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@PHDTHESIS{Brepols:751443,
author = {Brepols, Tim},
othercontributors = {Reese, Stefanie and Forest, Samuel},
title = {{T}heory and numerics of gradient-extended damage coupled
with plasticity},
school = {Rheinisch-Westfälische Technische Hochschule Aachen},
type = {Dissertation},
address = {Aachen},
reportid = {RWTH-2018-231363},
pages = {1 Online-Ressource (V, 268 Seiten) : Illustrationen,
Diagramme},
year = {2018},
note = {Veröffentlicht auf dem Publikationsserver der RWTH Aachen
University 2019; Dissertation, Rheinisch-Westfälische
Technische Hochschule Aachen, 2018},
abstract = {Numerical simulations for predicting damage and failure of
materials and structures are of fundamental importance in
many engineering disciplines, since they usually reduce the
number of costly and time-consuming practical experiments
and allow for deeper insights into processes that would
otherwise not or only hardly be possible. The significance
of such simulations depends to a large extent on the quality
of the applied material models which are themselves
constantly being further developed to take more and more
phenomena and effects into account that occur in real
materials. In this context, the coupled modeling of the
complex material phenomena 'damage' and 'plasticity' can be
mentioned as a challenging and practically relevant subject
the scientific literature has been dealing with for quite
some time already. There is still a pressing need for
further research in this scientific field. The present
cumulative dissertation aims at making a valuable
contribution in this regard. It essentially represents a
compilation of several published works of the author (and
his coauthors) related to the topic. The overall goal is the
development and investigation of novel gradient-extended
damage-plasticity material models, both for the
geometrically linear and nonlinear regime, which are based
on a so-called 'two-surface' approach. The latter means that
damage and plasticity are modeled as truly distinct (but
coupled) dissipative mechanisms by taking separate damage
loading and plastic yield criteria as well as loading /
unloading conditions into consideration, respectively.
Nonlinear Armstrong-Frederick kinematic hardening, nonlinear
Voce isotropic hardening and nonlinear damage hardening are
also accounted for by the models that can quite flexibly be
adapted to various situations in which the considered real
material shows either a (quasi-)brittle-type, ductile-type
or possibly a mixed-type damaging behavior. The
gradient-extension of damage (based on a micromorphic
approach) is used to avoid pathological mesh sensitivity
issues in finite element simulations that otherwise
typically occur when using conventional models involving
material softening behavior. After an introductory part with
a literature overview and a more detailed clarification of
the research-relevant questions, the thesis begins with two
works that are concerned with a numerical comparison of two
different and competing kind of formulations for large
deformation plasticity: hypo- and hyperelastic-based
plasticity formulations that rely upon an additive
decomposition of the rate of deformation tensor or a
multiplicative split of the deformation gradient. At this
point, no damage is being considered, yet. The main purpose
for the thesis is to clarify whether one of the two
formulations should generally be preferred when it later
comes to an extension of the geometrically linear
gradient-enhanced damage-plasticity model to large
deformations. Various simulations with single finite
elements finally reveal that the results, which are obtained
using the respective modeling approaches, can indeed
significantly differ from each other under extreme
conditions and that an incautious use of hypoelastic-based
plasticity formulations can even lead to physically
implausible model behavior. However, in more
application-oriented structural simulations these problems
are nearly insignificant and the results show a good
agreement which suggests that, in principal, both
formulations are well-suited for the development of new
material models involving large plastic deformations.
Afterwards, two works are presented that deal with the
theory and numerics of two slightly different two-surface
gradient-extended damage-plasticity models for the
geometrically linear regime. Among other things, the
following topics are discussed: the application of the
micromorphic approach to achieve the gradient-extension of
the models, the derivation of the strong and weak form of
the underlying boundary value problem, the thermodynamically
consistent derivation of the evolution equations, the
models' implementation into finite element codes, the
algorithmic handling of the discretized equations at the
integration point level and the computation of the
consistent tangent operators which are necessary to retain a
quadratic rate of convergence of the Newton scheme at the
global finite element level. The results of numerous
structural simulations demonstrate the good practical
performance and mesh regularizing properties of the models
in finite element simulations involving material softening.
In the last part of the thesis, the model formulation is
extended for its application to geometrically nonlinear
problems. For this, a hyperelastic-based plasticity
framework is used which relies upon an additional
multiplicative split of the plastic part of the deformation
gradient in order to allow for the modeling of nonlinear
Armstrong-Frederick kinematic hardening at large
deformations and which utilizes exclusively symmetric
internal variables. Besides the theory, also many
numerically relevant topics are discussed, such as a
suitable time integration scheme for the evolution equations
that preserves both the plastic incompressibility and
symmetry of the tensorial internal variables, or the
implementation of the model formulation into finite element
codes. Finally, the functionality of the geometrically
nonlinear model is exemplified by a structural finite
element simulation.},
cin = {311510},
ddc = {624},
cid = {$I:(DE-82)311510_20140620$},
typ = {PUB:(DE-HGF)11},
doi = {10.18154/RWTH-2018-231363},
url = {https://publications.rwth-aachen.de/record/751443},
}
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