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@PHDTHESIS{Lamm:989667,
author = {Lamm, Lukas},
othercontributors = {Reese, Stefanie and Nackenhorst, Udo},
title = {{C}ontinuum based modelling and simulation of
rate-dependent effects in inelastic solids: applications for
biological growth and damage mechanics},
school = {Rheinisch-Westfälische Technische Hochschule Aachen},
type = {Dissertation},
address = {Aachen},
publisher = {RWTH Aachen University},
reportid = {RWTH-2024-06926},
pages = {1 Online-Ressource : Illustrationen},
year = {2024},
note = {Veröffentlicht auf dem Publikationsserver der RWTH Aachen
University; Dissertation, Rheinisch-Westfälische Technische
Hochschule Aachen, 2024},
abstract = {Nowadays, model-based simulation methods play a major role
in the research and development of new technologies. This is
not least due to the time and cost savings associated with
their use. Ideally, however, physically motivated simulation
models also provide a deeper insight into the processes
depicted, which is otherwise difficult to achieve in many
places. In the context of engineering sciences, the
prediction of the behaviour of a wide variety of materials
under mechanical loading plays a particularly important
role. Since almost all materials tend to nonlinear material
behaviour under certain circumstances, the modelling can be
very challenging depending on the effect under
consideration. Especially in the area of rate- and
time-dependent modelling of a wide variety of material
properties, many open research questions remain yet to be
answered. These include, for example, the description of
time-dependent growth processes in biological materials or
the modelling of rate-dependent damage phenomena. The
present cumulative dissertation presents a compilation of
the author’s (and his coauthors’) work that has been
published on topics of continuum mechanical modelling of
rate-dependent material behaviour. After the introduction,
the overview of the current state of research and the
clarification of the research-relevant questions, four
published research papers are presented. The dissertation
starts with a paper on the topic of modelling growth
processes in artificially grown tissue. Based on
experimental observations, a so-called homeostatic state is
postulated in this work. Such a state describes a state of
tension preferred by the tissue, which the material always
tries to adopt through active contraction or expansion. This
consideration forms the basis for modelling the
corresponding growth-induced change in shape and volume.
Following classical models for the description of plastic
material behaviour, it is shown that by introducing a
homeostatic potential, the development of the
growth-related, inelastic strains can be elegantly
described. For the description of the temporal component in
the evolution of the inelastic strains, a classical Perzyna
approach is used. In addition to the theoretical derivation,
the numerical realization as well as the implementation in
finite element (FE) software will be discussed in the
following. Using numerical examples, it is shown that the
new formulation is able to predict the growth behaviour more
precisely than other well established models. This is
especially illustrated by considering the influence of
complex boundary conditions. Finally, a first investigation
of the prediction quality of the model based on experimental
data shows that the developed model is able to reasonably
approximate the growth-induced homeostatic stress in the
tissue. Besides growth process effects, many other inelastic
effects can occur in complex materials. Polymers show a
strong dependence in their deformation behaviour with
respect to both loading rate and temperature. Furthermore,
rate-dependent damage effects play an important role in
these materials. In the further course of this dissertation,
two articles and one conference proceeding are presented,
dealing with the thermodynamically consistent modelling of
ratedependent damage behaviour in polymers. In the first two
publications on this topic, the purely mechanical continuum
model is presented. Based on the multiplicative
decomposition of the deformation gradient, the viscoelastic
material behaviour is described via a viscous potential. A
Perzyna approach is used to model the rate-dependent
evolution of the scalar damage variable. The
thermodynamically consistent derivation is discussed in the
following as well as the numerical treatment of the
equations and their implementation in FE software. Finally,
it is shown that the developed model is able to adequately
represent creep damage and polymers. This is a great
advantage compared to classical, rate-independent models, as
these are not able to represent this effect in a meaningful
way. Building on the previous publications, the last article
in this work deals with the thermodynamically consistent
extension of the proposed damage model to take thermal
effects into account. For this purpose, a fully
thermomechanically coupled formulation is presented on the
basis of a further decomposition of the deformation
gradient. Using appropriate parameter studies and numerical
examples, the influence of temperature on the development of
damage is investigated. Finally, the results of various
structural calculations demonstrate the applicability of
this mutliphysical simulation model for various
applications. In the last chapter, this dissertation
concludes the research questions investigated herein and
gives an outlook for further potential research based on the
findings of this work.},
cin = {311510},
ddc = {624},
cid = {$I:(DE-82)311510_20140620$},
typ = {PUB:(DE-HGF)11},
doi = {10.18154/RWTH-2024-06926},
url = {https://publications.rwth-aachen.de/record/989667},
}
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