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On the Effect of Nanofillers on the Environmental Stress Cracking Resistance of Glassy Polymers
(2019)

It is well known that reinforcing polymers with small amounts of nano-sized fillers is one of the most effective methods for simultaneously improving their mechanical and thermal properties. However, only a small number of studies have focused on environ-mental stress cracking (ESC), which is a major issue for premature failures of plastic products in service. Therefore, the contribution of this work focused on the influence of nano-SiO2 particles on the morphological, optical, mechanical, thermal, as well as envi-ronmental stress cracking properties of amorphous-based nanocomposites.
Polycarbonate (PC), polystyrene (PS) and poly(methyl methacrylate) (PMMA) nanocom-posites containing different amounts and sizes of nano-SiO2 particles were prepared using a twin-screw extruder followed by injection molding. Adding a small amount of nano-SiO2 caused a reduction in optical properties but improved the tensile, toughness, and thermal properties of the polymer nanocomposites. The significant enhancement in mechanical and thermal properties was attributed to the adequate level of dispersion and interfacial interaction of the SiO2 nanoparticles in the polymer matrix. This situation possibly increased the efficiency of stress transfer across the nanocomposite compo-nents. Moreover, the data revealed a clear dependency on the filler size. The polymer nanocomposites filled with smaller nanofillers exhibited an outstanding enhancement in both mechanical properties and transparency compared with nanocomposites filled with larger particles. The best compromise of strength, toughness, and thermal proper-ties was achieved in PC-based nanocomposites. Therefore, special attention to the influ-ence of nanofiller on the ESC resistance was given to PC.
The ESC resistance of the materials was investigated under static loading with and without the presence of stress-cracking agents. Interestingly, the incorporation of nano-SiO2 greatly enhanced the ESC resistance of PC in all investigated fluids. This result was particularly evident with the smaller quantities and sizes of nano-SiO2. The enhancement in ESC resistance was more effective in mild agents and air, where the quality of the deformation process was vastly altered with the presence of nano-SiO2. This finding confirmed that the new structural arrangements on the molecular scale in-duced by nanoparticles dominate over the ESC agent absorption effect and result in greatly improving the ESC resistance of the materials. This effect was more pronounced with increasing molecular weight of PC due to an increase in craze stability and fibril density. The most important and new finding is that the ESC behavior of polymer-based nanocomposites/ stress-cracking agent combinations can be scaled using the Hansen solubility parameter. Thus allowed us to predict the risk of ESC as a function of the filler content for different stress-cracking agents without performing extensive tests. For a comparison of different amorphous polymer-based nanocomposites at a given nano-SiO2 particle content, the ESC resistance of materials improved in the following order: PMMA/SiO2 < PS/SiO2 < low molecular weight PC/SiO2 < high molecular weight PC/SiO2. In most cases, nanocomposites with 1 vol.% of nano-SiO2 particles exhibited the largest improvement in ESC resistance.
However, the remarkable improvement in the ESC resistance—particularly in PC-based nanocomposites—created some challenges related to material characterization because testing times (failure time) significantly increased. Accordingly, the superposition ap-proach has been applied to construct a master curve of crack propagation model from the available short-term tests at different temperatures. Good agreement of the master curves with the experimental data revealed that the superposition approach is a suitable comparative method for predicting slow crack growth behavior, particularly for long-duration cracking tests as in mild agents. This methodology made it possible to mini-mize testing time.
Additionally, modeling and simulations using the finite element method revealed that multi-field modeling could provide reasonable predictions for diffusion processes and their impact on fracture behavior in different stress cracking agents. This finding sug-gests that the implemented model may be a useful tool for quick screening and mitigat-ing the risk of ESC failures in plastic products.

The simulation of cutting process challenges established methods due to large deformations and topological changes. In this work a particle finite element method (PFEM) is presented, which combines the benefits of discrete modeling techniques and methods based on continuum mechanics. A crucial part of the PFEM is the detection of the boundary of a set of particles. The impact of this boundary detection method on the structural integrity is examined and a relation of the key parameter of the method to the eigenvalues of strain tensors is elaborated. The influence of important process parameters on the cutting force is studied and a comparison to an empirical relation is presented.

Areal optical surface topography measurement is an emerging technology for industrial quality control. However, neither calibration procedures nor the utilization of material measures are standardized. State of the art is the calibration of a set of metrological characteristics with multiple calibration samples (material measures). Here, we propose a new calibration sample (artefact) capable of providing the entire set of relevant metrological characteristics within only one single sample. Our calibration artefact features multiple material measures and is manufactured with two-photon laser lithography (direct laser writing, DLW). This enables a holistic calibration of areal topography measuring instruments with only one series of measurements and without changing the sample.

This research explores the development of web based reference software for
characterisation of surface roughness for two-dimensional surface data. The reference software used for verification of surface characteristics makes the evaluation methods easier for clients. The algorithms used in this software
are based on International ISO standards. Most software used in industrial measuring
instruments may give variations in the parameters calculated due to numerical changes in
calculation. Such variations can be verified using the proposed reference software.
The evaluation of surface roughness is carried out in four major steps: data capture, data
align, data filtering and parameter calculation. This work walks through each of these steps
explaining how surface profiles are evaluated by pre-processing steps called fitting and
filtering. The analysis process is then followed by parameter evaluation according to DIN EN
ISO 4287 and DIN EN ISO 13565-2 standards to extract important information from the
profile to characterise surface roughness.

Road accidents remain as one of the major causes of death and injuries globally. Several million people die every year due to road accidents all over the world. Although the number of accidents in European region have reduced in the past years, road safety still remains a major challenge. Especially in case of commercial trucks, due to the size and load of the vehicle, even minor collisions with other road users would lead to serious injuries or death. In order to reduce number of accidents, automotive industry is rapidly developing advanced driver assistance systems (ADAS) and automated driving technologies. Efficient and reliable solutions are required for these systems to sense, perceive and react to different environmental conditions. For vehicle safety applications such as collision avoidance with vulnerable road users (VRUs), it is not only important for the system to efficiently detect and track the objects in the vicinity of the vehicle but should also function robustly.
An environment perception solution for application in commercial truck safety systems and for future automated driving is developed in this work. Thereby a method for integrated tracking and classification of road users in the near vicinity of the vehicle is formulated. The drawbacks in conventional multi-object tracking algorithms with respect to state, measurement and data association uncertainties have been addressed with the recent advancements in the field of unified multi-object tracking solutions based on random finite sets (RFS). Gaussian mixture implementation of the recently developed labeled multi-Bernoulli (LMB) filter [RSD15] is used as the basis for multi-object tracking in this work. Measurement from an high-resolution radar sensor is used as the main input for detecting and tracking objects.
On one side, the focus of this work is on tracking VRUs in the near vicinity of the truck. As it is beneficial for most of the vehicle safety systems to also know the category that the object belongs to, the focus on the other side is also to classify the road users. All the radar detections believed to originate from a single object are clustered together with help of density based spatial clustering for application with noise (DBSCAN) algorithm. Each cluster of detections would have different properties based on the respective object characteristics. Sixteen distinct features based on radar detections, that are suitable for separating pedestrians, bicyclists and passenger car categories are selected and extracted for each of the cluster. A machine learning based classifier is constructed, trained and parameterised for distinguishing the road users based on the extracted features.
The class information derived from the radar detections can further be used by the tracking algorithm, to adapt the model parameters used for precisely predicting the object motion according to the category of the object. Multiple model labeled multi-Bernoulli filter (MMLMB) is used for modelling different object motions. Apart from the detection level, the estimated state of an object on the tracking level also provides information about the object class. Both these informations are fused using Dempster-Shafer theory (DST) of evidence, based on respective class probabilities Thereby, the output of the integrated tracking and classification with MMLMB filter are classified tracks that can be used by truck safety applications with better reliability.
The developed environment perception method is further implemented as a real-time prototypical system on a commercial truck. The performance of the tracking and classification approaches are evaluated with the help of simulation and multiple test scenarios. A comparison of the developed approaches to a conventional converted measurements Kalman filter with global nearest neighbour association (CMKF-GNN) shows significant advantages in the overall accuracy and performance.

The phase field approach is a powerful tool that can handle even complicated fracture phenomena within an apparently simple framework. Nonetheless, a profound understanding of the model is required in order to be able to interpret the obtained results correctly. Furthermore, in the dynamic case the phase field model needs to be verified in comparison to experimental data and analytical results in order to increase the trust in this new approach. In this thesis, a phase field model for dynamic brittle fracture is investigated with regard to these aspects by analytical and numerical methods

Fucoidan is a class of biopolymers mainly found in brown seaweeds. Due to its diverse medical importance, homogenous supply as well as a GMP-compliant product is of a special interest. Therefore, in addition to optimization of its extraction and purification from classical resources, other techniques were tried (e.g., marine tissue culture and heterologous expression of enzymes involved in its biosynthesis). Results showed that 17.5% (w/w) crude fucoidan after pre-treatment and extraction was obtained from the brown macroalgae F. vesiculosus. Purification by affinity chromatography improved purity relative to the commercial purified product. Furthermore, biological investigations revealed improved anti-coagulant and anti-viral activities compared with crude fucoidan. Furthermore, callus-like and protoplast cultures as well as bioreactor cultivation were developed from F. vesiculosus representing a new horizon to produce fucoidan biotechnologically. Moreover, heterologous expression of several enzymes involved in its biosynthesis by E. coli (e.g., FucTs and STs) demonstrated the possibility to obtain active enzymes that could be utilized in enzymatic in vitro synthesis of fucoidan. All these competitive techniques could provide the global demands from fucoidan.

The growing computational power enables the establishment of the Population Balance Equation (PBE)
to model the steady state and dynamic behavior of multiphase flow unit operations. Accordingly, the twophase
flow
behavior inside liquid-liquid extraction equipment is characterized by different factors. These
factors include: interactions among droplets (breakage and coalescence), different time scales due to the
size distribution of the dispersed phase, and micro time scales of the interphase diffusional mass transfer
process. As a result of this, the general PBE has no well known analytical solution and therefore robust
numerical solution methods with low computational cost are highly admired.
In this work, the Sectional Quadrature Method of Moments (SQMOM) (Attarakih, M. M., Drumm, C.,
Bart, H.-J. (2009). Solution of the population balance equation using the Sectional Quadrature Method of
Moments (SQMOM). Chem. Eng. Sci. 64, 742-752) is extended to take into account the continuous flow
systems in spatial domain. In this regard, the SQMOM is extended to solve the spatially distributed
nonhomogeneous bivariate PBE to model the hydrodynamics and physical/reactive mass transfer
behavior of liquid-liquid extraction equipment. Based on the extended SQMOM, two different steady
state and dynamic simulation algorithms for hydrodynamics and mass transfer behavior of liquid-liquid
extraction equipment are developed and efficiently implemented. At the steady state modeling level, a
Spatially-Mixed SQMOM (SM-SQMOM) algorithm is developed and successfully implemented in a onedimensional
physical spatial domain. The integral spatial numerical flux is closed using the mean mass
droplet diameter based on the One Primary and One Secondary Particle Method (OPOSPM which is the
simplest case of the SQMOM). On the other hand the hydrodynamics integral source terms are closed
using the analytical Two-Equal Weight Quadrature (TEqWQ). To avoid the numerical solution of the
droplet rise velocity, an analytical solution based on the algebraic velocity model is derived for the
particular case of unit velocity exponent appearing in the droplet swarm model. In addition to this, the
source term due to mass transport is closed using OPOSPM. The resulting system of ordinary differential
equations with respect to space is solved using the MATLAB adaptive Runge–Kutta method (ODE45). At
the dynamic modeling level, the SQMOM is extended to a one-dimensional physical spatial domain and
resolved using the finite volume method. To close the mathematical model, the required quadrature nodes
and weights are calculated using the analytical solution based on the Two Unequal Weights Quadrature
(TUEWQ) formula. By applying the finite volume method to the spatial domain, a semi-discreet ordinary
differential equation system is obtained and solved. Both steady state and dynamic algorithms are
extensively validated at analytical, numerical, and experimental levels. At the numerical level, the
predictions of both algorithms are validated using the extended fixed pivot technique as implemented in
PPBLab software (Attarakih, M., Alzyod, S., Abu-Khader, M., Bart, H.-J. (2012). PPBLAB: A new
multivariate population balance environment for particulate system modeling and simulation. Procedia
Eng. 42, pp. 144-562). At the experimental validation level, the extended SQMOM is successfully used
to model the steady state hydrodynamics and physical and reactive mass transfer behavior of agitated
liquid-liquid extraction columns under different operating conditions. In this regard, both models are
found efficient and able to follow liquid extraction column behavior during column scale-up, where three
column diameters were investigated (DN32, DN80, and DN150). To shed more light on the local
interactions among the contacted phases, a reduced coupled PBE and CFD framework is used to model
the hydrodynamic behavior of pulsed sieve plate columns. In this regard, OPOSPM is utilized and
implemented in FLUENT 18.2 commercial software as a special case of the SQMOM. The dropletdroplet
interactions
(breakage
and
coalescence)
are
taken
into
account
using
OPOSPM,
while
the
required
information
about
the
velocity
field
and
energy
dissipation
is
calculated
by
the
CFD
model.
In
addition
to
this,
the proposed coupled OPOSPM-CFD framework is extended to include the mass transfer. The
proposed framework is numerically tested and the results are compared with the published experimental
data. The required breakage and coalescence parameters to perform the 2D-CFD simulation are estimated
using PPBLab software, where a 1D-CFD simulation using a multi-sectional gird is performed. A very
good agreement is obtained at the experimental and the numerical validation levels.

A fast numerical method for an advanced electro-chemo-mechanical model is developed which is able to capture phase separation processes in porous materials. This method is applied to simulate lithium-ion battery cells, where the complex microstructure of the electrodes is fully resolved. The intercalation of ions into the popular cathode material LFP leads to a separation into lithium-rich and lithium-poor phases. The large concentration gradients result in high mechanical stresses. A phase-field method applying the Cahn-Hilliard equation is used to describe the diffusion. For the sake of simplicity, the linear elastic case is considered. Numerical tests for fully resolved three-dimensional granular microstructures are discussed in detail.

Epoxy belongs to a category of high-performance thermosetting polymers which have been used extensively in industrial and consumer applications. Highly cross-linked epoxy polymers offer excellent mechanical properties, adhesion, and chemical resistance. However, unmodified epoxies are prone to brittle fracture and crack propagation due to their highly crosslinked structure. As a result, epoxies are normally toughened to ensure the usability of these materials in practical applications.
This research work focuses on the development of novel modified epoxy matrices, with enhanced mechanical, fracture mechanical and thermal properties, suitable to be processed by filament winding technology, to manufacture composite based calender roller covers with improved performance in comparison to commercially available products.
In the first stage, a neat epoxy resin (EP) was modified using three different high functionality epoxy resins with two type of hardeners i.e. amine-based (H1) and anhydride-based (H2). Series of hybrid epoxy resins were obtained by systematic variation of high functionality epoxy resin contents with reference epoxy system. The resulting matrices were characterized by their tensile properties and the best system was chosen from each hardener system i.e. amine and anhydride. For tailored amine based system (MEP_H1) 14 % improvement was measured for bulk samples similarly, for tailored anhydride system (MEP_H2) 11 % improvement was measured when tested at 23 °C.
Further, tailored epoxy systems (MEP_H1 and MEP_H2) were modified using specially designed block copolymer (BCP), and core-shell rubber nanoparticles (CSR). Series of nanocomposites were obtained by systematic variation of filler contents. The resulting matrices were extensively characterized qualitatively and quantitatively to reveal the effect of each filler on the polymer properties. It was shown that the BCP confer better fracture properties to the epoxy resin at low filler loading without losing the other mechanical properties. These characteristics were accompanied by ductility and temperature stability. All composites were tested at 23 °C and at 80 °C to understand the effect of temperature on the mechanical and fracture properties.
Examinations on fractured specimen surfaces provided information about the mechanisms responsible for reinforcement. Nanoparticles generate several energy dissipating mechanisms in the epoxy, e.g. plastic deformation of the matrix, cavitation, void growth, debonding and crack pinning. These were closely related to the microstructure of the materials. The characteristic of the microstructure was verified by microscopy methods (SEM and AFM). The microstructure of neat epoxy hardener system was strongly influenced by the nanoparticles and the resulting interfacial interactions. The interaction of nanoparticles with a different hardener system will result in different morphology which will ultimately influence the mechanical and fracture mechanical properties of the nanocomposites. Hybrid toughening using a combination of the block-copolymer / core-shell rubber nanoparticles and block copolymer / TiO2 nanoparticles has been investigated in the epoxy systems. It was found out that addition of rigid phase with a soft phase recovers the loss of strength in the nanocomposites caused by a softer phase.
In order to clarify the relevant relationships, the microstructural and mechanical properties were correlated. The Counto’s, Halpin-Tsai, and Lewis-Nielsen equations were used to calculate the modulus of the composites and predicted modulus fit well with the measured values. Modeling was done to predict the toughening contribution from block copolymers and core-shell rubber nanoparticles. There was good agreement between the predicted values and the experimental values for the fracture energy.

Der Fokus der vorliegenden Arbeit liegt auf endlosfaser- und langfaserverstärkten
thermoplastischen Materialien. Hierfür wurde das „multilayered hybrid
(MLH)“ Konzept entwickelt und auf zwei Halbzeuge, den MLH-Roving und die MLHMat
angewendet. Der MLH-Roving ist ein Roving (bestehend aus Endlosfasern), der
durch thermoplastische Folien in mehrere Schichten geteilt wird. Der MLH-Roving
wird durch eine neuartige Spreizmethode mit anschließender thermischen Fixierung
und abschließender mehrfacher Faltung hergestellt. Dadurch können verschiedene
Faser-Matrix-Konfigurationen realisiert werden. Die MLH-Mat ist ein
glasmattenverstärktes thermoplastisches Material, das für hohe Fasergehalte bis 45
vol. % und verschiedene Matrixpolymere, z.B. Polypropylen (PP) und Polyamide 6
(PA6) geeignet ist. Sie zeichnet sich durch eine hohe Homogenität in der
Flächendichte und in der Faserrichtung aus. Durch dynamische Crashversuche mit
auf MLH-Roving und MLH-Mat basierenden Probekörpern wurden das
Crashverhalten und die Performance untersucht. Die Ergebnisse der Crashkörper
basierend auf langfaserverstärktem Material (MLH-Mat) und endlosfaserverstärktem
Material (MLH-Roving) waren vergleichbar. Die PA6-Typen zeigten eine bessere
Crashperformance als PP-Typen.
The present work deals with continuous fiber- and long fiber reinforced thermoplastic
materials. The concept of multilayered hybrid (MLH) structure was developed and
applied to the so-called MLH-roving and MLH-mat. The MLH-roving is a continuous
fiber roving separated evenly into several sublayers by thermoplastic films, through
the sequential processes of spreading with a newly derived equation, thermal fixing,
and folding. It was aimed to satisfy the variety of material configuration as well as the
variety in intermediate product. The MLH-mat is a glass mat reinforced thermoplastic
(GMT)-like material that is suitable for high fiber contents up to 45 vol. % and various
matrix polymers, e.g. polypropylene (PP), polyamide 6 (PA6). It showed homogeneity
in areal density, random directional fiber distribution, and reheating stability required
for molding process. On the MLH-roving and MLH-mat materials, the crash behavior
and performance were investigated by dynamic crash test. Long fiber reinforced
materials (MLH-mat) were equivalent to continuous fiber reinforced materials (MLHroving),
and PA6 grades showed higher crash performance than PP grades.

Due to their superior weight-specific mechanical properties, carbon fibre epoxy composites (CFRP) are commonly used in aviation industry. However, their brittle failure behaviour limits the structural integrity and damage tolerance in case of impact (e.g. tool drop, bird strike, hail strike, ramp collision) or crash events. To ensure sufficient robustness, a minimum skin thickness is therefore prescribed for the fuselage, partially exceeding typical service load requirements from ground or flight manoeuvre load cases. A minimum skin thickness is also required for lightning strike protection purposes and to enable state-of-the-art bolted repair technology. Furthermore, the electrical conductivity of CFRP aircraft structures is insufficient for certain applications; additional metal components are necessary to provide electrical functionality (e.g. metal meshes on the outer skin for lightning strike protection, wires for electrical bonding and grounding, overbraiding of cables to provide electromagnetic shielding). The corresponding penalty weights compromise the lightweight potential that is actually given by the structural performance of CFRP over aluminium alloys.
Former research attempts tried to overcome these deficits by modifying the resin system (e.g. by addition of conductive particles or toughening agents) but could not prove sufficient enhancements. A novel holistic approach is the incorporation of highly conductive and ductile continuous metal fibres into CFRP. The basic idea of this hybrid material concept is to take advantage of both the electrical and mechanical capabilities of the integrated metal fibres in order to simultaneously improve the electrical conductivity and the damage tolerance of the composite. The increased density of the hybrid material is over-compensated by omitting the need for additional electrical system installation items and by the enhanced structural performance, enabling a reduction of the prescribed minimum skin thickness. Advantages over state-of-the-art fibre metal laminates mainly arise from design and processing technology aspects.
In this context, the present work focuses on analysing and optimising the structural and electrical performance of such hybrid composites with shares of metal fibres up to 20 vol.%. Bundles of soft-annealed austenitic steel or copper cladded low carbon steel fibres with filament diameters of 60 or 63 µm are considered. The fibre bundles are distinguished by high elongation at break (32 %) and ultimate tensile strength (900 MPa) or high electrical conductivity (2.4 × 10^7 S/m). Comprehensive researches are carried out on the fibre bundles as well as on unidirectional and multiaxial laminates. Both hybrid composites with homogeneous and accumulated steel fibre arrangement are taken into account. Electrical in-plane conductivity, plain tensile behaviour, suitability for bolted joints as well as impact and perforation performance of the composite are analysed. Additionally, a novel non-destructive testing method based on measurement of deformation-induced phase transformation of the metastable austenitic steel fibres is discussed.
The outcome of the conductivity measurements verifies a correlation of the volume conductivity of the composite with the volume share and the specific electrical resistance of the incorporated metal fibres. Compared to conventional CFRP, the electrical conductivity in parallel to the fibre orientation can be increased by one to two orders of magnitude even for minor percentages of steel fibres. The analysis, however, also discloses the challenge of establishing a sufficient connection to the hybrid composite in order to entirely exploit its electrical conductivity.
In case of plain tensile load, the performance of the hybrid composite is essentially affected by the steel fibre-resin-adhesion as well as the laminate structure. Uniaxial hybrid laminates show brittle, singular failure behaviour. Exhaustive yielding of the embedded steel fibres is confined to the arising fracture gap. The high transverse stiffness of the isotropic metal fibres additionally intensifies strain magnification within the resin under transverse tensile load. This promotes (intralaminar) inter-fibre-failure at minor composite deformation. By contrast, multiaxial hybrid laminates exhibit distinctive damage evolution. After failure initiation, the steel fibres extensively yield and sustain the load-carrying capacity of angularly (e.g. ±45°) aligned CFRP plies. The overall material response is thus not only a simple superimposition but a complex interaction of the mechanical behaviour of the composite’s constituents. As a result of this post-damage performance, an ultimate elongation of over 11 % can be proven for the hybrid laminates analysed in this work. In this context, the influence of the steel fibre-resin adhesion on the failure behaviour of the hybrid composite is explicated by means of an analytical model. Long term exposure to corrosive media has no detrimental effect on the mechanical performance of stainless steel fibre reinforced composites. By trend, water uptake increases the maximum elongation at break of the hybrid laminate.
Moreover, the suitability of CFRP for bolted joints can partially be improved by the integration of steel fibres. While the bearing strength basically remains nearly unaffected, the bypass failure behaviour (ε_{max}: +363 %) as well as the head pull-through resistance (E_{a,BPT}: +81 %) can be enhanced. The improvements primarily concern the load-carrying capacity after failure initiation. Additionally, the integrated ductile steel fibres significantly increase the energy absorption capacity of the laminate in case of progressive bearing failure by up to 63 %.
However, the hybrid composite exhibits a sensitive low velocity/low mass impact behaviour. Compared to conventional CFRP, the damage threshold load of very thin hybrid laminates is lower, making them prone for delamination at minor, non-critical impact energies. At higher energy levels, however, the impact-induced delamination spreads less since most of the impact energy is absorbed by yielding of the ductile metal fibres instead of crack propagation. This structural advantage compared to CFRP gains in importance with increasing impact energy. The plastic deformation of the metastable austenitic steel fibres is accompanied by a phase transformation from paramagnetic γ-austenite to ferromagnetic α’-martensite. This change of the magnetic behaviour can be used to detect and evaluate impacts on the surface of the hybrid composite, which provides a simple non-destructive testing method. In case of low velocity/high mass impact, integration of ductile metal fibres into CFRP enables to address spacious areas of the laminate for energy absorption purposes. As a consequence, the perforation resistance of the hybrid composite is significantly enhanced; by addition of approximately 20 vol.% of stainless steel fibres, the perforation strength can be increased by 61 %, while the maximum energy absorption capacity rises by 194 %.

The detection and characterisation of undesired lead structures on shaft surfaces is a concern in production and quality control of rotary shaft lip-type sealing systems. The potential lead structures are generally divided into macro and micro lead based on their characteristics and formation. Macro lead measurement methods exist and are widely applied. This work describes a method to characterise micro lead on ground shaft surfaces. Micro lead is known as the deviation of main orientation of the ground micro texture from circumferential direction. Assessing the orientation of microscopic structures with arc minute accuracy with regard to circumferential direction requires exact knowledge of both the shaft’s orientation and the direction of surface texture. The shaft’s circumferential direction is found by calibration. Measuring systems and calibration procedures capable of calibrating shaft axis orientation with high accuracy and low uncertainty are described. The measuring systems employ areal-topographic measuring instruments suited for evaluating texture orientation. A dedicated evaluation scheme for texture orientation is based on the Radon transform of these topographies and parametrised for the application. Combining the calibration of circumferential direction with the evaluation of texture orientation the method enables the measurement of micro lead on ground shaft surfaces.

The main goal of this work was the study of the applicability of a polymer film heat exchanger concept for the applications in the chemical industry, such as the condensation of organic solvents. The polymer film heat exchanger investigated is a plate heat exchanger with very thin (0.025 – 0.1 mm) plates or films, which separate the fluids and enable the heat transfer. After a successful application of this concept to seawater desalination in a previous work, a further step is in chemical engineering, where the good chemical resistance of polymers in aggressive fluids is the challenge.
Two approaches were performed in this work. The first one was experimental and included the study of the chemical and mechanical resistance of preselected films, made of polymer materials, such as polyimide (PI), polyethylene terephthalate (PET) and polytetrafluoroethylene (PTFE). To simulate realistic operating conditions in a heat exchanger the films were exposed to a combined thermal (up to 90°C) and mechanical pressure loads (4-6 bar) with permanent contact with the relevant organic solvents, such as toluene, hexane, heptane and tetrahydrofuran (THF). Furthermore, a lab-scale apparatus and a full-scale demonstrator were manufactured in cooperation with two industrial partners. These were used for the investigation of the heat transfer performance for operating modes with and without phase change.
In addition to the experimental work, a coupled finite element –computational fluid dynamics (FEM-CFD)-model was developed, based on the fluid-structure-interaction (FSI). Two major tasks had to be solved here. The first one was the modelling of the condensation process, based on available mathematical models and energy balances. The second one was the consideration of the partially reversible deformation of the used film during operation. Since this deformation changes the geometry of the fluid channels also has an influence on the overall performance of the apparatus, a coupled FEM-CFD model was developed.
During the experimental study of the chemical resistance of the films, the PTFE film showed the best performance, and hence can be used for all four tested solvents. For the polyimide film, failures while exposed to THF were observed, and the PET film can only be used with water and hexane. With the used lab-scale heat exchanger and the full-scale demonstrator competitive overall heat transfer coefficients between 270 W/m²K and 700 W/m²K could be reached for the liquid-liquid (water-water, water-hexane) operation mode without phase change. For the condensation process, overall heat transfer coefficients of up to 1700/m²K could be obtained.
The numerical approach led to a well-functioning coupled model in a very small scale (1 cm²). An upscale, however, failed due to enormous hardware resources necessary required for the simulation of the entire full-scale demonstrator. The main reason for this is the very low thickness of the films, which leads to tiny mesh element sizes (<0.05 mm) necessary to model the deformation of the film. The modelling of the liquid-liquid heat transfer provided an acceptable accuracy (approx. 10%), but at very low rates the deviations were then higher (over 30%). The results of the condensation modelling were ambivalent. One the one hand a physically plausible model was developed, which could map the entire condensation process. On the other hand, the corresponding energy balance revealed major inaccuracy and hence could not be used for the determination of the overall heat transfer and showed the current limits of the FEM-CFD approach.

In this thesis viscoelastic material models are established to investigate the nature of continuous calving processes at Antarctic ice shelves. Physics-based descriptions of calving require appropriate fracture criteria to separate icebergs from the remaining ice shelf. Hence, criteria of the stress, the strain, and the self-similarity criterion are considered within finite-element computations. Crucial parameters in the models to determine the position of calving are the accurate knowledge of the geometry, especially the freeboard height, while the material parameters mainly influence the time span between two successive calving events. The extension to nonlinear material models is necessary to properly analyze the internal forces also for large deformations that occur for longer times of the viscous ice flow.

The present situation of control engineering in the context of automated production can be described as a tension field between its desired outcome and its actual consideration. On the one hand, the share of control engineering compared to the other engineering domains has significantly increased within the last decades due to rising automation degrees of production processes and equipment. On the other hand, the control engineering domain is still underrepresented within the production engineering process. Another limiting factor constitutes a lack of methods and tools to decrease the amount of software engineering efforts and to permit the development of innovative automation applications that ideally support the business requirements.
This thesis addresses this challenging situation by means of the development of a new control engineering methodology. The foundation is built by concepts from computer science to promote structuring and abstraction mechanisms for the software development. In this context, the key sources for this thesis are the paradigm of Service-oriented Architecture and concepts from Model-driven Engineering. To mold these concepts into an integrated engineering procedure, ideas from Systems Engineering are applied. The overall objective is to develop an engineering methodology to improve the efficiency of control engineering by a higher adaptability of control software and decreased programming efforts by reuse.

The mechanical properties of semi-crystalline polymers depend extremely on their
morphology, which is dependent on the crystallization during processing. The aim of
this research is to determine the effect of various nanoparticles on morphology
formation and tensile mechanical properties of polypropylene under conditions
relevant in polymer processing and to contribute ultimately to the understanding of
this influence.
Based on the thermal analyses of samples during fast cooling, it is found that the
presence of nanoparticle enhances the overall crystallization process of PP. The results
suggest that an increase of the nucleation density/rate is a dominant process that
controls the crystallization process of PP in this work, which can help to reduce the
cycle time in the injection process. Moreover, the analysis of melting behaviors
obtained after each undercooling reveals that crystal perfection increases significantly
with the incorporation of TiO2 nanoparticles, while it is not influenced by the SiO2
nanoparticles.
This work also comprises an analysis of the influence of nanoparticles on the
microstructure of injection-molded parts. The results clearly show multi-layers along
the wall thickness. The spherulite size and the degree of crystallinity continuously
decrease from the center to the edge. Generally both the spherulite size and the degree
of crystallinity decrease with higher the SiO2 loading. In contrast, an increase in the
degree of crystallinity with an increasing TiO2 nanoparticle loading was detected.
The tensile properties exhibit a tendency to increase in the tensile strength as the core
is reached. The tensile strength decreases with the addition of nanoparticles, while the
elongation at break of nanoparticle-filled PP decreases from the skin to the core. With
increasing TiO2 loading, the elongation at break decreases.

This thesis is concerned with a phase field model for martensitic transformations in metastable austenitic steels. Within the phase field approach an order parameter is introduced to indicate whether the present phase is austenite or martensite. The evolving microstructure is described by the evolution of the order parameter, which is assumed to follow the time-dependent Ginzburg-Landau equation. The elastic phase field model is enhanced in two different ways to take further phenomena into account. First, dislocation movement is considered by a crystal plasticity setting. Second, the elastic model for martensitic transformations is combined with a phase field model for fracture. Finite element simulations are used to study the single effects separately which contribute to the microstructure formation.

This thesis investigates the electromechanic coupling of dielectric elastomers for the static and dynamic case by numerical simulations. To this end, the fundamental equations of the coupled field problem are introduced and the discretisation procedure for the numerical implementation is described. Furthermore, a three field formulation is proposed and implemented to treat the nearly incompressible behaviour of the elastomer. Because of the reduced electric permittivity of the material, very high electric fields are required for actuation purposes. To improve the electromechanic coupling a heterogeneous microstructure consisting of an elastomer matrix with barium titanate inclusions is proposed and studied.

Thermoplastic composite materials are being widely used in the automotive and aerospace industries. Due to the limitations of shape complexity, different components
need to be joined. They can be joined by mechanical fasteners, adhesive bonding or
both. However, these methods have several limitations. Components can be joined
by fusion bonding due to the property of thermoplastics. Thermoplastics can be melted on heating and regain their shape on cooling. This property makes them ideal for
joining through fusion bonding by induction heating. Joining of non-conducting or
non-magnetic thermoplastic composites needs an additional material that can generate heat by induction heating.
Polymers are neither conductive nor electromagnetic so they don’t have inherent potential for inductive heating. A susceptor sheet having conductive materials (e.g. carbon fiber) or magnetic materials (e.g. nickel) can generate heat during induction. The
main issues related with induction heating are non-homogeneous and uncontrolled
heating.
In this work, it was observed that to generate heat with a susceptor sheet depends
on its filler, its concentration, and its dispersion. It also depends on the coil, magnetic
field strength and coupling distance. The combination of different fillers not only increased the heating rate but also changed the heating mechanism. Heating of 40ºC/
sec was achieved with 15wt.-% nickel coated short carbon fibers and 3wt.-% multiwalled carbon nanotubes. However, only nickel coated short carbon fibers (15wt-.%)
attained the heating rate of 24ºC/ sec. In this study, electrical conductivity, thermal
conductivity and magnetic properties testing were also performed. The results also
showed that electrical percolation was achieved around 15wt.-% in fibers and (13-
6)wt.-% with hybrid fillers. Induction heating tests were also performed by making
parallel and perpendicular susceptor sheet as fibers were uni-directionally aligned.
The susceptor sheet was also tested by making perforations.
The susceptor sheet showed homogeneous and fast heating, and can be used for
joining of non-conductive or non-magnetic thermoplastic composites.

Whole-body vibrations (WBV) have adverse effects on ride comfort and human health. Suspension seats have an important influence on the WBV severity. In this study, WBV were measured on a medium-sized compact wheel loader (CWL) in its typical operations. The effect of short-term exposure to the WBV on the ride comfort was evaluated according to ISO 2631-1:1985 and ISO 2631-1:1997. ISO 2631-1:1997 and ISO 2631-5:2004 were adopted to evaluate the effect of long-term exposure to the WBV on the human health. Reasons for the different evaluation results obtained according to ISO 2631-1:1997 and ISO 2631-5:2004 were explained in this study. The WBV measurements were carried out in cases where the driver wore a lap belt or a four-point seat harness and in the case where the driver did not wear any safety belt. The seat effective amplitude transmissibility (SEAT) and the seat transmissibility in the frequency domain in these three cases were analyzed to investigate the effect of a safety belt on the seat transmissibility. Seat tests were performed on a multi-axis shaking table in laboratory to study the dynamic behavior of a suspension seat under the vibration excitations measured on the CWL. The WBV intensity was reduced by optimizing the vertical and the longitudinal seat suspension systems with the help of computational simulations. For the optimization multi-body models of the seat-dummy system in the laboratory seat tests and the seat-driver system in the field vibration measurements were built and validated.

In this contribution a mortar-type method for the coupling of non-conforming NURBS surface patches is proposed. The connection of non-conforming patches with shared degrees of freedom requires mutual refinement, which propagates throughout the whole patch due to the tensor-product structure of NURBS surfaces. Thus, methods to handle non-conforming meshes are essential in NURBS-based isogeometric analysis. The main objective of this work is to provide a simple and efficient way to couple the individual patches of complex geometrical models without altering the variational formulation. The deformations of the interface control points of adjacent patches are interrelated with a master-slave relation. This relation is established numerically using the weak form of the equality of mutual deformations along the interface. With the help of this relation the interface degrees of freedom of the slave patch can be condensated out of the system. A natural connection of the patches is attained without additional terms in the weak form. The proposed method is also applicable for nonlinear computations without further measures. Linear and geometrical nonlinear examples show the high accuracy and robustness of the new method. A comparison to reference results and to computations with the Lagrange multiplier method is given.

This thesis treats the application of configurational forces for the evaluation of fracture processes in Antarctic ice shelves. FE simulations are used to analyze the influence of geometric scales, material parameters and boundary conditions on single surface cracks. A break-up event at the Wilkins Ice Shelf that coincided with a major temperature drop motivates the consideration of frost wedging as a mechanism for ice shelf disintegration. An algorithm for the evaluation of the crack propagation direction is used to analyze the horizontal growth of rifts. Using equilibrium considerations for a viscoelastic fluid, a method is introduced to compute viscous volume forces from measured velocity fields as loads for a linear elastic fracture mechanical analysis.

This thesis deals with the development of a tractor front loader scale which measures payload continuously, independent of the center of gravity of the payload, and unaffected of the position and movements of the loader. To achieve this, a mathematic model of a common front loader is simplified which makes it possible to identify its parameters by a repeatable and automatic procedure. By measuring accelerations as well as cylinder forces, the payload is determined continuously during the working process. Finally, a prototype was build and the scale was tested on a tractor.

On the Extended Finite Element Method for the Elasto-Plastic Deformation of Heterogeneous Materials
(2015)

This thesis is concerned with the extended finite element method (XFEM) for deformation analysis of three-dimensional heterogeneous materials. Using the "enhanced abs enrichment" the XFEM is able to reproduce kinks in the displacements and therewith jumps in the strains within elements of the underlying tetrahedral finite element mesh. A complex model for the micro structure reconstruction of aluminum matrix composite AMC225xe and the modeling of its macroscopic thermo-mechanical plastic deformation behavior is presented, using the XFEM. Additionally, a novel stabilization algorithm is introduced for the XFEM. This algorithm requires preprocessing only.

Computational Homogenization of Piezoelectric Materials using FE² Methods and Configurational Forces
(2015)

Piezoelectric materials are electro-mechanically coupled materials. In these materials it is possible to produce an electric field by applying a mechanical load. This phenomenon is known as the piezoelectric effect. These materials also exhibit a mechanical deformation in response to an external electric loading, which is known as the inverse piezoelectric effect. By using these smart properties of piezoelectric materials, applications are possible in sensors and actuators. Ferroelectric or piezoelectric materials show switching behavior of the polarization in the material under an external loading. Due to this property, these materials are used to produce random access memory (RAM) for the non-volatile storage of data in computing devices. It is essential to understand the material responses of piezoelectric materials properly in order to use them in the engineering applications in innovative manners. Due to the growing interest in determining the material responses of smart material (e.g., piezoelectric material), computational methods are becoming increasingly important.
Many engineering materials possess inhomogeneities on the micro level. These inhomogeneities in the materials cause some difficulties in the determination of the material responses computationally as well as experimentally. But on the other hand, sometimes these inhomogeneities help the materials to render some good physical properties, e.g., glass or carbon fiber reinforced composites are light weight, but show higher strength. Piezoelectric materials also exhibit intense inhomogeneities on the micro level. These inhomogeneities are originating from the presence of domains, domain walls, grains, grain boundaries, micro cracks, etc. in the material. In order to capture the effects of the underlying microstructures on the macro quantities, it is essential to homogenize material parameters and the physical responses. There are several approaches to perform the homogenization. A two-scale classical (first-order) homogenization of electro-mechanically coupled materials using a FE²-approach is discussed in this work. The main objective of this work is to investigate the influences of the underlying micro structures on the macro Eshelby stress tensor and on the macro configurational forces. The configurational forces are determined in certain defect situations. These defect situations include the crack tip of a sharp crack in the macro specimen.
A literature review shows that the macro strain tensor is used to determine the micro boundary condition for the FE²-based homogenization in a small strain setting. This approach is capable to determine the consistent homogenized physical quantities (e.g., stress, strain) and the homogenized material quantities (e.g., stiffness tensor). But the application of these type of micro boundaries for the homogenization does not generate physically consistent macro Eshelby stress tensor or the macro configurational forces. Even in the absence of the micro volume configurational forces, this approach of the homogenization of piezoelectric materials produces unphysical volume configurational forces on the macro level. After a thorough investigation of the boundary conditions on the representative volume elements (RVEs), it is found that a displacement gradient driven micro boundary conditions remedy this issue. The use of the displacement gradient driven micro boundary conditions also satisfies the Hill-Mandel condition. The macro Eshelby stress tensor of a pure mechanical problem in a small deformation setting can be determined in two possible ways: by using the homogenized mechanical quantities (displacement gradient and stress tensor), or by homogenizing the Eshelby stress tensor on the micro level by volume averaging. The first approach does not satisfy the Hill-Mandel condition incorporating the Eshelby stress tensor in the energy term, on the other hand, the Hill-Mandel condition is satisfied in the second approach. In the case of homogenized Eshelby stress tensor determined from the homogenized physical quantities, the Hill-Mandel condition gives an additional energy term. A body in a small deformation setting is deformed according to the displacement gradient. If the homogenization is done using strain driven micro boundary conditions, the micro domain is deformed according to the macro strain, but the tiny vicinity around the corresponding Gauß point is deformed according to the macro displacement gradient. This implies that some restrictions are imposed at every Gauß point on the macro level. This situation helps the macro system to produce nonphysical volume configurational forces.
A FE²-based computational homogenization technique is also considered for the homogenization of piezoelectric materials. In this technique a representative volume element, which comprises of the micro structural features in the material, is assigned to every Gauß point of the macro domain. The macro displacement gradient and the macro electric field, or the macro stress tensor and the macro electric displacement are passed to the RVEs at every macro Gauß point. After determining boundary conditions on the RVEs, the homogenization process is performed. The homogenized physical quantities and the homogenized material parameters are passed back to macro Gauß points. In this work numerical investigations are carried out for two distinct situations of the microstructures of the piezoelectric materials regarding the evolution on the micro level: a) homogenization by using stationary microstructures, and b) homogenization by using evolving microstructures.
For the first case, the domain walls remain at fixed positions through out the simulations for the homogenization of piezoelectric materials. For a considerably large external loading, the real situation is different. But to understand the effects of the underlying microstructures on the macro configurational forces, to some extent it is sufficient to do the homogenization with fixed or stationary microstructures. The homogenization process is carried out for different microstructures and for different loading conditions. If the mechanical load is applied in the direction of the polarization, a smaller crack tip configurational force is observed in comparison to the configurational force determined for a mechanical loading perpendicular to the polarization. If the polarizations in the microstructures are parallel or perpendicular to the applied electric field and the applied displacement, configurational forces parallel to the crack ligament of the macro crack are observed only. In the case of inclined polarizations in the microstructures, configurational forces inclined to the crack ligament are obtained. The simulation results also reveal that an application of an external electric field to the material reduces the value of the nodal configurational forces at the crack tip.
In the second case, the interfaces of the micro structures are allowed to move from their initial positions at every step of the applied incremental external loading. Thus, at every step of the application of the external loading, the microstructures are changed when the external loading is larger than the coercive field. The movement of the interfaces is realized through the nodal configurational forces on the micro level. At every step of the application of the external loading, the nodal configurational forces per unit length on the domain walls are determined in the post-processing of the FE-simulation on the micro domain. With the help of the domain wall kinetics, the new positions of the domain walls are determined. Numerical results show that the crack tip region is the most affected area in the macro domain. For that reason a very different distribution of the macro electric displacement is observed comparing the same produced by using fixed microstructures. Due to the movement of the domain walls, the energy is dissipated in the system. As a result, a smaller configurational force appears at the crack tip on the macro level in the case of the homogenization by using evolving microstructures. By using the homogenization technique involving the evolution of the microstructures, it is possible to produce the electric displacement vs. electric field hysteresis loop on the macro level. The shape of the hysteresis loop depends on the value of the rate of application of the external electric loading. A faster deployment of the external electric field widens the hysteresis loop.

A Consistent Large Eddy Approach for Lattice Boltzmann Methods and its Application to Complex Flows
(2015)

Lattice Boltzmann Methods have shown to be promising tools for solving fluid flow problems. This is related to the advantages of these methods, which are among others, the simplicity in handling complex geometries and the high efficiency in calculating transient flows. Lattice Boltzmann Methods are mesoscopic methods, based on discrete particle dynamics. This is in contrast to conventional Computational Fluid Dynamics methods, which are based on the solution of the continuum equations. Calculations of turbulent flows in engineering depend in general on modeling, since resolving of all turbulent scales is and will be in near future far beyond the computational possibilities. One of the most auspicious modeling approaches is the large eddy simulation, in which the large, inhomogeneous turbulence structures are directly computed and the smaller, more homogeneous structures are modeled.
In this thesis, a consistent large eddy approach for the Lattice Boltzmann Method is introduced. This large eddy model includes, besides a subgrid scale model, appropriate boundary conditions for wall resolved and wall modeled calculations. It also provides conditions for turbulent domain inlets. For the case of wall modeled simulations, a two layer wall model is derived in the Lattice Boltzmann context. Turbulent inlet conditions are achieved by means of a synthetic turbulence technique within the Lattice Boltzmann Method.
The proposed approach is implemented in the Lattice Boltzmann based CFD package SAM-Lattice, which has been created in the course of this work. SAM-Lattice is feasible of the calculation of incompressible or weakly compressible, isothermal flows of engineering interest in complex three dimensional domains. Special design targets of SAM-Lattice are high automatization and high performance.
Validation of the suggested large eddy Lattice Boltzmann scheme is performed for pump intake flows, which have not yet been treated by LBM. Even though, this numerical method is very suitable for this kind of vortical flows in complicated domains. In general, applications of LBM to hydrodynamic engineering problems are rare. The results of the pump intake validation cases reveal that the proposed numerical approach is able to represent qualitatively and quantitatively the very complex flows in the intakes. The findings provided in this thesis can serve as the basis for a broader application of LBM in hydrodynamic engineering problems.

The present thesis describes the development and validation of a viscosity adaption method for the numerical simulation of non-Newtonian fluids on the basis of the Lattice Boltzmann Method (LBM), as well as the development and verification of the related software bundle SAM-Lattice.
By now, Lattice Boltzmann Methods are established as an alternative approach to classical computational fluid dynamics
methods. The LBM has been shown to be an accurate and efficient tool for the numerical simulation of weakly compressible or incompressible fluids. Fields of application reach from turbulent simulations through thermal problems to acoustic calculations among others. The transient nature of the method and the need for a regular grid based, non body conformal discretization makes the LBM ideally suitable for simulations involving complex solids. Such geometries are common, for instance, in the food processing industry, where fluids are mixed by static mixers or agitators. Those fluid flows are often laminar and non-Newtonian.
This work is motivated by the immense practical use of the Lattice Boltzmann Method, which is limited due to stability issues. The stability of the method is mainly influenced by the discretization and the viscosity of the fluid. Thus, simulations of non-Newtonian fluids, whose kinematic viscosity depend on the shear rate, are problematic. Several authors have shown that the LBM is capable of simulating those fluids. However, the vast majority of the simulations in the literature are carried out for simple geometries and/or moderate shear rates, where the LBM is still stable. Special care has to be taken for practical non-Newtonian Lattice Boltzmann simulations in order to keep them stable. A straightforward way is to truncate the modeled viscosity range by numerical stability criteria. This is an effective approach, but from the physical point of view the viscosity bounds are chosen arbitrarily. Moreover, these bounds depend on and vary with the grid and time step size and, therefore, with the simulation Mach number, which is freely chosen at the start of the simulation. Consequently, the modeled viscosity range may not fit to the actual range of the physical problem, because the correct simulation Mach number is unknown a priori. A way around is, to perform precursor simulations on a fixed grid to determine a possible time step size and simulation Mach number, respectively. These precursor simulations can be time consuming and expensive, especially for complex cases and a number of operating points. This makes the LBM unattractive for use in practical simulations of non-Newtonian fluids.
The essential novelty of the method, developed in the course of this thesis, is that the numerically modeled viscosity range is consistently adapted to the actual physically exhibited viscosity range through change of the simulation time step and the simulation Mach number, respectively, while the simulation is running. The algorithm is robust, independent of the Mach number the simulation was started with, and applicable for stationary flows as well as transient flows. The method for the viscosity adaption will be referred to as the "viscosity adaption method (VAM)" and the combination with LBM leads to the "viscosity adaptive LBM (VALBM)".
Besides the introduction of the VALBM, a goal of this thesis is to offer assistance in the spirit of a theory guide to students and assistant researchers concerning the theory of the Lattice Boltzmann Method and its implementation in SAM-Lattice. In Chapter 2, the mathematical foundation of the LBM is given and the route from the BGK approximation of the Boltzmann equation to the Lattice Boltzmann (BGK) equation is delineated in detail.
The derivation is restricted to isothermal flows only. Restrictions of the method, such as low Mach number flows are highlighted and the accuracy of the method is discussed.
SAM-Lattice is a C++ software bundle developed by the author and his colleague Dipl.-Ing. Andreas Schneider. It is a highly automated package for the simulation of isothermal flows of incompressible or weakly compressible fluids in 3D on the basis of the Lattice Boltzmann Method. By the time of writing of this thesis, SAM-Lattice comprises 5 components. The main components are the highly automated lattice generator SamGenerator and the Lattice Boltzmann solver SamSolver. Postprocessing is done with ParaSam, which is our extension of the
open source visualization software ParaView. Additionally, domain decomposition for MPI
parallelism is done by SamDecomposer, which makes use of the graph partitioning library MeTiS. Finally, all mentioned components can be controlled through a user friendly GUI (SamLattice) implemented by the author using QT, including features to visually track output data.
In Chapter 3, some fundamental aspects on the implementation of the main components, including the corresponding flow charts will be discussed. Actual details on the implementation are given in the comprehensive programmers guides to SamGenerator and SamSolver.
In order to ensure the functionality of the implementation of SamSolver, the solver is verified in Chapter 4 for Stokes's First Problem, the suddenly accelerated plate, and for Stokes's Second Problem, the oscillating plate, both for Newtonian fluids. Non-Newtonian fluids are modeled in SamSolver with the power-law model according to Ostwald de Waele. The implementation for non-Newtonian fluids is verified for the Hagen-Poiseuille channel flow in conjunction with a convergence analysis of the method. At the same time, the local grid refinement as it is implemented in SamSolver, is verified. Finally, the verification of higher order boundary conditions is done for the 3D Hagen-Poiseuille pipe flow for both Newtonian and non-Newtonian fluids.
In Chapter 5, the theory of the viscosity adaption method is introduced. For the adaption process, a target collision frequency or target simulation Mach number must be chosen and the distributions must be rescaled according to the modified time step size. A convenient choice is one of the stability bounds. The time step size for the adaption step is deduced from the target collision frequency \(\Omega_t\) and the currently minimal or maximal shear rate in the system, while obeying auxiliary conditions for the simulation Mach number. The adaption is done in the collision step of the Lattice Boltzmann algorithm. We use the transformation matrices of the MRT model to map from distribution space to moment space and vice versa. The actual scaling of the distributions is conducted on the back mapping, because we use the transformation matrix on the basis of the new adaption time step size. It follows an additional rescaling of the non-equilibrium part of the distributions, because of the form of the definition for the discrete stress tensor in the LBM context. For that reason it is clear, that the VAM is applicable for the SRT model as well as the MRT model, where there is virtually no extra cost in the latter case. Also, in Chapter 5, the multi level treatment will be discussed.
Depending on the target collision frequency and the target Mach number, the VAM can be used to optimally use the viscosity range that can be modeled within the stability bounds or it can be used to drastically accelerate the simulation. This is shown in Chapter 6. The viscosity adaptive LBM is verified in the stationary case for the Hagen-Poiseuille channel flow and in the transient case for the Wormersley flow, i.e., the pulsatile 3D Hagen-Poiseuille pipe flow. Although, the VAM is used here for fluids that can be modeled with the power-law approach, the implementation of the VALBM is straightforward for other non-Newtonian models, e.g., the Carreau-Yasuda or Cross model. In the same chapter, the VALBM is validated for the case of a propeller viscosimeter developed at the chair SAM. To this end, the experimental data of the torque on the impeller of three shear thinning non-Newtonian liquids serve for the validation. The VALBM shows excellent agreement with experimental data for all of the investigated fluids and in every operating point. For reasons of comparison, a series of standard LBM simulations is carried out with different simulation Mach numbers, which partly show errors of several hundred percent. Moreover, in Chapter 7, a sensitivity analysis on the parameters used within the VAM is conducted for the simulation of the propeller viscosimeter.
Finally, the accuracy of non-Newtonian Lattice Boltzmann simulations with the SRT and the MRT model is analyzed in detail. Previous work for Newtonian fluids indicate that depending on the numerical value of the collision frequency \(\Omega\), additional artificial viscosity is introduced due to the finite difference scheme, which negatively influences the accuracy. For the non-Newtonian case, an error estimate in the form of a functional is derived on the basis of a series expansion of the Lattice Boltzmann equation. This functional can be solved analytically for the case of the Hagen-Poiseuille channel flow of non-Newtonian fluids. The estimation of the error minimum is excellent in regions where the \(\Omega\) error is the dominant source of error as opposed to the compressibility error.
Result of this dissertation is a verified and validated software bundle on the basis of the viscosity adaptive Lattice Boltzmann Method. The work restricts itself on the simulation of isothermal, laminar flows with small Mach numbers. As further research goals, the testing of the VALBM with minimal error estimate and the investigation of the VALBM in the case of turbulent flows is suggested.

An efficient multiscale approach is established in order to compute the macroscopic response of nonlinear composites. The micro problem is rewritten in an integral form of the Lippmann-Schwinger type and solved efficiently by Fast Fourier Transforms. Using realistic microstructure models complex nonlinear effects are reproduced and validated with measured data of fiber reinforced plastics. The micro problem is integrated in a Finite Element framework which is used to solve the macroscale. The scale coupling technique and a consistent numerical algorithm is established. The method provides an efficient way to determine the macroscopic response considering arbitrary microstructures, constitutive behaviors and loading conditions.

Accurate path tracking control of tractors became a key technology for automation in agriculture. Increasingly sophisticated solutions, however, revealed that accurate path tracking control of implements is at least equally important. Therefore, this work focuses on accurate path tracking control of both tractors and implements. The latter, as a prerequisite for improved control, are equipped with steering actuators like steerable wheels or a steerable drawbar, i.e. the implements are actively steered. This work contributes both new plant models and new control approaches for those kinds of tractor-implement combinations. Plant models comprise dynamic vehicle models accounting for forces and moments causing the vehicle motion as well as simplified kinematic descriptions. All models have been derived in a systematic and automated manner to allow for variants of implements and actuator combinations. Path tracking controller design begins with a comprehensive overview and discussion of existing approaches in related domains. Two new approaches have been proposed combining the systematic setup and tuning of a Linear-Quadratic-Regulator with the simplicity of a static output feedback approximation. The first approach ensures accurate path tracking on slopes and curves by including integral control for a selection of controlled variables. The second approach, instead, ensures this by adding disturbance feedforward control based on side-slip estimation using a non-linear kinematic plant model and an Extended Kalman Filter. For both approaches a feedforward control approach for curved path tracking has been newly derived. In addition, a straightforward extension of control accounting for the implement orientation has been developed. All control approaches have been validated in simulations and experiments carried out with a mid-size tractor and a custom built demonstrator implement.

This work presents a framework for the computation of complex geometries containing intersections of multiple patches with Reissner-Mindlin shell elements. The main objective is to provide an isogeometric finite element implementation which neither requires drilling rotation stabilization, nor user interaction to quantify the number of rotational degrees of freedom for every node. For this purpose, the following set of methods is presented. Control points with corresponding physical location are assigned to one common node for the finite element solution. A nodal basis system in every control point is defined, which ensures an exact interpolation of the director vector throughout the whole domain. A distinction criterion for the automatic quantification of rotational degrees of freedom for every node is presented. An isogeometric Reissner-Mindlin shell formulation is enhanced to handle geometries with kinks and allowing for arbitrary intersections of patches. The parametrization of adjacent patches along the interface has to be conforming. The shell formulation is derived from the continuum theory and uses a rotational update scheme for the current director vector. The nonlinear kinematic allows the computation of large deformations and large rotations. Two concepts for the description of rotations are presented. The first one uses an interpolation which is commonly used in standard Lagrange-based shell element formulations. The second scheme uses a more elaborate concept proposed by the authors in prior work, which increases the accuracy for arbitrary curved geometries. Numerical examples show the high accuracy and robustness of both concepts. The applicability of the proposed framework is demonstrated.

Continuum Mechanical Modeling of Dry Granular Systems: From Dilute Flow to Solid-Like Behavior
(2014)

In this thesis, we develop a granular hydrodynamic model which covers the three principal regimes observed in granular systems, i.e. the dilute flow, the dense flow and the solid-like regime. We start from a kinetic model valid at low density and extend its validity to the granular solid-like behavior. Analytical and numerical results show that this model reproduces a lot of complex phenomena like for instance slow viscoplastic motion, critical states and the pressure dip in sand piles. Finally we formulate a 1D version of the full model and develop a numerical method to solve it. We present two numerical examples, a filling simulation and the flow on an inclined plane where the three regimes are included.

In the present work, the phase transitions in different Fe/FeC systems were studied by using the molecular dynamics simulation and the Meyer-Entel interaction potential (also the Johnson potential for Fe-C interaction). Fe-bicrystal, thin film, Fe-C bulk and Fe-C nanowire systems were investigated to study the behaviour of the phase transition, where the energetics, dynamics and transformations pathways were analysed.

The study addresses the effect of multiple jet passes and other parameters namely feedrate, water pressure and standoff distance in waterjet peening of metallic
surfaces. An analysis of surface integrity was used to evaluate the performance of
different parameters in the process. An increase in the number of jet passes and
pressure leads to a higher roughness and more erosion and also a higher hardness.
In contrast, the feedrate shows a reverse effect on those surface characteristics.
There exists a specific value of standoff distance that results in the maximum surface
roughness, erosion as well as hardness. Analysis of the surface microstructure gave
a good insight into the mechanism material removal process involving initial and
evolved damage. Also, the waterjet peening process was optimized based on the
design of experiment approach. The developed empirical models had shown
reasonable correlations between the measured and predicted responses. A proper selection of waterjet peening parameters can be formulated to be used in practical
works.

In recent years the field of polymer tribology experienced a tremendous development
leading to an increased demand for highly sophisticated in-situ measurement methods.
Therefore, advanced measurement techniques were developed and established
in this study. Innovative approaches based on dynamic thermocouple, resistive electrical
conductivity, and confocal distance measurement methods were developed in
order to in-situ characterize both the temperature at sliding interfaces and real contact
area, and furthermore the thickness of transfer films. Although dynamic thermocouple
and real contact area measurement techniques were already used in similar
applications for metallic sliding pairs, comprehensive modifications were necessary to
meet the specific demands and characteristics of polymers and composites since
they have significantly different thermal conductivities and contact kinematics. By using
tribologically optimized PEEK compounds as reference a new measurement and
calculation model for the dynamic thermocouple method was set up. This method
allows the determination of hot spot temperatures for PEEK compounds, and it was
found that they can reach up to 1000 °C in case of short carbon fibers present in the
polymer. With regard to the non-isotropic characteristics of the polymer compound,
the contact situation between short carbon fibers and steel counterbody could be
successfully monitored by applying a resistive measurement method for the real contact
area determination. Temperature compensation approaches were investigated
for the transfer film layer thickness determination, resulting in in-situ measurements
with a resolution of ~0.1 μm. In addition to a successful implementation of the measurement
systems, failure mechanism processes were clarified for the PEEK compound
used. For the first time in polymer tribology the behavior of the most interesting
system parameters could be monitored simultaneously under increasing load
conditions. It showed an increasing friction coefficient, wear rate, transfer film layer
thickness, and specimen overall temperature when frictional energy exceeded the
thermal transport capabilities of the specimen. In contrast, the real contact area between
short carbon fibers and steel decreased due to the separation effect caused by
the transfer film layer. Since the sliding contact was more and more matrix dominated,
the hot spot temperatures on the fibers dropped, too. The results of this failure
mechanism investigation already demonstrate the opportunities which the new
measurement techniques provide for a deeper understanding of tribological processes,
enabling improvements in material composition and application design.

The demand of sustainability is continuously increasing. Therefore, thermoplastic
composites became a focus of research due to their good weight to performance
ratio. Nevertheless, the limiting factor of their usage for some processes is the loss of
consolidation during re-melting (deconsolidation), which reduces the part quality.
Several studies dealing with deconsolidation are available. These studies investigate
a single material and process, which limit their usefulness in terms of general
interpretations as well as their comparability to other studies. There are two main
approaches. The first approach identifies the internal void pressure as the main
cause of deconsolidation and the second approach identifies the fiber reinforcement
network as the main cause. Due to of their controversial results and limited variety of
materials and processes, there is a big need of a more comprehensive investigation
on several materials and processes.
This study investigates the deconsolidation behavior of 17 different materials and
material configurations considering commodity, engineering, and performance
polymers as well as a carbon and two glass fiber fabrics. Based on the first law of
thermodynamics, a deconsolidation model is proposed and verified by experiments.
Universal applicable input parameters are proposed for the prediction of
deconsolidation to minimize the required input measurements. The study revealed
that the fiber reinforcement network is the main cause of deconsolidation, especially
for fiber volume fractions higher than 48 %. The internal void pressure can promote
deconsolidation, when the specimen was recently manufactured. In other cases the
internal void pressure as well as the surface tension prevents deconsolidation.
During deconsolidation the polymer is displaced by the volume increase of the void.
The polymer flow damps the progress of deconsolidation because of the internal
friction of the polymer. The crystallinity and the thermal expansion lead to a
reversible thickness increase during deconsolidation. Moisture can highly accelerate
deconsolidation and can increase the thickness by several times because of the
vaporization of water. The model is also capable to predict reconsolidation under the
defined boundary condition of pressure, time, and specimen size. For high pressure
matrix squeeze out occur, which falsifies the accuracy of the model.The proposed model was applied to thermoforming, induction welding, and
thermoplastic tape placement. It is demonstrated that the load rate during
thermoforming is the critical factor of achieving complete reconsolidation. The
required load rate can be determined by the model and is dependent on the cooling
rate, the forming length, the extent of deconsolidation, the processing temperature,
and the final pressure. During induction welding deconsolidation can tremendously
occur because of the left moisture in the polymer at the molten state. The moisture
cannot fully diffuse out of the specimen during the faster heating. Therefore,
additional pressure is needed for complete reconsolidation than it would be for a dry
specimen. Deconsolidation is an issue for thermoplastic tape placement, too. It limits
the placement velocity because of insufficient cooling after compaction. If the
specimen after compaction is locally in a molten state, it deconsolidates and causes
residual stresses in the bond line, which decreases the interlaminar shear strength. It
can be concluded that the study gains new knowledge and helps to optimize these
processes by means of the developed model without a high number of required
measurements.
Aufgrund seiner guten spezifischen Festigkeit und Steifigkeit ist der
endlosfaserverstärkte Thermoplast ein hervorragender Leichtbauwerkstoff. Allerdings
kann es während des Wiederaufschmelzens durch Dekonsolidierung zu einem
Verlust der guten mechanischen Eigenschaften kommen, daher ist Dekonsolidierung
unerwünscht. In vielen Studien wurde die Dekonsolidierung mit unterschiedlichen
Ergebnissen untersucht. Dabei wurde meist ein Material und ein Prozess betrachtet.
Eine allgemeine Interpretation und die Vergleichbarkeit unter den Studien sind
dadurch nur begrenzt möglich. Aus der Literatur sind zwei Ansätze bekannt. Dem
ersten Ansatz liegt der Druckunterschied zwischen Poreninnendruck und
Umgebungsdruck als Hauptursache der Dekonsolidierung zu Grunde. Beim zweiten
Ansatz wird die Faserverstärkung als Hauptursache identifiziert. Aufgrund der
kontroversen Ergebnisse und der begrenzten Anzahl der Materialien und
Verarbeitungsverfahren, besteht die Notwendigkeit einer umfassenden Untersuchung
über mehrere Materialien und Prozesse. Diese Studie umfasst drei Polymere
(Polypropylen, Polycarbonat und Polyphenylensulfid), drei Gewebe (Köper, Atlas und
Unidirektional) und zwei Prozesse (Autoklav und Heißpressen) bei verschiedenen
Faservolumengehalten.
Es wurde der Einfluss des Porengehaltes auf die interlaminare Scherfestigkeit
untersucht. Aus der Literatur ist bekannt, dass die interlaminare Scherfestigkeit mit
der Zunahme des Porengehaltes linear sinkt. Dies konnte für die Dekonsolidierung
bestätigt werden. Die Reduktion der interlaminaren Scherfestigkeit für
thermoplastische Matrizes ist kleiner als für duroplastische Matrizes und liegt im
Bereich zwischen 0,5 % bis 1,5 % pro Prozent Porengehalt. Außerdem ist die
Abnahme signifikant vom Matrixpolymer abhängig.
Im Falle der thermisch induzierten Dekonsolidierung nimmt der Porengehalt
proportional zu der Dicke der Probe zu und ist ein Maß für die Dekonsolidierung. Die
Pore expandiert aufgrund der thermischen Gasexpansion und kann durch äußere
Kräfte zur Expansion gezwungen werden, was zu einem Unterdruck in der Pore
führt. Die Faserverstärkung ist die Hauptursache der Dickenzunahme
beziehungsweise der Dekonsolidierung. Die gespeicherte Energie, aufgebaut während der Kompaktierung, wird während der Dekonsolidierung abgegeben. Der
Dekompaktierungsdruck reicht von 0,02 MPa bis 0,15 MPa für die untersuchten
Gewebe und Faservolumengehalte. Die Oberflächenspannung behindert die
Porenexpansion, weil die Oberfläche vergrößert werden muss, die zusätzliche
Energie benötigt. Beim Kontakt von benachbarten Poren verursacht die
Oberflächenspannung ein Verschmelzen der Poren. Durch das bessere Volumen-
Oberfläche-Verhältnis wird Energie abgebaut. Der Polymerfluss bremst die
Entwicklung der Dickenzunahme aufgrund der erforderlichen Energie (innere
Reibung) der viskosen Strömung. Je höher die Temperatur ist, desto niedriger ist die
Viskosität des Polymers, wodurch weniger Energie für ein weiteres Porenwachstum
benötigt wird. Durch den reversiblen Einfluss der Kristallinität und der
Wärmeausdehnung des Verbundes wird während der Erwärmung die Dicke erhöht
und während der Abkühlung wieder verringert. Feuchtigkeit kann einen enormen
Einfluss auf die Dekonsolidierung haben. Ist noch Feuchtigkeit über der
Schmelztemperatur im Verbund vorhanden, verdampft diese und kann die Dicke um
ein Vielfaches der ursprünglichen Dicke vergrößern.
Das Dekonsolidierungsmodell ist in der Lage die Rekonsolidierung vorherzusagen.
Allerdings muss der Rekonsolidierungsdruck unter einem Grenzwert liegen
(0,15 MPa für 50x50 mm² und 1,5 MPa für 500x500 mm² große Proben), da es sonst
bei der Probe zu einem Polymerfluss aus der Probe von mehr als 2 % kommt. Die
Rekonsolidierung ist eine inverse Dekonsolidierung und weist die gleichen
Mechanismen in der entgegengesetzten Richtung auf.
Das entwickelte Modell basiert auf dem ersten Hauptsatz der Thermodynamik und
kann die Dicke während der Dekonsolidierung und der Rekonsolidierung
vorhersagen. Dabei wurden eine homogene Porenverteilung und eine einheitliche,
kugelförmige Porengröße angenommen. Außerdem wurde die Massenerhaltung
angenommen. Um den Aufwand für die Bestimmung der Eingangsgrößen zu
reduzieren, wurden allgemein gültige Eingabeparameter bestimmt, die für eine
Vielzahl von Konfigurationen gelten. Das simulierte Materialverhalten mit den
allgemein gültigen Eingangsparametern erzielte unter den definierten
Einschränkungen eine gute Übereinstimmung mit dem tatsächlichen
Materialverhalten. Nur bei Konfigurationen mit einer Viskositätsdifferenz von mehr als 30 % zwischen der Schmelztemperatur und der Prozesstemperatur sind die
allgemein gültigen Eingangsparameter nicht anwendbar. Um die Relevanz für die
Industrie aufzuzeigen, wurden die Effekte der Dekonsolidierung für drei weitere
Verfahren simuliert. Es wurde gezeigt, dass die Kraftzunahmegeschwindigkeit
während des Thermoformens ein Schlüsselfaktor für eine vollständige
Rekonsolidierung ist. Wenn die Kraft zu langsam appliziert wird oder die finale Kraft
zu gering ist, ist die Probe bereits erstarrt, bevor eine vollständige Konsolidierung
erreicht werden kann. Auch beim Induktionsschweißen kann Dekonsolidierung
auftreten. Besonders die Feuchtigkeit kann zu einer starken Zunahme der
Dekonsolidierung führen, verursacht durch die sehr schnellen Heizraten von mehr als
100 K/min. Die Feuchtigkeit kann während der kurzen Aufheizphase nicht vollständig
aus dem Polymer ausdiffundieren, sodass die Feuchtigkeit beim Erreichen der
Schmelztemperatur in der Probe verdampft. Beim Tapelegen wird die
Ablegegeschwindigkeit durch die Dekonsolidierung begrenzt. Nach einer scheinbar
vollständigen Konsolidierung unter der Walze kann die Probe lokal dekonsolidieren,
wenn das Polymer unter der Oberfläche noch geschmolzen ist. Die daraus
resultierenden Poren reduzieren die interlaminare Scherfestigkeit drastisch um 5,8 %
pro Prozent Porengehalt für den untersuchten Fall. Ursache ist die Kristallisation in
der Verbindungszone. Dadurch werden Eigenspannungen erzeugt, die in der
gleichen Größenordnung wie die tatsächliche Scherfestigkeit sind.

Tire-soil interaction is important for the performance of off-road vehicles and the soil compaction in the agricultural field. With an analytical model, which is integrated in multibody-simulation software, and a Finite Element model, the forces and moments generated on the tire-soil contact patch were studied to analyze the tire performance. Simulations with these two models for different tire operating conditions were performed to evaluate the mechanical behaviors of an excavator tire. For the FE model validation a single wheel tester connected to an excavator arm was designed. Field tests were carried out to examine the tire vertical stiffness, the contact pressure on the tire – hard ground interface, the longitudinal/vertical force and the compaction of the sandy clay from the test field under specified operating conditions. The simulation and experimental results were compared to evaluate the model quality. The Magic Formula was used to fit the curves of longitudinal and lateral forces. A simplified tire-soil interaction model based on the fitted Magic Formula could be established and further applied to the simulation of vehicle-soil interaction.

Aim of this work was the extension and development of a coupled Computational Fluid Dynamics (CFD) and population balance model (PBM) solver to enable a simulation aided design of stirred liquid-liquid extraction columns. The principle idea is to develop a new design methodology based on a CFD-PBM approach and verify it with existing data and correlations. On this basis, the separation performance in any apparatus geometry should be possible to predict without any experimental input. Reliable “experiments in silico” (computer calculations) should give the engineer a valuable and user-friendly tool for early design studies at minimal costs.
The layout of extraction columns is currently based on experimental investigations from miniplant to pilot plant and a scale-up to the industrial scale. The hydrodynamic properties can be varied by geometrical adjustments of the stirrer diameter, the stirrer height, the free cross sectional area of the stator, the compartment height as well as the positioning and the size of additional baffles. The key parameter for the liquid–liquid extraction is the yield which is mainly determined at the in- and outlets of the column. Local phenomena as the swirl structure are influenced by geometry changes. However, these local phenomena are generally neglected in state-of-the are design methodologies due to the complex required measurement techniques. A geometrical optimization of the column therefore still results in costs for validation experiments as assembly and operation of the column, which can be reduced by numerical investigations. The still mainly in academics used simulation based layout of counter-current extraction columns is based at the beginning of this work on one dimensional simulations of extraction columns and first three dimensional simulations. The one dimensional simulations are based on experimental derived, geometrical dependent correlations for the axial backmixing (axial dispersion), the hold-up, the phase fraction, the droplet sedimentation and the energy dissipation. A combination of these models with droplet population balance modeling resulted in a description of the complex droplet-droplet interactions (droplet size) along the column height. The three dimensional CFD simulations give local information about the flow field (velocity, swirl structure) based on the used numerical mesh corresponding to the real geometry. A coupling of CFD with population balance modeling further provides information about the local droplet size. A backcoupling of the droplet size with the CFD (drag model) results in an enhancement of the local hydrodynamics (e.g. hold-up, dispersed phase velocity). CFD provided local information about the axial dispersion coefficient of simple geometrical design (e.g. Rotating Disc Contactor (RDC) column). First simulations of the RDC column using a two dimensional rotational geometry combined with population balance modeling were performed and gave local information about the droplet size for different boundary conditions (rotational speed, different column sizes).
In this work, two different column types were simulated using an extended OpenSource CFD code. The first was the RDC column, which were mainly used for code development due to its simple geometry. The Kühni DN32 column is equipped with a six-baffled stirring device and flat baffles for disturbing the flow and requires a full three dimensional description. This column type was mainly used for experimental validation of the simulations due to the low required volumetric flow rate. The Kühni DN60 column is similar to the Kühni DN32 column with slight changes to the stirring device (4-baffles) and was used for scale up investigations. For the experimental validation of the hydrodynamics, laser based measurement techniques as Particle Image Velocimetry (PIV) and Laser Induced Fluorescence (LIF) were used. A good agreement between the experimental derived values for velocity, hold-up and energy dissipation, experimentally derived correlations from literature and the simulations with a modified Euler-Euler based OpenSource CFD code could be found. The experimental derived axial dispersion coefficient was further compared to Euler-Lagrange simulations. The experimental derived correlations for the Kühni DN32 in literature fit to the simulated values. Also the axial dispersion coefficient for the dispersed phase satisfied a correlation from literature. However, due to the complexity of the dispersed phase axial dispersion coefficient measurement, the available correlations gave no distinct agreement to each other.
A coupling of the modified Euler-Euler OpenSource CFD code was done with a one group population balance model. The implementation was validated to the analytical solution of the population balance equation for constant breakage and coalescence kernels. A further validation of the population balance transport equation was done by comparing the results of a five compartment section to the results of the commercial CFD code FLUENT using the Quadrature Method of Moments (QMOM).
For the simulation of the droplet-droplet interactions in liquid-liquid extraction columns, several breakage and coalescence models are available in the literature. The models were compared to each other using the one-group population balance model in Matlab which allows the determination of the minimum stable droplet diameter at a certain energy dissipation. Based on this representation, it was possible to determine the parameters for a specific breakage and coalescence model combination which allowed the simulation of a Kühni miniplant column at different rotational speeds. The resulting simulated droplet size was in very good agreement to the experimental derived droplet size from literature. Several column designs of the DN32 were investigated by changing the compartment height and the axial stirrer position. It could be shown that a decrease of the stirrer position increases the phase fraction inside the compartment. At the same time, the droplet size decreases inside the compartment, which allows a higher mass transfer due to a higher available interfacial area. However, the shifting results in an expected earlier flooding of the column due to a compressed flow structure underneath the stirring device. In a next step, the code was further extended by mass transfer equations based on the two-film theory. Mass transfer coefficient models for the dispersed and continuous phase were investigated for the RDC column design.
A first mass transfer simulation of a full miniplant column was done. The change in concentration was accounted by the mixture density, viscosity and interfacial tension in dependence of the concentration, which affects the calculation of the droplet size. The results of the column simulation were compared to own experimental data of the column. It could be shown that the concentration profile along the column height can be predicted by the presented CFD/population balance/mass transfer code. The droplet size decreases corresponding to the interfacial tension along the column height. Compared to the experimental derived droplet size at the outlet, the simulation is in good agreement.
Besides the occurrence of a mono dispersed droplet size, high breakage may lead to the generation of small satellite droplets and coalescence underneath the stator leads to larger droplets inside the column and hence to a change of the hold-up and of the flooding point. A multi-phase code was extended by the Sectional Quadrature Method of Moment (SQMOM) allowing a modeling of the droplet interactions of bimodal droplet interactions or multimodal distributions. The implementations were in good agreement to the analytical solution. In addition, the simulation of an RDC column section showed the different distribution of the smaller droplets and larger droplets. The smaller droplets tend to follow the continuous phase flow structure and show a higher distribution of inside the column. The larger droplets tend to rise directly through the column and show only a low influence to the continuous phase flow.
The current results strengthen the use of CFD for the layout of liquid-liquid extraction columns in future. The coupling of CFD/PBM and mass transfer using an OpenSource CFD code allows the investigation of computational intensive column designs (e.g. pilot plant columns). Furthermore the coupled code enhances the accuracy of the hydrodynamics simulations and leads to a better understanding of counter-current liquid-liquid extraction columns. The gained correlation were finally used as an input for one dimensional mass transfer simulations, where a perfect fit of the concentration profiles at varied boundary conditions could be obtained. By using the multi-scale approach, the computational time for mass transfer simulations could be reduced to minutes. In future, with increasing computational power, a further extend of the multiphase CFD/SQMOM model including mass transfer equation will provide an efficient tool to model multimodal and multivariate systems as bubble column reactors.

The noise issue in manufacturing system is widely discussed from legal and health aspects. Regarding the existing laws and guidelines, various investigation methods are implemented in industry. The sound pressure level can be measured and reduced by using established approaches in reality. However, a straightforward and low cost approach to study noise issue using existing digital factory models is not found.
This thesis attempts to develop a novel concept for sound pressure level investigation in a virtual environment. With this, the factory planners are able to investigate the noise issue during factory design and layout planning phase.
Two computer aided tools are used in this approach: acoustic simulation and virtual reality (VR). The former enables the planner to simulate the sound pressure level by given factory layout and facility sound features. And the latter provides a visualization environment to view and explore the simulation results. The combination of these two powerful tools provides the planners a new possibility to analyze the noise in a factory.
To validate the simulations, the acoustic measurements are implemented in a real factory. Sound pressure level and sound intensity are determined respectively. Furthermore, a software tool is implemented using the introduced concept and approach. With this software, the simulation results are represented in a Cave Automatic Virtual Environment (CAVE).
This thesis describes the development of the approach, the measurement of sound features, the design of visualization framework, and the implementation of VR software. Based on this know-how, the industry users are able to design their own method and software for noise investigation and analysis.

This thesis is concerned with a phase field model for brittle fracture.
The high potential of phase field modeling in computational fracture mechanics lies in the generality of the approach and the straightforward numerical implementation, combined with a good accuracy of the results in the sense of continuum fracture mechanics.
However, despite the convenient numerical application of phase field fracture models, a detailed understanding of the physical properties is crucial for a correct interpretation of the numerical results. Therefore, the driving mechanisms of crack propagation and nucleation in the proposed phase field fracture model are explored by a thorough numerical and analytical investigation in this work.

Hydrogels are known to be covalently or ionic cross-linked, hydrophilic three-dimensional
polymer networks, which exist in our bodies in a biological gel form such as the vitreous
humour that fills the interior of the eyes. Poly(N-isopropylacrylamide) (poly(NIPAAm))
hydrogels are attracting more interest in biomedical applications because, besides others, they
exhibit a well-defined lower critical solution temperature (LCST) in water, around 31–34°C,
which is close to the body temperature. This is considered to be of great interest in drug
delivery, cell encapsulation, and tissue engineering applications. In this work, the
poly(NIPAAm) hydrogel is synthesized by free radical polymerization. Hydrogel properties
and the dimensional changes accompanied with the volume phase transition of the
thermosensitive poly(NIPAAm) hydrogel were investigated in terms of Raman spectra,
swelling ratio, and hydration. The thermal swelling/deswelling changes that occur at different
equilibrium temperatures and different solutions (phenol, ethanol, propanol, and sodium
chloride) based on Raman spectrum were investigated. In addition, Raman spectroscopy has
been employed to evaluate the diffusion aspects of bovine serum albumin (BSA) and phenol
through the poly(NIPAAm) network. The determination of the mutual diffusion coefficient,
\(D_{mut}\) for hydrogels/solvent system was achieved successfully using Raman spectroscopy at
different solute concentrations. Moreover, the mechanical properties of the hydrogel, which
were investigated by uniaxial compression tests, were used to characterize the hydrogel and to
determine the collective diffusion coefficient through the hydrogel. The solute release coupled
with shrinking of the hydrogel particles was modelled with a bi-dimensional diffusion model
with moving boundary conditions. The influence of the variable diffusion coefficient is
observed and leads to a better description of the kinetic curve in the case of important
deformation around the LCST. A good accordance between experimental and calculated data
was obtained.

An isogeometric Reissner-Mindlin shell derived from the continuum theory is presented. The geometry is described by NURBS surfaces. The kinematic description of the employed shell theory requires the interpolation of the director vector and of a local basis system. Hence, the definition of nodal basis systems at the control points is necessary for the proposed formulation. The control points are in general not located on the shell reference surface and thus, several choices for the nodal values are possible. The proposed new method uses the higher continuity of the geometrical description to calculate nodal basis system and director vectors which lead to geometrical exact interpolated values thereof. Thus, the initial director vector coincides with the normal vector even for the coarsest mesh. In addition to that a more accurate interpolation of the current director and its variation is proposed. Instead of the interpolation of nodal director vectors the new approach interpolates nodal rotations. Account is taken for the discrepancy between interpolated basis systems and the individual nodal basis systems with an additional transformation. The exact evaluation of the initial director vector along with the interpolation of the nodal rotations lead to a shell formulation which yields precise results even for coarse meshes. The convergence behavior is shown to be correct for k-refinement allowing the use of coarse meshes with high orders of NURBS basis functions. This is potentially advantageous for applications with high numerical effort per integration point. The geometrically nonlinear formulation accounts for large rotations. The consistent tangent matrix is derived. Various standard benchmark examples show the superior accuracy of the presented shell formulation. A new benchmark designed to test the convergence behavior for free form surfaces is presented. Despite the higher numerical effort per integration point the improved accuracy yields considerable savings in computation cost for a predefined error bound.

The discrete nature of the dispersed phase (swarm of droplet) in stirred and pulsed liquid-liquid extraction columns makes its mathematical modelling of such complex system a tedious task. The dispersed phase is considered as a population of droplets distributed randomly with respect to their internal properties (such as: droplet size and solute concentration) at a specific location in space. Hence, the population balance equation has been emerged as a mathematical tool to model and describe such complex behaviour. However, the resulting model is too complicated. Accordingly, the analytical solution of such a mathematical model does not exist except for particular cases. Therefore, numerical solutions are resorted to in general. This is due to the inherent nonlinearities in the convective and diffusive terms as well as the appearance of many integrals in the source term. However, modelling and simulation of liquid extraction columns is not an easy task because of the discrete nature of the dispersed phase, which consist of population of droplets. The natural frame work for taking this into account is the population balance approach.
In part of this doctoral thesis work, a rigours mathematical model based on the bivariate population balance frame work (the base of LLECMOD ‘‘Liquid-Liquid Extraction Column Module’’) for the steady state and dynamic simulation of pulsed (sieve plate and packed) liquid-liquid extraction columns is developed. The model simulates the coupled hydrodynamic and mass transfer for pulsed (packed and sieve plate) extraction columns. The model is programmed using visual digital FORTRAN and then integrated into the LLECMOD program. Within LLECMOD the user can simulate different types of extraction columns including stirred and pulsed ones. The basis of LLECMOD depends on stable robust numerical algorithms based on an extended version of a fixed pivot technique after Attarakih et al., 2003 (to take into account interphase solute transfer) and advanced computational fluid dynamics numerical methods. Experimental validated correlations are used for the estimation of the droplet terminal velocity in extraction columns based on single and swarm droplet experiments in laboratory scale devices. Additionally, recent published correlations for turbulent energy dissipation, droplet breakage and coalescence frequencies are discussed as been used in this version of LLECMOD. Moreover, coalescence model from literature derived from a stochastical description have been modified to fit the deterministic population model. As a case study, LLECMOD is used here to simulate the steady state performance of pulsed extraction columns under different operating conditions, which include pulsation intensity and volumetric flow rates are simulated. The effect of pulsation intensity (on the holdup, mean droplet diameter and solute concentration) is found to have more profound effect on systems of high interfacial tension. On the hand, the variation of volumetric flow rates have substantial effect on the holdup, mean droplet diameter and solute concentration profiles for chemical systems with low interfacial tension. Two chemical test systems recommended by the European Federation of Chemical Engineering (water-acetone (solute)-n-butyl acetate and water-acetone (solute)-toluene) and an industrial test system are used in the simulation. Model predictions are successfully validated against steady state and transient experimental data, where good agreements are achieved. The simulated results (holdup, mean droplet diameter and mass transfer profiles) compared to the experimental data show that LLECMOD is a powerful simulation tool, which can efficiently predict the dynamic and steady state performance of pulsed extraction columns.
In other part of this doctoral thesis work, the steady state performance of extraction columns is studied taking into account the effect of dispersed phase inlet condition (light or heavy phase is dispersed) and the direction of mass transfer (from continuous to dispersed phase and vice versa) using the population balance framework. LLECMOD, a program that uses multivariate population balance models, is extended to take into account the direction of mass transfer and the dispersed phase inlet. As a case study, LLECMOD is used to simulate pilot plant RDC columns where the steady state mean flow properties (dispersed phase hold up and droplet mean diameter) and the solute concentration profiles are compared to the available experimental data. Three chemical systems were used: sulpholane–benzene–n-heptane, water–acetone–toluene and water–acetone–n-butyl acetate. The dispersed phase inlet and the direction of mass transfer as well as the chemical system physical properties are found to have profound effect on the steady state performance of the RDC column. For example, the mean droplet diameter is found to persist invariant when the heavy phase is dispersed and the extractor efficiency is higher when the direction of mass transfer is from the continuous to the dispersed phase. For the purpose of experimental validation, it is found that LLECMOD predictions are in good agreement with the available experimental data concerning the dispersed phase hold up, mean droplet diameter and solute concentration profiles in both phases.
In a further part of this doctoral thesis, a mathematical model is developed for liquid extraction columns based on the multivariate population balance equation (PBE) and the primary secondary particle method (PSPM) introduced by Attarakih, 2010 (US Patent Application: 0100106467). It is extended to include the momentum balance for the dispersed phase. The advantage of momentum balance is to eliminate the need for often conflicting correlations used in estimating the terminal velocity of single and swarm of droplets. The resulting mathematical model is complex due to the integral nature of the population balance equation. To reduce the complexity of this model, while maintaining most of the information drawn from the continuous population balance equation, the concept of the PSPM is used. Based on the multivariate population balance equation and the PSPM a mathematical model is developed for any liquid extraction column. The secondary particle could be envisaged as a fluid particle carrying information about the distribution as it is evolved in space and time, in the meanwhile the primary particles carry the mean properties of the population such as total droplet concentration; mean droplet diameter dispersed phase hold up and so on. This information reflects the particle-particle interactions (breakage and coalescence) and transport (convection and diffusion). The developed model is discretized in space using a first-order upwind method, while semi-implicit first-order scheme in time is used to simulate a pilot plant RDC extraction column. Here the effect of the number of primary particles (classes) on the final predicted solution is investigated. Numerical results show that the solution converge fast even as the number of primary particle is increased. The terminal droplet velocity of the individual primary particle is found the most sensitive to the number of primary particles. Other mean population properties like the droplet mean diameter, mean hold up and the concentration profiles are also found to converge along the column height by increasing the number of primary particles. The predicted steady state profiles (droplet diameter, holdup and the concentration profiles) along a pilot RDC extraction column are compared to the experimental data where good agreement is achieved.
In addition to this a robust rigorous mathematical model based on the bivariate population balance equation is developed to predict the steady state and dynamic behaviour of the interacting hydrodynamics and mass transfer in Kühni extraction columns. The developed model is extended to include the momentum balance for the calculation of the droplet velocity. The effects of step changes in the important input variables (such as volumetric flow rates, rotational speed, inlet solute concentrations etc.) on the output variables (dispersed phase holdup, mean droplet diameter and the concentration profiles) are investigated.
The last topic of this doctoral thesis is developed to transient problems. The unsteady state analysis reveals the fact that the largest time constant (slowest response) is due to the mass transfer. On the contrary, the hydrodynamic response of the dispersed phase holdup is very fast when compared to the mass transfer due to the relative fast motion of the dispersed droplets with respect to the continuous phase. The dynamic behaviour of the dispersed and continuous phases shows a lag time that increases away from the feed points of both phases. Moreover, the solute concentration response shows a highly nonlinear behaviour due to both positive and negative step changes in the input variables. The simulation results are in good agreement with the experimental ones and show the usefulness of the model.

Unidirectional (UD) composites are the most competitive materials for the production
of high-end structures. Their field of application spreads from the aerospace up to
automotive and general industry sector. Typical examples of components made of
unidirectional reinforced composite materials are rocket motor cases, drive shafts or
pressure vessels for hydrogen storage. The filament winding technology, the pultrusion
process and the tape placement are processes suitable for the manufacturing
using UD semi-finished products. The demand for parts made of UD composites is
constantly increasing over the last years. A key feature for the success of this technology
is the improvement of the manufacturing procedure.
Impregnation is one of the most important steps in the manufacturing process. During
this step the dry continuous fibers are combined with the liquid matrix in order to create
a fully impregnated semi-finished product. The properties of the impregnated roving
have a major effect on the laminate quality, and the efficient processing of the
liquid matrix has a big influence on the manufacturing costs.
The present work is related to the development of a new method for the impregnation
of carbon fiber rovings with thermoset resin. The developed impregnation unit consists
of a sinusoidal cavity without any moving parts. The unit in combination with an
automated resin mixing-dosing system allows complete wet-out of the fibers, precise
calibration of the resin fraction, and stable processing conditions.
The thesis focuses on the modeling of the impregnation process. Mathematical expressions
for the fiber compaction, the gradual increase of the roving tension, the
static pressure, the capillarity inside the filaments of the roving, and the fiber permeation
are presented, discussed, and experimentally verified. These expressions were
implemented in a modeling algorithm. The model takes into account all the relevant
material and process parameters. An experimental set-up based on the filament
winding process was used for the validation of the model. Trials under different conditions
have been performed. The results proved that the model can accurately simulate
the impregnation process. The good impregnation degree of the wound samples
confirmed the efficiency of the developed impregnation unit. A techno economical
analysis has proved that the developed system will result to the reduction of the
manufacturing costs and to the increase of the productivity.

Induction welding is a technique for joining of thermoplastic composites. An alternating
electromagnetic field is used for contact-free and fast heating of the parts to be
welded. In case of a suitable reinforcement structure heat generation occurs directly
in the laminate with complete heating in thickness direction in the vicinity of the coil.
The resulting temperature field is influenced by the distance to the induction coil with
decreasing temperature for increasing distance. Consequently, the surface facing the
inductor yields the highest, the opposite surface the lowest temperature.
The temperature field described significantly complicates the welding process. Due to
complete heating the laminate has to be loaded with pressure in order to prevent delamination,
which requires the usage of complex and expensive welding tools. Additionally,
the temperature difference between the inductor and the opposite side may
be greater than the processing window, which is determined by the properties of the
matrix polymer.
The induction welding process is influenced by numerous parameters. Due to complexity
process development is mainly based on experimental studies. The investigation
of parameter influences and interactions is cumbersome and the measurement
of quality relevant parameters, especially in the bondline, is difficult. Process simulation
can reduce the effort of parameter studies and contribute to further analysis of
the induction welding process.
The objective of this work is the development of a process variant of induction welding
preventing complete heating of the laminate in thickness direction. For optimal
welding the bondline has to reach the welding temperature whereas the other domains
should remain below the melting temperature of the matrix polymer.
For control of the temperature distribution localized cooling by an impinging jet of
compressed air was implemented. The effect was assessed by static heating experiments
with carbon fiber reinforced polyetheretherketone (CF/PEEK) and polyphenylenesulfide
(CF/PPS).
The application of localized cooling could influence the temperature distribution in
thickness direction of the laminate, according to the specifications of the welding
process. The temperature maximum was shifted from the inductor to the opposite side. This enables heating of the laminate to welding temperature in the bondline and
concurrently preventing melting and effects connected to this on the outer surface.
Inductive heating and the process variant with localized cooling were implemented in
three-dimensional finite-element process models. For that purpose, the finiteelement-
software Comsol Multiphysics 4.1 was used for the development of fully
coupled electromagnetic-thermal models which have been validated experimentally.
A sensitivity analysis for determination of different processing parameters of inductive
heating was conducted. The coil current, field frequency, and heat capacity were
identified as significant parameters. The cooling effect of the impinging jets was estimated
by appropriate convection coefficients.
For transfer of the developed process variant to the continuous induction welding
process, a process model was created. It represents a single overlap joint with continuous
feed. With the help of process modeling a parameter set for welding of
CF/PEEK was determined and used for joining of specimens. In doing so, the desired
temperature field was achieved and melting of the outer layers could be prevented.

Thermoplastic polymer-polymer composites consist of a polymeric matrix and a
polymeric reinforcement. The combination of these materials offers outstanding
mechanical properties at lower weight than standard fiber reinforced materials.
Furthermore, when both polymeric components originate from the same family or,
ideally, from the same polymer, their sustainability degree is higher than standard
fiber reinforced composites.
A challenge of polymer-polymer composites is the subsequent processing of their
semi-finished materials by heating techniques. Since the fibers are made of meltable
thermoplastic, the reinforcing fiber structure might be lost during the heating process.
Hence, the mechanical properties of an overheated polymer-polymer composite
would decline, and finally, they would be even lower than the neat matrix. A decrease
of process temperature to manage the heating challenge is not reasonable since the
cycle time would be increased at the same time. Therefore, this work pursues the
adaption of a fast and selective heating method on the use with polymer-polymer
composites. Inductively activatable particles, so-called susceptors, were distributed in
the matrix to evoke a local heating in the matrix when being exposed to an
alternating magnetic field. In this way, the energy input to the fibers is limited.
The experimental series revealed the induction particle heating effect to be mainly
related to susceptor material, susceptor fraction, susceptor distribution as well as
magnetic field strength, coupling distance, and heating time. A proper heating was
achieved with ferromagnetic particles at a filler content of only 5 wt-% in HDPE as
well as with its respective polymer fiber reinforced composites. The study included
the analysis of susceptor impact on mechanical and thermal matrix properties as well
as a degradation evaluation. The susceptors were identified to have only a marginal
impact on matrix properties. Furthermore, a semi-empiric simulation of the particle
induction heating was applied, which served for the investigation of intrinsic melting
processes.
The achieved results, the experimental as well as the analytic study, were
successfully adapted to a thermoforming process with a polymer-polymer material,
which had been preheated by means of particle induction.

Nanoparticle-Filled Thermoplastics and Thermoplastic Elastomer: Structure-Property Relationships
(2012)

The present work focuses on the structure-property relationships of
particulate-filled thermoplastics and thermoplastic elastomer (TPE). In this work
two thermoplastics and one TPE were used as polymer matrices, i.e. amorphous
bisphenol-A polycarbonate (PC), semi-crystalline isotactic polypropylene (iPP),
and a block copolymer poly(butylene terephthalate)-block-poly(tetramethylene
glycol) TPE(PBT-PTMG). For PC, a selected type of various Aerosil® nano-SiO2
types was used as filler to improve the thermal and mechanical properties by
maintaining the transparency of PC matrix. Different types of SiO2 and TiO2
nanoparticles with different surface polarity were used for iPP. The goal was to
examine the influence of surface polarity and chemical nature of nanoparticles on
the thermal, mechanical and morphological properties of iPP composites. For
TPE(PBT-PTMG), three TiO2 particles were used, i.e. one grade with hydroxyl
groups on the particle surface and the other two grades are surface-modified with
metal and metal oxides, respectively. The influence of primary size and dispersion
quality of TiO2 particles on the properties of TPE(PBT-PTMG)/TiO2 composites
were determined and discussed.
All polymer composites were produced by direct melt blending in a twin-screw
extruder via masterbatch technique. The dispersion of particles was examined by
using scanning electron microscopy (SEM) and micro-computerized tomography
(μCT). The thermal and crystalline properties of polymer composites were characterized by using thermogravimetric analysis (TGA) and differential
scanning calorimetry (DSC). The mechanical and thermomechanical properties
were determined by using mechanical tensile testing, compact tension and
Charpy impact as well as dynamic-mechanical thermal analysis (DMTA).
The SEM results show that the unpolar-surface modified nanoparticles are better
dispersed in polymer matrices as iPP than polar-surface nanoparticles, especially
in case of using Aeroxide® TiO2 nanoparticles. The Aeroxide® TiO2 nanoparticles
with a polar surface due to Ti-OH groups result in a very high degree of
agglomeration in both iPP and TPE matrices because of strong van der Waals
interactions among particles (hydrogen bonding). Compared to unmodified
Aeroxide® TiO2 nanoparticles, the other grades of surface modified TiO2 particles
are very homogenously dispersed in used iPP and TPE(PBT-PTMG). The
incorporation of SiO2 nanoparticles into bisphenol-A PC significantly increases
the mechanical properties of PC/SiO2 nanocomposites, particularly the resistance
against environmental stress crazing (ESC). However, the transparency of
PC/SiO2 nanocomposites decreases with increasing nanoparticle content and
size due to a mismatch of infractive indices of PC and SiO2 particles. The different
surface polarity of nanoparticles in iPP shows evident influence on properties of
iPP composites. Among iPP/SiO2 nanocomposites, the nanocomposite
containing SiO2 nanoparticles with a higher degree of hydrophobicity shows
improved fracture and impact toughness compared to the other iPP/SiO2
composites. The TPE(PBT-PTMG)/TiO2 composites show much better thermal and mechanical properties than neat TPE(PBT-PTMG) due to strong chemical
interactions between polymer matrix and TiO2 particles. In addition, better
dispersion quality of TiO2 particles in used TPE(PBT-PTMG) leads to dramatically
improved mechanical properties of TPE(PBT-PTMG)/TiO2 composites.

This thesis treats the extension of the classical computational homogenization scheme towards the multi-scale computation of material quantities like the Eshelby stresses and material forces. To this end, microscopic body forces are considered in the scale-transition, which may emerge due to inhomogeneities in the material. Regarding the determination of material quantities based on the underlying microscopic structure different approaches are compared by means of their virtual work consistency. In analogy to the homogenization of spatial quantities, this consistency is discussed within Hill-Mandel type conditions.

This thesis is concerned with the modeling of the domain structure evolution in ferroelectric materials. Both a sharp interface model, in which the driving force on a domain wall is used to postulate an evolution law, and a continuum phase field model are treated in a thermodynamically consistent framework. Within the phase field model, a Ginzburg-Landau type evolution law for the spontaneous polarization is derived. Numerical simulations (FEM) show the influence of various kinds of defects on the domain wall mobility in comparison with experimental findings. A macroscopic material law derived from the phase field model is used to calculate polarization yield surfaces for multiaxial loading conditions.

The primary objective of this work is the development of robust, accurate and efficient simulation methods for the optimal control of mechanical systems, in particular of constrained mechanical systems as they appear in the context of multibody dynamics. The focus is on the development of new numerical methods that meet the demand of structure preservation, i.e. the approximate numerical solution inherits certain characteristic properties from the real dynamical process.
This task includes three main challenges. First of all, a kinematic description of multibody systems is required that treats rigid bodies and spatially discretised elastic structures in a uniform way and takes their interconnection by joints into account. This kinematic description must not be subject to singularities when the system performs large nonlinear dynamics. Here, a holonomically constrained formulation that completely circumvents the use of rotational parameters has proved to perform very well. The arising constrained equations of motion are suitable for an easy temporal discretisation in a structure preserving way. In the temporal discrete setting, the equations can be reduced to minimal dimension by elimination of the constraint forces. Structure preserving integration is the second important ingredient. Computational methods that are designed to inherit system specific characteristics – like consistency in energy, momentum maps or symplecticity – often show superior numerical performance regarding stability and accuracy compared to standard methods. In addition to that, they provide a more meaningful picture of the behaviour of the systems they approximate. The third step is to take the previ- ously addressed points into the context of optimal control, where differential equation and inequality constrained optimisation problems with boundary values arise. To obtain meaningful results from optimal control simulations, wherein energy expenditure or the control effort of a motion are often part of the optimisation goal, it is crucial to approxi- mate the underlying dynamics in a structure preserving way, i.e. in a way that does not numerically, thus artificially, dissipate energy and in which momentum maps change only and exactly according to the applied loads.
The excellent numerical performance of the newly developed simulation method for optimal control problems is demonstrated by various examples dealing with robotic systems and a biomotion problem. Furthermore, the method is extended to uncertain systems where the goal is to minimise a probability of failure upper bound and to problems with contacts arising for example in bipedal walking.