Neben Reifen, Riemen und Schläuchen zählen speziell auch die Balgwände von Luftfedern zu den Kompositen, da deren weiche Elastomermatrix zur Verstärkung Gewebelagen aus textilen Corden enthält. Diese Verstärkungsträger bestehen aus miteinander verzwirnten Garnen, die ihrerseits einen Zwirn aus polymeren Filamenten darstellen. Luftfederbälge weisen dementsprechend eine hochkomplexe innere Geometrie auf und sind zudem durch stark anisotropes, nichtlineares Materialverhalten gekennzeichnet. Für die strukturmechanische Simulation von Luftfedern mit der Finite-Elemente-Methode (FEM) werden in der vorliegenden Arbeit neuartige, hochauflösende Modelle entwickelt, die diesen Eigenschaften Rechnung tragen. Zunächst wird ein mathematisches Modell formuliert, das die verzwirnte Geometrie von Corden auf allgemeinen räumlichen Bahnkurven beschreibt und mithilfe dessen sich auch die lokale Orientierung der Filamente bestimmen lässt. Zur konstitutiven Modellierung des Filamentmaterials wird zudem ein transversal isotropes, hyperelastisches Materialmodell so modifiziert, dass bei Druckbelastung in Filamentrichtung nur noch die der Regularisierung dienende, isotrope Grundsteifigkeit zum Tragen kommt. Das Geometriemodell der Corde ist die Basis für deren dreidimensionale Abbildung in FE-Netzen von Luftfederbälgen. Als erster Schwerpunkt wird ein auf zyklischer Symmetrie basierendes Streifenmodell entwickelt, das die Cordgeometrie im gesamten Balg vollständig auflöst. Ein besonderes Augenmerk gilt dabei der Generierung konformer Netze, um die Grenzflächen zwischen Matrix und Corden exakt darzustellen. Das Streifenmodell ermöglicht somit detaillierte Analysen zur lokalen Verteilung von Spannungen und Verzerrungen im Inneren der Balgwand. Als zweiter Schwerpunkt wird diese Art der Modellierung auf einen kleinen rechteckigen Ausschnitt der Balgwand übertragen. Dieser Teppich ist als Submodell konzipiert, das Verschiebungen für seine Schnittränder aus einem vereinfachten Globalmodell bezieht und demzufolge die Analyse allgemeiner, nicht axialsymmetrischer Lastfälle möglich macht. Abschließend werden die Modelle anhand einer Rollbalgluftfeder für Busanwendungen eingehend untersucht und einem Praxistest zum Vergleich zweier Konstruktionsvarianten unterzogen. / Tires, belts, hoses and, in particular, air spring bellows are regarded as composites due to layers of reinforcing textile cords that are embedded in a soft elastomer matrix. These cords are produced by twisting yarns which, for their part, represent a twisted structure of polymeric filaments. Hence, air spring bellows feature a highly complex internal geometry as well as strongly anisotropic, nonlinear material behavior. For structural simulations of air springs by means of the finite element method (FEM), new high resolution models are developed here, which reflect all the aforementioned properties. At first, a mathematical model capable of representing the twisted geometry of cords on three-dimensional curves is introduced, which also allows to derive local filament orientations. For the constitutive description of filament material, a transversally isotropic, hyperelastic material model is modified so that only the small isotropic stiffness introduced for regularization remains in case of compressive loads in filament direction. The cord geometry model serves as the basis for their three-dimensional representation in FE meshes of air spring bellows. Firstly, the focus lies on developing a slice model relying on cyclic symmetry, which takes cord geometry into account throughout the entire bellows. Special emphasis is put on building conforming meshes in order to incorporate all material interfaces explicitly. As a result, the slice model allows for detailed analyses of local stress and strain distribution inside the bellows. Secondly, this type of modeling is applied to a rectangular section of the bellows. This carpet is conceived as a submodel acquiring the displacements to be imposed on its cut faces from a simplified global model, and therefore provides the opportunity to analyze general load cases not complying with axial symmetry. Based on a rolling lobe air spring used in bus applications, both models are examined thoroughly and, at last, subjected to a practical test comparing two different designs.

<div>This body of work examines analytical and numerical models to simulate the response of structures in shock absorption applications. Specifically, the work examines the prediction of cushion curves of polymer foams, and a topological examination of a $\chi$ shape unit cell found in architected mechanical elastomeric metamaterials. The $\chi$ unit cell exhibits the same effective stress-strain relationship as a closed cell polymer foam. Polymer foams are commonly used in the protective packaging of fragile products. Cushion curves are used within the packaging industry to characterize a foam's impact performance. These curves are two-dimensional representations of the deceleration of an impacting mass versus static stress. The main drawback with cushion curves is that they are currently generated from an exhaustive set of experimental test data. This work examines modeling the shock response using a continuous rod approximation with a given impact velocity in order to generate cushion curves without the need of extensive testing. In examining the $\chi$ unit cell, this work focuses on the effects of topological changes on constitutive behavior and shock absorbing performance. Particular emphasis is placed on developing models to predict the onset of regions of quasi-zero-modulus (QZM), the length of the QZM region and the cushion curve produced by impacting the unit cell. The unit cell's topology is reduced to examining a characteristic angle, defining the internal geometry with the cell, and examining the effects of changing this angle.</div><div>However, the characteristic angle cannot be increased without tradeoffs; the cell's effective constitutive behavior evolves from long regions to shortened regions of quasi-zero modulus. Finally, this work shows that the basic $\chi$ unit cell can be tessellated to produce a nearly equivalent force deflection relationship in two directions. The analysis and results in this work can be viewed as new framework in analyzing programmable elastomeric metamaterials that exhibit this type of nonlinear behavior for shock absorption.</div>

This thesis deals with problems of biomechanics of soft tissues, namely of stress-strain analysis of abdominal aortic aneurysm (AAA). The introduction describes briefly the possibility of aneurysm occurrence with a focus on an aneurysm in the abdominal aorta.

Dans cette thèse, nous nous proposons d'étudier et de traiter conjointement plusieurs problèmes phares en traitement d'images incluant le recalage d'images qui vise à apparier deux images via une transformation, la segmentation d'images dont le but est de délimiter les contours des objets présents au sein d'une image, et la décomposition d'images intimement liée au débruitage, partitionnant une image en une version plus régulière de celle-ci et sa partie complémentaire oscillante appelée texture, par des approches variationnelles locales et non locales. Les relations étroites existant entre ces différents problèmes motivent l'introduction de modèles conjoints dans lesquels chaque tâche aide les autres, surmontant ainsi certaines difficultés inhérentes au problème isolé. Le premier modèle proposé aborde la problématique de recalage d'images guidé par des résultats intermédiaires de segmentation préservant la topologie, dans un cadre variationnel. Un second modèle de segmentation et de recalage conjoint est introduit, étudié théoriquement et numériquement puis mis à l'épreuve à travers plusieurs simulations numériques. Le dernier modèle présenté tente de répondre à un besoin précis du CEREMA (Centre d'Études et d'Expertise sur les Risques, l'Environnement, la Mobilité et l'Aménagement) à savoir la détection automatique de fissures sur des images d'enrobés bitumineux. De part la complexité des images à traiter, une méthode conjointe de décomposition et de segmentation de structures fines est mise en place, puis justifiée théoriquement et numériquement, et enfin validée sur les images fournies. / In this thesis, we study and jointly address several important image processing problems including registration that aims at aligning images through a deformation, image segmentation whose goal consists in finding the edges delineating the objects inside an image, and image decomposition closely related to image denoising, and attempting to partition an image into a smoother version of it named cartoon and its complementary oscillatory part called texture, with both local and nonlocal variational approaches. The first proposed model addresses the topology-preserving segmentation-guided registration problem in a variational framework. A second joint segmentation and registration model is introduced, theoretically and numerically studied, then tested on various numerical simulations. The last model presented in this work tries to answer a more specific need expressed by the CEREMA (Centre of analysis and expertise on risks, environment, mobility and planning), namely automatic crack recovery detection on bituminous surface images. Due to the image complexity, a joint fine structure decomposition and segmentation model is proposed to deal with this problem. It is then theoretically and numerically justified and validated on the provided images.