Rolling contacts are utilized in many technical applications, both in bearings and in the contact between gear teeth. These components are often highly loaded, which makes them susceptible to suffer from rolling contact fatigue. This work focuses on the rolling contact fatigue mechanism of pitting. In order to attain a better understanding of why pitting initiates and grows, detailed simulations of rolling contacts have been performed. In particular the contact between two gears in a truck retarder was here used as a case study. The investigated contact experienced elastohydrodynamic lubrication conditions since the load was high enough to causes the surfaces in contact to deform and the viscosity of the lubricant to increase significantly. In Paper A it was investigated if surface irregularities in the size of the surface roughness are large enough to cause surface initiated fatigue. The investigation focused on the pitch line since small surface initiated pits were found here even though there was no slip present. Since there were pits present at the pitch line, it is important that the theories of pitting can explain the development of pits also in the absence of slip. The conclusion of the work was that surface irregularities of the size of normal surface roughness are enough to cause surface initiated fatigue at the pitch line. In Paper B it was investigated why pits are more likely to initiate in the dedendum of pinion gears than in the addendum. In both areas slip is present but in different directions. In the dedendum the friction from slip is against the rolling direction which enhances the risk for pitting. The investigation was performed by studying the effect of the temperature rise in the contact caused by the slip. The conclusion drawn was that the temperature rise in the contact explained why pitting was more common in the dedendum than in the addendum. / Rullande kontakter förekommer i många applikationer, till exempel i lager och mellan kugghjulständer. Både lager och kugghjul utsätts ofta för höga laster vilket gör att dess ytor löper stor risk att utmattas, vilket kallas rullande kontaktutmattning. Denna studie fokuserar på pitting, även kallat spalling, vilket är en typ av rullande kontaktutmattning där en utmattninsspricka växer fram som får delar av ytan att ramla av. För att få en bättre förståelse varför pittingskador uppkommer har noggranna simuleringar utförts av rullande kontakter. Kontakten mellan två tänder på kugghjul i en lastbilsretarder har används som underlag då många pittingskador påträffats på dem.  För att minska friktionen och nötningen i kontakten mellan kuggtänderna användes smörjmedel. De höga lasterna lastbilsretardern utsattes för deformerade kuggarnas ytor elastiskt samtidigt de kraftigt ökade viskositeten hos smörjmedlet. Dessa förhållanden gör att kontakten kallas för elastohydrodynamiskt smord, vilket på engelska förkortas till EHL. I Artikel A undersöktes om små ytojämnheter kan orsaka ytinitierade pittingskador. Eftersom skadan påträffats i friktionslösa kontakter, så som vid rullcirkeln på de undersökta kugghjulen, är det viktigt att teorierna som förklarar uppkomsten inte är beroende av friktion. Undersökningen fokuserade därför på förhållandena vid rullcirkeln.  Slutsatsen från arbetet var att små ytojämnheter, av samma storleksordning som ytojämnheterna på de undersökta kugghjulen, är tillräckligt stora för att orsaka utmattningsskador. I Artikel B undersöktes varför det är vanligare att pitts initieras i dedendum än addendum på drivande kugghjul. Kontakten på båda sidorna om rullcirkeln slirar svagt åt olika håll. Att kontakten slirar skapar friktion som är motriktad rullriktningen i dedendum vilket ökar risken för pittingskador. För att undersöka varför dessa förhållanden ökar risken för skador fördjupades analysen av kontakten genom att inkludera temperaturfältet. Simuleringarna visade att temperaturen ökar genom kontakten vilket orsakar en asymmetrisk spänningsfördelning. Denna asymmetriska spänningsfördelning gör att ytojämnheter i dedendum är troligare att orsaka skador än ytojämnheter i addendum. / <p>QC 20180213</p>

This work investigates the velocity-dependent coefficient of friction between concrete and 300 Maraging steel over short displacements. A modified torsional Hopkinson bar is utilized for rotating thin-walled steel rings in contact with a concrete disk under static precompression. Rotational velocity is varied between tests to determine the velocity dependence of the friction coefficient. Normal force is varied between certain tests to determine the pressure dependence of the friction coefficient between the concrete and steel. Three different types of concrete are tested to deduce any composition effect on the friction coefficient. Dry and greased conditions’ impact on the friction coefficient are also evaluated. Lastly, the displacement dependence (fade) is considered for the concrete with regards to the steel. Discussion of the usefulness of this data in modeling and experimentation of impact between concrete and steel is disclosed.

This dissertation describes the synthesis, antimicrobial properties, and catalytic activity of a variety of eta5-ligand rhodium and iridium complexes. Cp*RM(beta-diketonato)Cl (Cp*R = R-substituted tetramethylcyclopentadienyl ligand) complexes were found to have selective activity against Mycobacterium smegmatis, with activity highly dependent upon the substituents on the Cp*R ligand as well as on the beta-diketonato ligand. These complexes were synthesized in good yield from the reaction of the chloro bridged dimers ([Cp*RMCl2]2) with the desired beta-diketonato ligand under basic conditions. All complexes were fully characterized by 1H and 13C NMR. Twenty single crystal X-ray structures were solved. The success of these syntheses led to investigation of another beta-diketonato ligand: 1,1,1,5,5,5-hexafluoroacetylacetonate (hfac). Though many metal complexes of this ligand are known, reaction with [Cp*MCl2]2 did not yield the desired Cp*M(hfac)Cl complexes. Instead, a variety of products were obtained, three of which were characterized crystallographically. The most interesting structure featured a non-coordinating trifluoroacetate (TFA) anion and a [Cp*Ir]3Na1O4 cubane structure, which is an unprecedented and highly unusual arrangement for iridium. Attempts to synthesize this cluster rationally through reactions of [Cp*IrCl2]2 with TFA yielded instead a chloro bridged [Cp*IrCl(TFA)] dimer. Reaction of [Cp*MCl2]2 with 1,1,1-trifluoroacetylacetonate (tfac) yielded the expected Cp*M(tfac)Cl complex, indicating that the problem lies with using hfac as a ligand for Cp*M(III) complexes. Finally, the indenyl effect was investigated for the oxidative annulation of 2-phenylimidazole with 1-phenyl-1-propyne catalyzed by a series of methyl-substituted [(indenyl)RhCl2] dimers. [(Ind*)RhCl2]2 was found to have significantly greater activity than [Cp*RhCl2]2 (100% vs. 51%). Two plausible catalytic cycles were proposed, one of which invokes a ring slip transition state. Though it is unclear if the "indenyl effect" is responsible for this differing activity, it is certainly apparent that using an indenyl ligand has a notable effect in this catalytic reaction. Cyclometalation was also investigated stoichiometrically for 2-phenyl-1H-imidazole and 1-phenylpyrazole and found to proceed readily for [(Ind*)RhCl2]2. Additionally, the crystallographic structure of a Rh+ /Rh– ionic pair was solved. Ionic pairs such as this are rarely found in the literature. / Doctor of Philosophy / This dissertation deals with the uses of a series of unusual compounds containing the metals rhodium and iridium. Though these are rare and expensive metals, the uses and benefits described in this dissertation far outweigh the costs. Overall, the compounds described in this dissertation are colorfully characterized as “piano stool” compounds because of their overall shape and appearance. The metal, either rhodium or iridium, occupies a central point in the complex. On top of the metal is a “flat” organic group that gives the appearance of the seat of the piano stool. Below the metal, there are three other groups that look like the legs of the piano stool. By appropriate choice of the metals and the surrounding groups, special properties can be designed into these “piano stool” complexes. Chapter 2 describes the synthesis of a series of complexes where the “flat” group is a variant of a five-membered carbon ring compound known as cyclopentadienyl, the metal is rhodium or iridium, and two of the three legs come from a family of compounds known as acetylacetonates (acac). This series of piano stool compounds display antimicrobial activity against a class of pathogens known as mycobacteria, an example of which causes the disease tuberculosis. Changing the cyclopentadienyl group and the acac group allows for this antimicrobial activity to be tuned. In the following chapter, attempts to make the same type of compound described in the paragraph above with fluorine-substituted acacs gave some very unexpected results. The most surprising result was a very unusual cube-shaped structure containing 3 iridium atoms, 1 sodium atom, and 4 oxygen atoms, which is an unprecedented arrangement for iridium. Finally, there is a specific example of a flat group for the piano stool known as indenyl. Indenyl is intriguing because it can change shape from a flat group to a bent group. In doing this, it provides more space around the metal for other molecules to bind. The result of this work shows that piano stool compounds created with this indenyl group are more active and selective for carrying out a catalytic reaction to make new ring systems that could have potential use in the synthesis of new flavorings, fragrances, and even pharmaceuticals.

Reinforced concrete (RC) moment frame structures make up a notable proportion of buildings in earthquake-prone regions in the United States and throughout the world. The beam-column (BC) joints are the most crucial regions in a RC moment frame structure as any deterioration of strength and/or stiffness in these areas can lead to global collapse of the structure. Thus, accurate simulations of the joint behavior are important for assessment of the local and global performance of both one-way and two-way interior BC joints. Such simulations can be used to study the flexural-shear-bond interaction, the failure modes, and sensitivity of various parameters of structural elements. Most of the existing analytical approaches for interior BC joints have either failed to account for the cyclic bond-slip behavior and the triaxial compressive state of confined concrete in the joint correctly or require so many calibrations on parameters as to render them impractical. The core motivation for this study is the need to develop robust models to test current design recommendations for 3D beam-column-slab subassemblies subjected to large drifts. The present study aims to first evaluate the flexural-shear-bond interactive behavior of two-way beam-column-slab interior connections by both finite element and nonlinear truss methodologies. The local performance such as bond-slip and strain history of reinforcing steel are compared with the experimental results for the first time. The reliability of applied finite element approach is evaluated against a series of one-way interior BC joints and a two-way interior beam-column-slab joint. The accuracy and efficiency of the nonlinear truss methodology is also evaluated by the same series of joints. Results show good agreement for finite element method against both global and local response, including hysteretic curve, local bond-slip development and beam longitudinal bar stress/strain distributions. The nonlinear truss model is also capable in obtaining satisfactory global response, especially in capturing large shear cracks. A parametric study is exhibited for a prototype two-way interior beam-column-slab joint described in an example to ACI 352R-02, to quantify several non-consensus topics in the design of interior BC connections, such as the joint shear force subjected to bidirectional cyclic loading, the development of bond-slip behavior, and the failure modes of two-way interior joints with slab. Results from connections with different levels of joint shear force subjected to unidirectional loading show that meeting the requirements from ACI 352 is essential to maintain the force transfer mechanism and the integrity of the joint. The connections achieved satisfactory performance under unidirectional loading, while the bidirectional monotonic loading decreases the joint shear force calculated by ACI 352 by 10%~26% based on current results. Poorer performance is obtained for wider beams and connections fail by shear in the joint rather than bond-slip behavior when subjected to bidirectional cyclic loading. In general, the study indicates that the ACI352-02 design methodology generally results in satisfactory performance when applied to 2D joints (planar) under monotonic and cyclic loads. Less satisfactory performance was found for cases of 3D joints with slabs. / Doctor of Philosophy / Reinforced concrete (RC) moment frames are one of the most popular structure types because of their economical construction and adaptable spaces. Moment frames consist of grid-like assemblages of vertical columns and horizontal beams joined by cruciform connections commonly labelled as beam-column joints. Because of the regularity of the grid and the ability to have long column spacing, moment frames are easy to form and cast and result in wide open bays that can be adapted and readapted to many uses. In RC structures, steel bars embedded in the concrete are used to take tensile forces, as concrete is relatively weak when loaded in tension. Forces are transferred between the steel and concrete components by so-called “bond” forces at the perimeter of the bars. The proper modeling of the behavior of bond forces inside the beam-column joints of reinforced concrete moment frames is the primary objective of this dissertation. Reinforced concrete moment frames constitute a notable proportion of the existing buildings in earthquake-prone regions in the United States and throughout the world. The beam-column joints are the most crucial elements in a RC moment frame structure as any deterioration of strength and/or stiffness in these areas can lead to global collapse of the structure. Physical experimentation is the most reliable means of studying the performance of beam-column joints. However, experimental tests are expensive and time-consuming. This is why computational simulation must always be used as a supplemental tool. Accurate simulations of the behavior of beam-column joints is important for assessment of the local and global behavior of beam-column joints. However, most of the existing analytical approaches for interior beam-column joints have either failed to account for the bond-slip behavior and the triaxial compressive state of confined concrete in the joint correctly or require so many calibration parameters as to render them impractical. The present study aims to provide reliable numerical methods for evaluating the behavior of two-way beam-column-slab interior joints. Two methods are developed. The v first method is a complex finite element model in which the beam-column joint is subdivided into many small 3D parts with the geometrical and material characteristics of each part carefully defined. Since the number of parts may be in the hundreds of thousands and the geometry and material behavior highly non-linear, setting up the problem and its solution of this problem requires large effort on the part of the structural engineer and long computation times in supercomputers. Finite element models of this type are generally accurate and are used to calibrate simpler models. The second method developed herein is a nonlinear truss analogy model. In this case the structure is modelled as nonlinear truss elements, or elements carrying only axial forces. When properly calibrated, this method can produce excellent results especially in capturing large shear cracks. To evaluate the accuracy and to quantify the current seismic design procedure for beam-column joints, a prototype two-way interior beam-column-slab joint described in an example to ACI 352R-02, the current design guide used for these elements in the USA, is analytically studied by the finite element methodology. The study indicates that the ACI352-02 design methodology generally results in satisfactory performance when applied to one-way (planar) joints under monotonic and cyclic loads. Less satisfactory performance was found for cases of three-dimensional (3D) joints with slabs.

In this work, we develop an interface-preserving level-set method in the finite-element framework for interfacial flows with moving contact lines. In our method, the contact line is advected naturally by the flow field. Contact angle hysteresis can be easily implemented without explicit calculation of the contact angle or the contact line velocity, and meshindependent results can be obtained following a simple computational strategy. We have implemented the method in three dimensions and provide numerical studies that compare well with analytical solutions to verify our algorithm. We first develop a high-order numerical method for interface-preserving level-set reinitialization. Within the interface cells, the gradient of the level set function is determined by a weighted local projection scheme and the missing additive constant is determined such that the position of the zero level set is preserved. For the non-interface cells, we compute the gradient of the level set function by solving a Hamilton-Jacobi equation as a conservation law system using the discontinuous Galerkin method. This follows the work by Hu and Shu [SIAM J. Sci. Comput. 21 (1999) 660-690]. The missing constant for these cells is recovered using the continuity of the level set function while taking into account the characteristics. To treat highly distorted initial conditions, we develop a hybrid numerical flux that combines the Lax-Friedrichs flux and a penalty flux. Our method is accurate for non-trivial test cases and handles singularities away from the interface very well. When derivative singularities are present on the interface, a second-derivative limiter is designed to suppress the oscillations. At least (N + 1)th order accuracy in the interface cells and Nth order accuracy in the whole domain are observed for smooth solutions when Nth degree polynomials are used. Two dimensional test cases are presented to demonstrate superior properties such as accuracy, long-term stability, interface-preserving capability, and easy treatment of contact lines. We then develop a level-set method in the finite-element framework. The contact line singularity is removed by the slip boundary condition proposed by Ren and E [Phys. Fluids, vol. 19, p. 022101, 2007], which has two friction coefficients: βN that controls the slip between the bulk fluids and the solid wall and βCL that controls the deviation of the microscopic dynamic contact angle from the static one. The predicted contact line dynamics from our method matches the Cox theory very well. We further find that the same slip length in the Cox theory can be reproduced by different combinations of (βN; βCL). This combination leads to a computational strategy for mesh-independent results that can match the experiments. There is no need to impose the contact angle condition geometrically, and the dynamic contact angle automatically emerges as part of the numerical solution. With a little modification, our method can also be used to compute contact angle hysteresis, where the tendency of contact line motion is readily available from the level-set function. Different test cases, including code validation and mesh-convergence study, are provided to demonstrate the efficiency and capability of our method. Lastly, we extend our method to three-dimensional simulations, where an extension equation is solved on the wall boundary to obtain the boundary condition for level-set reinitializaiton with contact lines. Reinitialization of ellipsoidal interfaces is presented to show the accuracy and stability of our method. In addition, simulations of a drop on an inclined wall are presented that are in agreement with theoretical results. / Doctor of Philosophy / When a liquid droplet is sliding along a solid surface, a moving contact line is formed at the intersection of the three phases: liquid, air and solid. This work develops a numerical method to study problems with moving contact lines. The partial differential equations describing the problem are solved by finite element methods. Our numerical method is validated against experiments and theories. Furthermore, we have implemented our method in three-dimensional problems.

An experimental technique for conducting low speed impact of adhesively bonded automotive composite joints is presented. Based on the use of a modified drop tower, mode I, II, and mixed mode values for critical energy release rate were determined for a composite/epoxy system and used to create a fracture failure envelope. Because load measurements become erratic and unreliable at higher test rates, displacement-based relationships were used to quantify these energy release rates. Displacement data was collected with an imaging system that utilized edge detection to determine displacement profiles, end displacements, and opening displacements where applicable. Because of the resolution of the image-based approach used, determining crack length experimentally was extremely difficult. As a result, numerical methods were developed to objectively determine the crack length based on the available experimental data in mode I, II, and mixed mode I/II configurations. This numerical method uses a nonlinear fit to determine mode I crack lengths and a theoretical model based on cubic equations for mode II and mixed-mode I/II, where the coefficients of the equations are determined by using both boundary and transition conditions that are a result of the test setup. A double cantilever beam (DCB) geometry was chosen to collect mode I data, an end-loaded split (ELS) geometry was used for mode II, and a single leg bend (SLB) geometry was used for mixed-mode I/II. These geometries were used to determine the fracture characteristics of adhesively bonded automotive composites to create fracture failure envelopes as well as provide mode I, II, and mixed-mode I/II data to be used in finite element models. The chosen adhesive exhibited unstable, stick-slip crack growth, which resulted in very few data points being collected from each static DCB specimen as well as drastic drops in energy release rate between initiation and arrest points. Unstable growth also created issues in dynamic testing, as data points surrounding these "stick-slip" events were lost due to the insufficient sampling rate of the available imaging system. Issues also arose with differences between thick and thin composite adherend specimens. These differences could result from additional curing in thick adherend composite specimens due to the adherends retaining heat. DSC testing was conducted on uncured adhesive using a 2, 5, and 10 minute hold at the cure temperature, and significant additional curing was observed between the two and five minute cures. Due to the difference in relative stiffness between the 12 and 36 ply composite, the local loading rate at the crack tip was lower in the 12 ply adherends, possibly allowing for a larger plastic zone and thus a higher energy release rate. As a result, tests were conducted on 36 ply composite specimens at rates of 1 mm/min and 0.1 mm/min to determine if there were loading rate effects. This testing showed that higher initiation energy relase rates were found at the lower test rate, thus reinforcing the local loading rate theory. Due to issues with plastic deformation in aluminum adherends, mode II and mixed-mode I/II data were collected using only composite adherends. Only one data point was collected per specimen as the crack propagated directly into the composite after initiating from the precrack, thus multiple tests were conducted to collect sufficient data for constructing a failure envelope. Once mode I, II and mixed-mode I/II fracture data was collected, a fracture failure envelope was created. This failure envelope, combined with a predetermined factor of safety, could provide some of the necessary tools for design with this adhesive/composite system. / Master of Science

The behavior of soils during surface fault rupture is a serious concern in the planning and design of infrastructure that may be located within or near a fault zone. Challenges associated with developing mitigation measures for surface fault rupture include the uncertainty of fault rupture and the variability of fault behavior. Current analytical procedures define surface fault rupture according to the type of fault movement (strike slip, normal or reverse), the amount of displacement on the fault, and the mechanics of the material overlying the fault. The purpose of this thesis is to reconfirm analytical solutions and gain a better understanding of the mechanics of dip slip surface fault rupture. Specifically, this study focuses on analyzing the influence of soil density/stiffness and fault angle on rupture propagation and distributed surface displacements. While direct experimental results are not obtained, a constructed fault box and planned trials inform a framework for predicting the outcomes of these trials using existing literature. These prior studies provide a basis for forecasting the surface deformation patterns and propagation behavior that the planned trials would have revealed, offering valuable insights into fault rupture mechanics. The fault box, a 2-meter-long by 0.5-meter-wide fault box filled with 0.45 meters of Monterey #2/16 sand, was designed to examine the factors that influence the rupture propagation of alluvial soils overlying dip slip faults. The faulting apparatus consists of a scissor jack mechanism that replicates basal displacement by moving one half of the box relative to the stationary half at interchangeable fault angles. Planned trials involved using Monterey #2/16 sand prepared configurations of dense, loose, and layered loose-over-dense material to represent different geological conditions. In these planned experiments, ruptures would be driven until a clear shear band developed in the overlying sand and reached the surface. By synthesizing findings from prior studies, this research predicts that dense sands create concentrated shear bands with larger surface displacements and distinct surface ruptures, while loose sands result in more diffuse deformations over broader shear bands with less defined surface expressions. Additionally, shallow fault angles result in broader deformation zones, as the lower angle directs stress over a wider area. In layered soil configurations, density contrasts further influence deformation patterns, with transitions between layers influencing the extent and localization of surface displacements. These findings demonstrate that fault orientation and soil density control the nature of surface fault rupture.

No description available.

[pt] Nesta tese, a teoria das hastes de Cosserat é revisitada e aplicada à dinâmica de coluna de perfuração. O objetivo é estudar o comportamento dessas estruturas dentro de poços de petróleo curvos. Para atingir este objetivo, um modelo estrutural determinístico é construído onde as tubos de perfuração (drill-pipes) e o conjunto de fundo (bottom hole assembly) são considerados como uma estrutura unidimensional de Cosserat. Em seguida, é desenvolvida uma estratégia para tratar o contato lateral em poços com configuração curvilínea. Depois disso, o problema de contorno livre é tratado mediante uma estratégia que considera como a condição de borda evolui à medida que a estrutura de perfuração avança. Isto é feito mediante uma formulação de interação broca-rocha que deve considerar a dinâmica de corte. Para isso, uma equação extra, de advecção, é resolvida junto com as equações de movimento de Cosserat. Em seguida, alguns casos de aplicação são apresentados. Numa primeira instancia, alguns elementos do problema são avaliados separadamente. Seguidamente, eles são integrados e analisados de forma conjunta. Por exemplo, primeiramente uma coluna de perfuração sem contato de fundo (off-bottom) é simulada, ou seja, sem contato broca-rocha, para estudar o comportamento e a implementação da estratégia para o contato lateral. Aqui também são calibrados alguns dos parâmetros do modelo de atrito. Em seguida, a estratégia para contabilizar o corte na rocha é implementada em um modelo 2-DOF de baixa dimensão e em um semi-discreto onde a dinâmica de torção é modelada como uma equação de onda. Os resultados mostram que o uso de abordagens contínuas resulta mais apropriade que aquelas onde se utilizam modelos de baixa dimensãom, particularmente quando são consideradas colunas longas, e quando há interesse em analisar não apenas o comportamento da broca, mas também o comportamento do sistema mecânico ao longo dos tubos de perfuração. Isso é reforçado por outro exemplo onde a dinâmica de corte é combinada com a formulação de Cosserat. Observações semelhantes do ponto de vista qualitativo são encontradas. Resumindo os resultados obtidos, as diferenças nas previsões dadas pelos modelos de baixa dimensão e o de unidimensional de Cosserat justificam o desenvolvimento e aplicação da abordagem com esta formulação em estruturas de perfuração. Finalmente, a modo de introduzir outro aspecto importante em colunas de perfuração e que pode ser uma linha de pesquisa para continuar o trabalho, a variabilidades presente em elementos como rocha, inclui-se um caso de aplicação considerando um poço horizontal e um campo estocástico de atrito. / [en] In this thesis, the theory of Cosserat rods is applied to the dynamics of drill-strings. The main objective is to evaluate the behaviour of these strings when they move within curved wells. To achieve this goal, a deterministic structural model is constructed, where the drill-pipes and the bottom hole assembly are taken as a Cosserat rod. Next, a strategy to deal with the lateral contact in curved well configurations is developed. After that, the free boundary problem is assessed: while drilling, the boundary changes due to cutting, modifying the position of the soil and, consequently, changing the bit-rock interaction forces. For this reason, a bit-rock model that can account for the cutting dynamics is adopted, in which an extra advection equation is solved together with the equations of motion of the Cosserat rod. Next, application cases are provided. First, some effects included in the model are tested in isolation, such as the lateral friction, the lateral contact, and the cutting. After that, they are all combined. In the first analysis, an off-bottom string is simulated, i.e. without contact at the bit. This allows testing the formulation associated with the lateral contact. Also, the calibration of the lateral friction parameters is made. Following that, the strategy to account for the cutting at the bit is implemented in a low-dimensional 2-DOF model, and in a semi-discrete model with a continuous wave equation for the torsional dynamics. The results show that the use of continuous approaches is more appropriate than low-dimensional models. Especially when long columns are considered, and when there is interest in understanding not only the behaviour at the bit but also along drill-pipes. This finding is reinforced by another application where the cutting dynamics are combined with the Cosserat rod formulation. Again, similar observations from a qualitative point of view are found. Overall, the differences in the results between the lumped low-dimensional models and the continuous Cosserat rod justify the development and application of the Cosserat approach to drilling structures. Finally, an introductory stochastic analysis concerning the variability of the rock is presented as an introduction to a future line of research, where stochasticity is included. / [es] En esta tesis, la teoria de Cosserat para elementos unidimensionales es revisitada y aplicada a la simulación de columnas de perforación. El objetivo es estudiar el comportamiento de estas estructuras en pozos de geometría curva. Para alcanzar este objetivo se construye un modelo determinístico. En este modelo, los caños de perforación (drill-pipes) y el conjunto de fondo (bottom hole assembly) son modelados como una estructura unidimensional de Cosserat. Seguidamente, una estrategia para tratar con el contacto lateral en pozos curvos es desarrollada. Luego, el problema de frontera libre es estudiado: durante la perforación, la condición de borde cambia debido al cambio del perfil altimétrico del terreno, alterando su posición y consecuentemente las fuerzas asociadas a la interacción broca-roca. Por esta razón, se decide utilizar un modelo de interacción broca-roca que tiene en cuenta la dinámica del corte. En este abordaje una ecuación extra, la ecuación de advección, es resuelta en forma acoplada con las ecuaciones del movimiento de la estructura de Cosserat. Algunos ejemplos de aplicación son presentados. En una primera instancia, algunos de los elementos del problema son estudiados en forma aislada. Luego combinados en un modelo completo. Por ejemplo, el caso de una columna sin contacto de fondo (off-bottom) es tratado para evaluar el comportamiento y la implementación de la estrategia mencionada para detectar el contacto lateral. Además, se efectúa la calibración de alguno de los parámetros relacionados con la fricción lateral. Luego, la estrategia para considerar el corte en la punta es implementada en un modelo de 2-DOF, y en otro semi-discreto donde se considera un modelo de ecuación de onda para la dinámica torsional. Los resultados muestran que el uso de formulaciones continuas es más apropiado que aquellas formulaciones donde se utilizan modelos de dimensiones reducidas, particularmente cuando se estudia columnas largas donde el interés se centra en entender no solo el comportamiento de la broca sino también a lo largo de la tubería. Este resultado es reforzado por otro caso de aplicación en donde se combina la dinámica de corte con un modelo de Cosserat. Observaciones similares son vistas en el comportamiento cualitativo de la solución. En resumen, las diferencias observadas en los diferentes ejemplos de aplicación entre los modelos de dimensiones reducidas y el modelo continuo de Cosserat justifican el desarrollo y la aplicación de la teoría de Cosserat a estructuras de perforación. Finalmente, dado que uno de los objetivos planteados también es considerar la variabilidad en algunos elementos como ser las propiedades de la roca, un caso de aplicación considerando un pozo horizontal es mostrado.

This research investigates the modeling of randomly distributed surface-breaking microcracks and their effects on higher harmonic generation in Rayleigh surface waves. The modeling is based on micromechanical considerations of rough surface contact. The nonlinear behavior of a single microcrack is described by a hyperelastic effective stress-strain relationship. Finite element simulations of nonlinear wave propagation in a solid with distributed microcracks are performed. The evolution of fundamental and second harmonic amplitudes along the propagation distance is studied and the acoustic nonlinearity parameter is calculated. The results show that the nonlinearity parameter increases with crack density and root mean square roughness of the crack faces. While, for a dilute concentration of microcracks, the increase in acoustic nonlinearity is proportional to the crack density, this is not valid for higher crack densities, as the microcracks start to interact. Finally, it is shown that odd higher harmonic generation in Rayleigh surface waves due to sliding crack faces introduces a friction nonlinearity.