Aquesta tesi proporciona un marc per l'anàlisi dels experiments d'indentació. En primer lloc, s'estén el concepte dels règims de deformació al contacte a materials metàl·lics que presenten efectes d'enduriment per deformació. El principal resultat d'aquests estudis es el desenvolupament d'un mapa de modes de deformació en indentació que permet predir el règim de deformació actiu per donada una combinació de propietats mecàniques del material indentat. El mapa està construït a base de simulacions per elements finits en un gran nombre de sòlids, fonamentant-nos en les característiques del flux plàstic i la forma de la zona plàstica que presenten diferents metalls deformats segons un mode elasto-plàstic o un de completament plàstic. S'han obtingut dues correlacions generals entre els valors de duresa i la magnitud d'apilament o enfonsament que s'ha desenvolupat al voltant de l'empremta d'indentació, i les propietats mecàniques uniaxials. Aquestes correlacions són el centre d'una nova metodologia per extreure les propietats mecàniques a partir de mesures directes de la topografia de l'empremta i la corba de càrrega (P) - profunditat de penetració (hs) d'un assaig d'indentació instrumentada. A la part final de la tesi es presenta un marc general per a l'anàlisi de la influencia de la fricció que existeix entre material i indentador. Aquest coneixement ens permetrà estendre la metodologia a contactes amb fricció. Finalment, s'analitza detalladament l'analogia entre els experiments d'indentació i el problema de l'expansió d'una cavitat esfèrica. Primer es solucionen les equacions del problema de l'inflat d'una cavitat esfèrica en un sòlid que presenta enduriment per deformació. Les simulacions per elements finits permeten elaborar una analogia entre els paràmetres que regeixen el contacte i els de l'expansió de la cavitat esfèrica. Un dels resultats més immediats és el desenvolupament d'una nova formulació que permet avaluar la mida de la zona plàstica en experiments d'indentació punxeguda en materials metàl·lics. / This thesis provides a sound physical rationale to the analysis of indentation experiments. First, it extends the concept of the contact deformation regimes to metallic materials exhibiting strain hardening effects. The main outcome along these lines is the development of a contact deformation map, which predicts the active contact regime for a given combination of mechanical properties of the indented material. The map is based upon extensive finite element simulations elucidating the fundamental features of the plastic flow patterns and plastic zone shape in metals deforming within the elasto-plastic and the fully plastic contact regimes. General relations are then found between hardness and the amount of material pileup and sinking-in developing at the contact boundary with uniaxial mechanical properties. These relations are central in devising a novel methodology for mechanical property extraction based on direct assessments of the imprint's topography and instrumented indentation applied load (P) penetration depth (hs) curves. The final part of the thesis presents a general framework to the analysis of frictional effects between indenter and material. This knowledge allows one to extend the aforementioned methodology in dealing with frictional contacts. Finally, a detailed analysis is made on the analogy between indentation experiments and the problem of the expansion of a spherical cavity. Closed-form solutions for the expansion of the cavity in strain hardening solids are first derived. The finite element simulations provide a strict parametrical analogy between contact variables and those from expanding cavity formulations. The main outcome of this analysis is the development of new formulations which evaluate the plastic zone size in sharp indentation experiments of strain hardening metallic materials.

En este trabajo abordan diversos problemas relacionados con los flujos de fluido en régimen turbulento. El principal problema tratado es el de la dispersión de partículas en tiempos intermedios. Se analizan también las funciones de estructura a pequeña escala.En la primera parte, además de las ecuaciones de fundamentales de la Dinámica de Fluidos y de algunas herramientas estadísticas básicas, se tratan los temas de turbulencia bidimensional, espectro de energía, correlaciones de velocidad, escalas de la turbulencia, intermitencia, métodos numéricos y dipersión de partículas en flujo turbulento.En la segunda parte de la Tesis se analizan dos métodos numéricos de base muy diferente. El primero es una Simulación Numérica Directa (DNS), con la que se resuelve, de forma explícita, todas las escalas de un flujo turbulento a partir de las ecuaciones de la dinámica. Esto limita fuertemente el número de Reynolds de la simulación. El segundo método es conocido como Simulación Cinemática (KS), donde la única ecuación de la dinámica que se considera es la condición de continuidad.En la KS el flujo turbulento es simulado como la superposición de una serie de modos de Fourier. A cada modo le correponde una escala, determinada por un vecor número de onda, y una energía, dada por el coeficiente del modo. Estos coeficientes son calculados a partir del espectro de energía del campo que se pretende simular. Las características más importantes del campo simulado mediante la KS son:"No hay malla de discretización ni extrapolación a pequeñas escalas de espacio y tiempo. El campo es calculado en cualquier instante y cualquier posición. Esto lo hace especialmente atractivo para análisis Lagrangiano."Es posible elegir diferentes parámetros del flujo: espectro de energía, escalas, energía total, número de Reynolds.En la última parte de la Tesis se muestran los resultados de dos análisis diferentes realizados con la KS.En primer lugar se realiza una comparación exhaustiva de un flujo bidimensional generado mediante KS con otro, con idéntico espectro de energía, simulado con una DNS. Sobre ambos se realiza un análisis comparativo tanto Euleriano como Lagrangiano. El análisis Euleriano muestra bastantes diferencias entre ambos flujos. Las funciones de estructura, sin embargo, con muy semejantes a pequeña escala. El análisis Lagrangiano ofrece resultados sorprendentes en cuanto a semejanza entre un flujo y otro. El valor de la escala integral Lagrangiana de tiempo permite ajustar la evolución temporal de la KS. La dispersión absoluta es afectada por las estructuras coherentes debidas a la dinámica presente en el flujo simulado mediante la DNS, y ausentes en la KS. Estas estructuras coherentes dinámicas no parecen afectar a la evolución temporal de la dispersión relativa.En segundo lugar se realizan dos series de experimentos con la KS, analizando diferentes aspectos de la variación de la ley espectral del flujo turbulento. En la primera serie de experimentos se varia la ley espectral manteniendo uniforme la energia total del campo. Se analizan, por un lado, la estructura de la turbulencia para diferente ley espectral de potencia, y se propone una expresión para la función de estructura de orden p en función de la escala y de la ley espectral, para escalas menores que la microescala de Taylor. Por otro lado, se analiza también el efecto sobre la dispersión relativa.En la segunda serie de experimentos se varia la ley espectral manteniendo uniformes las escalas características del campo, de forma que se obtienen fuertes variaciones de energía. Se analiza el efecto sobre la dipersión relativa, observándose que se cumple la ley de Richardson generalizada, independientemente de la energia del campo, para espectros con potencia menor que 2. / In this work we study different problems related to the flow of fluids in turbulent motion. The main problem on which we focus is the particle dispersion for middle times. Structure functions on a small scale are analised as well.In the first part, besides the fundamental dynamic equations and some basic statistical tools, the following points are discussed: bidimensional turbulence, energy spectrum, velocity correlations, scales of turbulence, intermitence, numerical methods and particle dispersion in turbulent flow.In the second part, two numerical methods with very different bases are analised. The first one is a Direct Numerical Simulation (DNS), where all the scales of the flow are explicitly resolved from the dynamic equations. The second model is known as Kinematic Simulation (KS), where the only dynamic equation involved is the continuity condition.With the KS the turbulent flow is simulated as a superposition of a Fourier modes series. Every mode is related to a scale which is brougth about by a wavenumber vector, and an energy which is given by the mode coefficient. These coefficients are calculated from the energy spectrum of the simulated field.The most important characteristics of the KS simulated field are:"There is no discretitation grid nor small time and space scales interpolation. The field can be calculated in any time and any position. This makes this model specially attractive for Lagrangian analysis."It is possible to choose between different parameters: energy spectrum, scales, total energy, Reynolds number.In the last part of the thesis, the results of two different analysis carried out with KS are shown.In first place, an exhaustive comparison of a bidimensional flow generated by KS and another with an identical energy spectrum generated by DNS, is performed. With both a comparative analysis Eulerian and Lagrangian is carried out. The Eulerian analysis shows various differences between both flows. However, the structure functions are very similar on small scales. The Lagrangian analysis gives surprising results with regard to the similarity between both flows. The value of the Lagrangian integral time scale allows the KS temporary evolution to be adjusted. The absolute dispersion is affected by the coherent structures due to the dynamic present in the DNS simulated flow, which are absent in the KS. These dynamic coherent structures don't seem to affect the temporary evolution of the relative dispersion.In second place, two experimental series with KS are carried out, analysing different aspects of the variation of the spectral law of turbulent flow. In the first experimental series, the spectral law is modified keeping the total energy of the field uniform. On one hand, the structure of the turbulence for different spectral laws are analysed and an expression for the p-order structure function for scales smaller than the Taylor microscale, is proposed. On the other hand, the effect on the relative dispersion is analysed.In the second experimental series, the spectral law is modified keeping the field characteristic scales uniform, obtaining strong energy variations. The effect on the relative dispersion is analysed, observing that the generalized Richardson law is fulfilled, independently of the field energy, and for spectra with

L'estudi de la formació de microstructures en processos de solidificació té importants aplicacions científiques i tecnològiques. L'aparició d'aquestes estructures determina les propietats elèctriques i mecàniques del material solidificat, i té per tant un important interès tecnològic. La majoria d'aquestes estructures tenen el seu origen en una desestabilització morfològica de la interfase sòlid-líquid que es produeix a mesura que el front avança. Per aquest motiu, l'estudi del comportament dinàmic de la interfase resulta essencial per entendre els mecanismes que intervenen en la creació d'aquests patrons. Els processos de solidificació solen descriure's mitjançant problemes de contorn mòbil. Aquestes formulacions consten d'equacions per a la difusió del calor i de massa en les fases sòlida i líquida, que s'han de resoldre imposant l'acompliment de diverses condicions de contorn mòbils a la interfase. Els problemes de contorn mòbil, malgrat contenir tots els elements que intervenen en la dinàmica i ser de molta utilitat en l'àmbit de l'enginyeria, requereixen un cost computacional que no permet simular sistemes reals en règims interfacials complexos. Els mètodes de camp de fase (phase-field methods), van aparèixer a principis dels anys vuitanta com una eina computacional que permetia l'estudi de fenòmens interfacials de caire general. Aquests mètodes descriuen la forma de la interfase mitjançant un camp continu que pren valors diferents i constants en les dues fases. La dinàmica d'aquest camp és llavors acoblada al camp de difusió de calor o massa que determina l'avanç del front de solidificació. Un dels avantatges d'aquests mètodes és que la seva simulació no requereix d'algorismes de seguiment de la interfase (front tracking algorithsms). És ben conegut que les característiques principals de les microestructures en solidificació, es determinen durant els transitoris inicials en els que els corrents de massa i calor s'adapten a la evolució dinàmica del front. Un dels objectius en aquesta tesi és el de fer servir mètodes de camp de fase per descriure de forma quantitativa aquests transitoris. Per comprovar la validesa del nostre procediment, es realitza una comparació quantitativa entre els resultats numèrics obtinguts i diferents prediccions analítiques derivades del problema de contorn mòbil. Per un altra banda, la desestabilització del front es veu afectada per la presència de fluctuacions al sistema. Aquestes pertorbacions microscòpiques poden tenir el seu origen a les fluctuacions termodinàmiques internes, o bé ser conseqüència de imperfeccions experimentals que actuen com a font externa de soroll. El segon objectiu d'aquesta tesi és la introducció de fluctuacions en mètodes de camp de fase, de forma que es pugui estudiar l'amplificació dinàmica de les pertorbacions microscòpiques que acaben donant lloc a estructures macroscòpiques. Per finalitzar, analitzem el problema de la selecció en solidificació direccional. Estudiem els règims lineal i no-lineal, tot determinant les condicions, el moment i la forma en que apareixen les estructures dendrítiques i cel·lulars. / Crystal growth is a non-equilibrium process which involves physical mechanisms at very different scales. When a solidification front advances, mass and heat diffusion processes are combined with interfacial phenomena like capillarity or kinetic attachment. A complex interplay between these mechanisms gives rise to complex interfacial structures like snowflakes or cellular patterns. The formation of microstructures in solidification has both a scientific and a technological interest. On one hand, the study of the different interfacial structures constitutes a fundamental problem in the field of non-equilibrium pattern-forming systems. On the other side, from a technological point of view, the presence of microstructures determines the final mechanical and electrical properties of the processed material. Directional solidification is a controlled solidification technique which reproduces the conditions occurring in some important metallurgical processes like material casting or zone melting refining procedures. In a directional solidification experiment, the alloy sample is pulled at a constant velocity towards the cold region of an externally-imposed temperature gradient. Depending on the growth conditions, a morphological destabilization of the solid-liquid interface occurs during early transient stages. These initial transients are associated to a solute redistribution process due to the adaptation of the concentration field to the forced motion of the sample. The main objective of this thesis is to study the dynamical evolution of the morphological deformations of the front from these initial transients to the final stages where the properties of the interfacial pattern are determined. An important point in this process is that the internal fluctuations of the system play the role of an initiation mechanism for the morphological deformations of the front. During the initial transients, some of these microscopic perturbations are amplified by several orders of magnitude, and a range of wavelengths becomes morphologically unstable. The interfacial deformations of the front can be then characterized by means of power spectrum techniques. In order to study the dynamical evolution of the solidification front in directional solidification, we have used both theoretical and computational approaches: The main computational technique used in this thesis is the phase-field approach, which is a powerful method to simulate complex interfacial phenomena. The model equations describe the evolution of a continuous field , which takes different constant values at the solid and liquid bulks of the system. This field is then coupled with equations for the mass diffusion, and allows performing numerical studies without simulating the standard Stefan-like moving boundary problem. The phase-field method provides a diffuse interface description in which the transition from solid to liquid happens in a region of a certain thickness. The interface thickness introduces a new length in the simulations which must be taken into account to recover quantitative results. One major point in this thesis concerns with the introduction of fluctuations in phase-field methods. In the particular case of variational phase-field formulations -in which the model equations can be derived from a single free energy functional for the whole system-, the introduction of fluctuations can be done by applying the Fluctuation-Dissipation theorem. Variational formulations, however, although their appealing structure, present a poor computational efficiency and cannot be used to obtain quantitative results. To this extent, we have derived a general approach which does not relay in the Fluctuation-Dissipation assumption and permits to introduce fluctuations in both variational and non-variational phase-field formulations. Well-established analytical techniques like boundary integral methods for the transient front position and linear stability analysis of the interface during the transient have been used as theoretical predictions for the computational results. The dynamical evolution of the solidification front can be divided in two stages: A linear regime where the initial noise is amplified, and a non-linear coarsening process where the final properties of the interfacial pattern are selected. We have studied these different stages of the solidification process by using the phase-field approach, and good agreement is obtained when comparing with well-established theoretical and experimental predictions.

CERN is presently constructing the LHC, which will produce collisions of 7 TeV protons in 4 interaction points at a design luminosity of 1034 cm-2 s-1. The radiation dose resulting from the operation at high luminosity will cause a serious deterioration of the silicon tracker performance. The state-of-art silicon microstrip detectors can tolerate a fluence of about 3·1014 cm-2 of hadrons or charged leptons. This is insufficient for long-term operation in the central parts of the LHC trackers, in particular after the possible luminosity upgrade. By operating the detectors at cryogenic temperatures the radiation hardness can be improved by a factor 10. This work proposes a cryogenic microstrip detector module concept which has the features required for the upgraded LHC experiments at CERN. The module can hold an edgeless sensor, being a good candidate for improved luminosity and total cross-section measurements. The design of such a module is constrained by the requirements on radiation hardness and minimal mass. The choice of the component materials is guided by the properties of the silicon sensors, and the main criteria include best possible matching of the thermal dilatation, high thermal conductivity and appropriate elastic properties, in addition to the radiation resistance. A module design is proposed where, apart from the silicon sensor, both the support plate and the pitch adapter are processed on silicon. Future design options may also feature hybrids processed in silicon using thick-film techniques and cooling microchannels directly micromachined into the support plate. The best performance and highest degree of integration of the cooling is achieved with two-phase flow (high heat transfer coefficient) argon running through capillary pipes embedded in a CFC spacer close to the heat sources. A series of thermal tests have shown that silicon is an excellent heat spreader and its use as a structural material leads to a uniform temperature distribution in the sensor and support plate. The thermal resistance due to the glue layers dominates the thermal behaviour. The thermoelastic properties of the epoxies are key factors in the design. A series of samples were prepared to measure these properties of Araldite® 2011, Stycast® 1266 and Type L epoxies filled with fused quartz powder, as a function of temperature. Filling these epoxies reduces their thermal dilatation, nearly matching that of metals. This reduces the stress in the joints when cooling down. However, filling increases the Young modulus (E) of the epoxy so much, that the thermal stress increases with the filling factor. Furthermore, filling increases the viscosity and leads to thicker glue layers, which also increases the thermal stress in silicon. The idea of using filled epoxy was therefore abandoned. The E of unfilled epoxies at 77 K is between 4 and 8 times higher than that measured at 300 K. Thin layers of epoxy should be used to minimize the stress on the silicon substrate.Precision gluing jigs were designed and produced to assemble the prototype modules. The alignment with respect to the beam is done using a warm support plate, placed between the module and the vacuum chamber. The module is attached to this support structure through three thermally isolating precision support posts with dowels. The position of the module and its readout strips is thus accurately referred to the vacuum chamber, which itself can be aligned in the test beam line using optical targets.A first electrical prototype module was assembled using a 50 ?m pitch silicon microstrip sensor (32.5 cm2). Pitch adapter and support plate were processed on silicon. The CMS hybrid with APV25 readout chips was characterized at low temperature. First results were obtained down to 210 K, showing a decrease of the noise and the rise time and an increase of the pulse peak height with respect to the room temperature behaviour. A pair of edgeless silicon diode pad sensors was exposed to the X5 high-energy pion beam, in order to determine the edge sensitivity. A high-resistivity silicon p+-i-n+ planar diode detector (0.25 cm2) was diced through its front p+ implant to produce two halves of edgeless diode pad sensors. A large surface current on such an edge prevents the normal reverse biasing of this device but it can be sufficiently reduced by the use of a suitable cutting method, followed by edge treatment and by operating the sensor at low temperature. The gap width between the edgeless sensors, determined using the tracks measured by a reference telescope, was compared with metrology measurements. It was concluded that the depth of the dead layer is compatible with zero within the statistical accuracy of 8 µm and systematic accuracy of 6 µm.

La tesis propone una metodología para el análisis de la degradación a fatiga que produce la aplicación de cargas cíclicas en un composite laminado de fibras largas.En primer lugar se han estudiado los mecanismos de degradación que son responsables del deterioro irreversible de las propiedades de rigidez y resistencia de los composites bajo cargas cíclicas. Se ha tratado de obtener una visión de los fenómenos de degradación que tienen lugar en un elemento estructural de polímero reforzado con fibras (FRP) describiendo de forma cualitativa los distintos modos de daño en laminados. A continuación, mediante una revisión de los modelos de fatiga propuestos por otros autores, se han estudiado las estrategias más comunes para la predicción del tiempo de vida de un material sometido a cargas cíclicas. En este estudio se ha dado una especial importancia al enfoque del estudio de la fatiga en composites a través de modelos de daño en la mecánica de medios continuos (MMC). En la tesis se propone un método para la formulación de la degradación por el fenómeno de la fatiga. De este modo se ha ideado una metodología que ha permitido desarrollar un modelo constitutivo integrado en la MMC para la modelización de la degradación por fatiga. El modelo permite estudiar el comportamiento del composite bajo solicitación de tensiones cíclicas de características variables. Se ha definido una formulación generalizada para las curvas S-N y otra para las curvas de resistencia residual. Se ha elaborado un modelo de acumulación de la degradación sensitivo a las características cambiantes de las tensiones cíclicas. Se ha realizado, también, la implementación del modelo de degradación de la fatiga en un sistema de cálculo numérico de elementos finitos que permite acoplar la degradación a fatiga con cualquier modelo constitutivo del material (elástico, degradación progresiva y localizada, plasticidad, etc.). Para agilizar el proceso de cálculo, la implementación numérica se ha completado con la inclusión de una metodología que permite una linealización en el avance temporal aplicando bloques representativos de conjuntos de ciclos de carga. Finalmente, se han desarrollado unos ejemplos de validación de los modelos formulados la tesis. Además, se han generado ejemplos de aplicación de la metodología para analizar del comportamiento de laminados y/o para predecir la vida de elementos estructurales de FRP durante la fase de diseño. / The present thesis proposes a methodology for the analysis of the fatigue degradation due to the application of cyclic loads to a composite laminate.First, the fatigue degradation mechanisms responsible for the irreversible loss of stiffness and strength in the laminate are studied. A global vision of the degradation phenomena involved in a structural fiber-reinforced polymer (FRP) element is obtained.After, a revision of the fatigue life models present in the literature allows the analysis of the more common strategies for the life prediction of a material under cyclic loads. Special attention is given to the continuum damage mechanics (CDM) approach for the fatigue life of composite materials.A method for the formulation of the fatigue degradation is proposed. The methodology for a constitutive model for the fatigue degradation integrated in the CDM is obtained. This model allows the study of the composite behavior under variable cyclic stresses. A generalized formulation for the S-N curves and for the residual strength curves is defined. The model for the accumulation of the degradation is sensitive to the varying characteristics of the cyclic stresses.The model for the fatigue degradation is also implemented in a Finite Element program. This makes possible to couple the fatigue degradation with other constitutive models for the material (elastic, progressive and localized degradation, plasticity, etc.). In order to prompt the calculating process, the numeric implementation is completed with a methodology for the linearization of the temporal progression by applying representative blocks of load cycles.Finally, a set of validation examples are included, as well as some examples of the application of the methodology for the analysis of the behavior of laminates and/or to predict the fatigue life of structural FRP elements during the design process.

Path integral Monte Carlo (PIMC) is a method suitable for quantum liquid simulations at finite temperature. We present in this thesis a study of PIMC dealing with the theory and algorithms related to it, and then two applications of PIMC to current research problems of quantum fluids in the Bolzmann regime. The first part encompasses a study of the different ingredients of a PIMC code: action, sampling and physical property estimators. Particular attention has been paid to Li-Broughton's higher order approximation to the action. Regarding sampling, several collective movement methods have been derived, including the bisection algorithm, that has been thoroughly tested. We also include a study of estimators for different physical properties, such as, the energy (through the thermodynamic and virial estimators), the pair distribution function, the structure factor, and the momentum distribution. In relation to the momentum distribution, we have developed a novel algorithm for its estimation, the trail method. It surmounts some of the problems exposed by previous approaches, such as the open chain method or McMillan's algorithm.The Richardson extrapolation used within PIMC simulations, is another contribution of this thesis. Up until now, this extrapolation has not been used in this context. We present studies of the energy dependence on the number of "beads", along with the betterment provide by the Richardson extrapolation. Inasmuch as our goal is to perform research of quantum liquids at finite temperature, we have produced a library of codes, written from scratch, that implement most of the features theoretically developed. The most elaborated parts of these codes are included in some of the appendixes.The second part shows two different applications of the algorithms coded. We present results of a PIMC calculation of the momentum distribution of Ne and normal 4He at low temperatures. In the range of temperatures analysed, exchanges can be disregarded and both systems are considered Boltzmann quantum liquids. Their quantum character is well reflected in their momentum distributions witch show clear departures from the classical limit. The PIMC momentum distributions which show clear departures from the classical limit. The PIMC momentum distributions are sampled using the trail method. Kinetic energies of both systems, as a function of temperature and at a fixed density, are also reported. Finally, the solid-liquid neon phase transition along the 35 K isotherm has been characterized.While thermodynamic properties of the solid phase are well known the behaviour of some properties, such as the energy or the dessity, during the trasition presen6 some uncertainties For example, experimental data for the place diagram, which determines solid and liquid boundaries, present sizeable differences. The temperature chosen is high enough so that Bose or Fermi statistics corrections are small, although the system is strongly quantum mechanical. The results obtained show a discontinuity in the kinetic energy during the transition.

La tesis se centra en el desarrollo de técnicas numéricas específicas para la resolución de problemas de mecánica de sólidos, tomando como referencia aquellos que involucran geomateriales (suelos, rocas, materiales granulares,...). Concretamente, se tratan los siguientes puntos: 1) formulaciones Arbitrariamente Lagrangianas Eulerianas (ALE) para problemas con grandes desplazamientos del contorno; 2) métodos de resolución para problemas no lineales en el campo de la mecánica de sólidos y 3) modelización del comportamiento mecánico de materiales granulares mediante leyes constitutivas elastoplásticas. Las principales aportaciones de la tesis son: el desarrollo de una formulación ALE para modelos hyperelastoplásticos y el cálculo de operadores tangentes para distintas leyes constitutivas y esquemas de integración temporal no triviales (uso de esquemas de derivación numérica, técnicas de subincrementación y modelos elastoplásticos con endurecimiento y/o reblandecimiento dependientes del trabajo plástico o la densidad). Se presentan diversas aplicaciones que muestran las principales características de los desarrollos presentados (análisis del ensayo del molinete para arcillas blandas, del ensayo triaxial para arenas, de la rotura bajo una cimentación, del proceso de estricción de una barra metálica circular y de un proceso de estampación en frío), dedicando una especial atención a los aspectos computacionales de la resolución de dichos problemas. Por último, se dedica un capítulo específico a la modelización y la simulación numérica de procesos de compactación fría de polvos metálicos y cerámicos. / Numerical modelling of problems involving geomaterials (i.e. soils, rocks, concrete and ceramics) has been an area of active research over the past few decades. This fact is probably due to three main causes: the increasing interest of predicting the material behaviour in practical engineering situations, the great change of computer capabilities and resources, and the growing interaction between computational mechanics, applied mathematics and different engineering fields (concrete, soil mechanics...). This thesis fits within this last multidisciplinary approach. Based on constitutive modelling and applied mathematics and using both languages the numerical simulation of some complex geomechanical problems has been studied.The state of the art regarding experiments, constitutive modelling, and numerical simulations involving geomaterials is very extensive. The thesis focuses in three of the most important and actual ongoing research topics within this framework: 1) the treatment of large boundary displacements by means of Arbitrary Lagrangian-Eulerian (ALE) formulations; 2) the numerical solution of highly nonlinear systems of equations in solid mechanics; and 3) the constitutive modelling of the nonlinear mechanical behaviour of granular materials. The three topics have been analysed and different contributions for each one of them have been developed. Moreover, some of the new developments have been applied to the numerical modelling of cold compaction processes of powders. The process consists in transforming a loose powder into a compacted sample through a large volume reduction. This problem has been chosen as a reference application of the thesis because it involves large boundary displacements, finite deformations and highly nonlinear material behaviour. Therefore, it is a challenging geomechanical problem from a numerical modelling point of view.The most relevant contributions of the thesis are the following: 1) with respect to the treatment of large boundary displacements: quasistatic and dynamic analyses of the vane test for soft materials using a fluid-based ALE formulation and different non-newtonian constitutive laws, and the development of a solid-based ALE formulation for finite strain hyperelastic-plastic models, with applications to isochoric and non-isochoric cases; 2) referent to the solution of nonlinear systems of equations in solid mechanics: the use of simple and robust numerical differentiation schemes for the computation of tangent operators, including examples with several non-trivial elastoplastic constitutive laws, and the development of consistent tangent operators for different substepping time-integration rules, with the application to an adaptive time-integration scheme; and 3) in the field of constitutive modelling of granular materials: the efficient numerical modelling of different problems involving elastoplastic models, including work hardening-softening models for small strain problems and density-dependent hyperelastic-plastic models in a large strain context, and robust and accurate simulations of several powder compaction processes, with detailed analysis of spatial density distributions and verification of the mass conservation principle.

This thesis makes two noteworthy contributions in the are of mesh-free methods: a Pseudo-Divergence-Free (PDF) Element Free Galerkin (EFG) method which alleviates the volumetric locking and a Stabilized Updated Lagrangian formulation which allows to solve fast-transient dynamic problems involving large distortions. The thesis is organized in the following way. First of all, this thesis dedicates one chapter to the state of the art of mesh-free methods. The main reason is because there are many mesh-free methods that can be found in the literature which can be based on different ideas and with different properties. There is a real need of classifying, ordering and comparing these methods: in fact, the same or almost the same method can be found with different names in the literature. Secondly, a novel improved formulation of the (EFG) method is proposed in order to alleviate volumetric locking. It is based on a pseudo-divergence-free interpolation. Using the concept of diffuse derivatives an a convergence theorem of these derivatives to the ones of the exact solution, the new approximation proposed is obtained imposing a zero diffuse divergence. In this way is guaranteed that the method verifies asymptotically the incompressibility condition and in addition the imposition can be done a priori. This means that the main difference between standard EFG and the improved method is how is chosen the interpolation basis. Modal analysis and numerical results for two classical benchmark tests in solids corroborate that, as expected, diffuse derivatives converge to the derivatives of the exact solution when the discretization is refined (for a fixed dilation parameter) and, of course, that diffuse divergence converges to the exact divergence with the expected theoretical rate. For standard EFG the typical convergence rate is degrade as the incompressible limit is approached but with the improved method good results are obtained even for a nearly incompressible case and a moderately fine discretization. The improved method has also been used to solve the Stokes equations. In this case the LBB condition is not explicitly satisfied because the pseudo-divergence-free approximation is employed. Reasonable results are obtained in spite of the equal order interpolation for velocity and pressure. Finally, several techniques have been developed in the past to solve the well known tensile instability in the SPH (Smooth Particle Hydrodynamics) mesh-free method. It has been proved that a Lagrangian formulation removes completely the instability (but zero energy modes exist). In fact, Lagrangian SPH works even better than the Finite Element Method in problems involving distortions. Nevertheless, in problems with very large distortions a Lagrangian formulation will need of frequent updates of the reference configuration. When such updates are incorporated then zero energy modes are more likely to be activated. When few updates are carried out the error is small but when updates are performed frequently the solution is completely spoilt because of the zero energy modes. In this thesis an updated Lagrangian formulation is developed. It allows to carry out updates of the reference configuration without suffering the appearance of spurious modes. To update the Lagrangian formulation an incremental approach is used: an intermediate configuration will be the new reference configuration for the next time steps. It has been observed that this updated formulation suffers from similar numerical fracture to the Eulerian case. A modal analysis has proven that there exist zero energy modes. In the paper the updated Lagrangian method is exposed in detail, a stability analysis is performed and finally a stabilization technique is incorporated to preclude spurious modes.

En los últimos años, los trabajos de investigación están muy motivados por todo aquello que contribuye a reducir el ruido emitido por los sistemas oleohidráulicos. Como ha sido demostrado por varios investigadores, el origen de estas perturbaciones hay que buscarlo en el proceso de generación de las pulsaciones de caudal como característica intrínseca del propio funcionamiento real de la bomba, y en consecuencia, cualquier avance en este terreno debe pasar ineludiblemente por la simulación del comportamiento dinámico de estas unidades.El presente trabajo de investigación se circunscribe al estudio de una bomba gerotor, con el fin disponer de un estudio global, coherente y unificado que comprende la geometría de los perfiles trocoidales del engranaje, la cinemática del engrane, las características volumétricas, las tensiones en los puntos de contacto y su comportamiento dinámico.La geometría y cinemática de engrane del engranaje trocoidal se han deducido analíticamente mediante las ecuaciones de los perfiles de los dientes y la línea de puntos de contacto en función de cuatro parámetros básicos, sentando la base para el desarrollo de los estudios posteriores. Las características volumétricas se han desarrollado, puesto a punto y comparado mediante dos métodos: uno numérico que se fundamenta en un análisis integral-derivativo, y el otro que se fundamenta en un análisis derivativo-integral en sus dos posibles versiones, la analítica y la numérica. La concordancia de resultados obtenidos utilizando estos métodos es muy satisfactoria. En el cálculo de las tensiones de contacto, también se han propuesto y desarrollado dos metodologías de cálculo. Un primer método parte de la teoría desarrollada por Colbourne, implementado con una variante para el cálculo de los puntos de contacto. Este método es adecuado para ruedas dentadas exteriores donde el perfil del lóbulo o diente es ajustable a un arco circular. Puesto que su aplicación es muy restrictiva, se ha creído oportuno proponer un método alternativo implementado con el Método de los Elementos Finitos mucho más genérico. Este último ha proporcionado los valores de la magnitud de la máxima tensión de contacto más fiables y ha demostrado un alto nivel de flexibilidad que facilita en gran medida el proceso de optimización de la forma geométrica de los perfiles de los dientes.El comportamiento fluidodinámico de la bomba gerotor se estudia proponiendo un método de simulación física (Método de BondGraph) que incida directamente en el cálculo de las pulsaciones de caudal. El modelo de simulación fluidodinámico presenta un análisis matemático que parte del submodelo de una cámara y se completa con la interacción engranaje-bomba y las fugas de caudal. Esta metodología numérica desarrollada se contrasta con una técnica experimental (Método de la 'Fuente Secundaria') que permite la comparación directa de los resultados obtenidos por ambas vías. Son dos los bancos de ensayo empleados y desarrollados de acuerdo con la norma ISO 10767, uno en el Fluid Power Centre de la University of Bath, y otro diseñado y construido específicamente para esta tesis en el laboratorio del centro LABSON. Se observa que las amplitudes (pico a pico) de las pulsaciones de caudal obtenidas por vía experimental en el Fluid Power Centre son inferiores y más regulares que las obtenidas en el laboratorio del centro LABSON.La comparativa de resultados de la pulsación de caudal 'ideal' obtenida de la simulación y la pulsación de caudal de los ensayos experimentales muestran ser muy precisos en su forma, a pesar de existir diferencias de amplitud. El modelo de simulación muestra que describe con gran grado de exactitud la interacción engranaje-bomba y las fugas de caudal de una bomba gerotor. / In recent years, there has been a growing awareness of the hazards of industrial noise and how to reduce it in hydraulic systems. A great number of studies have been carried out in the past in this field and it has been shown that the source of these perturbations has to be sought in the process of the generation of flow ripple as an intrinsic characteristic of the pump. As a consequence of this, any advance in this field has to inevitably pass the simulation of the dynamic behaviour of the pump.The investigation work presented in this thesis is concentrated on the performance analysis of a gerotor pump in order to develop a coherent and unified global study of the trochoidal profiles geometry of the gear, the kinematics of the mesh, the volumetric characteristics, the contact stress at the contact points and its fluid dynamic behaviour.The geometry and kinematics of the mesh of the trochoidal gear has been analytically deduced through the equations of the teeth profiles and the line of contact, which are in turn function of four basic parameters and were the basis for further studies. The volumetric characteristics have been developed and compared by using two approaches: the integral-derivative approach solved by a numerical differentiation and the derivative-integral approach solved by a numerical and analytical integration. The coherence of the results obtained by both approaches is very satisfactory.Contact stress calculation is also proposed and developed by using two methodologies. The first method is based on Colbourne's theory and it is implemented by a new approach to the calculation of the contact points. This method is only valid for external gears formed by circular-arc teeth. Because of the limitation of this method, an alternative and more generic method has been proposed by implementing the Finite Element Method. This last method provides more reliable magnitude values of the maximum contact stress and it has shown a high flexibility that aids the process of optimization of the teeth profiles geometry.The fluid dynamic behaviour of the gerotor pump study is based on a physical simulation method (BondGraph's Method) which is focused on the flow ripple calculation. The simulation model presents an analytical approach which starts with a submodel of a single chamber and it is completed by the interaction of gear-pump and leakage flows. This numerical methodology is contrasted with an experimental methodology (Secondary Source Method) which allows a direct comparison between results from both methodologies. Two test rigs have been employed and developed according to the ISO normative 10767-192/84247: one of the test rigs is at the Fluid Power Centre of the University of Bath and the other test rig is specifically designed and constructed for this thesis at the LABON Centre. A comparison of the experimental results has shown that the amplitude (peak to peak) of the flow ripple of the Fluid Power Centre is more accurate than those obtained at the LABSON Centre.The comparison between the 'ideal' flow ripple from the simulation and the 'real' flow ripple from the experimental work are shown to be very precise in shape and form, despite of the discrepancies observed between amplitudes. It has been proved that the simulation model describes with a high accuracy the interaction of gear-pump and leakage flows of the gerotor pump.

Se ha llevado a cabo un estudio con el fin de observar diferencias en el comportamiento de fluencia en caliente de los cobres refinados al fuego con una pureza de 99.9%, dicho estudio ha permitido proponer modelos para predecir la curva esfuerzo-deformación y para predecir el tamaño de grano recristalizado dinámicamente. Los cobres refinados al fuego con una pureza de 99.9% se caracterizan por tener una composición residual de varios otros elementos, en algunos casos hasta 1000ppm. En los cobres con por lo menos 99.9% de pureza que tengan pocos elementos residuales, las diferencias observadas durante la fluencia en caliente se atribuyen a las interacciones entre átomos disueltos y dislocaciones, específicamente las interacciones con oxígeno intersticial. En el cobre electrolítico, el cual contiene principalmente altos contenidos de oxigeno, las diferencias de fluencia se atribuyen a cantidades cada vez mayores de partículas de Cu2O. Este trabajo más bien demuestra que las diferencias de esfuerzo encontradas en cobres refinados al fuego con una pureza de 99.9% son debidas a la cantidad de oxígeno residual, el cual forma finos precipitados a temperaturas intermedias que refuerzan la matriz metálica. A pesar del bajo contenido en oxígeno en los cobres estudiados (26-62ppm) se han caracterizado precipitados de Cu2O y se han utilizado teorías del endurecimiento por precipitación que han indicado que los precipitados de Cu2O eran los responsables del incremento en resistencia. Las interacciones entre átomos de oxígeno y dislocaciones son poco probables que causen un retro esfuerzo adicional a temperaturas superiores a los 600º C, en donde se ha llevado a cabo este trabajo. Se han comprimido tres cobres con 26, 46 y 62ppm de oxígeno a unas velocidades de deformación de 0.3s-1, 0.1s-1, 0.03s-1, 0.01s-1, 0.003s-1 y 0.001s-1 y a unas temperaturas desde 600º C hasta 950º C en intervalos de 50º. En este trabajo se presenta evidencia de cómo bajos contenidos de oxígeno en cobres 99.9% puros pueden afectar el comportamiento esfuerzo-deformación y el tamaño de grano recristalizado dinámicamente.Además de haber encontrado el elemento y el mecanismo responsable del retro esfuerzo adicional también se presenta un algoritmo matemático para estudiar y predecir las oscilaciones de esfuerzo durante la recristalización dinámica de pico múltiple. Intentos anteriores utilizando Modelos Computarizados de Monte Carlo, Modelos de Autómatas Celulares o Modelos Matemáticos para la Recristalización Dinámica (DRX) no predicen las oscilaciones de esfuerzo de materiales reales y su tiempo de computo los hace inviables para procesos de simulación industrial. El nuevo Modelo de Avrami con Coseno Amortiguado para la DRX es capaz de predecir la transición de DRX de pico simple a DRX de pico múltiple. Además el nuevo modelo define el esfuerzo de estado estable sin tener que escoger un valor de una curva experimental que posiblemente no haya alcanzado un estado estable. Otra contribución del nuevo modelo es que demuestra que las oscilaciones son completamente predecibles en términos de la velocidad de deformación y la temperatura, una característica que antes se había dicho ser improbable. El nuevo modelo para la DRX junto con un modelo modificado de Voce-Kocks para la restauración dinámica han sido exitosamente implementados para predecir la fluencia en caliente.Adicionalmente a las anteriores contribuciones este trabajo también da a conocer la relación que tiene el tamaño de grano recristalizado con la temperatura y la velocidad de deformación. Se asume que los cobres 99.9% puros, como los estudiados, tenderán a un tamaño de grano de estado estable el cual cuando esté a temperatura ambiente determinará las propiedades mecánicas del producto forjado.