15.08.2025, 7:33 AM CEST

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Waimann, Johanna
Gierden, Christian
Schmidt, Annika
Svendsen, Bob
Reese, Stefanie

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