Comportamiento estructural de elementos de f��brica reforzados con materiales compuestos avanzados solicitados a flexi��n y flexocompresi��n

El refuerzo de estructuras existentes mediante el encolado exterior de l��minas de pol��meros reforzados con fibras (FRP) se ha convertido en la aplicaci��n m��s com��n de los materiales compuestos avanzados en construcci��n. Estos materiales presentan muchas ventajas frente a los materiales convencionales (sin corrosi��n, ligeros, de f��cil aplicaci��n, etc.). Pero a pesar de las numerosas investigaciones realizadas, a��n persisten ciertas dudas sobre algunos aspectos de su comportamiento y las aplicaciones pr��cticas se llevan a cabo s��lo con la ayuda de gu��as, sin que haya una normativa oficial. El objetivo de este trabajo es incrementar el conocimiento sobre esta t��cnica de refuerzo, y m��s concretamente, sobre el refuerzo a flexi��n de estructuras de f��brica. Con frecuencia el elemento reforzado es de hormig��n armado y las l��minas de FRP encoladas al exterior sirven para mejorar su resistencia a flexi��n, cortante o compresi��n (encamisados). Sin embargo su empleo en otros materiales como las estructuras de f��brica resulta muy prometedor. Las f��bricas se caracterizan por soportar muy bien los esfuerzos de compresi��n pero bastante mal los de tracci��n. Adherir l��minas de materiales compuestos puede servir para mejorar la capacidad resistente de elementos de f��brica sometidos a esfuerzos de flexi��n. Pero para ello, debe quedar garantizada una correcta adherencia entre el FRP y la f��brica, especialmente en edificios antiguos cuya superficie puede estar deteriorada por encontrarse a la intemperie o por el propio paso del tiempo. En el cap��tulo II se describen los objetivos fundamentales del trabajo y el m��todo seguido. En el cap��tulo III se hace una amplia revisi��n del estado de conocimiento sobre el tema. En el apartado III.1 se detallan las principales caracter��sticas y propiedades mec��nicas de fibras, matrices y materiales compuestos as�� como sus principales aplicaciones, haciendo especial hincapi�� en aspectos relativos a su durabilidad. En el apartado III.2 se incluye una revisi��n hist��rica de las l��neas de investigaci��n, tanto te��ricas como emp��ricas, publicadas sobre estructuras de hormig��n reforzadas a flexi��n encolando materiales compuestos. El apartado III.3 se centra en el aspecto fundamental de la adherencia refuerzo-soporte. Se hace un repaso a distintos modelos propuestos para prevenir el despegue distinguiendo si ��ste se inicia en la zona de anclaje o si est�� inducido por fisuras en la zona interior del elemento. Se observa falta de consenso en las propuestas. Adem��s en este punto se relatan las campa��as experimentales publicadas acerca de la adherencia entre materiales compuestos y f��bricas. En el apartado III.4 se analizan las particularidades de las estructuras de f��brica. Adem��s, se revisan algunas de las investigaciones relativas a la mejora de su comportamiento a flexi��n mediante l��minas de FRP. El comportamiento mec��nico de muros reforzados solicitados a flexi��n pura (sin compresi��n) ha sido documentado por varios autores, si bien es una situaci��n poco frecuente en f��bricas reales. Ni el comportamiento mec��nico de muros reforzados solicitados a flexocompresi��n ni la incidencia que el nivel de compresi��n soportado por la f��brica tiene sobre la capacidad resistente del elemento reforzado han sido suficientemente tratados. En cuanto a los trabajos te��ricos, las diferentes propuestas se basan en los m��todos utilizados para hormig��n armado y comparten los principios habituales de c��lculo. Sin embargo, presentan diferencias relativas, sobre todo, a tres aspectos: 1) la forma de modelar el comportamiento de la f��brica, 2) el valor de deformaci��n de c��lculo del refuerzo, y 3) el modo de fallo que se considera recomendable buscar con el dise��o. A pesar de ello, el ajuste con la parte experimental de cada trabajo suele ser bueno debido a una enorme disparidad en las variables consideradas. Cada campa��a presenta un modo de fallo caracter��stico y la formulaci��n que se propone resulta apropiada para ��l. Parece necesario desarrollar un m��todo de c��lculo para f��bricas flexocomprimidas reforzadas con FRP que pueda ser utilizado para todos los posibles fallos, tanto atribuibles a la l��mina como a la f��brica. En el apartado III.4 se repasan algunas lesiones habituales en f��bricas solicitadas a flexi��n y se recogen ejemplos de refuerzos con FRP para reparar o prevenir estos da��os. Para mejorar el conocimiento sobre el tema, se llevan a cabo dos peque��as campa��as experimentales realizadas en el Instituto de Ciencias de la Construcci��n Eduardo Torroja. La primera acerca de la adherencia de materiales compuestos encolados a f��bricas deterioradas (apartado IV.1) y la segunda sobre el comportamiento estructural a flexocompresi��n de probetas de f��brica reforzadas con estos materiales (apartado IV.2). En el cap��tulo V se analizan algunos de los modelos de adherencia propuestos para prevenir el despegue del extremo del refuerzo. Se confirma que las predicciones obtenidas con ellos resultan muy dispares. Se recopila una base de datos con los resultados experimentales de campa��as sobre adherencia de FRP a f��bricas extra��das de la literatura y de los resultados propios de la campa��a descrita en el punto IV.1. Esta base de datos permite conocer cual de los m��todos analizados resulta m��s adecuado para dimensionar el anclaje de l��minas de FRP adheridas a f��bricas. En el cap��tulo VI se propone un m��todo para la comprobaci��n en agotamiento de secciones de f��brica reforzadas con materiales compuestos sometidas a esfuerzos combinados de flexi��n y compresi��n. Est�� basado en el procedimiento de c��lculo de la capacidad resistente de secciones de hormig��n armado pero adaptado a las f��bricas reforzadas. Para ello, se utiliza un diagrama de c��lculo tensi��n deformaci��n de la f��brica de tipo bilineal (acorde con el CTE DB SE-F) cuya simplicidad facilita el desarrollo de toda la formulaci��n al tiempo que resulta adecuado para predecir la capacidad resistente a flexi��n tanto para fallos debidos al refuerzo como a la f��brica. Adem��s se limita la deformaci��n de c��lculo del refuerzo teniendo en consideraci��n ciertos aspectos que provocan que la l��mina adherida no pueda desarrollar toda su resistencia, como el desprendimiento inducido por fisuras en el interior del elemento o el deterioro medioambiental. En concreto, se propone un ���coeficiente reductor por adherencia��� que se determina a partir de una base de datos con 68 resultados experimentales procedentes de publicaciones de varios autores y de los ensayos propios de la campa��a descrita en el punto IV.2. Tambi��n se revisa la formulaci��n propuesta con ayuda de la base de datos. En el cap��tulo VII se estudia la incidencia de las principales variables, como el axil, la deformaci��n de c��lculo del refuerzo o su rigidez, en la capacidad final del elemento. Las conclusiones del trabajo realizado y las posibles l��neas futuras de investigaci��n se exponen en el cap��tulo VIII. ABSTRACT Strengthening of existing structures with externally bonded fiber reinforced polymers (FRP) has become the most common application of advanced composite materials in construction. These materials exhibit many advantages in comparison with traditional ones (corrosion resistance, light weight, easy to apply, etc.). But despite countless researches have been done, there are still doubts about some aspects of their behaviour and applications are carried out only with the help of guidelines, without official regulations. The aim of this work is to improve the knowledge on this retrofitting technique, particularly in regard to flexural strengthening of masonry structures. Reinforced concrete is often the strengthened material and external glued FRP plates are used to improve its flexural, shear or compressive (by wrapping) capacity. However the use of this technique on other materials like masonry structures looks promising. Unreinforced masonry is characterized for being a good material to support compressive stresses but really bad to withstand tensile ones. Glue composite plates can improve the flexural capacity of masonry elements subject to bending. But a proper bond between FRP sheet and masonry must be ensured to do that, especially in old buildings whose surface can be damaged due to being outside or ageing. The main objectives of the work and the methodology carried out are described In Chapter II. An extensive overview of the state of art is done in Chapter III. In Section III.1 physical and mechanical properties of fibers, matrix and composites and their main applications are related. Durability aspects are especially emphasized. Section III.2 includes an historical overview of theoretical and empirical researches on concrete structures strengthened gluing FRP plates to improve their flexural behaviour. Section III.3 focuses on the critical point of bonding between FRP and substrate. Some theoretical models to prevent debonding of FRP laminate are reviewed, it has made a distinction between models for detachment at the end of the plate or debonding in the intermediate zones due to the effects of cracks. It is observed a lack of agreement in the proposals. Some experimental studies on bonding between masonry and FRP are also related in this chapter. The particular characteristics of masonry structures are analyzed in Section III.4. Besides some empirical and theoretical investigations relative to improve their flexural capacity with FRP sheets are reviewed. The mechanical behaviour of strengthened walls subject to pure bending (without compression) has been established by several authors, but this is an unusual situation for real masonry. Neither mechanical behaviour of walls subject to bending and compression nor influence of axial load in the final capacity of the strengthened element are adequately studied. In regard to theoretical studies, the different proposals are based on reinforced concrete analytical methods and share common design principles. However, they present differences, especially, about three aspects: 1) the constitutive law of masonry, 2) the value of ultimate FRP strain and 3) the desirable failure mode that must be looked for. In spite of them, a good agreement between each experimental program and its theoretical study is often exhibited due to enormous disparity in considered test parameters. Each experimental program usually presents a characteristic failure mode and the proposed formulation results appropriate for this one. It seems necessary to develop a method for FRP strengthened walls subject to bending and compression enable for all failure modes (due to FRP or masonry). Some common damages in masonry subject to bending are explained in Section III.4. Examples of FRP strengthening to repair or prevent these damages are also written. Two small experimental programs are carried out in Eduardo Torroja Institute to improve the knowledge on this topic. The first one is concerned about the bond between FRP plates and damaged masonry (section IV.1) and the second one is related to the mechanical behaviour of the strengthened masonry specimens subject to out of plane bending combined with axial force (section IV.2). In the Chapter V some bond models to prevent the debonding at the FRP plate end are checked. It is confirmed that their predictions are so different. A pure-shear test database is compiled with results from the existing literature and others from the experimental program described in section IV.1. This database lets know which of the considered model is more suitable to design anchorage lengths of glued FRP to masonry. In the Chapter VI a method to check unreinforced masonry sections with external FRP strengthening subject to bending and compression to the ultimate limit state is proposed. This method is based on concrete reinforced one, but it is adapted to strengthened masonry. A bilinear constitutive law is used for masonry (according to CTE DB SE-F). Its simplicity helps to develop the model formulation and it has proven to be suitable to predict bending capacity either for FRP failures or masonry crushing. With regard to FRP, the design strain is limited. It is taken into account different aspects which cause the plate can���t reach its ultimate strength, like intermediate FRP debonding induced by opening cracking or environmental damage. A ���bond factor��� is proposed. It is obtained by means of an experimental bending test database that includes 68 results from the existing literature and from the experimental program described in section IV.2. The proposed formulation has also been checked with the help of bending database. The effects of the main parameters, like axial load, FRP design effective strain or FRP stiffness, on the bending capacity of the strengthened element are studied in Chapter VII. Finally, the main conclusions from the work carried out are summarized in Chapter VIII. Future lines of research to be explored are suggested as well.

Polypropylene/glass fiber hierarchical composites incorporating inorganic fullerene-like nanoparticles for advanced technological applications

Novel isotactic polypropylene (iPP)/glass fiber (GF) laminates reinforced with inorganic fullerene-like tungsten disulfide (IF-WS2) nanoparticles as environmentally friendly fillers have been successfully fabricated by simple melt-blending and fiber impregnation in a hot-press without the addition of any compatibilizer. The influence of IF-WS2 concentration on the morphology, viscosity. and thermal and mechanical behavior of the hierarchical composites has been investigated. Results revealed an unprecedented 62 ��C increase in the degradation temperature of iPP/GF upon addition of only 4.0 wt % IF-WS2. The coexistence of both micro- and nanoscale fillers resulted in synergistic effects on enhancing the stiffness, strength, crystallinity, thermal stability, glass transition (Tg) and heat distortion temperature (HDT) of the matrix. The approach used in this work is an efficient, versatile, scalable and economic strategy to improve the mechanical and thermal behavior of GF-reinforced thermoplastics with a view to extend their use in advanced technological applications. This new type of composite materials shows great potential to improve the efficiency and sustainability of many forms of transport.

Microstructure and mechanical properties at high temperature of SiC-matrix by electrophoretic deposition and polymer infiltration and pyrolysis process

The EFDA-ITER programme for materials wants to develop new structural materials for future nuclear magnetic fusion reactors. In this context, special attention must be paid in the development of new composite materials that could support the hard working conditions of the nuclear fusion reactors: high temperature, high stresses, and high radiation.

High fidelity simulations of failure in fiber-reinforced composites

Los ensayos virtuales de materiales compuestos han aparecido como un nuevo concepto dentro de la industria aeroespacial, y disponen de un vasto potencial para reducir los enormes costes de certificaci��n y desarrollo asociados con las tediosas campa��as experimentales, que incluyen un gran n��mero de paneles, subcomponentes y componentes. El objetivo de los ensayos virtuales es sustituir algunos ensayos por simulaciones computacionales con alta fidelidad. Esta tesis es una contribuci��n a la aproximaci��n multiescala desarrollada en el Instituto IMDEA Materiales para predecir el comportamiento mec��nico de un laminado de material compuesto dadas las propiedades de la l��mina y la intercara. La mec��nica de da��o continuo (CDM) formula el da��o intralaminar a nivel constitutivo de material. El modelo de da��o intralaminar se combina con elementos cohesivos para representar da��o interlaminar. Se desarroll�� e implement�� un modelo de da��o continuo, y se aplic�� a configuraciones simples de ensayos en laminados: impactos de baja y alta velocidad, ensayos de tracci��n, tests a cortadura. El an��lisis del m��todo y la correlaci��n con experimentos sugiere que los m��todos son razonablemente adecuados para los test de impacto, pero insuficientes para el resto de ensayos. Para superar estas limitaciones de CDM, se ha mejorado la aproximaci��n discreta de elementos finitos enriqueciendo la cinem��tica para incluir discontinuidades embebidas: el m��todo extendido de los elementos finitos (X-FEM). Se adapt�� X-FEM para un esquema expl��cito de integraci��n temporal. El m��todo es capaz de representar cualitativamente los mecanismos de fallo detallados en laminados. Sin embargo, los resultados muestran inconsistencias en la formulaci��n que producen resultados cuantitativos err��neos. Por ��ltimo, se ha revisado el m��todo tradicional de X-FEM, y se ha desarrollado un nuevo m��todo para superar sus limitaciones: el m��todo cohesivo X-FEM estable. Las propiedades del nuevo m��todo se estudiaron en detalle, y se concluy�� que el m��todo es robusto para implementaci��n en c��digos expl��citos din��micos escalables, resultando una nueva herramienta ��til para la simulaci��n de da��o en composites. Virtual testing of composite materials has emerged as a new concept within the aerospace industry. It presents a very large potential to reduce the large certification costs and the long development times associated with the experimental campaigns, involving the testing of a large number of panels, sub-components and components. The aim of virtual testing is to replace some experimental tests by high-fidelity numerical simulations. This work is a contribution to the multiscale approach developed in Institute IMDEA Materials to predict the mechanical behavior of a composite laminate from the properties of the ply and the interply. Continuum Damage Mechanics (CDM) formulates intraply damage at the the material constitutive level. Intraply CDM is combined with cohesive elements to model interply damage. A CDM model was developed, implemented, and applied to simple mechanical tests of laminates: low and high velocity impact, tension of coupons, and shear deformation. The analysis of the results and the comparison with experiments indicated that the performance was reasonably good for the impact tests, but insuficient in the other cases. To overcome the limitations of CDM, the kinematics of the discrete finite element approximation was enhanced to include mesh embedded discontinuities, the eXtended Finite Element Method (X-FEM). The X-FEM was adapted to an explicit time integration scheme and was able to reproduce qualitatively the physical failure mechanisms in a composite laminate. However, the results revealed an inconsistency in the formulation that leads to erroneous quantitative results. Finally, the traditional X-FEM was reviewed, and a new method was developed to overcome its limitations, the stable cohesive X-FEM. The properties of the new method were studied in detail, and it was demonstrated that the new method was robust and can be implemented in a explicit finite element formulation, providing a new tool for damage simulation in composite materials.

Optimizaci��n de la densidad de energ��a en vigas de material compuesto (PRF) sometidas a flexi��n pura

Las necesidades energ��ticas actuales requieren el desarrollo de tecnolog��as eficaces y eficientes en producci��n, transporte y distribuci��n de energ��a. Estas necesidades han impulsado nuevos desarrollos en el ��mbito energ��tico, entre los cuales se encuentran sistemas de almacenamiento de energ��a. El avance en ingenier��a de materiales permite pensar en la posibilidad de almacenamiento mediante deformaci��n el��stica de vigas. Concretamente se parte de un concepto de mecanismo acumulador de energ��a basado en la deformaci��n el��stica de resortes espirales a torsi��n. Dichos resortes se pueden considerar como elementos vigas sometidos a flexi��n pura y grandes deflexiones. Esta Tesis de centra en el dise��o y optimizaci��n de estos elementos con el fin de maximizar la densidad de energ��a que son capaces de absorber. El proceso de optimizaci��n comienza con la identificaci��n del factor cr��tico del que depende dicho proceso, en este caso de trata de la densidad de energ��a. Dicho factor depende de la geometr��a de la secci��n resistente y del material empleado en su construcci��n. En los ��ltimos a��os ha existido un gran desarrollo de los materiales compuestos de tipo polim��rico reforzados con fibras (PRF). Estos materiales est��n sustituyendo gradualmente a otros materiales, como los metales, debido principalmente a su excelente relaci��n entre propiedades mec��nicas y peso. Por otro lado, analizando las posibles geometr��as para la secci��n resistente, se observ�� que la m��s adecuada es una estructura tipo s��ndwich. Se implementa as�� un procedimiento de dise��o de vigas s��ndwich sometidas a flexi��n pura, con las pieles fabricadas en materiales compuestos tipo PRF y un n��cleo que debe garantizar el bajo peso de la estructura. Se desarrolla as�� un procedimiento sistem��tico que se puede particularizar dependiendo de los par��metros de entrada de la viga, y que tiene en cuenta y analiza la aparici��n de todos los posibles modos de fallo posibles. As�� mismo se desarrollan una serie de mapas o ��bacos de dise��o que permiten seleccionar r��pidamente las dimensiones preliminares de la viga. Finalmente se llevan a cabo ensayos que permiten, por un lado, validar el concepto del mecanismo acumulador de energ��a a trav��s del ensayo de un muelle con secci��n monol��tica, y por otro validar los distintos dise��os de vigas s��ndwich propuestos y mostrar el incremento de la densidad de energ��a con respecto a la alternativa monol��tica. Como l��neas futuras de investigaci��n se plantean la investigaci��n en nuevos materiales, como la utilizaci��n de nanotubos de carbono, y la optimizaci��n del mecanismo de absorci��n de energ��a; optimizando el mecanismo de absorci��n a flexi��n pura e implementando sistemas que permitan acumular energ��a mediante la deformaci��n el��stica debida a esfuerzos de tracci��n-compresi��n. ABSTRACT Energy supply requires the development of effective and efficient technologies for the production, transport and distribution of energy. In recent years, many energy storage systems have been developed. Advances in the field of materials engineering has allowed the development of new concepts as the energy storage by elastic deformation of beams. Particularly, in this Thesis an energy storage device based on the elastic deformation of torsional springs has been studied. These springs can be considered as beam elements subjected to pure bending loads and large deflections. This Thesis is focused on the design and optimization of these beam elements in order to maximize its density of stored energy. The optimization process starts with the identification of the critical factors for the elastic energy storage: the density. This factor depends on the geometry of the cross section of the beam and the materials from which it is made. In the last 20 years, major advances in the field of composite materials have been made, particularly in the field of fiber reinforced polymers (FRP). This type of material is substituting gradually metallic materials to their excellent weight-mechanical properties ratio. In the other side, several possible geometries are analyzed for its use in the cross section of the beam; it was concluded that the best option, for maximum energy density, is using a sandwich beam. A design procedure for sandwich beams with skins made up with FRP composites and a light weight core is developed. This procedure can be particularized for different input parameters and it analyzes all the possible failure modes. Abacus and failure mode maps have been developed in order to simplify the design process. Finally several tested was made. Firstly, a prototype of the energy storage system which uses a monolithic composite beam was tested in order to validate the concept of the energy storage by elastic deformation. After that sandwich beam samples are built and tested, validating the design and showing the increase of energy density with respect to the monolithic beam. As futures research lines the following are proposed: research in new materials, as carbon nanotubes; and the optimization of the energy storage mechanism, that means optimizing the pure bending storage mechanism and developing new ones based on traction-compression mechanisms.

Methodology based on FBG sensors for monitoring of FRP-strengthened beams

Advanced composite materials are increasingly used in the strengthening of reinforced concrete (RC) structures. The use of externally bonded strips made of fibre-reinforced plastics (FRP) as strengthening method has gained widespread acceptance in recent years since it has many advantages over the traditional techniques. However, unfortunately, this strengthening method is often associated with a brittle and sudden failure caused by some form of FRP bond failure, originated at the termination of the FRP material or at intermediate areas in the vicinity of flexural cracks in the RC beam. Up to date, little effort in the early prediction of the debonding in its initial instants even though this effect is not noticeable by simple visual observation. An early detection of this phenomenon might help in taking actions to prevent future catastrophes. Fibre-optic Bragg grating (FBG) sensors are able to measure strains locally with high resolution and accuracy. Furthermore, as their physical size is extremely small compared with other strain measuring components, it enables to be embedded at the concrete-FRP interface for determining the strain distribution without influencing the mechanical properties of the host materials. This paper shows the development of a debonding identification methodology based on strains experimentally measured. For, it a simplified model is implemented to simulate the behaviour of FRP-strengthened reinforced concrete beams. This model is taken as a basis to. develop an model updating procedure able to detect minor debonding at the concrete-FRP interface from experimental strains obtained by using FBG sensors embedded at the interface

Hierarchical and hybrid polymer nanocomposites based on carbon nanotubes and inorganic fullerene type nanoparticles

The influence of singlewalled carbon nanotubes (SWCNT) and inorganic fullerenelike tungsten disulfide nanoparticles (IFWS2) on the morphology and thermal, mechanical and electrical performance of multifunctional fibrereinforced polymer composites has been investigated. Significant improvements were observed in stiffness, strength and toughness in poly (ether ether ketone) (PEEK) / (SWCNT) / glass fibre (GF) laminates when a compatibilizer was used for wrapping the CNTs. Hybrid poly(phenylene sulphide) (PPS)/IFWS2/ carbon fibre (CF) reinforced polymer composites showed improved mechanical and tribological properties attributed to a synergetic effect between the IF nanoparticles and CF.

Thermoplastic Polymer Nanocomposites Based on Inorganic Fullerene-like Nanoparticles and Inorganic Nanotubes

Using inorganic fullerene-like (IF) nanoparticles and inorganic nanotubes (INT) in organic-inorganic hybrid composite, materials provide the potential for improving thermal, mechanical, and tribological properties of conventional composites. The processing of such high-performance hybrid thermoplastic polymer nanocomposites is achieved via melt-blending without the aid of any modifier or compatibilizing agent. The incorporation of small quantities (0.1-4 wt.%) of IF/INTs (tungsten disulfide, IF-WS2 or molybdenum disulfide, MoS2) generates notable performance enhancements through reinforcement effects and excellent lubricating ability in comparison with promising carbon nanotubes or other inorganic nanoscale fillers. It was shown that these IF/INT nanocomposites can provide an effective balance between performance, cost effectiveness, and processability, which is of significant importance for extending the practical applications of diverse hierarchical thermoplastic-based composites.

An��lisis param��trico determinista y aleatorio de problemas din��micos en estructuras aeroespaciales

Los fen��menos din��micos pueden poner en peligro la integridad de estructuras aeroespaciales y los ingenieros han desarrollado diferentes estrategias para analizarlos. Uno de los grandes problemas que se plantean en la ingenier��a es c��mo atacar un problema din��mico estructural. En la presente tesis se plantean distintos fen��menos din��micos y se proponen m��todos para estimar o simular sus comportamientos mediante un an��lisis param��trico determinista y aleatorio del problema. Se han propuesto desde problemas sencillos con pocos grados de libertad que sirven para analizar las diferentes estrategias y herramientas a utilizar, hasta fen��menos muy din��micos que contienen comportamientos no lineales, da��os y fallos. Los primeros ejemplos de investigaci��n planteados cubren una amplia gama de los fen��menos din��micos, como el an��lisis de vibraciones de elementos m��sicos, incluyendo impactos y contactos, y el an��lisis de una viga con carga arm��nica aplicada a la que tambi��n se le a��aden par��metros aleatorios que pueden responder a un desconocimiento o incertidumbre de los mismos. Durante el desarrollo de la tesis se introducen conceptos y se aplican distintos m��todos, como el m��todo de elementos finitos (FEM) en el que se analiza su resoluci��n tanto por esquemas impl��citos como expl��citos, y m��todos de an��lisis param��tricos y estad��sticos mediante la t��cnica de Monte Carlo. M��s adelante, una vez ya planteadas las herramientas y estrategias de an��lisis, se estudian fen��menos m��s complejos, como el impacto a baja velocidad en materiales compuestos, en el que se busca evaluar la resistencia residual y, por lo tanto, la tolerancia al da��o de la estructura. Se trata de un suceso que puede producirse por la ca��da de herramienta, granizo o restos en la pista de aterrizaje. Otro de los fen��menos analizados tambi��n se da en un aeropuerto y se trata de la colisi��n con un dispositivo frangible, el cual tiene que romperse bajo ciertas cargas y, sin embargo, soportar otras. Finalmente, se aplica toda la metodolog��a planteada en simular y analizar un posible incidente en vuelo, el fen��meno de la p��rdida de pala de un turboh��lice. Se trata de un suceso muy particular en el que la estructura tiene que soportar unas cargas complejas y excepcionales con las que la aeronave debe ser capaz de completar con ��xito el vuelo. El an��lisis incluye comportamientos no lineales, da��os, y varios tipos de fallos, y en el que se trata de identificar los par��metros clave en la secuencia del fallo. El suceso se analiza mediante an��lisis estructurales deterministas m��s habituales y tambi��n mediante otras t��cnicas como el m��todo de Monte Carlo con el que se logran estudiar distintas incertidumbres en los par��metros con variables aleatorias. Se estudian, entre otros, el tama��o de pala perdida, la velocidad y el momento en el que se produce la rotura, y la rigidez y resistencia de los apoyos del motor. Se tiene en cuenta incluso el amortiguamiento estructural del sistema. Las distintas estrategias de an��lisis permiten obtener unos resultados valiosos e interesantes que han sido objeto de distintas publicaciones. ABSTRACT Dynamic phenomena can endanger the integrity of aerospace structures and, consequently, engineers have developed different strategies to analyze them. One of the major engineering problems is how to deal with the structural dynamics. In this thesis, different dynamic phenomena are introduced and several methods are proposed to estimate or simulate their behaviors. The analysis is considered through parametric, deterministic and statistical methods. The suggested issues are from simple problems with few degrees of freedom, in order to develop different strategies and tools to solve them, to very dynamic phenomena containing nonlinear behaviors failures, damages. The first examples cover a wide variety of dynamic phenomena such as vibration analysis of mass elements, including impacts and contacts, and beam analysis with harmonic load applied, in which random parameters are included. These parameters can represent the unawareness or uncertainty of certain variables. During the development of the thesis several concepts are introduced and different methods are applied, such as the finite element method (FEM), which is solved through implicit and explicit schemes, and parametrical and statistical methods using the Monte Carlo analysis technique. Next, once the tools and strategies of analysis are set out more complex phenomena are studied. This is the case of a low-speed impact in composite materials, the residual strength of the structure is evaluated, and therefore, its damage tolerance. This incident may occur from a tool dropped, hail or debris throw on the runway. At an airport may also occur, and it is also analyzed, a collision between an airplane and a frangible device. The devise must brake under these loads, however, it must withstand others. Finally, all the considered methodology is applied to simulate and analyze a flight incident, the blade loss phenomenon of a turboprop. In this particular event the structure must support complex and exceptional loads and the aircraft must be able to successfully complete the flight. Nonlinear behavior, damage, and different types of failures are included in the analysis, in which the key parameters in the failure sequence are identified. The incident is analyzed by deterministic structural analysis and also by other techniques such as Monte Carlo method, in which it is possible to include different parametric uncertainties through random variables. Some of the evaluated parameters are, among others, the blade loss size, propeller rotational frequency, speed and angular position where the blade is lost, and the stiffness and strength of the engine mounts. The study does also research on the structural damping of the system. The different strategies of analysis obtain valuable and interesting results that have been already published.

Fatiga en CFRP: Caracterizaci��n y M��todo ��ptico para la Estimaci��n del Da��o

El desarrollo de nuevas estructuras aeroespaciales optimizadas, utilizan materiales compuestos, para los componentes cr��ticos y subsistemas, principalmente pol��meros reforzados con fibra de carbono (CFRP). Un conocimiento profundo del estado de da��o por fatiga de estructuras de CFRP avanzado, es esencial para predecir la vida residual y optimizar los intervalos de inspecci��n estructural, reparaciones y/o sustituci��n de componentes. Las t��cnicas actuales se basan principalmente en la medici��n de cargas estructurales a lo largo de la vida ��til de la estructura mediante galgas extensom��tricas el��ctricas. Con esos datos, se estima la vida a fatiga utilizando modelos de acumulaci��n de da��o. En la presente tesis, se eval��a la metodolog��a convencional para la estimaci��n de la vida a fatiga de un CFRP aeron��utico. Esta metodolog��a est�� basada en la regla de acumulaci��n de da��o lineal de Palmgren-Miner, y es aplicada para determinar la vida a fatiga de estructuras sometidas a cargas de amplitud variable. Se ha realizado una campa��a de ensayos con cargas de amplitud constante para caracterizar un CFRP aeron��utico a fatiga, obteniendo las curvas cl��sicas S-N, en diferentes relaciones de esfuerzo. Se determinaron los diagramas de vida constante, (CLD), tambi��n conocidos como diagramas de Goodman, utilizando redes neuronales artificiales debido a la ausencia de modelos coherentes para materiales compuestos. Se ha caracterizado la degradaci��n de la rigidez debido al da��o por fatiga. Se ha ensayado un segundo grupo de probetas con secuencias estandarizadas de cargas de amplitud variable, para obtener la vida a fatiga y la degradaci��n de rigidez en condiciones realistas. Las cargas aplicadas son representativas de misiones de aviones de combate (Falstaff), y de aviones de transporte (Twist). La vida a fatiga de las probetas cicladas con cargas de amplitud variable, se compar�� con el ��ndice de da��o te��rico calculado en base a la regla de acumulaci��n de da��o lineal convencional. Los resultados obtenidos muestran predicciones no conservativas. Esta tesis tambi��n presenta el estudio y desarrollo, de una nueva t��cnica de no contacto para evaluar el estado de da��o por fatiga de estructuras de CFRP por medio de cambios de los par��metros de rugosidad. La rugosidad superficial se puede medir f��cilmente en campo con m��todos sin contacto, mediante t��cnicas ��pticas tales como speckle y perfil��metros ��pticos. En el presente estudio, se han medido par��metros de rugosidad superficial, y el factor de irregularidad de la superficie, a lo largo de la vida de las probetas cicladas con cargas de amplitud constante y variable, Se ha obtenido una buena tendencia de ajuste al correlacionar la magnitud de la rugosidad y el factor de irregularidad de la superficie con la degradaci��n de la rigidez de las probetas fatigadas. Estos resultados sugieren que los cambios en la rugosidad superficial medida en zonas estrat��gicas de componentes y estructuras hechas de CFRP, podr��an ser indicativas del nivel de da��o interno debido a cargas de fatiga. Los resultados tambi��n sugieren que el m��todo es independiente del tipo de carga de fatiga que ha causado el da��o. Esto ��ltimo hace que esta t��cnica de medici��n sea aplicable como inspecci��n para una amplia gama de estructuras de materiales compuestos, desde tanques presurizados con cargas de amplitud constante, estructuras aeron��uticas como alas y colas de aeronaves cicladas con cargas de amplitud variable, hasta aplicaciones industriales como automoci��n, entre otros. ABSTRACT New optimized aerospace structures use composite materials, mainly carbon fiber reinforced polymer composite (CFRP), for critical components and subsystems. A strong knowledge of the fatigue state of highly advanced (CFRP) structures is essential to predict the residual life and optimize intervals of structural inspection, repairs, and/or replacements. Current techniques are based mostly on measurement of structural loads throughout the service life by electric strain gauge sensors. These sensors are affected by extreme environmental conditions and by fatigue loads in such a way that the sensors and their systems require exhaustive maintenance throughout system life. In the present thesis, the conventional methodology based on linear damage accumulation rules, applied to determine the fatigue life of structures subjected to variable amplitude loads was evaluated for an aeronautical CFRP. A test program with constant amplitude loads has been performed to obtain the classical S-N curves at different stress ratios. Constant life diagrams, CLDs, where determined by means of Artificial Neural Networks due to the absence of consistent models for composites. The stiffness degradation due to fatigue damage has been characterized for coupons under cyclic tensile loads. A second group of coupons have been tested until failure with a standardized sequence of variable amplitude loads, representative of missions for combat aircraft (Falstaff), and representative of commercial flights (Twist), to obtain the fatigue life and the stiffness degradation under realistic conditions. The fatigue life of the coupons cycled with variable amplitude loads were compared to the theoretical damage index calculated based on the conventional linear damage accumulation rule. The obtained results show non-conservative predictions. This thesis also presents the evaluation of a new non-contact technique to evaluate the fatigue damage state of CFRP structures by means of measuring roughness parameters to evaluate changes in the surface topography. Surface roughness can be measured easily on field with non-contact methods by optical techniques such as speckle and optical perfilometers. In the present study, surface roughness parameters, and the surface irregularity factor, have been measured along the life of the coupons cycled with constant and variable amplitude loads of different magnitude. A good agreement has been obtained when correlating the magnitude of the roughness and the surface irregularity factor with the stiffness degradation. These results suggest that the changes on the surface roughness measured in strategic zones of components and structures made of CFRP, could be indicative of the level of internal damage due to fatigue loads. The results also suggest that the method is independent of the type of fatigue load that have caused the damage. It makes this measurement technique applicable for a wide range of inspections of composite materials structures, from pressurized tanks with constant amplitude loads, to variable amplitude loaded aeronautical structures like wings and empennages, up to automotive and other industrial applications.

Incorporaci��n de escorias de aluminio en la fabricaci��n de productos de Arcilla cocida

Las sociedades desarrolladas generan una gran cantidad de residuos, que necesitan una adecuada gesti��n. Esta problem��tica requiere, de este modo, una atenci��n creciente por parte de la sociedad, debido a la necesidad de proteger el medio ambiente. En este sentido, los esfuerzos se centran en reducir al m��ximo la generaci��n de residuos y buscar v��as de aprovechamiento de aquellos que son inevitables, soluciones mucho m��s aconsejables desde el punto de vista t��cnico, ecol��gico y econ��mico que su vertido o destrucci��n. Las industrias deben adoptar las medidas precisas para fomentar la reducci��n de estos residuos, desarrollar tecnolog��as limpias que permitan el ahorro de los recursos naturales que poseemos, y sobre todo buscar m��todos de reutilizaci��n, reciclado, inertizaci��n y valorizaci��n de los residuos generados en su producci��n. La industria de la construcci��n es un campo muy receptivo para el desarrollo de nuevos materiales en los que incorporar estos residuos. La incorporaci��n de diferentes residuos industriales en matrices cer��micas se plantea como una v��a barata de fijar las diferentes especies met��licas presentes en transformaci��n de rocas ornamentales, lodos de galvanizaci��n o metal��rgicos, etc. En todos los casos, la adici��n de estos residuos requiere su caracterizaci��n previa y la optimizaci��n de las condiciones de conformado y cocci��n en el caso de su incorporaci��n a la arcilla cocida. Entre los residuos incorporados en materiales de construcci��n se encuentran las escorias de aluminio. La industria metal��rgica produce durante sus procesos de fusi��n diferentes tipos de escorias. Su reciclado es una de las l��neas de inter��s para estas industrias. En el caso de las escorias de aluminio, su tratamiento inicial consiste en una recuperaci��n del aluminio mediante m��todos mec��nicos seguido de un tratamiento qu��mico, o plasma. Este m��todo conduce a que la escoria final apenas contenga aluminio y sea rica en sales solubles lo que limita su almacenamiento en escombreras. La escoria es una mezcla de aluminio metal y productos no met��licos como ��xidos, nitruros y carburos de aluminio, sales y otros ��xidos met��licos. En este estudio se ha analizado la posibilidad de la adici��n de escorias de aluminio procedentes de la metalurgia secundaria en materiales de construcci��n, de forma que tras un procesado de las mismas permita la obtenci��n de materiales compuestos de matriz cer��mica. En la presente Tesis Doctoral se ha analizado la viabilidad t��cnica de la incorporaci��n de las escorias de aluminio procedentes de la metalurgia secundaria en una matriz de arcilla cocida. Para ello se han aplicado diferentes tratamientos a la escoria y se han aplicado diferentes variables en su procesado como la energ��a de molienda o la temperatura de sinterizacion, adem��s del contenido de escoria. Su compactaci��n con agua entre el 5-10 %, secado y sinterizaci��n permite obtener piezas rectangulares de diverso tama��o. Desde el punto de vista del contenido de la escoria, se incorpor�� entre un 10 y 40% de escoria TT, es decir sometida una calcinaci��n previa a 750��C en aire. Los mejores resultados alcanzados corresponden a un contenido del 20% ESC TT, sinterizada a 980��C, por cuanto altos contenidos en escoria condicen a piezas con coraz��n negro. Los productos obtenidos con la adici��n de 20% de escoria de aluminio a la arcilla, presentan una baja expansi��n tras sinterizaci��n, mejores propiedades f��sicas y mec��nicas, y mayor conductividad t��rmica que los productos obtenidos con arcilla sin adiciones. Aumenta su densidad, disminuye su absorci��n y aumenta sus resistencias de flexi��n y compresi��n, al presentar una porosidad cerrada y una interacci��n escoria-matriz. En todos los casos se produce una exudaci��n superficial de aluminio met��lico, cuyo volumen est�� relacionado con la cantidad de escoria adicionada. Mediante la incorporaci��n de este contenido de escoria, tras un tratamiento de disoluci��n de sales y posterior calcinaci��n (ESC TTQ), se mejoran las propiedades del material compuesto, no s��lo sobre la de la escoria calcinada (ESC TT), sino tambi��n, sobre la escoria sin tratamiento (ESC). Si adem��s, la adici��n del 20% de escoria a��adida, est�� tratada, no s��lo t��rmicamente sino tambi��n qu��micamente (ESC TTQ), ��stas mejoran a��n m��s las propiedades del material compuesto, siendo el producto m��s compacto, con menos poros, por lo que los valores de densidad son m��s elevados, menores son las absorciones y mayores resistencias de flexi��n y compresi��n, que los productos obtenidos con la adici��n de escoria s��lo tratada t��rmicamente. Alcanzando valores de resistencias caracter��sticas a compresi��n del orden de 109 MPa. Los valores de conductividad t��rmica obtenidos tambi��n son mayores. Los ensayos tecnol��gicos con piezas de 160 x 30 x 5 mm y el material compuesto optimizado de arcilla+ 20%ESCTTQ, consistieron en la determinaci��n de su expansi��n por humedad, eflorescencia y heladicidad, mostrando en general un mejor comportamiento que la arcilla sin adiciones. As��, se han obtenido nuevos materiales compuestos de matriz cer��mica para la construcci��n, mejorando sus propiedades f��sicas, mec��nicas y t��rmicas, utilizando escorias de aluminio procedentes de la metalurgia secundaria, como opci��n de valorizaci��n de estos residuos, evitando as��, que se viertan a vertederos y contaminen el medio ambiente. ABSTRACT Developed societies generate a lot of waste, which need proper management. Thus, this problem requires increased attention from the society, due to the need to protect the environment. In this regard, efforts are focused on to minimize the generation of waste and find ways of taking advantage of those who are inevitable, much more advisable solutions from the technical, ecological and economic viewpoint to disposal or destruction. Industries should adopt precise measures to promote waste reduction, develop clean technologies that allow the saving of natural resources that we possess, and above all seek methods of reuse, recycling, recovery and valorisation of the waste generated in their production. The industry of the construction is a very receptive field for the development of new materials in which to incorporate these residues. The incorporation of different industrial residues in ceramic counterfoils appears as a cheap route to fix the different metallic present species in transformation of ornamental rocks, muds of galvanization or metallurgical, etc. In all the cases, the addition of these residues needs his previous characterization and the optimization of the conditions of conformed and of baking in case of his incorporation to the baked clay. Residues incorporated into construction materials include aluminium slag. The metallurgical industry produces during their fusion processes different types of slags. Recycling is one of the lines of interest to these industries. In the case of aluminium slag, their initial treatment consists of a recovery of the aluminium using mechanical methods followed by chemical treatment, or plasma. This method leads to that final slag just contains aluminium and is rich in soluble salts which limits storage in dumps. The slag is a mixture of aluminium metal and non-metallic such as oxides, nitrides and carbides of aluminium salts products and other metal oxides. The present Doctoral thesis has analysed the technical viability of the incorporation of aluminium slag from secondary Metallurgy in an array of baked clay. So they have been applied different treatments to the slag and have been applied different variables in its processing as the temperature of sintering, in addition to the content of slag or energy grinding. Its compaction with water between 5-10%, drying and sintering allows rectangular pieces of different size. From the point of view of the content of the slag, it is incorporated between 10 and 40% slag TT, that is to say, submitted a calcination prior to 750 �� C in air. The best results achieved correspond to 20% ESC TT, sintered at 980 �� C, as high levels of slag in accordance to pieces with black heart. The products obtained with the addition of 20% of slag from aluminium to clay, present a low expansion after sintering, better physical properties and mechanical, and higher thermal conductivity than the products obtained with clay, without addictions. Its density increases, decreases its absorption and increases its resistance to bending and compression, introducing a closed porosity and slag-matrix interaction. In all cases there is a superficial exudation of metallic aluminium, whose volume is related to the amount of slag added. By incorporating this content of slag, following a treatment of salt solution and subsequent calcination (ESC TTQ), are improved the properties of composite material not only on the calcined slag (ESC TT), but also in the slag without treatment (ESC). If the addition of 20% of slag added, is also treated, not only thermally but also chemically (ESC TTQ), they further improve the properties of the composite material, the product is more compact, less porous, so the values are higher density, minors are absorptions and greater resistance in bending and compression, to the products obtained with the addition of slag only treated thermally. Reaching values of compressive resistance characteristic of the order of 109 MPa. The thermal conductivity values obtained are also higher. Testing technology with pieces of 160 x 30 x 5 mm and optimized composite material of clay 20% ESCTTQ, consisted in the determination of its expansion by moisture, efflorescence and frost resistance, in general, showing a better performance than the clay without additions. Thus, we have obtained new ceramic matrix composite materials for construction, improving its physical, mechanical and thermal properties, using aluminium slag secondary metallurgy, as an option Valuation of these wastes, thus preventing them from being poured to landfills and pollute environment.

Comportamiento de pilares de hormig��n armado confinados con materiales compuestos sometidos a compresi��n centrada

En la actualidad muchas estructuras de hormig��n armado necesitan ser reforzadas debido a diversas razones: errores en el proyecto o construcci��n, deterioro debido a efectos ambientales, cambios de uso o mayores requerimientos en los c��digos. Los materiales compuestos, tambi��n conocidos como pol��meros reforzados con fibras (FRP), est��n constituidos por fibras continuas de gran resistencia y rigidez embebidas en un material polim��rico. Los FRP se utilizan cada vez m��s en aplicaciones estructurales debido a sus excelentes propiedades (elevadas resistencia y rigidez espec��ficas y resistencia a la corrosi��n). Una de las aplicaciones m��s atractivas es el refuerzo de pilares mediante confinamiento para incrementar su resistencia y ductilidad. El confinamiento puede conseguirse pegando capas de FRP envolviendo el pilar en la direcci��n de los cercos (con las fibras orientadas en direcci��n perpendicular al eje del elemento). Se han realizado numerosos estudios experimentales en probetas cil��ndricas peque��as confinadas con encamisados de FRP y sometidas a compresi��n axial, y se han propuesto varios modelos sobre el hormig��n confinado con FRP. Es sabido que el confinamiento de pilares de secci��n no circular es menos eficiente. En una secci��n circular, el FRP ejerce una presi��n de confinamiento uniforme sobre todo el per��metro, mientras que en una secci��n rectangular la acci��n de confinamiento se concentra en las esquinas. Esta tesis presenta los resultados de una investigaci��n experimental sobre el comportamiento de probetas de hormig��n de secci��n cuadrada confinadas con FRP y sometidas a compresi��n centrada. Se realizaron un total de 42 ensayos investig��ndose el comportamiento en las direcciones axial y transversal. Las variables del estudio incluyen: la resistencia del hormig��n, el tipo de fibras (vidrio o carbono), la cuant��a de refuerzo y el radio de curvatura de las esquinas. Los resultados de los ensayos realizados muestran que el confinamiento con FRP puede mejorar considerablemente la resistencia y ductilidad de pilares de hormig��n armado de secci��n cuadrada con las esquinas redondeadas. La mejora conseguida es mayor en los hormigones de baja resistencia que en los de resistencia media. La deformaci��n de rotura de la camisa de FRP es menor que la que se obtiene en ensayos de tracci��n normalizados del laminado, y la eficiencia del confinamiento depende en gran medida del radio de redondeo de las esquinas. Los resultados se han comparado con los obtenidos seg��n los modelos te��ricos m��s aceptados. Hay dos par��metros cr��ticos en el ajuste de los modelos: el factor de eficiencia de la deformaci��n y el efecto de confinamiento en secciones no circulares. Nowadays, many existing RC structures are in need of repair and strengthening for several reasons: design or construction errors, deterioration caused by environmental effects, change in use of the structures or revisions of code requirements. Composite materials, also known as fibre reinforced polymers (FRP), are composed of high strength and stiffness continuous fibres embedded in a polymer material. FRP materials are being increasingly used in many structural applications due to their excellent properties (high strength- and stiffness-toweight ratio, good corrosion behaviour). One of the most attractive applications of FRP is the confinement of concrete columns to enhance both strength and ductility. Concrete confinement can be achieved by bonding layers of hoop FRP around the column (fibres oriented perpendicular to the longitudinal axis). Many experimental studies have been conducted on small-scale plain concrete specimens of circular cross-sections confined with FRP and subjected to pure axial compressive loading, and several design models have been proposed to describe the behaviour of FRP-confined concrete. It is widely accepted that the confinement of non-circular columns is less efficient than the confinement of circular columns. In a circular cross section, the jacket exerts a uniform confining pressure over the entire perimeter. In the case of a rectangular cross section, the confining action is mostly concentrated at the corners. This thesis presents the results of a comprehensive experimental investigation on the behaviour of axially loaded square concrete specimens confined with FRP. A total of 42 compression tests were conducted, and the behaviour of the specimens in the axial and transverse directions were investigated. The parameters considered in this study are: concrete strength, type of fibres (glass or carbon), amount of FRP reinforcement and corner radius of the cross section. The tests results indicate that FRP confinement can enhance considerably the compressive strength and ductility of RC square columns with rounded corners. The enhancement is more pronounced for low- than for normal-strength concrete. The rupture strain of the FRP jacket is lower than the ultimate strain obtained by standard tensile testing of the FRP material, and the confinement efficiency significantly depends on the corner radius. The confined concrete behaviour was predicted according to the more accepted theoretical models and compared with experimental results. There are two key parameters which critically influence the fitting of the models: the strain efficiency factor and the effect of confinement in non-circular sections.

Anhydrite/aerogel composites for thermal insulation

High performance thermal insulating composite materials can be produced with mineral binders and hydrophobic aerogel particles through a hydrophilization process for the latter with surfactants. The present study is focused on the development of aerogel/calcium sulfate composites by the hydrophilization of hydrophobic silica aerogel particles through a polymer-based surfactant. Its effects on the microstructure and hydration degree are examined as well as their relation to the resulting mechanical and physical properties. Results show that composites with an around 60 % of aerogel by volume can achieve a thermal conductivity <30 mW/m �� K. Interestingly, a surfactant addition of 0.1 % by wt% of the water in the mixtures provides better material properties compared to a surfactant wt% addition of 5 %. However, it has been found around 40 % entrained air, affecting the material properties by reducing the binder and aerogel volume fractions within the composites. Moreover, gypsum crystallization starts to be inhibited at aerogel volume fractions >35 %. Towards material optimization, a model for the calculation of thermal conductivity of composites and an equation for the compressive strength are proposed.

Modelo num��rico mecanobiol��gico para a obten����o da matriz de rigidez estrutural e da densidade mineral na remodelagem ��ssea

Neste trabalho �� proposto um modelo mecanobiol��gico de remodelagem ��ssea para a estimativa de varia����es, provocadas por perturba����es mec��nicas ou biol��gicas, na matriz de rigidez estrutural da escala macrosc��pica e na densidade mineral em uma regi��o do osso. Na coopera����o entre as ��reas da sa��de e da engenharia, como nos estudos estruturais de biomec��nica no sistema esquel��tico, as propriedades mec��nicas dos materiais devem ser conhecidas, entretanto os ossos possuem uma constitui����o material altamente complexa, din��mica e variante entre indiv��duos. Sua din��mica decorre dos ciclos de absor����o e deposi����o de matriz ��ssea na remodelagem ��ssea, a qual ocorre para manter a integridade estrutural do esqueleto e adapt��-lo aos est��mulos do ambiente, sejam eles biol��gicos, qu��micos ou mec��nicos. Como a remodelagem ��ssea pode provocar altera����es no material do osso, espera-se que suas propriedades mec��nicas tamb��m sejam alteradas. Na literatura cient��fica h�� modelos matem��ticos que preveem a varia����o da matriz de rigidez estrutural a partir do est��mulo mec��nico, por��m somente os modelos mais recentes inclu��ram explicitamente processos biol��gicos e qu��micos da remodelagem ��ssea. A densidade mineral ��ssea �� um importante par��metro utilizado no diagn��stico de doen��as ��sseas na ��rea m��dica. Desse modo, para a obten����o da varia����o da rigidez estrutural e da densidade mineral ��ssea, prop��e-se um modelo num��rico mecanobiol��gico composto por cinco submodelos: da din��mica da popula����o de c��lulas ��sseas, da resposta das c��lulas ao est��mulo mec��nico, da porosidade ��ssea, da densidade mineral ��ssea e, baseado na Lei de Voigt para materiais comp��sitos, da rigidez estrutural. Os valores das constantes das equa����es dos submodelos foram obtidos de literatura. Para a solu����o das equa����es do modelo, prop��e-se uma implementa����o num��rica e computacional escrita em linguagem C. O m��todo de Runge-Kutta-Dorman-Prince, cuja vantagem consiste no uso de um passo de solu����o vari��vel, �� utilizado no modelo para controlar o erro num��rico do resultado do sistema de equa����es diferenciais. Foi realizada uma avalia����o comparativa entre os resultados obtidos com o modelo proposto e os da literatura dos modelos de remodelagem ��ssea recentes. Conclui-se que o modelo e a implementa����o propostos s��o capazes de obter varia����es da matriz de rigidez estrutural macrosc��pica e da densidade mineral ��ssea decorrentes da perturba����o nos par��metros mec��nicos ou biol��gicos do processo de remodelagem ��ssea.

An��lise elastopl��stica bidimensional de meios refor��ados com fibras

De modo a satisfazer aspectos de resist��ncia, custo ou conforto, o aperfei��oamento do desempenho das estruturas �� uma meta sempre almejada na Engenharia. Melhorias t��m sido alcan��adas dado ao crescente uso de materiais comp��sitos, pois estes apresentam propriedades f��sicas diferenciadas capazes de atender as necessidades de projeto. Associado ao emprego de comp��sitos, o estudo da plasticidade demonstra uma interessante alternativa para aumentar o desempenho estrutural ao conferir uma capacidade resistente adicional ao conjunto. Entretanto, alguns problemas podem ser encontrados na an��lise elastopl��stica de comp��sitos, al��m das pr��prias dificuldades inerentes �� incorpora����o de fibras na matriz, no caso de comp��sitos refor��ados. A forma na qual um comp��sito refor��ado por fibras e suas fases t��m sua representa����o e simula����o �� de extrema import��ncia para garantir que os resultados obtidos sejam compat��veis com a realidade. �� medida que se desenvolvem modelos mais refinados, surgem problemas referentes ao custo computacional, al��m da necessidade de compatibiliza����o dos graus de liberdade entre os n��s das malhas de elementos finitos da matriz e do refor��o, muitas vezes exigindo a coincid��ncia das referidas malhas. O presente trabalho utiliza formula����es que permitem a representa����o de comp��sitos refor��ados com fibras sem que haja a necessidade de coincid��ncia entre malhas. Al��m disso, este permite a simula����o do meio e do refor��o em regime elastopl��stico com o objetivo de melhor estudar o real comportamento. O modelo constitutivo adotado para a plasticidade �� o de von Mises 2D associativo com encruamento linear positivo e a solu����o deste modelo foi obtida atrav��s de um processo iterativo. A formula����o de elementos finitos posicional �� adotada com descri����o Lagrangeana Total e apresenta as posi����es do corpo no espa��o como par��metros nodais. Com o intuito de averiguar a correta implementa����o das formula����es consideradas, exemplos para valida����o e apresenta����o das funcionalidades do c��digo computacional desenvolvido foram analisados.