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@PHDTHESIS{Holthusen:963830,
author = {Holthusen, Hagen},
othercontributors = {Reese, Stefanie and Kuhl, Ellen},
title = {{M}odeling and numerics of anisotropic and inelastic
materials: plasticity, damage and growth},
school = {Rheinisch-Westfälische Technische Hochschule Aachen},
type = {Dissertation},
address = {Aachen},
publisher = {RWTH Aachen University},
reportid = {RWTH-2023-07973},
pages = {1 Online-Ressource : Illustrationen, Diagramme},
year = {2023},
note = {Veröffentlicht auf dem Publikationsserver der RWTH Aachen
University; Dissertation, Rheinisch-Westfälische Technische
Hochschule Aachen, 2023},
abstract = {There has been tremendous technological progress, both in
the manufacturing of ever more sophisticated materials and
in the steadily increasing computational power. Thus,
materials showing a pronounce kind of anisotropy --
initially and/or induced -- found their way into various
fields of engineering applications. On the one hand, for
example, fusion deposition modeling as used in 3D printing
creates materials that behave anisotropically to increase
load-bearing capacity. On the other hand, the power of
modern computers enables numerical simulations that provide
deeper insights into the underlying material behavior.
However, in order to accurately predict material behavior
while keeping the computational time cost relatively low,
continuum mechanical models are needed that are capable of
capturing a broad spectrum of anisotropy, in particular
those anisotropic effects caused by various inelastic
material behaviors. In this regard, almost all materials,
regardless of whether they are non-living or living, undergo
inelastic deformation at some point. May it be irreversible
deformation, rate dependence, degradation up to failure or
even growth of living organisms. Macroscopically, all of
these phenomena can cause the material to behave
anisotropically if it did not already do so initially. For
instance, the material's stiffness might fail completely in
one direction due to microcracks, while being less degraded
in another direction. Further well-known inelastic effects
might be caused by anisotropic yield criteria such as Hill's
one, or even by kinematic (plastic strain) hardening. In
addition, one of the currently most challenging topics in
continuum mechanics is the modeling of (direction-dependent)
growth of biological tissues. From a continuum mechanical
point of view, all these phenomena are modeled based on two
essential concepts: The multiplicative decomposition of the
deformation gradient and structural tensors. Besides
theoretical modeling, numerical implementation can be highly
challenging as well and is known to be error-prone due to
the complexity typically associated with such models.
Therefore, the continuum mechanical framework employed
should be designed in such a way that it can be easily
implemented in algorithmic differentiation (AD) tools to
enable robust and efficient computations. This cumulative
dissertation is intended to make a valuable contribution in
this regard. The overall objective is to develop generic
continuum mechanical formulations for inelastic phenomena
associated with anisotropy in a geometrically nonlinear
context. Therefore, a compilation of several publications by
the author (and his co-authors) is presented. These should
contribute to the development of more advanced material
models in the future. In the beginning of this thesis the
motivation, the research relevant questions and a
comprehensive literature overview regarding the
state-of-the-art are presented. After this introductory
part, the first paper deals with initially anisotropic
materials such as fiber reinforced plastics. For the fiber,
different failure mechanisms under tensile or compressive
loadings are taken into account, while for the matrix
isotropic damage coupled to plasticity is considered.
Therefore, in addition to the initial anisotropy, further
anisotropic effects arise due to the involved
tension-compression asymmetry as well as the change in the
stiffness ratio between fiber and matrix. Since three scalar
(local) damage variables are used in this work, each of them
is gradient-extended using the micromorphic approach to
obtain mesh-independent results. The entire framework is
formulated in a geometrically nonlinear sense and
investigated using several numerical simulations.
Thereafter, the following three articles address the
anisotropy induced by plasticity and anisotropic damage
within initially isotropic materials. As in the first work,
a `two-surface' approach is employed to treat plasticity and
damage as independent but strongly coupled mechanisms. The
governing equations are described in logarithmic strain
space using an additive split, while damage is represented
by a symmetric second order tensor. Moreover, the proposed
framework satisfies the damage growth criterion, which
prevents the model from artificial stiffening effects. Once
again, the micromorphic approach is used, whereas the damage
tensor's invariants are gradient-extended. Several
representative structural examples are examined to
investigate the model's ability to provide mesh-independent
results in uniaxial and multiaxial settings, as well as two-
and three-dimensional boundary value problems. The last two
articles of this dissertation deal with the combination of
the multiplicative decomposition and AD in the context of
biomechanics. For this purpose, a co-rotated configuration
of the intermediate configuration is introduced, which
shares the same characteristics with the intermediate
configuration, but is uniquely defined. Thus, it can be
implemented using AD in an efficient and physically sound
manner. In addition, the concept of structural tensors, an
additional split of the inelastic part of the deformation
gradient and hardening effects are discussed in a
thermodynamically consistent manner. The stress-driven
kinematic growth model, which is formulated in terms of the
co-rotated configuration, utilizes the concept of
homeostatic surfaces to describe growth and remodeling
processes of soft biological tissues. In this regard, two
parallel decompositions of the deformation gradient are
employed, in order to treat direction-dependent and
independent constituents separately. Moreover, remodeling of
collagen fibers is taken into account in a stress-driven
manner. The model is fully implemented using AD using an
implicit approach. The predicted growth and remodeling
behavior is compared with experiments found in literature
and agrees qualitatively well with these data.},
cin = {311510},
ddc = {624},
cid = {$I:(DE-82)311510_20140620$},
typ = {PUB:(DE-HGF)11},
doi = {10.18154/RWTH-2023-07973},
url = {https://publications.rwth-aachen.de/record/963830},
}
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