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TY - THES AU - Gierden, Christian TI - Model order reduction for FE-FFT-based multiscale material modeling PB - Rheinisch-Westfälische Technische Hochschule Aachen VL - Dissertation CY - Aachen M1 - RWTH-2024-05191 SP - 1 Online-Ressource : Illustrationen PY - 2024 N1 - Veröffentlicht auf dem Publikationsserver der RWTH Aachen University N1 - Dissertation, Rheinisch-Westfälische Technische Hochschule Aachen, 2024 AB - The material behavior of a structural component is determined by the underlying microstructure and its associated features and local interactions. Therefore, multiscale simulations can provide valuable information on the overall constitutive response of the material and thus on its use in practical applications. Since these simulations are generally computationally expensive, the application of suitable multiscale methods is a challenging task. In order to reduce the numerical costs, various model order reduction techniques have been developed and applied. The goal, and at the same time the challenge, of model order reduction techniques is to decrease the computational complexity and effort of the numerical simulations while maintaining high accuracy of the numerical results. The given cumulative dissertation presents a collection of journal articles and conference proceedings contributing to this research field. It aims to generalize a framework for an efficient and accurate two-scale FE-FFT-based method, which is based on a coarsely discretized microstructure. Additionally, the thesis intends to significantly improve the accuracy of a reduced FFT-based microscale simulation, in which the computations in Fourier space are performed using a reduced set of Fourier modes. Starting by addressing the motivation and research relevant questions of this dissertation, next a comprehensive literature review on the current trends in computational multiscale modeling as well as the latest developments in FFT-based microscale and FE-FFT-based two-scale methods is presented. Earlier works in this field are discussed in the first journal article, which provides an overview of several FFT-based algorithms and solvers including their applications, methods to reduce the effect of Gibbs oscillations, specific model order reduction techniques, and the FFT-based method in the context of FE-FFT-based two-scale simulations. Subsequently, two papers deal with an efficient FE-FFT-based two-scale simulation framework applied to model the material behavior of viscoplastic polycrystals. Within this framework a coarsely discretized microstructure is used for the two-scale simulations, where the minimum number of grid points, which is required to generate accurate macroscopic results, is defined in a pre-processing step. Highly resolved microstructural results can be generated in a post-processing step. The papers focus on generalizing this framework to the finite strain regime and to the thermomechanically coupled case. The following five works focus on a reduced FFT-based microscale simulation utilizing a decreased number of Fourier modes for the computations in Fourier space, wherein the accuracy of the obtained results directly depends on the choice of the considered Fourier modes. First, for the investigation of two-phase microstructures, a geometrically adapted sampling pattern is introduced, which consists of the Fourier modes with the highest amplitudes resulting from a Fourier transformation of the characteristic function of the given microstructure. The characteristic function captures the representation of phases within the microstructure. Thereafter a strain-based sampling pattern is suggested, where the aforementioned characteristic function is replaced by the microstructural strain field. Compared to the results obtained with the geometrically adapted sampling pattern, this strain-based sampling pattern leads to even more accurate results. Furthermore, since the definition of a characteristic function is no longer required, it can be used to investigate complex polycrystalline microstructures with challenging microstructural effects, e.g., considering crystal plasticity or solid-solid phase transformations. Finally, to demonstrate the universality of the model order reduction technique, its application is shown in the context of various improvements for the FFT-based method. It is implemented, for example, in combination with finite-difference-based operator approximations to reduce the effect of Gibbs oscillations, or with fast gradient solvers to reduce the number of iterations required to reach a converged solution. LB - PUB:(DE-HGF)11 DO - DOI:10.18154/RWTH-2024-05191 UR - https://publications.rwth-aachen.de/record/986443 ER -