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The prediction of fracture is of utmost importance regarding the design of modern, specifically tailored engineering materials. These materials are often heterogeneous, \ie their properties vary in space. This can either be achieved purposefully by combining two or more constituents to profit from a more resilient composite material, or happen due to unavoidable imperfections. In any case, purely experimental assessment of failure is tedious and circuitous as soon as the structure of interest gets more complex, and the involvement of numerical models is inevitable. In this work, the phase-field approach to fracture is applied which is able to capture manifold crack phenomena inherently and sidesteps the need for remeshing by describing the crack as a continuous field. The phase-field model is extended to a fully diffuse incorporation of heterogeneities: A static order parameter smoothly transitions from one to the other bulk material constituent, while the weak, brittle interface is incorporated via a continuous fracture toughness distribution. The sharp interface jump conditions still hold for the diffuse representation since a partial rank-1 relaxation is employed in accordance with the unilateral contact condition of the phase-field model. Moreover, a compensation procedure ensures the independence of the interface fracture toughness from interface and phase-field length scales. The model is validated by a comparison to analytical results and the predictive power is demonstrated by the deduction of direction-dependent, effective fracture properties of heterogeneous microstructures. / Die Vorhersage des Bruchverhaltens ist für die Entwicklung moderner, speziell zugeschnittener technischer Werkstoffe von größter Bedeutung. Diese Materialien sind oft heterogen, d.h. ihre Eigenschaften variieren im Raum. Dies kann entweder absichtlich durch die Kombination zweier oder mehrerer Bestandteile erreicht werden, um von einem widerstandsfähigeren Verbundwerkstoff zu profitieren, oder durch unvermeidbare Imperfektionen geschehen. In jedem Fall ist eine rein experimentelle Versagensbewertung komplexer Strukturen mühsam und umständlich, und die Nutzung numerischer Modelle unvermeidlich. In dieser Arbeit werden Brüche mittels Phasenfeldmethode modelliert, wodurch vielfältige Rissphänomene erfasst werden können und die Notwendigkeit einer Neuvernetzung durch die Beschreibung des Risses als kontinuierliches Feld entfällt. Das Phasenfeldmodell wird um eine vollständig diffuse Einbindung von Heterogenitäten erweitert: Ein statischer Orderparameter beschreibt den glatten Übergang zwischen zwei Bestandteilen des Materials, während die geschwächte, spröde Grenzfläche durch eine kontinuierliche Bruchzähigkeitsverteilung eingebunden wird. Die scharfen Grenzflächensprungbedingungen gelten auch für die diffuse Darstellung, da eine partielle Rang-1 Relaxation in Übereinstimmung mit der unilateralen Rissflächenkontaktbedingung genutzt wird. Darüber hinaus gewährleistet ein Kompensationsverfahren die Unabhängigkeit der Grenzflächenbruchzähigkeit von inhärenten Längenskalen der Grenzfläche und des Rissphasenfelds. Das Modell wird durch einen Vergleich mit analytischen Ergebnissen validiert und die Vorhersagekraft wird durch die Ableitung richtungsabhängiger, effektiver Brucheigenschaften heterogener Mikrostrukturen demonstriert.

Multiphase flow is a familiar phenomenon from daily life and occupies an important role in physics, engineering, and medicine. The understanding of multiphase flows relies largely on the theory of interfaces, which is not well understood in many cases. To date, the Navier-Stokes-Korteweg equations and the Cahn-Hilliard equation have represented two major branches of phase-field modeling. The Navier-Stokes-Korteweg equations describe a single component fluid material with multiple states of matter, e.g., water and water vapor; the Cahn-Hilliard type models describe multi-component materials with immiscible interfaces, e.g., air and water. In this dissertation, a unified multiphase fluid modeling framework is developed based on rigorous mathematical and thermodynamic principles. This framework does not assume any ad hoc modeling procedures and is capable of formulating meaningful new models with an arbitrary number of different types of interfaces. In addition to the modeling, novel numerical technologies are developed in this dissertation focusing on the Navier-Stokes-Korteweg equations. First, the notion of entropy variables is properly generalized to the functional setting, which results in an entropy-dissipative semi-discrete formulation. Second, a family of quadrature rules is developed and applied to generate fully discrete schemes. The resulting schemes are featured with two main properties: they are provably dissipative in entropy and second-order accurate in time. In the presence of complex geometries and high-order differential terms, isogeometric analysis is invoked to provide accurate representations of computational geometries and robust numerical tools. A novel periodic transformation operator technology is also developed within the isogeometric context. It significantly simplifies the procedure of the strong imposition of periodic boundary conditions. These attributes make the proposed technologies an ideal candidate for credible numerical simulation of multiphase flows. A general-purpose parallel computing software, named PERIGEE, is developed in this work to provide an implementation framework for the above numerical methods. A comprehensive set of numerical examples has been studied to corroborate the aforementioned theories. Additionally, a variety of application examples have been investigated, culminating with the boiling simulation. Importantly, the boiling model overcomes several challenges for traditional boiling models, owing to its thermodynamically consistent nature. The numerical results indicate the promising potential of the proposed methodology for a wide range of multiphase flow problems. / text

This thesis is devoted to several aspects of geometry and morphology in wetting problems and hard sphere packings. First, we propose a new method to simulate wetting and slip on nanostructured substrates: a phase field model associated with a dynamical density theory approach. We showed omniphobicity, meaning repellency, no matter the chemical properties of the liquid on monovalued surfaces, i.e. surfaces without overhangs, which is in contradiction with the macroscopic Cassie-Baxter-Wenzel theory, can produce so-called We checked systematically the impact of the surface parameters on omniphobic repellency, and we show that the key ingredient are line tensions, which emerge from needle shaped surface structures. Geometrical effects have also an important influence on glassy or jammed systems, for example amorphous hard sphere systems in infinite pressure limit. Such hard sphere packings got stuck in a so-called jammed phase, and we shall demonstrate that the local structure in such systems is universal, i.e. independent of the protocol of the generation. For this, robust order parameters - so-called Minkowski tensors - are developed, which overcome robustness deficiencies of widely used order parameters. This leads to a unifying picture of local order parameters, based on geometrical principles. Furthermore, we find with the Minkowski tensor analysis crystallization in jammed sphere packs at the random closed packing point

L'Inconel 718 est un superalliage base-nickel très utilisé pour la fabrication de pièces aéronautiques soumises à de fortes contraintes et de hautes températures. La maîtrise de la microstructure finale issue de la mise en forme à chaud est un des éléments clés pour le contrôle des propriétés mécaniques et pour répondre aux exigences strictes du secteur. Dans cette étude, l'évolution de la microstructure de l'Inconel 718 est étudiée au moyen d'essais de torsion suivis d'une trempe à l'eau (pour examiner les évolutions dynamiques) ou d'un maintien à la température de déformation puis d'une trempe à l'eau (pour examiner les évolutions post-dynamiques). Ces essais sont réalisés dans les domaines de température δ-supersolvus et δ-subsolvus et pour des vitesses de déformation de 10-2 à 0.1 s-1. Des analyses microstructurales par microscopie électronique à balayage et cartographie des orientations cristallographiques par EBSD sont réalisées pour suivre l'évolution de la fraction recristallisée, de la taille de grains recristallisés ainsi que de l'état de précipitation lors de la déformation et des maintiens pré- et post-déformation. Sur base de ces observations expérimentales, les principaux mécanismes métallurgiques actifs sont identifiés, puis modélisés : écrouissage, germination de nouveaux grains, migration de joints de grains, et interaction avec les particules de seconde-phases. Un modèle d'évolution microstructurale en champ moyen a été enrichi pour prendre en compte l'ensemble de ces mécanismes élémentaires et leur dépendance aux conditions thermomécaniques. Ce modèle permet de décrire, pour les domaines δ-subsolvus et δ-supersolvus, les cinétiques de recristallisation dynamique et post-dynamique de l'Inconel 718, les cinétiques de précipitation et dissolution de la phase δ, ainsi que l'évolution de la taille de grains. Il prédit également les courbes contrainte-déformation dans le domaine de température δ-supersolvus. / Inconel 718 is nickel-based Superalloy widely used in the aeronautic industry to manufacture aircraft parts subjected to extreme in-service conditions of high stresses at elevated temperatures. Controlling the microstructure after hot forming is a key element to control the mechanical properties of the final products and meet the tight specifications imposed by the aeronautic industry.In this work, the microstructure evolution of Inconel 718 was investigated via isothermal and iso-strain rate torsion tests followed by water quenching (to investigate dynamic evolution) or by annealing at deformation temperature then water quenching (to investigate post-dynamic evolution). These tests were conducted in both δ-Supersolvus and δ-Subsolvus temperature domains and for strain rates of 0.01 to 0.1 s-1.Scanning electron microscopy (SEM) and Electron Back Scattered Diffraction (EBSD) were used to characterize the microstructure and follow the evolution of the recrystallized fraction, the recrystallized grain size and the δ-phase precipitation after deformation and during pre-deformation and post-deformation annealing. Based on these experimental observations, the main metallurgical mechanisms have been identified and modelled: hardening, nucleation of new grains, grain boundaries migration and the δ-phase- recrystallization interaction.A two-site mean field approach having a low computational cost was chosen to model the microstructural evolution at different thermomechanical conditions. This model describes the main mechanisms taking place during hot forming of Inconel 718 in both δ-Supersolvus and δ-Subsolvus domains and predicts the recrystallization kinetics in both dynamic and post-dynamic regimes , the δ-phase precipitation and dissolution kinetics and the grain size evolution. The model predicts also the strain-stress curves at high temperatures in the absence of δ-phase particles.

Phase field models have played an important role in shaping our understanding of a variety of micro structural phenomena in materials. Their attractive features include (a) their ability to capture instabilities in microstructures, and (b) their ability to handle topological transitions { such as splitting or coalescence { gracefully. Therefore, we have chosen to use a phase field model in our study of instabilities in cylindrical pores in nanoporous membranes which eventually lead to their failure. Our study is motivated by recent studies on thermal stability of nanoporous membranes of alumina, titania and zirconia. The key feature in our model is its ability to incorporate surface discussion as the mechanism for mass transport. We first benchmark the model through a critical comparison of our results on early stages of surface evolution during Rayleigh instability and grain boundary grooving with those from linear theories of these phenomena. We have then used longer simulations (which go beyond early stages, and therefore, can incorporate non-lineare effects) to study instabilities in a hollow cylinder in three different systems: single crystal or amorphous solid (which fails through Rayleigh instability), a model sys-tem with parallel grain boundaries (which fails through grain boundary grooving), and a polycrystal (whose failure depends on a combination of grain growth and grooving). In all the cases, the surface energy is assumed to be isotropic, and the operative mechanism for mass transport is assumed to be surface discussion.

We present a new diffuse interface model for the dynamics of inextensible vesicles in a viscous fluid with inertial forces. A new feature of this work is the implementation of the local inextensibility condition in the diffuse interface context. Local inextensibility is enforced by using a local Lagrange multiplier, which provides the necessary tension force at the interface. We introduce a new equation for the local Lagrange multiplier whose solution essentially provides a harmonic extension of the multiplier off the interface while maintaining the local inextensibility constraint near the interface. We also develop a local relaxation scheme that dynamically corrects local stretching/compression errors thereby preventing their accumulation. Asymptotic analysis is presented that shows that our new system converges to a relaxed version of the inextensible sharp interface model. This is also verified numerically. To solve the equations, we use an adaptive finite element method with implicit coupling between the Navier-Stokes and the diffuse interface inextensibility equations. Numerical simulations of a single vesicle in a shear flow at different Reynolds numbers demonstrate that errors in enforcing local inextensibility may accumulate and lead to large differences in the dynamics in the tumbling regime and smaller differences in the inclination angle of vesicles in the tank-treading regime. The local relaxation algorithm is shown to prevent the accumulation of stretching and compression errors very effectively. Simulations of two vesicles in an extensional flow show that local inextensibility plays an important role when vesicles are in close proximity by inhibiting fluid drainage in the near contact region.

For some alloys martensitic transformation is responsible for the so-called shape memory effect and pseudoelasticity. These properties are used in a wide range of industry applications. Each of these materials is transformed to the shape it was manufactured in when heated to its critical temperature (austenite phase) no matter how seriously it was deformed at lower temperatures (martensite phase). Looking at the microstructure, one can observe significant change of crystalographic lattice depending on temperature and deformation. This the- sis focuses on modelling the evolution of microstructure during deformation for materials in the martensite phase. In this case, the creation of multiple variants of martensite is observed, divided by interfaces where a part of energy is stored. This behaviour can be described by the phase-field model. The numerical im- plementation of this model using the standard finite element method requires large computational costs. The aim of this thesis is to implement this model in MATLAB using a spectral method based on the fast Fourier transform, which is suitable for solving problems on a periodic domain. It is interesting to com- pare the computation using spectral method on a conventional PC with the computation written in FEniCS computed on a cluster. However, the...

Infant visual attention develops rapidly over the first year of life, significantly altering the way infants respond to peripheral visual events. Here we present data from 5-, 7- and 10-month-old infants using the Infant Orienting With Attention (IOWA) task, designed to capture developmental changes in visual spatial attention and saccade planning. Results indicate rapid development of spatial attention and visual response competition between 5 and 10 months. We use a dynamic neural field (DNF) model to link behavioral findings to neural population activity, providing a possible mechanistic explanation for observed developmental changes. Together, the behavioral and model simulation results provide new insights into the specific mechanisms that underlie spatial cueing effects, visual competition, and visual interference in infancy.

De nos jours, il est bien accepté que le cycle magnétique de 11 ans du Soleil est l'oeuvre d'une dynamo interne présente dans la zone convective. Bien qu'avec la puissance de calculs des ordinateurs actuels il soit possible, à l'aide de véritables simulations magnétohydrodynamiques, de résoudre le champ magnétique et la vitessse dans toutes les directions spatiales, il n'en reste pas moins que pour étudier l'évolution temporelle et spatiale de la dynamo solaire à grande échelle, il reste avantageux de travailler avec des modèles plus simples. Ainsi, nous avons utilisé un modèle simplifié de la dynamo solaire, nommé modèle de champ moyen, pour mieux comprendre les mécanismes importants à l'origine et au maintien de la dynamo solaire. L'insertion d'un tenseur-alpha complet dans un modèle dynamo de champ moyen, provenant d'un modèle global-MHD [Ghizaru et al., 2010] de la convection solaire, nous a permis d'approfondir le rôle que peut jouer la force électromotrice dans les cycles magnétiques produits par ce modèle global. De cette façon, nous avons pu reproduire certaines caractéristiques observées dans les cycles magnétiques provenant de la simulation de Ghizaru et al., 2010. Tout d'abord, le champ magnétique produit par le modèle de champ moyen présente deux modes dynamo distincts. Ces modes, de périodes similaires, sont présents et localisés sensiblement aux mêmes rayons et latitudes que ceux produits par le modèle global. Le fait que l'on puisse reproduire ces deux modes dynamo est dû à la complexité spatiale du tenseur-alpha. Par contre, le rapport entre les périodes des deux modes présents dans le modèle de champ moyen diffère significativement de celui trouvé dans le modèle global. Par ailleurs, on perd l'accumulation d'un fort champ magnétique sous la zone convective dans un modèle où la rotation différentielle n'est plus présente. Ceci suggère que la présence de rotation différentielle joue un rôle non négligeable dans l'accumulation du champ magnétique à cet endroit. Par ailleurs, le champ magnétique produit dans un modèle de champ moyen incluant un tenseur-alpha sans pompage turbulent global est très différent de celui produit par le tenseur original. Le pompage turbulent joue donc un rôle fondamental au sein de la distribution spatiale du champ magnétique. Il est important de souligner que les modèles dépourvus d'une rotation différentielle, utilisant le tenseur-alpha original ou n'utilisant pas de pompage turbulent, parviennent tous deux à produire une dynamo oscillatoire. Produire une telle dynamo à l'aide d'un modèle de ce type n'est pas évident, a priori. Finalement, l'intensité ainsi que le type de profil de circulation méridienne utilisés sont des facteurs affectant significativement la distribution spatiale de la dynamo produite. / It is generally agreed upon that the 11-year magnetic cycle of the Sun arises through the action of an internal dynamo operating in the convective zone, and perhaps also immediately beneath it. Although the computing power of current supercomputers is sufficient to allow fairly realistic magnetohydrodynamical simulations of this dynamo process, to study the temporal and spatial evolution of the large-scale solar magnetic field over long timescales, it remains advantageous to work with simpler models. Thus, to better understand the physical mechanisms at the origin and maintenance of the solar dynamo, we used a simplified formulation, known as a mean-field model. By using a complete alpha-tensor extracted from a global MHD model of solar convection [Ghizaru et al., 2010] as input to a kinematic axisymmetric mean-field dynamo model [Charbonneau & MacGregor, 1997], it becomes possible to study the effect of the electromotive force on the magnetic cycles produced by the global model. In this way, we are able to reproduce some of the observed characteristics of the Ghizaru et al., 2010 simulation, in particular magnetic cycles. The axisymmetric magnetic field produced by the mean-field dynamo model exhibits two distincts dynamo modes. These modes, with similar periods, are present and peak at substantially at the same radii and latitudes as the sonlly-averaged magnetic fields extracted from the global model. Thanks to the spatial complexity of the alpha-tensor, we can reproduce these two dynamo modes. In contrast, the ratio of the periods of the two modes present in the mean field model differs significantly from that found in the global model. In addition, the accumulation of strong magnetic fields at the base of the convective zone disappears in a model where differential rotation has been removed. This suggests that differential rotation plays a significant role in the accumulation of magnetic fields in this region. Furthermore, removing the turbulent pumping component of the alpha-tensor produces a very different magnetic field cycle. Therefore, turbulent pumping plays a crucial role in the spatial distribution of the magnetic field. It is important to underline that the models without differential rotation, with or without turbulent pumping, both succeed in producing an oscillatory dynamo using only the turbulent electromotive force. However, the dynamos materializing in these modified models are significantly different from that using the full alpha-tensor. Finally, both the intensity and form of meridional circulation profiles are significant factors affecting the dynamo modes.