Interactions between three immiscible phases, including incompressible viscoelastic structures and fluids, form standard constellations for countless scenarios in natural science. The complexity of many such scenarios has motivated various research efforts in scientific computing. This work presents novel numerical approaches for two specific of these ternary fluid-structure interaction constellations. The potential of these approaches is demonstrated by diverse applications. First, a phase field model is developed describing the interaction between a fluid and a viscoelastic solid. For this purpose, a Navier-Stokes-Cahn-Hilliard system is considered together with a hyperelastic neo-Hookean model. Based on this, an arbitrary Lagrangian-Eulerian (ALE) method is implemented to simulate the indentation of the solid material in the context of atomic force microscopy, capable of predicting physical parameters. Next, the second approach is developed to describe the interaction between a two-phase fluid and a viscoelastic solid, where fluid and solid are defined on separate domains but aligned at the interface between them. The previously introduced phase field model is used to represent the fluid and an ALE method is used for the motion of the grid, where the fluid-solid interface moves with flow velocity. A unified system is solved in all subdomains, which includes both the balance of mass and momentum and the balance of forces at the fluid-solid interface. Simulations of static and dynamic soft wetting are subsequently presented, in particular a contact line moving over a substrate with oscillating stick-slip behavior. This work combines the advantages of phase field and ALE methods for meaningful simulations and emphasizes validity and numerical stability in all approaches.

<div> Porous lithium ion battery (LIB) electrodes are comprised of electrochemically active material particles that store lithium and a surrounding conductive binder, liquid electrolyte, carbon black mixture that facilitates ionic and electronic transport. Typically, lithium diffusivity is several orders of magnitude smaller in the active material as compared to the surrounding electrolyte, making the electrode microstructure a governing factor in determining the balance between its lithium storage capacity and transport rate. Here, the effects of microstructure on the performance of LIBs are systematically analyzed at three length scales - the single particle length scale, the spatially resolved multiple particle length scale, and the porous electrode layer (homogenized) length scale. At the single particle length scale, a thermodynamically consistent variational framework is presented to examine the effects of crystallographic anisotropy, crystallographic texture, grain size, and grain morphology on the LiNi_1/3Mn_1/3Co_1/3O₂ (NMC111) chemistry. The theory was extended to the spatially resolved multiple particle length scale and the porous electrode layer length scale to explain the microstructural origin of experimentally observed instances of apparent phase separation in NMC111. At the electrode length scale, a data driven framework is presented to evaluate the electrochemical performance of a wide range of particle morphologies and battery architectures. Specifically, microstructural characteristics of 53 356 microstructures are assessed, and strategies to optimize electrode design parameters such as active particle morphology, spatial orientation, electrode porosity, and cell thickness are presented.</div><p></p>

The phase-field formulation for fracture based on the framework of representative crack elements is extended to transient thermo-mechanics. The finite element formulation is derived starting from the variational principle of total virtual power. The intention of this manuscript is to demonstrate the potential of the framework for multi-physical fracture models and complex processes inside the crack. The present model at hand allows to predict realistic deformation kinematics and heat fluxes at cracks. At the application of fully coupled, transient thermo-elasticity to a pre-cracked plate, the opened crack yields thermal isolation between both parts of the plate. Inhomogeneous thermal strains result in a curved crack surface, inhomogeneous recontact and finally heat flow through the crack regions in contact. The novel phase-field framework further allows to study processes inside the crack, which is demonstrated by heat radiation between opened crack surfaces. Finally, numerically calculated crack paths at a disc subjected to thermal shock load are compared to experimental results from literature and a curved crack in a three-dimensional application are presented.

La cristallisation sous tension (SIC) du caoutchouc naturel (NR) a fait l’objet d’un nombre considérable d’études depuis sa découverte il y a près d’un siècle. Cependant, il existe peu d’informations dans la littérature concernant le comportement du caoutchouc à des vitesses de sollicitation proches des temps caractéristiques de cristallisation. L’objectif de cette thèse est alors de contribuer à la compréhension du phénomène de cristallisation sous tension grâce à des essais dynamiques à grandes vitesses. Pour répondre à cet objectif, nous avons développé une machine de traction permettant de déformer des échantillons d’élastomères à des vitesses de sollicitation pouvant aller jusqu’à 290s-1. Les essais ont été réalisés sur quatre NR avec des taux de soufre variables, deux NR chargés comportant des taux de noir de carbone différents. Nous avons également étudié un matériau synthétique à base de polyisoprène (IR) afin de comparer ses performances à celle du NR. Les essais dynamiques étant relativement difficiles à interpréter, un travail conséquent a donc été d’abord réalisé à basse vitesse. En outre, l’approche expérimentale proposée a été couplée à une approche thermodynamique de la SIC. Les mécanismes généraux associés à la cristallisation que nous identifions sont les suivants: lors d’une traction, la cristallisation consiste en l’apparition de populations cristallines conditionnée par l’hétérogénéité de réticulation des échantillons. Cette cristallisation semble nettement accélérée dès lors que ce cycle est réalisé au-dessus de la déformation de fusion. Nous attribuons ce phénomène à un effet mémoire dû à un alignement permanent des chaînes. Enfin, l’effet de la vitesse est décrit théoriquement en intégrant un terme de diffusion des chaînes dans la cinétique de SIC. Cette approche couplée à des essais mécaniques suggère que la SIC est essentiellement gouvernée par la cinétique de nucléation. Lors des tests dynamiques, la combinaison de l’effet mémoire et d’une accélération de la fusion pendant le cycle entraine une nette diminution voire une disparition de l’hystérèse cristalline. En outre, l’auto-échauffement, qui augmente progressivement avec la fréquence du cycle, tend à supprimer l’effet mémoire en provoquant le passage du cycle en dessous de la déformation de fusion. Lors de ces essais dynamiques, la SIC semble favorisée pour le matériau le moins réticulé. Nous attribuons cet effet au blocage d’enchevêtrements jouant le rôle de sites nucléants pour la SIC. Le matériau chargé semble avoir une moins bonne aptitude à cristalliser à hautes vitesses, par rapport à l’élastomère non chargé, en raison d’un auto-échauffement important à l’interface entre charges et matrice. Enfin, nous notons une convergence des cinétiques de cristallisation du caoutchouc naturel et synthétique à grande déformation et grande vitesse de sollicitation, que nous attribuons à la prédominance du terme énergétique d’origine entropique dans la cinétique de nucléation. / Strain induced crystallization (SIC) of Natural Rubber (NR) has been the subject of a large number of studies since its discovery in 1929. However, the literature is very poor concerning the study of SIC when samples are deformed with a stretching time in the range of the SIC characteristic time (around 10msec-100msec). Thus, the aim of this thesis is to contribute to the understanding of the SIC phenomenon thanks to dynamic tensile tests at high strain rates. To meet this goal, we have developed a dynamic tensile test machine allowing stretching samples of elastomers at strain rates up to 290 s-1. The tests are carried out on four NR with different sulphur amount, two NR with different carbon black filler amounts. We also studied a synthetic rubber made of polyisoprene chains (IR) able to crystallize under strain. Dynamic tests are relatively difficult to interpret; a significant work has thus been first performed at slow strain rate. Moreover, the experiments are coupled with a thermodynamic approach. First, the general mechanisms associated to the crystallization are identified as follows: during mechanical loading or during cooling in the deformed state, SIC is the result of successive appearance of crystallite populations whose nucleation and growth depend on the local network density. Crystallization is enhanced when the cycle is performed above the melting stretching ratio. This phenomenon is attributed to a memory effect due to a permanent alignment of the chains. Finally, the effect of the strain rate is theoretically described thanks to a diffusion term. This approach, coupled with experiments suggests that SIC is mainly governed by the nucleation kinetics. For the dynamic test, the combination of the memory effect and the acceleration of the melting during the cycle lead to a reduction or even disappearance of the crystalline hysteresis. In addition, self-heating, which progressively increases with the frequency of the cycle, causes the delay of the melting stretching ratio. This well explains why the crystallinity index decreases at the minimum stretching ratio of the dynamic cycles when the frequency increases. We finally compared the ability of our different rubbers to crystallize at high strain rates. SIC is enhanced for the weakly crosslinked rubber. This might be related to the dynamics of its free entanglements, these ones acting as supplementary crosslinks at high strain rates. Then, a filled rubber is compared to the unfilled one. We found that the filled sample has a lower ability to crystallize at high strain rates as compared to the unfilled one. This is likely due to the strong self-heating at the interface between the fillers and the rubbery matrix. Finally, we observe a convergence of crystallization kinetics in natural and synthetic rubbers at high strains and high strain rates. This is attributed to the predominance of the entropic energy in the nucleation kinetics in these experimental conditions.

La cristallisation induite par déformation des élastomères est un processus cinétique qui conduit à la formation de nano-cristallites thermodynamiquement stables. La présence de ces nano-cristallites au sein de la phase amorphe modifie considérablement les propriétés mécaniques des élastomères cristallisables. Ces élastomères ont en effet la propriété intéressante d'être auto-renforçants. L’objectif de ce travail est de développer un modèle physique capable de décrire localement l’évolution de la microstructure sous l’effet d’un champ de contrainte élastique durant la cristallisation. Dans ce but, un modèle de champ de phase est élaboré et mis en œuvre dans le cadre de la mécanique des milieux continus en couplant thermodynamique et mécanique avec une dynamique de transition de phase d’Allen-Cahn. La description thermodynamique de la cristallisation induite par déformation à petite échelle est basée sur la fonctionnelle d’énergie libre du système amorphe-cristal. Les conséquences du choix de cette formulation sont discutées, on étudie en particulier les effets de contraintes élastiques sur l’équilibre des phases en volumes ainsi que sur la cinétique de croissance des domaines cristallins au sein de l’amorphe. L’introduction de l’élasticité du réseau des contraintes topologiques induite par les enchevêtrements et/ou les nœuds de réticulation dans le modèle de champ de phase a permis de mettre en évidence l’existence d’un état stable de cristallites formées (modèle énergétique) mais aussi des instabilités de croissance (modèle cinétique). Sur la base de ces deux modèles, cinétique et énergétique, nous avons étudié systématiquement l’influence des contraintes topologiques sur la cinétique de croissance et nous montrons que cette cinétique est en effet contrôlée par l’accumulation de contraintes élastiques à l’interface. La prise en compte de l’élasticité du réseau des contraintes topologiques dans l’approche thermodynamique de cristallisation prédit une augmentation de la tension de surface et par conséquent un arrêt du mécanisme de croissance en donnant lieu à la formation de cristallites stables. Enfin, nous avons adopté le modèle énergétique pour modéliser le couplage entre nucléation, croissance et déformation cyclique. Pour valider le modèle local proposé une comparaison entre les résultats des simulations par champ de phase et les données expérimentales issues de la caractérisation d’un caoutchouc naturel réticulé est effectuée et nous montrons qualitativement l’accord entre l’expérience et le modèle. / Natural rubber NR and more generally elastomer presents unique physical properties that are very important for many engineering applications. Strain induced crystallization of elastomer presents a major interest because it improves considerably the mechanical properties. In fact, the presence of crystallites within the amorphous phase in a polymer network induces a strengthening of this material, giving NR a self-reinforcement character. In this thesis, we develop a mesoscopic model to describe the crystallization of elastomers under strain. In this context, we present a kinetic model using a new physical approach: a phase field model. This model combines the crystallization thermodynamics with the local stress field. The thermodynamic description of the phase transition is based on a Gibbs free energy functional F which contains all energy contributions of the system: the bulk contributions (enthalpy and entropy) and surface tension. To understand the experimental observation of nanometer size crystalites, an explicit account of the topological constraints induced by both entanglements and/or crosslinks is necessary. We investigated two limiting mechanisms, a kinetic limitation of the growth, and an energetic limitation. Based on both the kinetic and the energetic approaches, we have systematically studied the influence of topological constraints on the growth process. We have shown that the growth process is affected by the accumulation of elastic stress at the interface. The kinetic model predicts the existence of instabilities during the growth. These instabilities induce a heterogeneous dynamical growth which leads to the formation of dendrite like structures. On the contrary, the energetic approach predicts an exponential increase of the surface tension during the growth that limits the size of the crystallites very efficiently. In the last part we investigated elastomer crystallization under cyclic deformation. To this end, we coupled the previous energetic model with the nucleation process. Finally the simulation data are compared with experimental measurements.

The investigation of failure in brittle materials, subjected to dynamic transient loading conditions, represents one of the ongoing challenges in the mechanics community. Progresses on this front are required to support the design of engineering components which are employed in applications involving extreme operational regimes. To this purpose, this thesis is devoted to the development of a framework which provides the capabilities to model how crack patterns form and evolve in brittle materials and how they affect the quantitative description of failure. The proposed model is developed within the context of diffusive interfaces which are at the basis of a new class of theories named phase field models. In this work, a set of additional features is proposed to expand their domain of applicability to the modelling of (i) rate and (ii) pressure dependent effects. The path towards the achievement of the first goal has been traced on the desire to account for micro-inertia effects associated with high rates of loading. Pressure dependency has been addressed by postulating a mode-of-failure transition law whose scaling depends upon the local material triaxiality. The governing equations have been derived within a thermodynamically-consistent framework supplemented by the employment of a micro-forces balance approach. The numerical implementation has been carried out within an updated lagrangian finite element scheme with explicit time integration. A series of benchmarks will be provided to appraise the model capabilities in predicting rate-pressure-dependent crack initiation and propagation. Results will be compared against experimental evidences which closely resemble the boundary value problems examined in this work. Concurrently, the design and optimization of a complimentary, improved, experimental characterization platform, based on the split Hopkinson pressure bar, will be presented as a mean for further validation and calibration.

Les simulations numériques des fissures fragiles par les modèles d’endommagement à gradient deviennent main- tenant très répandues. Les résultats théoriques et numériques montrent que dans le cadre de l’existence d’une pre-fissure la propagation suit le critère de Griffith. Alors que pour le problème à une dimension la nucléation de la fissure se fait à la contrainte critique, cette dernière propriété dimensionne le paramètre de longueur interne.Dans ce travail, on s’attarde sur le phénomène de nucléation de fissures pour les géométries communément rencontrées et qui ne présentent pas de solutions analytiques. On montre que pour une entaille en U- et V- l’initiation de la fissure varie continument entre la solution prédite par la contrainte critique et celle par la ténacité du matériau. Une série de vérifications et de validations sur diffèrent matériaux est réalisée pour les deux géométries considérées. On s’intéresse ensuite à un défaut elliptique dans un domaine infini ou très élancé pour illustrer la capacité du modèle à prendre en compte les effets d’échelles des matériaux et des structures.Dans un deuxième temps, ce modèle est étendu à la fracturation hydraulique. Une première phase de vérification du modèle est effectuée en stimulant une pré-fissure seule par l’injection d’une quantité donnée de fluide. Ensuite on étudie la simulation d’un réseau parallèle de fissures. Les résultats obtenus montrent qu’il a qu’une seule fissure qui se propage et que ce type de configuration minimise mieux l’énergie la propagation d’un réseau de fractures. Le dernier exemple se concentre sur la stabilité des fissures dans le cadre d’une expérience d’éclatement à pression imposée pour l’industrie pétrolière. Cette expérience d’éclatement de la roche est réalisée en laboratoire afin de simuler les conditions de confinement retrouvées lors des forages.La dernière partie de ce travail se concentre sur la rupture ductile en couplant le modèle à champ de phase avec les modèles de plasticité parfaite. Grâce à l’approche variationnelle du problème on décrit l’implantation numérique retenue pour le calcul parallèle. Les simulations réalisées montrent que pour une géométrie légèrement entaillée la phénoménologie des fissures ductiles comme par exemple la nucléation et la propagation sont en concordances avec ceux reportées dans la littérature. / Phase-field models, sometimes referred to as gradient damage, are widely used methods for the numerical simulation of crack propagation in brittle materials. Theoretical results and numerical evidences show that they can predict the propagation of a pre-existing crack according to Griffith’s criterion. For a one- dimensional problem, it has been shown that they can predict nucleation upon a critical stress, provided that the regularization parameter is identified with the material’s internal characteristic length.In this work, we draw on numerical simulations to study crack nucleation in commonly encountered geometries for which closed-form solutions are not available. We use U- and V-notches to show that the nucleation load varies smoothly from the one predicted by a strength criterion to the one of a toughness criterion when the strength of the stress concentration or singularity varies. We present validation and verification of numerical simulations for both types of geometries. We consider the problem of an elliptic cavity in an infinite or elongated domain to show that variational phase field models properly account for structural and material size effects.In a second movement, this model is extended to hydraulic fracturing. We present a validation of the model by simulating a single fracture in a large domain subject to a control amount of fluid. Then we study an infinite network of pressurized parallel cracks. Results show that the stimulation of a single fracture is the best energy minimizer compared to multi-fracking case. The last example focuses on fracturing stability regimes using linear elastic fracture mechanics for pressure driven fractures in an experimental geometry used in petroleum industry which replicates a situation encountered downhole with a borehole called burst experiment.The last part of this work focuses on ductile fracture by coupling phase-field models with perfect plasticity. Based on the variational structure of the problem we give a numerical implementation of the coupled model for parallel computing. Simulation results of a mild notch specimens are in agreement with the phenomenology of ductile fracture such that nucleation and propagation commonly reported in the literature.

The prediction of fracture in thin-walled structures is decisive for a wide range of applications. Modeling methods such as the phase-field method usually consider cracks to be constant over the thickness which, especially in load cases involving bending, is an imperfect approximation. In this contribution, fracture phenomena along the thickness direction of structural elements (plates or shells) are addressed with a phase-field modeling approach. For this purpose, a new, so called “mixed-dimensional” model is introduced, which combines structural elements representing the displacement field in the two-dimensional shell midsurface with continuum elements describing a crack phase-field in the three-dimensional solid space. The proposed model uses two separate finite element discretizations, where the transfer of variables between the coupled twoand three-dimensional fields is performed at the integration points which in turn need to have corresponding geometric locations. The governing equations of the proposed mixed-dimensional model are deduced in a consistent manner from a total energy functional with them also being compared to existing standard models. The resulting model has the advantage of a reduced computational effort due to the structural elements while still being able to accurately model arbitrary through-thickness crack evolutions as well as partly along the thickness broken shells due to the continuum elements. Amongst others, the higher accuracy aswell as the numerical efficiency of the proposed model are tested and validated by comparing simulation results of the new model to those obtained by standard models using numerous representative examples.

The realistic approximation of structural behavior in a post fracture state by the phase-field method requires information about the spatial orientation of the crack surface at the material point level. For the directional phase-field split, this orientation is specified by the crack orientation vector, that is defined perpendicular to the crack surface. An alternative approach to the determination of the orientation based on standard fracture mechanical arguments, i.e. in alignment with the direction of the largest principle tensile strain or stress, is investigated by considering the amount of dissipated strain energy density during crack evolution. In contrast to the application of gradient methods, the analytical approach enables the determination of all local maxima of strain energy density dissipation and, in consequence, the identification of the global maximum, that is assumed to govern the orientation of an evolving crack. Furthermore, the evaluation of the local maxima provides a novel aspect in the discussion of the phenomenon of crack branching. As the directional split differentiates into crack driving contributions of tension and shear stresses on the crack surface, a consistent relation to Mode I and Mode II fracture is available and a mode dependent fracture toughness can be considered. Consequently, the realistic simulation of rock-like fracture is demonstrated. In addition, a numerical investigation of Ƭ-convergence for an AT-2 type crack surface density is presented in a two-dimensional setup. For the directional split, also the issues internal locking as well as lateral phase-field evolution are addressed.

In this thesis, we study mathematical models that describe the morphology of a generalized biological cell in equilibrium or under the influence of external forces. Within these models, the cell is considered as a thermodynamic system, where streaming effects in the cell bulk and the surrounding are coupled with a Helfrich-type model for the cell membrane. The governing evolution equations for the cell given in a continuum formulation are derived using an energy variation approach. Such two-phase flow problems that combine streaming effects with a free boundary problem that accounts for bending and surface tension can be described effectively by a diffuse interface approach. An advantage of the diffuse interface approach is that models for e.g. different biophysical processes can easily be combined. That makes this method suitable to describe complex phenomena such as cell motility and multi-cell dynamics. Within the first model for cell motility, we combine a biological network for GTPases with the hydrodynamic Helfrich-type model. This model allows to account for cell motility driven by membrane protrusion as a result of actin polymerization. Within the second model, we moreover extend the Helfrich-type model by an active gel theory to account for the actin filaments in the cell bulk. Caused by contractile stress within the actin-myosin solution, a spontaneous symmetry breaking event occurs that lead to cell motility. In this thesis, we further study the dynamics of multiple cells which is of wide interest since it reveals rich non-linear behavior. To apply the diffuse interface framework, we introduce several phase field variables to account for several cells that are coupled by a local interaction potential. In a first application, we study white blood cell margination, a biological phenomenon that results from the complex relation between collisions, different mechanical properties and lift forces of red blood cells and white blood cells within the vascular system. Here, it is shown that inertial effects, which can become of relevance in various parts of the cardiovascular system, lead to a decreasing tendency for margination with increasing Reynolds number. Finally, we combine the active polar gel theory and the multi-cell approach that is capable of studying collective migration of cells. This hydrodynamic approach predicts that collective migration emerges spontaneously forming coherently-moving clusters as a result of the mutual alignment of the velocity vectors during inelastic collisions. We further observe that hydrodynamics heavily influence those systems. However, a complete suppression of the onset of collective migration cannot be confirmed. Moreover, we give a brief insight how such highly coupled systems can be treated numerically using finite elements and how the numerical costs can be limited using operator splitting approaches and problem parallelization with OPENMP. / Diese Dissertation beschäftigt sich mit mathematischen Modellen zur Beschreibung von Gleichgewichts- und dynamischen Zuständen von verallgemeinerten biologischen Zellen. Die Zellen werden dabei als thermodynamisches System aufgefasst, bei dem Strömungseffekte innerhalb und außerhalb der Zelle zusammen mit einem Helfrich-Modell für Zellmembranen kombiniert werden. Schließlich werden durch einen Energie-Variations-Ansatz die Evolutionsgleichungen für die Zelle hergeleitet. Es ergeben sie dabei Mehrphasen-Systeme, die Strömungseffekte mit einem freien Randwertproblem, das zusätzlich physikalischen Einflüssen wie Biegung und Oberflächenspannung unterliegt, vereinen. Um solche Probleme effizient zu lösen, wird in dieser Arbeit die Diffuse-Interface-Methode verwendet. Ein Vorteil dieser Methode ist, dass es sehr einfach möglich ist, Modelle, die verschiedenste Prozesse beschreiben, miteinander zu vereinen. Dies erlaubt es, komplexe biologische Phänomene, wie zum Beispiel Zellmotilität oder auch die kollektive Bewegung von Zellen, zu beschreiben. In den Modellen für Zellmotilität wird ein biologisches Netzwerk-Modell für GTPasen oder auch ein Active-Polar-Gel-Modell, das die Aktinfilamente im Inneren der Zellen als Flüssigkristall auffasst, mit dem Multi-Phasen-Modell kombiniert. Beide Modelle erlauben es, komplexe Vorgänge bei der selbst hervorgerufenen Bewegung von Zellen, wie das Vorantreiben der Zellmembran durch Aktinpolymerisierung oder auch die Kontraktionsbewegung des Zellkörpers durch kontraktile Spannungen innerhalb des Zytoskelets der Zelle, zu verstehen. Weiterhin ist die kollektive Bewegung von vielen Zellen von großem Interesse, da sich hier viele nichtlineare Phänomene zeigen. Um das Diffuse-Interface-Modell für eine Zelle auf die Beschreibung mehrerer Zellen zu übertragen, werden mehrere Phasenfelder eingeführt, die die Zellen jeweils kennzeichnen. Schließlich werden die Zellen durch ein lokales Abstoßungspotential gekoppelt. Das Modell wird angewendet, um White blood cell margination, das die Annäherung von Leukozyten an die Blutgefäßwand bezeichnet, zu verstehen. Dieser Prozess wird dabei bestimmt durch den komplexen Zusammenhang zwischen Kollisionen, den jeweiligen mechanischen Eigenschaften der Zellen, sowie deren Auftriebskraft innerhalb der Adern. Die Simulationen zeigen, dass diese Annäherung sich in bestimmten Gebieten des kardiovaskulären Systems stark vermindert, in denen die Blutströmung das Stokes-Regime verlässt. Schließlich wird das Active-Polar-Gel-Modell mit dem Modell für die kollektive Bewegung vom Zellen kombiniert. Dies macht es möglich, die kollektive Bewegung der Zellen und den Einfluss von Hydrodynamik auf diese Bewegung zu untersuchen. Es zeigt sich dabei, dass der Zustand der kollektiven gerichteten Bewegung sich spontan aus der Neuausrichtung der jeweiligen Zellen durch inelastische Kollisionen ergibt. Obwohl die Hydrodynamik einen großen Einfluss auf solche Systeme hat, deuten die Simulationen nicht daraufhin, dass Hydrodynamik die kollektive Bewegung vollständig unterdrückt. Weiterhin wird in dieser Arbeit gezeigt, wie die stark gekoppelten Systeme numerisch gelöst werden können mit Hilfe der Finiten-Elemente-Methode und wie die Effizienz der Methode gesteigert werden kann durch die Anwendung von Operator-Splitting-Techniken und Problemparallelisierung mittels OPENMP.