% IMPORTANT: The following is UTF-8 encoded. This means that in the presence
% of non-ASCII characters, it will not work with BibTeX 0.99 or older.
% Instead, you should use an up-to-date BibTeX implementation like “bibtex8” or
% “biber”.
@PHDTHESIS{Gierden:986443,
author = {Gierden, Christian},
othercontributors = {Reese, Stefanie and Svendsen, Bob},
title = {{M}odel order reduction for {FE}-{FFT}-based multiscale
material modeling},
school = {Rheinisch-Westfälische Technische Hochschule Aachen},
type = {Dissertation},
address = {Aachen},
publisher = {RWTH Aachen University},
reportid = {RWTH-2024-05191},
pages = {1 Online-Ressource : Illustrationen},
year = {2024},
note = {Veröffentlicht auf dem Publikationsserver der RWTH Aachen
University; Dissertation, Rheinisch-Westfälische Technische
Hochschule Aachen, 2024},
abstract = {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.},
cin = {311510},
ddc = {624},
cid = {$I:(DE-82)311510_20140620$},
typ = {PUB:(DE-HGF)11},
doi = {10.18154/RWTH-2024-05191},
url = {https://publications.rwth-aachen.de/record/986443},
}
guest ::