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Autor(en): Leuschner, Matthias
Titel: Numerically efficient computational homogenization : Fourier-accelerated nodal solvers and reduced basis model order reduction
Erscheinungsdatum: 2018
Verlag: Stuttgart : Institute of Applied Mechanics, University of Stuttgart
Dokumentart: Dissertation
Seiten: X, 206
Serie/Report Nr.: Publication series of the Institute of Applied Mechanics (IAM);1
URI: http://elib.uni-stuttgart.de/handle/11682/10134
http://nbn-resolving.de/urn:nbn:de:bsz:93-opus-ds-101343
http://dx.doi.org/10.18419/opus-10117
ISBN: 978-3-937399-50-8
Zusammenfassung: Many engineering materials exhibit heterogeneous microstructures, whose compositions and formations may to some extend be controlled during manufacturing processes. Homogenization methods predicting effective macroscopic properties of microheterogeneous materials are important tools for the development of high performance materials and for multiscale analyses of structures made thereof. Conventional computational homogenization techniques usually suffer from long computing times. For microstructures represented by pixel or voxel images, a reduction of computational effort can be achieved using fast Fourier transform algorithms. A method combining Fourier-based acceleration with a finite element discretization is presented with numerical examples of thermal and mechanical homogenization. In addition, a reduced basis approach for materials with viscoplastic constituents and imperfect interfaces at the phase boundaries is developed. Systematic offline analyses of precomputed training data allow for efficient online algorithms, which yield good predictions for test scenarios that deviate moderately from the training cases.
Enthalten in den Sammlungen:02 Fakultät Bau- und Umweltingenieurwissenschaften

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