A robust numerical framework to the analysis of material failure of fibre reinforced soft tissue

In this work, robustness and stability of continuum damage models applied to material failure in soft tissues are addressed. In the implicit damage models equipped with softening, the presence of negative eigenvalues in the tangent elemental matrix degrades the condition number of the global matrix, leading to a reduction of the computational performance of the numerical model. Two strategies have been adapted from literature to improve the aforementioned computational performance degradation: the IMPL-EX integration scheme [Oliver,2006], which renders the elemental matrix contribution definite positive, and arclength-type continuation methods [Carrera,1994], which allow to capture the unstable softening branch in brittle ruptures. The IMPL-EX integration scheme has as a major drawback the need to use small time steps to keep numerical error below an acceptable value. A convergence study, limiting the maximum allowed increment of internal variables in the damage model, is presented. Finally, numerical simulation of failure problems with fibre reinforced materials illustrates the performance of the adopted methodology.

Pulsatile flow in coronary bifurcations for different stenting techniques

The objective of this work is to analyze the local hem odynamic changes caused in a coronary bifurcation by three different stenting techniques: simple stenting of the main vessel, simple stenting of the main vessel with kissing balloon in the side branch and culotte. To carry out this study an idealized geometry of a coronary bifurcation is used, and two bifurcation angles, 45º and 90º, are chosen as representative of the wide variety of re al configurations. In order to quantify the influence of the stenting technique on the local blood flow, both numeri- cal simulations and experimental measurements are performed. First, steady simulations are carried out with the commercial code ANSYS-Fluent, and then, experimental measurements with PIV (Particle Image Velocimetry) obtained in the laboratory are used to validate the numerical simulation. The steady computational simulations show a good overall agreement with the experimental data. Second, pulsatile flow is considered to take into account the tran- sient effects. The time averaged wall shear stress, scillatory shear index and pressure drop obtained numerically are used to compare the behavior of the stenting techniques.

Fatigue in laser shock peened open-hole thin aluminium specimens

An experimental study was performed in order to determine the influence of the sequence of operations on the effectiveness of Laser Shock Peening (LSP) treatment in increasing the fatigue performances of open-hole aluminium specimens. Residual stress measurements, fractographic analysis and FEM analysis were performed, indicating the presence of compressive residual stresses on the surface of the treated specimens and tensile residual stresses in the mid-section along the thickness of the specimens. Negative effects on fatigue lives were encountered on the specimens with the hole already present, while positive effect were observed in specimens in which the hole was drilled after LSP treatment. These results indicate that LSP can be a good solution for “in production” application, in which open holes are to be drilled after the LSP treatment. The application in which LSP is used “in service” on structures with pre-existing cut-outs, has proven to be impracticable in the investigated configuration.

Simulation, Design and Analysis of Air-Breathing Combined-Cycle Engines for High Speed Propulsion

Desde la aparición del turborreactor, el motor aeróbico con turbomaquinaria ha demostrado unas prestaciones excepcionales en los regímenes subsónico y supersónico bajo. No obstante, la operación a velocidades superiores requiere sistemas más complejos y pesados, lo cual ha imposibilitado la ejecución de estos conceptos. Los recientes avances tecnológicos, especialmente en materiales ligeros, han restablecido el interés por los motores de ciclo combinado. La simulación numérica de estos nuevos conceptos es esencial para estimar las prestaciones de la planta propulsiva, así como para abordar las dificultades de integración entre célula y motor durante las primeras etapas de diseño. Al mismo tiempo, la evaluación de estos extraordinarios motores requiere una metodología de análisis distinta. La tesis doctoral versa sobre el diseño y el análisis de los mencionados conceptos propulsivos mediante el modelado numérico y la simulación dinámica con herramientas de vanguardia. Las distintas arquitecturas presentadas por los ciclos combinados basados en sendos turborreactor y motor cohete, así como los diversos sistemas comprendidos en cada uno de ellos, hacen necesario establecer una referencia común para su evaluación. Es más, la tendencia actual hacia aeronaves "más eléctricas" requiere una nueva métrica para juzgar la aptitud de un proceso de generación de empuje en el que coexisten diversas formas de energía. A este respecto, la combinación del Primer y Segundo Principios define, en un marco de referencia absoluto, la calidad de la trasferencia de energía entre los diferentes sistemas. Esta idea, que se ha estado empleando desde hace mucho tiempo en el análisis de plantas de potencia terrestres, ha sido extendida para relacionar la misión de la aeronave con la ineficiencia de cada proceso involucrado en la generación de empuje. La metodología se ilustra mediante el estudio del motor de ciclo combinado variable de una aeronave para el crucero a Mach 5. El diseño de un acelerador de ciclo combinado basado en el turborreactor sirve para subrayar la importancia de la integración del motor y la célula. El diseño está limitado por la trayectoria ascensional y el espacio disponible en la aeronave de crucero supersónico. Posteriormente se calculan las prestaciones instaladas de la planta propulsiva en función de la velocidad y la altitud de vuelo y los parámetros de control del motor: relación de compresión, relación aire/combustible y área de garganta. ABSTRACT Since the advent of the turbojet, the air-breathing engine with rotating machinery has demonstrated exceptional performance in the subsonic and low supersonic regimes. However, the operation at higher speeds requires further system complexity and weight, which so far has impeded the realization of these concepts. Recent technology developments, especially in lightweight materials, have restored the interest towards combined-cycle engines. The numerical simulation of these new concepts is essential at the early design stages to compute a first estimate of the engine performance in addition to addressing airframe-engine integration issues. In parallel, a different analysis methodology is required to evaluate these unconventional engines. The doctoral thesis concerns the design and analysis of the aforementioned engine concepts by means of numerical modeling and dynamic simulation with state-of-the-art tools. A common reference is needed to evaluate the different architectures of the turbine and the rocket-based combined-cycle engines as well as the various systems within each one of them. Furthermore, the actual trend towards more electric aircraft necessitates a common metric to judge the suitability of a thrust generation process where different forms of energy coexist. In line with this, the combination of the First and the Second Laws yields the quality of the energy being transferred between the systems on an absolute reference frame. This idea, which has been since long applied to the analysis of on-ground power plants, was extended here to relate the aircraft mission with the inefficiency of every process related to the thrust generation. The methodology is illustrated with the study of a variable- combined-cycle engine for a Mach 5 cruise aircraft. The design of a turbine-based combined-cycle booster serves to highlight the importance of the engine-airframe integration. The design is constrained by the ascent trajectory and the allocated space in the supersonic cruise aircraft. The installed performance of the propulsive plant is then computed as a function of the flight speed and altitude and the engine control parameters: pressure ratio, air-to-fuel ratio and throat area.

Induction of engineered residual stresses fields and enhancement of fatigue life of high reliability metallic components by laser shock processing

Laser shock processing (LSP) is being increasingly applied as an effective technology for the improvement of metallic materials mechanical and surface properties in different types of components as a means of enhancement of their corrosion and fatigue life behavior. As reported in previous contributions by the authors, a main effect resulting from the application of the LSP technique consists on the generation of relatively deep compression residual stresses field into metallic alloy pieces allowing an improved mechanical behaviour, explicitly the life improvement of the treated specimens against wear, crack growth and stress corrosion cracking. Additional results accomplished by the authors in the line of practical development of the LSP technique at an experimental level (aiming its integral assessment from an interrelated theoretical and experimental point of view) are presented in this paper. Concretely, follow-on experimental results on the residual stress profiles and associated surface properties modification successfully reached in typical materials (especially Al and Ti alloys characteristic of high reliability components in the aerospace, nuclear and biomedical sectors) under different LSP irradiation conditions are presented along with a practical correlated analysis on the protective character of the residual stress profiles obtained under different irradiation strategies. Additional remarks on the improved character of the LSP technique over the traditional “shot peening” technique in what concerns depth of induced compressive residual stresses fields are also made through the paper

Finite element simulation of sandwich panels of plasterboard and rock wool under mixed mode fracture

This paper presents the results of research on mixed mode fracture of sandwich panels of plasterboard and rock wool. The experimental data of the performed tests are supplied. The specimens were made from commercial panels. Asymmetrical three-point bending tests were performed on notched specimens. Three sizes of geometrically similar specimens were tested for studying the size effect. The paper also includes the numerical simulation of the experimental results by using an embedded cohesive crack model.The involved parameters for modelling are previously measured by standardised tests.

Caracterización dinámica del glaciar Hurd combinando observaciones de campo y simulaciones numéricas

El objetivo fundamental de esta tesis es la caracterización de la morfología y del estado de deformaciones y tensiones del Glaciar Hurd (Isla Livingston, Archipiélago de las Shetland del Sur, Antártida), mediante una combinación de observaciones de campo, registros de georradar y simulaciones numéricas. La morfología y el estado de deformaciones y tensiones actuales son la expresión de la evolución dinámica del glaciar desde tiempos pretéritos hasta recientes, y su análisis nos dará las pautas con las cuales ser capaces de predecir, con el apoyo de las simulaciones numéricas, su evolución futura. El primer aspecto que se aborda es el estudio de las estructuras que pueden observarse en la superficie del glaciar. Describimos las distintas técnicas utilizadas (medidas de campo, fotointerpretación de ortofotografías, análisis geoquímico de cenizas volcánicas, etc.) y presentamos el análisis e interpretación de los resultados morfo-estructurales, así como la correlación, mediante análisis geoquímicos (fluorescencia de rayos X), entre las cenizas volcánicas que extruyen en la superficie del Glaciar Hurd y las del volcán Decepción, origen de las cenizas. Esto nos permite realizar una datación de las mismas como Tefra 1, correspondiente a la erupción de 1970, Tefra 2, correspondiente a las erupciones pre-1829, y el conjunto Tefra 3, asociado a las erupciones más antiguas. En segundo lugar nos ocupamos de las estructuras presentes en el interior del glaciar, cuya herramienta de detección fundamental es el georradar. Identificadas estas estructuras internas, las vinculamos con las observadas en la superficie del glaciar. También hemos estudiado la estructura hidrotérmica del glaciar, obteniendo una serie de evidencias adicionales de su carácter politérmico. Entre éstas se contaban, hasta ahora, las basadas en el valor del parámetro de rigidez de la relación constitutiva del hielo determinada por ajuste de modelos dinámicos y observaciones realizados por Otero (2008) y las basadas en las velocidades de las ondas de radar en el hielo determinadas con el método de punto medio común por Navarro y otros (2009). Las evidencias adicionales que aportamos en esta tesis son: 1) la presencia de estructuras típicas de régimen compresivo en la zona terminal del glaciar y de cizalla en los márgenes del mismo, y 2) la presencia de un estrato superficial de hielo frío (por encima de otro templado) en la zona de ablación de los tres lóbulos del Glaciar Hurd –Sally Rocks, Argentina y Las Palmas–, que alcanzan espesores de 70, 50 y 40 m, respectivamente. Este estrato de hielo frío está probablemente congelado al lecho subglaciar en la zona terminal (Molina y otros, 2007; esta tesis). Por último, nos ocupamos de la simulación numérica de la dinámica glaciar. Presentamos el modelo físico-matemático utilizado, discutimos sus condiciones de contorno y cómo éstas se miden en los trabajos de campo, y describimos el procedimiento de resolución numérica del sistema de ecuaciones parciales del modelo. Presentamos los resultados para los campos de velocidades, deformaciones y tensiones, comparando estos resultados con las estructuras observadas. También incluimos el análisis de las elipses de deformación acumulativa, que proporcionan información sobre las estructuras a las que puede dar lugar la evolución del estado de deformaciones y tensiones a las que se ve sometido el hielo según avanza, lentamente, desde la cabecera hasta la zona terminal del glaciar, con tiempos de tránsito de hasta 1.250 años, recogiendo así la historia de deformaciones en el glaciar. Concluyendo, ponemos de manifiesto en esta tesis que las medidas de campo de las estructuras y niveles de cenizas, las medidas de georradar y las simulaciones numéricas de la dinámica glaciar, realizadas de forma combinada, permiten caracterizar el régimen actual de velocidades, deformaciones y tensiones del glaciar, entender su evolución en el pasado y predecir su evolución futura. ABSTRACT The main objective of this thesis is to characterize the morphology and the state of strains and stresses of Hurd Glacier (Livingston Island, South Shetland Islands archipelago, Antarctica) through a combination of field observations, ground-penetrating radar measurements and numerical simulations. The morphology and the current state of strain and stresses are the expression of the dynamic evolution of the glacier from the past to recent times, and their analysis gives us the guidelines to be able to predict, with the support of numerical simulations, its future evolution. The first subject addressed is the study of structures that can be observed on the glacier surface. We describe the different techniques used (field measurements, photointerpretation of orthophotos, geochemical analysis of volcanic ashes, etc.) and we present the analysis and interpretation of the morpho-structural results, as well as the correlation with geochemical analysis (XRF) between the volcanic ashes extruded to the surface of Hurd Glacier and those of Deception Island volcano, from which the ashes originate. This allows us dating the ashes as Tephra 1, corresponding to the 1970 eruption, Tephra 2, corresponding to the pre-1829 eruptions, and the Tephra 3 group, associated with older eruptions. Secondly we focus on the study of the structures present within the glacier, which are detected with the help of ground-penetrating radar. Once identified, we link these internal structures with those observed on the glacier surface. We also study the hydrothermal structure of the glacier, getting a series of additional evidences of its polythermal structure. Among the evidences available so far, we can mention those based on the value of the stiffness parameter of the constitutive relation of ice, determined by fitting dynamic models to observations, as done by Otero (2008), and those based on the velocity of propagation of the radar waves through the glacier ice, measured using the common midpoint method, as done by Navarro et al. (2009). The additional evidences that we provide in this thesis are: 1) the presence of structures typical of compressive regime in the terminal zone of the glacier, together with shear at its margins, and 2) the presence of a surface layer of cold ice (overlying a layer of temperate ice) in the ablation zone of the three lobes of Hurd Glacier –Sally Rocks, Argentina and Las Palmas–, reaching thicknesses of 70, 50 and 40 m, respectively. This cold layer is probably frozen to the subglacial bed in the terminal zone (Molina and others 2007; this thesis). Finally, we deal with the numerical simulation of glacier dynamics. We present the physical-mathematical model, discuss its boundary conditions and how they are measured in the field work, and describe the method of numerical solution of the model’s partial differential equations. We present the results for the velocity, strain and stress fields, comparing these results with the observed structures. We also include an analysis of the ellipses of cumulative deformation, which provide information about the structures that can result from the evolution of the strain and stress regime of the glacier ice as it moves slowly from the head to the snout of the glacier, with transit times of up to 1,250 years, so picking the history of deformation of the glacier. Summarizing, we show in this thesis that field measurements of structures and ash layers, ground-penetrating radar measurements and numerical simulations of glacier dynamics, performed in combination, allow us to characterize the current regime of velocities, strains and stresses of the glacier, to understand its past evolution and to predict its future evolution.

Overall vs. local mechanical behaviour of ferritic austenitic steel joints made by laser welding

The present investigation addresses the overall and local mechanical performance of dissimilar joints of low carbon steel (CS) and stainless Steel (SS) thin sheets achieved by laser welding in case of heat source displacement from the weld gap centreline towards CS. Welding was performed on a Nd:YAG laser DY033 (3300 W) in a continuos wave (CW), keyhole mode. The tensile behavior of the joint different zones assessed by using a video-image based system (VIC-2D) reveals that the residual stress field, together with the positive difference in yield between the weld metal and the base materials protects the joint from being plastically deformed. The tensile loadings of flat transverse specimens generate the strain localization and failure in CS, far away from the weld.

A discrete spectral model for intermediate crack debonding in FRP-strengthened RC beams

One of the common failure modes of reinforced concrete (RC) beams strengthened in flexure with a bonded fibre-reinforced polymer (FRP) is intermediate crack (IC) debonding, which is originated at a critical section in the vicinity of flexural cracks and propagates to a plate end. Despite considerable research over the last years, few reliable and simplified IC debonding strength models have been developed. This paper firstly presents a one-dimensional model based on the discrete crack approach for concrete and the spectral element method for the numerical simulation of the IC debonding process. The progressive formation of flexural cracks and subsequent concrete-FRP interfacial debonding is formulated by the introduction of a new element able to represent both phenomena simultaneously without perturbing the numerical procedure. Furthermore, with the proposed model, high frequency dynamic response for these kinds of structures can also be obtained in a very simple and non-expensive way, which makes this procedure very useful as a tool for diagnoses and detection of debonding in its initial stage by monitoring the change in local dynamic characteristics.

Time-resolved evolution of coherent structures in turbulent channels

El objetivo de esta tesis es estudiar la dinámica de la capa logarítmica de flujos turbulentos de pared. En concreto, proponemos un nuevo modelo estructural utilizando diferentes tipos de estructuras coherentes: sweeps, eyecciones, grupos de vorticidad y streaks. La herramienta utilizada es la simulación numérica directa de canales turbulentos. Desde los primeros trabajos de Theodorsen (1952), las estructuras coherentes han jugado un papel fundamental para entender la organización y dinámica de los flujos turbulentos. A día de hoy, datos procedentes de simulaciones numéricas directas obtenidas en instantes no contiguos permiten estudiar las propiedades fundamentales de las estructuras coherentes tridimensionales desde un punto de vista estadístico. Sin embargo, la dinámica no puede ser entendida en detalle utilizando sólo instantes aislados en el tiempo, sino que es necesario seguir de forma continua las estructuras. Aunque existen algunos estudios sobre la evolución temporal de las estructuras más pequeñas a números de Reynolds moderados, por ejemplo Robinson (1991), todavía no se ha realizado un estudio completo a altos números de Reynolds y para todas las escalas presentes de la capa logarítmica. El objetivo de esta tesis es llevar a cabo dicho análisis. Los problemas más interesantes los encontramos en la región logarítmica, donde residen las cascadas de vorticidad, energía y momento. Existen varios modelos que intentan explicar la organización de los flujos turbulentos en dicha región. Uno de los más extendidos fue propuesto por Adrian et al. (2000) a través de observaciones experimentales y considerando como elemento fundamental paquetes de vórtices con forma de horquilla que actúan de forma cooperativa para generar rampas de bajo momento. Un modelo alternativo fué ideado por del Álamo & Jiménez (2006) utilizando datos numéricos. Basado también en grupos de vorticidad, planteaba un escenario mucho más desorganizado y con estructuras sin forma de horquilla. Aunque los dos modelos son cinemáticamente similares, no lo son desde el punto de vista dinámico, en concreto en lo que se refiere a la importancia que juega la pared en la creación y vida de las estructuras. Otro punto importante aún sin resolver se refiere al modelo de cascada turbulenta propuesto por Kolmogorov (1941b), y su relación con estructuras coherentes medibles en el flujo. Para dar respuesta a las preguntas anteriores, hemos desarrollado un nuevo método que permite seguir estructuras coherentes en el tiempo y lo hemos aplicado a simulaciones numéricas de canales turbulentos con números de Reynolds lo suficientemente altos como para tener un rango de escalas no trivial y con dominios computacionales lo suficientemente grandes como para representar de forma correcta la dinámica de la capa logarítmica. Nuestros esfuerzos se han desarrollado en cuatro pasos. En primer lugar, hemos realizado una campaña de simulaciones numéricas directas a diferentes números de Reynolds y tamaños de cajas para evaluar el efecto del dominio computacional en las estadísticas de primer orden y el espectro. A partir de los resultados obtenidos, hemos concluido que simulaciones con cajas de longitud 2vr y ancho vr veces la semi-altura del canal son lo suficientemente grandes para reproducir correctamente las interacciones entre estructuras coherentes de la capa logarítmica y el resto de escalas. Estas simulaciones son utilizadas como punto de partida en los siguientes análisis. En segundo lugar, las estructuras coherentes correspondientes a regiones con esfuerzos de Reynolds tangenciales intensos (Qs) en un canal turbulento han sido estudiadas extendiendo a tres dimensiones el análisis de cuadrantes, con especial énfasis en la capa logarítmica y la región exterior. Las estructuras coherentes han sido identificadas como regiones contiguas del espacio donde los esfuerzos de Reynolds tangenciales son más intensos que un cierto nivel. Los resultados muestran que los Qs separados de la pared están orientados de forma isótropa y su contribución neta al esfuerzo de Reynolds medio es nula. La mayor contribución la realiza una familia de estructuras de mayor tamaño y autosemejantes cuya parte inferior está muy cerca de la pared (ligada a la pared), con una geometría compleja y dimensión fractal « 2. Estas estructuras tienen una forma similar a una ‘esponja de placas’, en comparación con los grupos de vorticidad que tienen forma de ‘esponja de cuerdas’. Aunque el número de objetos decae al alejarnos de la pared, la fracción de esfuerzos de Reynolds que contienen es independiente de su altura, y gran parte reside en unas pocas estructuras que se extienden más allá del centro del canal, como en las grandes estructuras propuestas por otros autores. Las estructuras dominantes en la capa logarítmica son parejas de sweeps y eyecciones uno al lado del otro y con grupos de vorticidad asociados que comparten las dimensiones y esfuerzos con los remolinos ligados a la pared propuestos por Townsend. En tercer lugar, hemos estudiado la evolución temporal de Qs y grupos de vorticidad usando las simulaciones numéricas directas presentadas anteriormente hasta números de Reynolds ReT = 4200 (Reynolds de fricción). Las estructuras fueron identificadas siguiendo el proceso descrito en el párrafo anterior y después seguidas en el tiempo. A través de la interseción geométrica de estructuras pertenecientes a instantes de tiempo contiguos, hemos creado gratos de conexiones temporales entre todos los objetos y, a partir de ahí, definido ramas primarias y secundarias, de tal forma que cada rama representa la evolución temporal de una estructura coherente. Una vez que las evoluciones están adecuadamente organizadas, proporcionan toda la información necesaria para caracterizar la historia de las estructuras desde su nacimiento hasta su muerte. Los resultados muestran que las estructuras nacen a todas las distancias de la pared, pero con mayor probabilidad cerca de ella, donde la cortadura es más intensa. La mayoría mantienen tamaños pequeños y no viven mucho tiempo, sin embargo, existe una familia de estructuras que crecen lo suficiente como para ligarse a la pared y extenderse a lo largo de la capa logarítmica convirtiéndose en las estructuras observas anteriormente y descritas por Townsend. Estas estructuras son geométricamente autosemejantes con tiempos de vida proporcionales a su tamaño. La mayoría alcanzan tamaños por encima de la escala de Corrsin, y por ello, su dinámica está controlada por la cortadura media. Los resultados también muestran que las eyecciones se alejan de la pared con velocidad media uT (velocidad de fricción) y su base se liga a la pared muy rápidamente al inicio de sus vidas. Por el contrario, los sweeps se mueven hacia la pared con velocidad -uT y se ligan a ella más tarde. En ambos casos, los objetos permanecen ligados a la pared durante 2/3 de sus vidas. En la dirección de la corriente, las estructuras se desplazan a velocidades cercanas a la convección media del flujo y son deformadas por la cortadura. Finalmente, hemos interpretado la cascada turbulenta, no sólo como una forma conceptual de organizar el flujo, sino como un proceso físico en el cual las estructuras coherentes se unen y se rompen. El volumen de una estructura cambia de forma suave, cuando no se une ni rompe, o lo hace de forma repentina en caso contrario. Los procesos de unión y rotura pueden entenderse como una cascada directa (roturas) o inversa (uniones), siguiendo el concepto de cascada de remolinos ideado por Richardson (1920) y Obukhov (1941). El análisis de los datos muestra que las estructuras con tamaños menores a 30η (unidades de Kolmogorov) nunca se unen ni rompen, es decir, no experimentan el proceso de cascada. Por el contrario, aquellas mayores a 100η siempre se rompen o unen al menos una vez en su vida. En estos casos, el volumen total ganado y perdido es una fracción importante del volumen medio de la estructura implicada, con una tendencia ligeramente mayor a romperse (cascada directa) que a unirse (cascade inversa). La mayor parte de interacciones entre ramas se debe a roturas o uniones de fragmentos muy pequeños en la escala de Kolmogorov con estructuras más grandes, aunque el efecto de fragmentos de mayor tamaño no es despreciable. También hemos encontrado que las roturas tienen a ocurrir al final de la vida de la estructura y las uniones al principio. Aunque los resultados para la cascada directa e inversa no son idénticos, son muy simétricos, lo que sugiere un alto grado de reversibilidad en el proceso de cascada. ABSTRACT The purpose of the present thesis is to study the dynamics of the logarithmic layer of wall-bounded turbulent flows. Specifically, to propose a new structural model based on four different coherent structures: sweeps, ejections, clusters of vortices and velocity streaks. The tool used is the direct numerical simulation of time-resolved turbulent channels. Since the first work by Theodorsen (1952), coherent structures have played an important role in the understanding of turbulence organization and its dynamics. Nowadays, data from individual snapshots of direct numerical simulations allow to study the threedimensional statistical properties of those objects, but their dynamics can only be fully understood by tracking them in time. Although the temporal evolution has already been studied for small structures at moderate Reynolds numbers, e.g., Robinson (1991), a temporal analysis of three-dimensional structures spanning from the smallest to the largest scales across the logarithmic layer has yet to be performed and is the goal of the present thesis. The most interesting problems lie in the logarithmic region, which is the seat of cascades of vorticity, energy, and momentum. Different models involving coherent structures have been proposed to represent the organization of wall-bounded turbulent flows in the logarithmic layer. One of the most extended ones was conceived by Adrian et al. (2000) and built on packets of hairpins that grow from the wall and work cooperatively to gen- ´ erate low-momentum ramps. A different view was presented by del Alamo & Jim´enez (2006), who extracted coherent vortical structures from DNSs and proposed a less organized scenario. Although the two models are kinematically fairly similar, they have important dynamical differences, mostly regarding the relevance of the wall. Another open question is whether such a model can be used to explain the cascade process proposed by Kolmogorov (1941b) in terms of coherent structures. The challenge would be to identify coherent structures undergoing a turbulent cascade that can be quantified. To gain a better insight into the previous questions, we have developed a novel method to track coherent structures in time, and used it to characterize the temporal evolutions of eddies in turbulent channels with Reynolds numbers high enough to include a non-trivial range of length scales, and computational domains sufficiently long and wide to reproduce correctly the dynamics of the logarithmic layer. Our efforts have followed four steps. First, we have conducted a campaign of direct numerical simulations of turbulent channels at different Reynolds numbers and box sizes, and assessed the effect of the computational domain in the one-point statistics and spectra. From the results, we have concluded that computational domains with streamwise and spanwise sizes 2vr and vr times the half-height of the channel, respectively, are large enough to accurately capture the dynamical interactions between structures in the logarithmic layer and the rest of the scales. These simulations are used in the subsequent chapters. Second, the three-dimensional structures of intense tangential Reynolds stress in plane turbulent channels (Qs) have been studied by extending the classical quadrant analysis to three dimensions, with emphasis on the logarithmic and outer layers. The eddies are identified as connected regions of intense tangential Reynolds stress. Qs are then classified according to their streamwise and wall-normal fluctuating velocities as inward interactions, outward interactions, sweeps and ejections. It is found that wall-detached Qs are isotropically oriented background stress fluctuations, common to most turbulent flows, and do not contribute to the mean stress. Most of the stress is carried by a selfsimilar family of larger wall-attached Qs, increasingly complex away from the wall, with fractal dimensions « 2. They have shapes similar to ‘sponges of flakes’, while vortex clusters resemble ‘sponges of strings’. Although their number decays away from the wall, the fraction of the stress that they carry is independent of their heights, and a substantial part resides in a few objects extending beyond the centerline, reminiscent of the very large scale motions of several authors. The predominant logarithmic-layer structures are sideby- side pairs of sweeps and ejections, with an associated vortex cluster, and dimensions and stresses similar to Townsend’s conjectured wall-attached eddies. Third, the temporal evolution of Qs and vortex clusters are studied using time-resolved DNS data up to ReT = 4200 (friction Reynolds number). The eddies are identified following the procedure presented above, and then tracked in time. From the geometric intersection of structures in consecutive fields, we have built temporal connection graphs of all the objects, and defined main and secondary branches in a way that each branch represents the temporal evolution of one coherent structure. Once these evolutions are properly organized, they provide the necessary information to characterize eddies from birth to death. The results show that the eddies are born at all distances from the wall, although with higher probability near it, where the shear is strongest. Most of them stay small and do not last for long times. However, there is a family of eddies that become large enough to attach to the wall while they reach into the logarithmic layer, and become the wall-attached structures previously observed in instantaneous flow fields. They are geometrically self-similar, with sizes and lifetimes proportional to their distance from the wall. Most of them achieve lengths well above the Corrsin’ scale, and hence, their dynamics are controlled by the mean shear. Eddies associated with ejections move away from the wall with an average velocity uT (friction velocity), and their base attaches very fast at the beginning of their lives. Conversely, sweeps move towards the wall at -uT, and attach later. In both cases, they remain attached for 2/3 of their lives. In the streamwise direction, eddies are advected and deformed by the local mean velocity. Finally, we interpret the turbulent cascade not only as a way to conceptualize the flow, but as an actual physical process in which coherent structures merge and split. The volume of an eddy can change either smoothly, when they are not merging or splitting, or through sudden changes. The processes of merging and splitting can be thought of as a direct (when splitting) or an inverse (when merging) cascade, following the ideas envisioned by Richardson (1920) and Obukhov (1941). It is observed that there is a minimum length of 30η (Kolmogorov units) above which mergers and splits begin to be important. Moreover, all eddies above 100η split and merge at least once in their lives. In those cases, the total volume gained and lost is a substantial fraction of the average volume of the structure involved, with slightly more splits (direct cascade) than mergers. Most branch interactions are found to be the shedding or absorption of Kolmogorov-scale fragments by larger structures, but more balanced splits or mergers spanning a wide range of scales are also found to be important. The results show that splits are more probable at the end of the life of the eddy, while mergers take place at the beginning of the life. Although the results for the direct and the inverse cascades are not identical, they are found to be very symmetric, which suggests a high degree of reversibility of the cascade process.

Simulation and geometrical design of multi-section tapered semiconductor optical amplifiers at 1.57 µm

Fully integrated semiconductor master-oscillator power-amplifiers (MOPA) with a tapered power amplifier are attractive sources for applications requiring high brightness. The geometrical design of the tapered amplifier is crucial to achieve the required power and beam quality. In this work we investigate by numerical simulation the role of the geometrical design in the beam quality and in the maximum achievable power. The simulations were performed with a Quasi-3D model which solves the complete steady-state semiconductor and thermal equations combined with a beam propagation method. The results indicate that large devices with wide taper angles produce higher power with better beam quality than smaller area designs, but at expenses of a higher injection current and lower conversion efficiency.

Numerical issues in Lagrangian tracking and topological evolution of fluid particles in wallbounded turbulent flows

The determination of the local Lagrangian evolution of the flow topology in wall-bounded turbulence, and of the Lagrangian evolution associated with entrainment across the turbulent / non-turbulent interface into a turbulent boundary layer, require accurate tracking of a fluid particle and its local velocity gradients. This paper addresses the implementation of fluid-particle tracking in both a turbulent boundary layer direct numerical simulation and in a fully developed channel flow simulation. Determination of the sub-grid particle velocity is performed using both cubic B-spline, four-point Hermite spline and higher-order Hermite spline interpolation. Both wall-bounded flows show similar oscillations in the Lagrangian tracers of both velocity and velocity gradients, corresponding to the movement of particles across the boundaries of computational cells. While these oscillation in the particle velocity are relatively small and have negligible effect on the particle trajectories for time-steps of the order of CFL = 0.1, they appear to be the cause of significant oscillations in the evolution of the invariants of the velocity gradient tensor.

Tridimensional simulation of the speed, pressure and turbulence fields of the air flow on the geometry of a freight truck inside a wind tunnel

This study shows the air flow behavior through the geometry of a freight truck inside a AF6109 wind tunnel with the purpose to predict the speed, pressure and turbulence fields made by the air flow, to decrease the aerodynamic resistance, to calculate the dragging coefficient, to evaluate the aerodynamics of the geometry of the prototype using the CFD technique and to compare the results of the simulation with the results obtained experimentally with the “PETER 739 HAULER” scaled freight truck model located on the floor of the test chamber. The Geometry went through a numerical simulation process using the CFX 5,7. The obtained results showed the behavior of the air flow through the test chamber, and also it showed the variations of speed and pressure at the exit of the chamber and the calculations of the coefficient and the dragging force on the geometry of the freight truck. The evaluation of the aerodynamics showed that the aerodynamic deflector is a device that helped the reduction the dragging produced in a significant way by the air. Furthermore, the dragging coefficient and force on the prototype freight truck could be estimated establishing an incomplete similarity.

A study of the mechanical behaviour of the human aortic artery by means of non-linear finite element models

En la presente tesis desarrollamos una estrategia para la simulación numérica del comportamiento mecánico de la aorta humana usando modelos de elementos finitos no lineales. Prestamos especial atención a tres aspectos claves relacionados con la biomecánica de los tejidos blandos. Primero, el análisis del comportamiento anisótropo característico de los tejidos blandos debido a las familias de fibras de colágeno. Segundo, el análisis del ablandamiento presentado por los vasos sanguíneos cuando estos soportan cargas fuera del rango de funcionamiento fisiológico. Y finalmente, la inclusión de las tensiones residuales en las simulaciones en concordancia con el experimento de apertura de ángulo. El análisis del daño se aborda mediante dos aproximaciones diferentes. En la primera aproximación se presenta una formulación de daño local con regularización. Esta formulación tiene dos ingredientes principales. Por una parte, usa los principios de la teoría de la fisura difusa para garantizar la objetividad de los resultados con diferentes mallas. Por otra parte, usa el modelo bidimensional de Hodge-Petruska para describir el comportamiento mesoscópico de los fibriles. Partiendo de este modelo mesoscópico, las propiedades macroscópicas de las fibras de colágeno son obtenidas a través de un proceso de homogenización. En la segunda aproximación se presenta un modelo de daño no-local enriquecido con el gradiente de la variable de daño. El modelo se construye a partir del enriquecimiento de la función de energía con un término que contiene el gradiente material de la variable de daño no-local. La inclusión de este término asegura una regularización implícita de la implementación por elementos finitos, dando lugar a resultados de las simulaciones que no dependen de la malla. La aplicabilidad de este último modelo a problemas de biomecánica se estudia por medio de una simulación de un procedimiento quirúrgico típico conocido como angioplastia de balón. In the present thesis we develop a framework for the numerical simulation of the mechanical behaviour of the human aorta using non-linear finite element models. Special attention is paid to three key aspects related to the biomechanics of soft tissues. First, the modelling of the characteristic anisotropic behaviour of the softue due to the collagen fibre families. Secondly, the modelling of damage-related softening that blood vessels exhibit when subjected to loads beyond their physiological range. And finally, the inclusion of the residual stresses in the simulations in accordance with the opening-angle experiment The modelling of damage is addressed with two major and different approaches. In the first approach a continuum local damage formulation with regularisation is presented. This formulation has two principal ingredients. On the one hand, it makes use of the principles of the smeared crack theory to avoid the mesh size dependence of the structural response in softening. On the other hand, it uses a Hodge-Petruska bidimensional model to describe the fibrils as staggered arrays of tropocollagen molecules, and from this mesoscopic model the macroscopic material properties of the collagen fibres are obtained using an homogenisation process. In the second approach a non-local gradient-enhanced damage formulation is introduced. The model is built around the enhancement of the free energy function by means of a term that contains the referential gradient of the non-local damage variable. The inclusion of this term ensures an implicit regularisation of the finite element implementation, yielding mesh-objective results of the simulations. The applicability of the later model to biomechanically-related problems is studied by means of the simulation of a typical surgical procedure, namely, the balloon angioplasty.

Relationship between residual stresses and mechanical behavior in ceramic composites

En este trabajo, materiales de tipo alúmina/Y-TZP (ZrO2 tetragonal, estabilizada con 3 mol. % Y2O3), como sistema cerámico popular por sus mejoradas propiedades mecánicas en comparación con las cerámicas de alúmina puras, han sido estudiados en términos de propiedades mecánicas y tensiones residuales. El novedoso método de colado en cinta, consistente en el apilamiento de cintas de cerámica verde a temperatura ambiente y el uso de bajas presiones, se ha escogido para la presente investigación con el fin de poder aprovechar al máximo el futuro desarrollo de materiales laminados de alúmina-óxido de circonio. Se han determinado las propiedades de los materiales obtenidos por este nuevo método de procesamiento comparándolas con las de los materiales obtenidos por “slip casting”, con el fin de analizar si el método propuesto afecta a la microestructura y, por tanto, a las propiedades mecánicas y tensiones residuales propias de estos materiales. Para analizar la idoneidad del proceso de fabricación, utilizado para evitar la presencia de discontinuidades en las intercaras entre las láminas así como otros fenómenos que puedan interferir con las propiedades mecánicas, se estudiaron materiales cerámicos con la misma composición en cintas. Por otra parte también se analizó el efecto de la adición de óxido de circonio sobre la aparición de tensiónes residuales en cerámicas Al2O3/Y-TZP, teniendo en cuenta su notable influencia sobre las propiedades microestructurales y mecánicas de los materiales, así como el requisito de co-sinterización de capas con diferentes materiales compuestos en materiales laminados. La caracterización del material incluye la determinación de la densidad, el análisis de la microestructura, la obtención de las propiedades mecánicas (módulo de elasticidad, dureza, resistencia a la flexión y tenacidad de fractura) así como de las tensiones residuales. En combinación con otros métodos de medida tradicionales, la nanoindentación también se empleó como una técnica adicional para la medida del módulo de elasticidad y de la dureza. Por otro lado, diferentes técnicas de difracción con neutrones, tanto las basadas en longitud de onda constante (CW) como en tiempo de vuelo (TOF), han sido empleadas para la medición fiable de la deformación residual a través del grosor en muestras a granel. Las tensiones residuales fueron determinadas con elevada precisión, aplicando además métodos de análisis apropiados, como por ejemplo el refinamiento de Rietveld. Las diferentes fases en cerámicas sinterizadas, especialmente las de zirconia, se examinaron con detalle mediante el análisis de Rietveld, teniendo en cuenta el complicado polimorfismo del Óxido de Zirconio (ZrO2) así como las posibles transformaciones de fase durante el proceso de fabricación. Los efectos del contenido de Y-TZP en combinación con el nuevo método de procesamiento sobre la microestructura, el rendimiento mecánico y las tensiones residuales de los materiales estudiados (Al2O3/Y-TZP) se resumen en el presente trabajo. Finalmente, los mecanismos de endurecimiento, especialmente los relacionados con las tensiones residuales, son igualmente discutidos. In present work, Alumina/Y-TZP (tetragonal ZrO2 stabilized with 3 mol% Y2O3) materials, as an popular ceramic system with improved mechanical properties compared with the pure alumina ceramics, have been studied in terms of mechanical properties and residual stresses. The novel tape casting method, which involved the stacking of green ceramics tapes at room temperature and using low pressures, is selected for manufacturing and investigation, in order to take full advantage of the future development of alumina-zirconia laminated materials. Features of materials obtained by the new processing method are determined and compared with those of materials obtained by conventional slip casting in a plaster mold, in order to study whether the proposed method of processing affects microstructure and thereby the mechanical properties and residual stresses characteristics of materials. To analyse the adequacy of the manufacturing process used to avoid the presence of discontinuities at the interfaces between the sheets and other phenomena that interfere with the mechanical properties, ceramic materials with the same composition in tapes were investigated. Moreover, the effect of addition of zirconia on residual stress development of Al2O3/Y-TZP ceramics were taken into investigations, considering its significantly influence on the microstructure and mechanical properties of materials as well as the requirement of co-sintering of layers with different composites in laminated materials. The characterization includes density, microstructure, mechanical properties (elastic modulus, hardness, flexure strength and fracture toughness) and residual stresses. Except of the traditional measurement methods, nanoindentation technique was also used as an additional measurement of the elastic modulus and hardness. Neutron diffraction, both the constant-wavelength (CW) and time-of-flight (TOF) neutron diffraction techniques, has been used for reliable through-thickness residual strain measurement in bulk samples. Residual stresses were precisely determined combined with appropriate analysis methods, e.g. the Rietveld refinement. The phase compositions in sintered ceramics especially the ones of zirconia were accurately examined by Rietveld analysis, considering the complex polymorph of ZrO2 and the possible phase transformation during manufacturing process. Effects of Y-TZP content and the new processing method on the microstructure, mechanical performance and residual stresses were finally summarized in present studied Al2O3/Y-TZP materials. The toughening mechanisms, especially the residual stresses related toughening, were theoretically discussed.