Percutaneous transluminal balloon angioplasty followed by drug-eluting stent implantation has been of great benefit in coronary applications, whereas in peripheral applications, success rates remain low. Analysis of healing patterns in successful deployments shows that six months after implantation the artery has reorganized itself to accommodate the increase in caliber and there is no purpose for the stent to remain, potentially provoking inflammation and foreign body reaction. Thus, a fully biodegradable polymeric stent that fulfills the mission and steps away is of great benefit. Biodegradable polymers have a widespread usage in the biomedical field, such as sutures, scaffolds and implants. Degradation refers to bond scission process that breaks polymeric chains down to oligomers and monomers. Extensive degradation leads to erosion, which is the process of mass loss from the polymer bulk. The prevailing mechanism of biodegradation of aliphatic polyesters (the main class of biodegradable polymers used in biomedical applications) is random scission by passive hydrolysis and results in molecular weight reduction and softening. In order to understand the applicability and efficacy of biodegradable polymers, a two pronged approach involving experiments and theory is necessary. A constitutive model involving degradation and its impact on mechanical properties was developed through an extension of a material which response depends on the history of the motion and on a scalar parameter reflecting the local extent of degradation and depreciates the mechanical properties. A rate equation describing the chain scission process confers characteristics of stress relaxation, creep and hysteresis to the material, arising due to the entropy-producing nature of degradation and markedly different from their viscoelastic counterparts. Several initial and boundary value problems such as inflation and extension of cylinders were solved and the impacts of the constitutive model analyzed. In vitro degradation of poly(L-lactic acid) fibers under tensile load was performed and degradation and reduction in mechanical properties was dependent on the mechanical environment. Mechanical testing of degraded fibers allowed the proper choice of constitutive model and its evolution. Analysis of real stent geometries was made possible with the constitutive model integration into finite element setting and stent deformation patterns in response to pressurization changed dramatically as degradation proceeded.

Solid oxide fuel cells (SOFC) in a flat-plate configuration require a hermetic seal between the fuel and air sides of the electrodes, and this seal must withstand a variety of thermally-induced stresses over the lifetime of the cell. In this study, quantitative microstructure-property relationships are developed to predict optimum seal structures for mechanical properties and thermal expansion coefficient criteria. These relationships are used to create an inverse approach to characterizing the processing method from the desired microstructure. The main focus of the work concentrates on providing tools to enable macroscopic property predictions from the constituent properties using homogenization techniques based on the individual phase properties and microstructure morphology. The microstructure is represented by two-point correlation functions. Statistical continuum mechanics models were then employed and developed to predict the mechanical and thermal properties of the material. The models enable the prediction of elastic modulus and coefficient of thermal expansion of the multi-phase material. The inelastic mechanical behavior was also studied, indicating microstructure dependence. These models will aid in predicting the a proper seal microstructure (with desired elastic stiffness, coefficient of thermal expansion, and viscoelastic behaviors) based on a desired level of crystallization glass-ceramic materials.

Nanostructured materials are gaining an ongoing demand because of their exceptional chemical and physical properties. Due to complexities and costs of experimental studies at nanoscale, computer simulations are getting more attractive asexperimental alternatives. In this PhD work, we tried to use combination of atomistic simulations and continuum modeling for the evaluation of thermal conductivity and elastic stiffness of nanostructured materials. We used molecular dynamics simulations to probe and investigate the thermal and mechanical response of materials at nanoscale. The finite element and micromechanics methods that are on the basis of continuum mechanics theories were used to evaluate the bulk properties of materials. The predicted properties are then compared with existing experimental results.

Thesis deals with solving the problems of continuum mechanics by method of Isogeometric analysis. This relatively young method combines the advantages of precise NURBS geometry and robustness of the classical finite element method. The method is described on procedure of solving a plane Poissons boundary value problem. Solver is implemented in MatLab and algorithms are attached to the text.

This Master's thesis relates to continuum mechanics and its connection with selected directions of modern differential geometry, which deal with geometric structures and objects. These are mainly tensors, bundles, varieties and jets. The first part is devoted to the mechanics of the continuum itself and its description in several areas, others deal with mathematical concepts and their possible application in mechanics.

Das Promotionsthema war die numerische Untersuchung des Einflusses der mechanisch induzierten martensitischen Phasenumwandlung auf das Bruchverhalten hochlegierter TRIP-Stähle. Die Analyse der Spannungsfelder vor einer abstumpfenden Rissspitze hat ergeben, dass die Phasenumwandlung zu höheren rissöffnenden Spannungen führt. Außerdem wurden charakteristische Spannungsverläufe mit Wendepunkten beobachtet. Für duktiles Versagen wurde ein positiver Einfluss der Phasenumwandlung geschlussfolgert, da die umwandlungsinduzierte Verfestigung das Porenwachstum in der Bruchprozesszone erschwert. Dies wurde an Hand mikromechanischer Simulationen der duktilen Rissausbreitung demonstriert. Im Rahmen der Theorie materieller Kräfte konnte eine abschirmende Wirkung des TRIP-Effekts auf die Rissspitze nachgewiesen werden. Durch Phasenumwandlung wird Arbeit dissipiert, die nicht mehr für Rissfortschritt verfügbar ist. Die energetische Triebkraft für Risswachstum wird demzufolge reduziert. Die Rissausbreitung im TRIP-Stahl wurde mit einer Kohäsivzone modelliert. Die Parameter des Kohäsivzonenmodells charakterisieren den Bruchprozess und konnten unter Verwendung experimenteller Daten identifiziert werden. Um zukünftig die Rolle der Phasenumwandlung bei Ermüdungsrisswachstum untersuchen zu können, wurde ein Materialmodell für TRIP-Stähle unter zyklischer Beanspruchung entwickelt. Die erforderlichen Materialparameter wurden mit Hilfe der Daten aus Wechselverformungsversuchen bestimmt. / This thesis is focused on the numerical investigation of the fracture behavior of high alloy austenitic TRIP-steels and especially on the effect of mechanically induced martensitic phase transformation. The analysis of stress fields in front of a blunting crack tip has shown that phase transformation leads to higher crack opening stresses. Additionally, characteristic courses of the stress components with inflection points were observed. A positive influence of phase transformation on ductile fracture was concluded, because transformation induced hardening retards void growth in the fracture process zone. This was demonstrated by micromechanical simulations of ductile crack extension. In order to investigate the shielding effect of phase transformation on the crack tip, the theory of material forces was applied. Mechanical work is dissipated due to the TRIP-effect, which is no longer available for crack growth. Hence, the energetic driving force for fracture is reduced. Furthermore, crack extension is modeled with a cohesive zone. The parameters of the cohesive zone model, which characterize the fracture process, are identified based on experimental data. In future work the role of phase transformation during fatigue crack growth should by studied. Therefore, a material model for TRIP-steels under cyclic loading was developed. The associated material parameters were estimated based on the results of cyclic deformation experiments.

Almost all animal cells maintain a thin layer of actin filaments and associated proteins underneath the cell membrane. The actomyosin cortex is subject to internal stress patterns which result from the spatiotemporally regulated activity of non-muscle myosin II motors in the actin network. We study how these active stresses drive changes in cell shape and flows within the cortical layer, and how these cytoskeletal deformations and flows govern processes such as cell migration, cell division and organelle transport. Following a continuum mechanics approach, we develop theoretical descriptions for three different cellular processes, to obtain - in collaboration with experimental groups - a detailed and quantitative understanding of the underlying cytoskeletal mechanics. We investigate the forces and cortex flows involved in adhesion-independent cell migration in confinement. Many types of cell migration rely on the extension of protrusions at the leading edge, where the cells attach to the substrate with specific focal adhesions, and pull themselves forward, exerting stresses in the kPa range. In confined environments however, cells exhibit migration modes which are independent of specific adhesions. Combining hydrodynamic theory, microfluidics and quantitative imaging of motile, non-adherent carcinosarcoma cells, we analyze the mechanical behavior of cells during adhesion-independent migration. We find that the accumulation of active myosin motors in the rear part of these cells results in a retrograde cortical flow as well as the contraction of the cell body in the rear and expansion in the front, and we describe how both processes contribute to the translocation of the cells, depending on the geometric and mechanical parameters of the system. Importantly, we find that the involved propulsive forces are several orders of magnitude lower than during adhesive motility while the achieved migration velocities are similar. Moreover, the distribution of forces on the substrate during non-adhesive migration is fundamentally different, giving rise to a positive force dipole. In contrast to adhesive migration modes, non-adhesive cells move by exerting pushing forces at the rear, acting to expand rather than contract their substrate as they move. These differences may strongly affect hydrodynamic and/or deformational interactions between collectively migrating cells. In addition to the work outlined above, we study contractile ring formation in the actin cytoskeleton before and during cell division. While in disordered actin networks, myosin motor activity gives rise to isotropic stresses, the alignment of actin filaments in the cortex during cell division introduces a preferred direction for motor-filament interactions, resulting in anisotropies in the cortical stress. Actin filaments align in myosin-dependent shear flows, resulting in possible feedback between motor activity, cortical flows and actin organization. We investigate how the mechanical interplay of these different cortical properties gives rise to the formation of a cleavage furrow during cell division, describing the level of actin filament alignment at different points on the cortex with a nematic order parameter, in analogy to liquid crystal physics. We show that cortical anisotropies arising from shear-flow induced alignment patterns are sufficient to drive the ingression of cellular furrows, even in the absence of localized biochemical myosin up-regulation. This mechanism explains the characteristic appearance of pseudocleavage furrows in polarizing cells. Finally, we study the characteristic nuclear movements in pseudostratified epithelia during development. These tissues consist of highly proliferative, tightly packed and elongated cells, with nuclei actively travelling to the apical side of the epithelium before each cell division. We explore how cytoskeletal properties act together with the mechanics of the surrounding tissue to control the shape of single cells embedded in the epithelium, and investigate potential mechanisms underlying the observed nuclear movements. These findings form a theoretical basis for a more detailed characterization of processes in pseudostratified epithelia. Taken together, we present a continuum mechanics description of the actomyosin cell cortex, and successfully apply it to several different cell biological processes. Combining our theory with experimental work from collaborating groups, we provide new insights into different aspects of cell mechanics.

A new theoretical formalism is developed for the study of the mechanical behaviour of magneto-sensitive elastomers (MSEs) under a uniform external magnetic field. This formalism allows us to combine macroscopic continuum-mechanics and microscopic approaches for complex analysis of MSEs with different shapes and with different particle distributions. It is shown that starting from a model based on an explicit discrete particle distribution one can separate the magnetic field inside the MSE into two contributions: one which depends on the shape of the sample with finite size and the other, which depends on the local spatial particle distribution. The magneto-induced deformation and the change of elastic modulus are found to be either positive or negative, their dependences on the magnetic field being determined by a non-trivial interplay between these two contributions. Mechanical properties are studied for two opposite types of coupling between the particle distribution and the magneto-induced deformation: absence of elastic coupling and presence of strong affine coupling. Predictions of a new formalism are in a qualitative agreement with existing experimental data.

La fonction respiratoire chez l'homme est indissociable du mouvement de déformation du poumon : les échanges gazeux entre l'organisme et son environnement sont rendus possibles, lors de l'inspiration, par le gonflement des alvéoles du parenchyme pulmonaire, et lors de l'expiration, par un retour passif à l'état d'équilibre statique du poumon. Les propriétés viscoélastiques des tissus pulmonaires jouent un rôle clé dans la fonction même de cet organe. Ces éléments de la mécanique respiratoire pourraient être des biomarqueurs très sensibles de l'état physiopathologique du poumon puisqu'ils dépendent de la structure des tissus et des conditions biologiques qui sont considérablement altérées par la plupart des maladies pulmonaires comme le cancer, l'emphysème, l'asthme ou la fibrose interstitielle. L'imagerie par résonance magnétique permet aujourd'hui, de manière non-invasive, l'obtention d'images anatomiques tridimensionnelles permettant, grâce aux résolutions spatiales et temporelles accessibles ainsi qu'aux contrastes riches observés au sein des tissus mous, la mesure de l'état de déformation d'un organe à un instant donné. Par ailleurs, par l'application de gradients d'encodage du mouvement, l'élastographie par résonance magnétique permet de suivre, sur la phase du signal de résonance magnétique, la réponse des organes à une contrainte mécanique externe afin de révéler leurs propriétés viscoélastiques, ce qui permet d'envisager l'exploration quantitative et spatialement résolue d'organes profonds que la main du médecin ne peut atteindre. Dans le poumon, l'IRM conventionnelle est cependant relativement inadaptée : la faible densité tissulaire, les grandes différences de susceptibilité magnétique à l'interface entre le gaz et le tissu et, corrélativement, les très faibles durées de vie du signal de résonance magnétique, conduisent à des rapports signal-à-bruit difficilement exploitables. De plus, les durées des acquisitions IRM tridimensionnelles sont généralement supérieures à la période du mouvement respiratoire, ce qui nécessite de prendre en considération ce mouvement au sein du processus d'imagerie. Ce projet de thèse, réalisé en collaboration avec GE Healthcare, vise à contourner les limitations citées précédemment en s'appuyant sur des techniques d'acquisition à temps d'écho sub-milliseconde de type UTE et ZTE, associées à des approches originales et innovantes de suivi intrinsèque des mouvements physiologiques ainsi qu'à des techniques de reconstruction d'images quadridimensionnelles tenant compte à la fois du mouvement respiratoire, de la redondance de l'information entre les différents canaux d'acquisition de données et de la parcimonie des images reconstruites à travers certaines représentations mathématiques. L'objectif ultime du projet est le développement et la validation de techniques d'exploration fonctionnelle respiratoire locales et quantitatives, mais aussi d'élastographie dynamique du poumon par résonance magnétique, afin d'extraire les paramètres ventilatoires et les modules viscoélastiques de cisaillement locaux du poumon au cours du cycle respiratoire. / The respiratory function in human cannot be separated from the deformation motion of the lung: the gas exchanges between the organism and its environment are made possible, during the inspiration, by the swelling of the alveoli in the pulmonary parenchyma, and during the expiration, by a passive return to the static equilibrium state of the lung. The viscoelastic properties of lung tissue play a key role in the function of this organ. These elements of respiratory mechanics may prove to be very sensitive biomarkers of the pathophysiological state of the lung since they depend on the structure of tissues and biological conditions that are considerably altered by most pulmonary diseases such as cancer, emphysema, asthma or interstitial fibrosis. Magnetic resonance imaging enables non-invasive measurement of three-dimensional anatomical images that allow, thanks to the accessible spatial and temporal resolutions as well as the rich contrasts observed in the soft tissues, the measurement of the deformation state of an organ at a given moment. Moreover, by applying motion encoding gradients, magnetic resonance elastography gives the possibility to follow, onto to the magnetic resonance phase signal, the mechanical strain response of organs to an external mechanical stress in order to reveal their viscoelastic properties, which makes possible a quantitative and spatially-resolved exploration of deep organs that are nor reachable by the medical doctor's hand. In the lung, conventional MRI is, however, relatively difficult: the low tissue density, the large differences in magnetic susceptibility at the interface between gas and tissue and, correlatively, the very short lifetimes of the magnetic resonance signal, lead to signal-to-noise ratios that are difficult to exploit. In addition, the durations of three-dimensional MRI scans are generally longer than the period of the respiratory motion, which requires consideration of this motion within the imaging process. This PhD project, carried out in collaboration with GE Healthcare, aims at circumventing the limitations mentioned above by using UTE and ZTE sub-millisecond echo-time acquisition techniques, combined with original and innovative approaches of intrinsic physiological motions monitoring as well as four-dimensional image reconstruction techniques taking into account the respiratory motion, the redundancy of information between the different data acquisition channels and the sparsity of the reconstructed images through some mathematical representations. The ultimate goal of this project is the development and the validation of local and quantitative techniques to explore the respiratory function, as well as dynamic magnetic resonance lung elastography, in order to extract local ventilation parameters and viscoelastic shear moduli in the lung during the breathing cycle.

<p>A wide variety of phase evolution phenomena observed in solids such as intermetallic growth at the junction between two metals subjected to high temperature, growth of oxide on metal surfaces due to atmospheric exposure and void evolution induced by electromigration in microelectronic devices for example, can be classified as being driven by reaction-diffusion processes. These phase evolution phenomena have a significant impact on material reliability for critical applications, and therefore, there is a requirement for modeling such reaction-diffusion driven phase evolution phenomena. It is difficult to analyze these due to the complexity of modeling the evolving interface between solid phases. Additional complexity is  due to the multi-physics nature of the diffusive and reactive processes. Diffusion in solids is driven by a variety of stimuli such as current, temperature and stress, in addition to the chemical potential. Therefore, there is a need for a model that accounts for the influence of such factors on phase evolution. In this thesis,  a generalized continuum based reaction-diffusion theory for phase and void evolution in solid state is developed. The derivation starts off with generalized interface balance laws for mass, momentum and energy. The thermodynamic entropy inequality for irreversible phase growth is derived for arbitrary anisotropic and inhomogeneous surface stress. These interface relations are combined with governing relations in the material bulk for the temperature, stress, electrical and concentration fields, to develop a general model capable of analyzing and describing phase evolution in solids. This theory is then applied to a variety of intermetallic phase and void evolution phenomena observed in microelectronics.</p> <p><br></p> <p>Electromigration induced voiding in thin metal films is an example of phase evolution that is an important reliability concern in microelectronics. Studies have reported that the electromigration induced void growth rate is inversely related to the adhesion of metal thin films with the base and capping layers. Electromigration experiments are performed on fabricated test devices with Cu thin films with SiNx and TiN capping layers. The observations from electromigration experiments on thin Cu metal films at a range of temperatures indicate that the contribution of interface adhesion strength to electromigration resistance decreases with an increase in temperature. The generalized reaction-diffusion theory developed here is modified to develop an expression to account for the effect of base and passivation layer adhesion and temperature on electromigration resistance of metal thin films. The void growth rates measured in the experiments are analyzed with the expression for void growth rate to estimate the interface adhesion strength for the Cu-TiN and Cu-SiNx interfaces. </p> <p><br></p> <p>Demand for increased bandwidth, power efficiency and performance requirements have resulted in a trend of reduction in size and pitch of Cu pillar-Solder micro-bump interconnects used in heterogeneously integrated packages. As the size of micro-bumps reduce, reliability challenges due to voiding in the solder joint and the growth of Cu-Sn intermetallics are observed. The underlying reaction-diffusion mechanisms responsible for Cu-Sn intermetallic growth and voiding in solder joints are unclear at this stage and require further investigation. The current practice of material characterization in micro-bumps involve destructive cross-sectioning and polishing of the micro-bumps after testing. These processes result in loss of continuity in the samples used for the experiments, and material removal due to abrasive polishing might result in a loss of critical information. Therefore, a novel test device capable of non-destructive characterization of Cu-Sn intermetallic growth and voiding in sub-30 micron size micro-bumps is designed and fabricated in this work. The fabricated test devices are subjected to thermal aging for over 1000 h and the underlying reaction-diffusion mechanisms behind the intermetallic phase and void evolution are investigated. </p> <p><br></p> <p>A reaction-diffusion mechanism is proposed explaining the evolution of  various Cu-Sn intermetallic phases and solder joint void observed from experiments. Using the reaction-diffusion mechanism inferred from the thermal aging experiments and the generalized reaction-diffusion theory for phase evolution developed in this thesis, a sharp interface model is developed for the evolution of Cu-Sn intermetallic phases and solder joint void. The diffuse interface phase field equivalent equations for the sharp interface model governing equations are developed using matched formal asymptotic analysis. The evolution of Cu-Sn intermetallic phase and voids in the solder joint are simulated for different temperatures and current density to demonstrate the validity of the phase field and sharp interface models.  </p> <p><br></p>