Estudio numérico y experimental del efecto de tamaño en modo mixto de los paneles de yeso laminado y lana de roca

Los paneles sándwich de yeso laminado y lana de roca presentan una abundante patología de fisuración debida a flechas excesivas de forjados. Existe, por tanto, la necesidad de avanzar en la simulación y predicción de comportamiento bajo solicitaciones de tracción y cortante de ese tipo de paneles, a pesar de que en las aplicaciones habituales no tienen responsabilidad estructural. El comportamiento de este material puede ser considerado cuasi-frágil, y en base a ello en este trabajo ha sido estudiado haciendo uso de modelos de fisura cohesiva, cuya aplicación a otros materiales cuasifrágiles, como el hormigón, ha aportado resultados muy satisfactorios. En esta comunicación se presenta el trabajo realizado para estudiar el efecto del tamaño del elemento de yeso laminado y lana de roca en su comportamiento mecánico-resistente. Para ello se diseñó una campaña de ensayos en modo mixto sobre probetas de diferente tamaño. Se han realizado ensayos de flexión en tres puntos en modo mixto de unas probetas entalladas, geométricamente similares y de diferente tamaño, obteniéndose las curvas carga-desplazamiento y cargaabertura de la boca de la entalla. Para simular numéricamente el comportamiento en fractura del panel en modo mixto se ha utilizado un modelo de elementos finitos con fisura embebida basado en la fisura cohesiva en el que se introducen como entrada los parámetros obtenidos a partir de la experimentación de trabajos anteriores, obteniéndose un buen ajuste. En función de estos resultados se analiza el efecto del tamaño en los paneles. Sandwich panels of laminated gypsum and rockwool have an abundant pathology of cracking due to excessive slabs deflection. Therefore, it is necessary to progress in the simulation and prediction of behaviour under tensile and shear load of such panels, although in typical applications have no structural responsability. The behaviour of this material may be considered quasi-brittle and, based on this idea, in this work has been studied using a cohesive crack model that has been applied to other quasi-brittle materials, such as concrete, and has provided very satisfactory results. This communication presents the work carried out to study the size effect of the specimen of plasterboard and rockwool in its mechanical and resistant behaviour. The authors designed an experimental campaign under mixed mode composed by testing specimens of different sizes. Assymetrical three-point bending tests have been performed on notched specimens, geometrically similar and of different size, to obtain load-displacement and load-crack moutn opening displacement curves. To numerically simulate the mixed-mode fracture behaviour of the panels we have used a finite element model with embedded crack, based on the cohesive crack model, using as input the experimental parameters obtained in previous work, obtaining a good adjustment. Based on these results we analyze the size effect of the panels

Maximum Likelihood Estimation of Modal Parameters in Structures Using the Expectation Maximization Algorithm

This paper presents a time-domain stochastic system identification method based on maximum likelihood estimation (MLE) with the expectation maximization (EM) algorithm. The effectiveness of this structural identification method is evaluated through numerical simulation in the context of the ASCE benchmark problem on structural health monitoring. The benchmark structure is a four-story, two-bay by two-bay steel-frame scale model structure built in the Earthquake Engineering Research Laboratory at the University of British Columbia, Canada. This paper focuses on Phase I of the analytical benchmark studies. A MATLAB-based finite element analysis code obtained from the IASC-ASCE SHM Task Group web site is used to calculate the dynamic response of the prototype structure. A number of 100 simulations have been made using this MATLAB-based finite element analysis code in order to evaluate the proposed identification method. There are several techniques to realize system identification. In this work, stochastic subspace identification (SSI)method has been used for comparison. SSI identification method is a well known method and computes accurate estimates of the modal parameters. The principles of the SSI identification method has been introduced in the paper and next the proposed MLE with EM algorithm has been explained in detail. The advantages of the proposed structural identification method can be summarized as follows: (i) the method is based on maximum likelihood, that implies minimum variance estimates; (ii) EM is a computational simpler estimation procedure than other optimization algorithms; (iii) estimate more parameters than SSI, and these estimates are accurate. On the contrary, the main disadvantages of the method are: (i) EM algorithm is an iterative procedure and it consumes time until convergence is reached; and (ii) this method needs starting values for the parameters. Modal parameters (eigenfrequencies, damping ratios and mode shapes) of the benchmark structure have been estimated using both the SSI method and the proposed MLE + EM method. The numerical results show that the proposed method identifies eigenfrequencies, damping ratios and mode shapes reasonably well even in the presence of 10% measurement noises. These modal parameters are more accurate than the SSI estimated modal parameters.

The Dynamics of High-Speed Railway Bridges: A Review of Design Issues and New Research for Lateral Dynamics

The dynamic effects of high-speed trains on viaducts are important issues for the design of the structures, as well as for the consideration of safe running conditions for the trains. In this work we start by reviewing the relevance of some basic design aspects. The significance of impact factor envelopes for moving loads is considered first. Resonance which may be achieved for high-speed trains requires dynamic analysis, for which some key aspects are discussed. The relevance of performing a longitudinal distribution of axle loads, the number of modes taken in analysis, and the consideration of vehicle-structure interaction are discussed with representative examples. The lateral dynamic effects of running trains on bridges is of importance for laterally compliant viaducts, such as some very tall structures erected in new high-speed lines. The relevance of this study is mainly for the safety of the traffic, considering both internal actions such as the hunting motion as well as external actions such as wind or earthquakes [1]. These studies require three-dimensional dynamic coupled vehicle-bridge models, and consideration of wheel to rail contact, a phenomenon which is complex and costly to model in detail. We describe here a fully nonlinear coupled model, described in absolute coordinates and incorporated into a commercial finite element framework [2]. The wheel-rail contact has been considered using a FastSim algorithm which provides a compromise between accuracy and computational cost, and captures the main nonlinear response of the contact interface. Two applications are presented, firstly to a vehicle subject to a strong wind gust traversing a bridge, showing the relevance of the nonlinear wheel-rail contact model as well as the dynamic interaction between bridge and vehicle. The second application is to a real HS viaduct with a long continuous deck and tall piers and high lateral compliance [3]. The results show the safety of the traffic as well as the importance of considering features such as track alignment irregularities.

Goal-oriented self-adaptive hp-strategies for finite element analysis of electromagnetic scattering and radiation problems

In this paper, a fully automatic goal-oriented hp-adaptive finite element strategy for open region electromagnetic problems (radiation and scattering) is presented. The methodology leads to exponential rates of convergence in terms of an upper bound of an user-prescribed quantity of interest. Thus, the adaptivity may be guided to provide an optimal error, not globally for the field in the whole finite element domain, but for specific parameters of engineering interest. For instance, the error on the numerical computation of the S-parameters of an antenna array, the field radiated by an antenna, or the Radar Cross Section on given directions, can be minimized. The efficiency of the approach is illustrated with several numerical simulations with two dimensional problem domains. Results include the comparison with the previously developed energy-norm based hp-adaptivity.

WYPIWYG Hyperelasticity

In this paper we describe a new promising procedure to model hyperelastic materials from given stress-strain data. The main advantage of the proposed method is that the user does not need to have a relevant knowledge of hyperelasticity, large strains or hyperelastic constitutive modelling. The engineer simply has to prescribe some stress strain experimental data (whether isotropic or anisotropic) in also user prescribed stress and strain measures and the model almost exactly replicates the experimental data. The procedure is based on the piece-wise splines model by Sussman and Bathe and may be easily generalized to transversely isotropic and orthotropic materials. The model is also amenable of efficient finite element implementation. In this paper we briefly describe the general procedure, addressing the advantages and limitations. We give predictions for arbitrary ?experimental data? and also give predictions for actual experiments of the behaviour of living soft tissues. The model may be also implemented in a general purpose finite element program. Since the obtained strain energy functions are analytic piece-wise functions, the constitutive tangent may be readily derived in order to be used for implicit static problems, where the equilibrium iterations must be performed and the material tangent is needed in order to preserve the quadratic rate of convergence of Newton procedures.

Crack mechanical failure in lithium niobate crystal under ion irradiation; novel simulation by extended finite elements

Swift heavy ion irradiation (ions with mass heavier than 15 and energy exceeding MeV/amu) transfer their energy mainly to the electronic system with small momentum transfer per collision. Therefore, they produce linear regions (columnar nano-tracks) around the straight ion trajectory, with marked modifications with respect to the virgin material, e.g., phase transition, amorphization, compaction, changes in physical or chemical properties. In the case of crystalline materials the most distinctive feature of swift heavy ion irradiation is the production of amorphous tracks embedded in the crystal. Lithium niobate is a relevant optical material that presents birefringence due to its anysotropic trigonal structure. The amorphous phase is certainly isotropic. In addition, its refractive index exhibits high contrast with those of the crystalline phase. This allows one to fabricate waveguides by swift ion irradiation with important technological relevance. From the mechanical point of view, the inclusion of an amorphous nano-track (with a density 15% lower than that of the crystal) leads to the generation of important stress/strain fields around the track. Eventually these fields are the origin of crack formation with fatal consequences for the integrity of the samples and the viability of the method for nano-track formation. For certain crystal cuts (X and Y), these fields are clearly anisotropic due to the crystal anisotropy. We have used finite element methods to calculate the stress/strain fields that appear around the ion-generated amorphous nano-tracks for a variety of ion energies and doses. A very remarkable feature for X cut-samples is that the maximum shear stress appears on preferential planes that form +/-45º with respect to the crystallographic planes. This leads to the generation of oriented surface cracks when the dose increases. The growth of the cracks along the anisotropic crystal has been studied by means of novel extended finite element methods, which include cracks as discontinuities. In this way we can study how the length and depth of a crack evolves as function of the ion dose. In this work we will show how the simulations compare with experiments and their application in materials modification by ion irradiation.

Crack mechanical failure in ceramic materials under ion irradiation: case of lithium niobate crystal

Swift heavy ion irradiation (ions with mass heavier than 15 and energy exceeding MeV/amu) transfer their energy mainly to the electronic system with small momentum transfer per collision. Therefore, they produce linear regions (columnar nano-tracks) around the straight ion trajectory, with marked modifications with respect to the virgin material, e.g., phase transition, amorphization, compaction, changes in physical or chemical properties. In the case of crystalline materials the most distinctive feature of swift heavy ion irradiation is the production of amorphous tracks embedded in the crystal. Lithium niobate is a relevant optical material that presents birefringence due to its anysotropic trigonal structure. The amorphous phase is certainly isotropic. In addition, its refractive index exhibits high contrast with those of the crystalline phase. This allows one to fabricate waveguides by swift ion irradiation with important technological relevance. From the mechanical point of view, the inclusion of an amorphous nano-track (with a density 15% lower than that of the crystal) leads to the generation of important stress/strain fields around the track. Eventually these fields are the origin of crack formation with fatal consequences for the integrity of the samples and the viability of the method for nano-track formation. For certain crystal cuts (X and Y), these fields are clearly anisotropic due to the crystal anisotropy. We have used finite element methods to calculate the stress/strain fields that appear around the ion- generated amorphous nano-tracks for a variety of ion energies and doses. A very remarkable feature for X cut-samples is that the maximum shear stress appears on preferential planes that form +/-45º with respect to the crystallographic planes. This leads to the generation of oriented surface cracks when the dose increases. The growth of the cracks along the anisotropic crystal has been studied by means of novel extended finite element methods, which include cracks as discontinuities. In this way we can study how the length and depth of a crack evolves as function of the ion dose. In this work we will show how the simulations compare with experiments and their application in materials modification by ion irradiation.

Computational Methods for Identification of Vibrating Structures

System identification deals with the problem of building mathematical models of dynamical systems based on observed data from the system" [1]. In the context of civil engineering, the system refers to a large scale structure such as a building, bridge, or an offshore structure, and identification mostly involves the determination of modal parameters (the natural frequencies, damping ratios, and mode shapes). This paper presents some modal identification results obtained using a state-of-the-art time domain system identification method (data-driven stochastic subspace algorithms [2]) applied to the output-only data measured in a steel arch bridge. First, a three dimensional finite element model was developed for the numerical analysis of the structure using ANSYS. Modal analysis was carried out and modal parameters were extracted in the frequency range of interest, 0-10 Hz. The results obtained from the finite element modal analysis were used to determine the location of the sensors. After that, ambient vibration tests were conducted during April 23-24, 2009. The response of the structure was measured using eight accelerometers. Two stations of three sensors were formed (triaxial stations). These sensors were held stationary for reference during the test. The two remaining sensors were placed at the different measurement points along the bridge deck, in which only vertical and transversal measurements were conducted (biaxial stations). Point estimate and interval estimate have been carried out in the state space model using these ambient vibration measurements. In the case of parametric models (like state space), the dynamic behaviour of a system is described using mathematical models. Then, mathematical relationships can be established between modal parameters and estimated point parameters (thus, it is common to use experimental modal analysis as a synonym for system identification). Stable modal parameters are found using a stabilization diagram. Furthermore, this paper proposes a method for assessing the precision of estimates of the parameters of state-space models (confidence interval). This approach employs the nonparametric bootstrap procedure [3] and is applied to subspace parameter estimation algorithm. Using bootstrap results, a plot similar to a stabilization diagram is developed. These graphics differentiate system modes from spurious noise modes for a given order system. Additionally, using the modal assurance criterion, the experimental modes obtained have been compared with those evaluated from a finite element analysis. A quite good agreement between numerical and experimental results is observed.

Modelo simplificado de pocos grados de libertad, para simular el impacto de una roca sobre una viga de hormigón armado

Durante mucho tiempo se han estudiado los efectos producidos por el impacto de objetos sobre estructuras, inicialmente la gran mayoría de los estudios se centraban en el impacto de proyectiles de tipo balístico dado el interés que se tenía en el diseño de estructuras capaces de soportar el impacto de dichos proyectiles. Dada la falta de capacidad de cálculo para resolver el problema que tuviera en cuenta el comportamiento global de la estructura junto con el comportamiento local, los estudios se centraban básicamente en la zona de impacto. El momento en el cual se pueden realizar cálculos que requieren de múltiples iteraciones para llegar a una solución satisfactoria al complejo problema planteado no se produce hasta la llegada de los modernos ordenadores. En el presente estudio se establece un sistema de múltiples grados de libertad (SMDF, System of Multiple Degrees of Freedom), que permite el estudio del impacto de una roca sobre una viga de hormigón armado teniendo en cuenta factores que afectan al ámbito local y global de la estructura analizada. El sistema se resuelve a través de un método de resolución implícita como es el método de Newmark, el cual nos permite, sin tener que acceder a un programa de elementos finitos, obtener una solución suficientemente aproximada al problema planteado con un coste computacional relativamente bajo. En el documento se comprueba el modelo propuesto con los resultados existentes de unos ensayos a escala real, y se plantean diversas hipótesis analizando las diferentes respuestas del sistema a la variación de las condiciones de partida. The effects produced by the impact of objects on structures have been studied for a long time. Initially, the vast majority of studies focused on the impact of ballistic missiles, due to the particular interest in the design of these structures being capable to withstand the impact such projectiles. Due to the lack of calculation capacity to solve the problem of taking into account the global behavior of the structure together with the local behavior, the studies focused mainly on the impact zone. The moment in which calculations that required multiple iterations could be performed with satisfactory solutions for the complex problem presented did not arrive until the introduction of modern computers. The present study establishes a System of Multiple Degrees of Freedom, which allows the study of the impact of a rock on a reinforced concrete beam, taking into account factors that affect the local and global behavior of the structure analyzed. The system is solved using an implicit solution method as is the Newmark method, which allows us, without using a finite element program, to obtain a sufficiently approximate solution to the problem with a relatively low computational cost. This paper tests the proposed model with existing results obtained in large-scale tests, and analyses the response of the system to various changing scenarios to the starting conditions.

Análisis del comportamiento en servicio de los puentes de fábrica ante las nuevas condiciones de explotación

Los puentes arco de fábrica representan una parte importante del inventario de puentes en España y en Europa. De aquí, la importancia cuantitativa de estas estructuras y el interés que representa tanto para las Administraciones, organismos públicos y privados como para la sociedad en general, mantener estos puentes en servicio. Para poder alargar su vida útil, aún más si cabe, se plantea imprescindible llevar a cabo una labor de conservación y mantenimiento adecuada. La importancia de la evaluación estructural de los puentes de fábrica se basa en la conveniencia de conocer el comportamiento estructural tanto en condiciones de servicio como en agotamiento. El comportamiento en Estado Límite Último ha sido estudiado en profundidad y como resultado, la seguridad frente a agotamiento ha quedado definida con cierta confianza. Sin embargo, el comportamiento en Estado Límite de Servicio no es tan conocido. Se considera necesaria una revisión del concepto de ELS en puentes arco de fábrica puesto que muchos de ellos, cumpliendo las comprobaciones establecidas para ELU, presentan daños asociados a las actuales condiciones de explotación existentes actuales. El presente trabajo se enmarca dentro de un proyecto que está llevando a cabo la UIC (Union Internationale de Chemins de Fer) desde 2004. El objetivo general del mismo es conocer el comportamiento de los puentes arco de fábrica y mejorar los métodos de evaluación, mantenimiento y reparación existentes. Con este estudio, se pretende contribuir a mejorar la caracterización del comportamiento en servicio de estas estructuras. Para ello se ha realizado un análisis del estado tensional de la bóveda y el relleno estudiando la influencia de la configuración geométrica de los puentes y las propiedades de los materiales que los componen. Entender el funcionamiento de estas estructuras y conocer sus peculiares características ha sido el paso previo al desarrollo del estudio. Para ello, se ha acudido al minucioso trabajo desarrollado por diversos autores, desde los primeros análisis mediante la línea de presiones hasta los actuales métodos basados en elementos finitos. En primer lugar, se ha realizado un estudio paramétrico de diferentes configuraciones geométricas. El objetivo es comprobar la influencia de las dimensiones absolutas y las relaciones existentes entre las mismas en el comportamiento en servicio de los puentes. A continuación, se ha estudiado la influencia de las propiedades mecánicas de los rellenos rígido y granular (modificando su módulo de deformabilidad) en el estado tensional de la bóveda y el propio relleno. Para las dos etapas anteriores se emplea un modelo simplificado de puente arco de fábrica. A continuación, se crea un modelo más completo del mismo, para estudiar la influencia de las propiedades mecánicas del substrato de cimentación en el comportamiento estructural en servicio de la estructura. El objetivo final de este trabajo fin de máster, es conocer el comportamiento en servicio de los puentes arco de fábrica, para poder establecer las variables que condicionan el mismo. El siguiente paso en este campo de estudio, consiste en fijar unos valores límite para las mismas. Como síntesis de las conclusiones obtenidas, se menciona que el comportamiento estructural de los puente arco de fábrica, en mayor o menor medida, está influenciado por su geometría y las propiedades de los rellenos y substrato de cimentación que forman parte del mismo. Masonry arch bridges represent an important part of the total bridges, both in Spain and Europe. For this reason, these structures are so important in terms of quantity. They play an essential role for public administration and people in general. In order to remain those bridges serviceable, suitable inspections and repairs are required. It is necessary to have knowledge of the bridge condition so that an assessment can be made with confidence. It is therefore necessary to check that bridges behave properly under Ultimate Limit State criterion and Serviceability Limit State criterion. ULS has been studied thoroughly and as result, requirements under collapse are well described. However, structural behaviour under conditions of serviceability is not well evaluated. Serviceability Limit State criterion should be redefined for masonry arch bridges assessment. This is because many bridges that fulfil SLS criterion have damages. The purpose of this work is to take part in the improvement of assessment under serviceability. A vault and fill structural behaviour analysis has been performed from two points of view: geometry of the bridge and materials’ properties. The starting point was learning about masonry arch bridges behaviour and their special features. For this task, a revision of several authors’ thorough study has been made, from the line of thrust analysis to the current finite element analysis. Firstly, a parametric study of typologies of bridge has been made. The aim is to know how vault and fill behaviour changes modifying both absolute dimensions and relation between them. In the next step, a study of both surface fill and backfill properties has been done. The aim is to know how vault and fill behaviour changes modifying Young’s modulus. The principal conclusion achieved along this work is that the structural behaviour of masonry bridges depends of the bridge geometry and its material properties.

Estudio numérico y experimental del efecto de tamaño en modo mixto de los paneles de yeso laminado y lana de roca

Los paneles sándwich de yeso laminado y lana de roca presentan una abundante patología de fisuración debida a flechas excesivas de forjados. Existe, por tanto, la necesidad de avanzar en la simulación y predicción de comportamiento bajo solicitaciones de tracción y cortante de ese tipo de paneles, a pesar de que en las aplicaciones habituales no tienen responsabilidad estructural. El comportamiento de este material puede ser considerado cuasi-frágil, y en base a ello en este trabajo ha sido estudiado haciendo uso de modelos de fisura cohesiva, cuya aplicación a otros materiales cuasifrágiles, como el hormigón, ha aportado resultados muy satisfactorios. En esta comunicación se presenta el trabajo realizado para estudiar el efecto del tamaño del elemento de yeso laminado y lana de roca en su comportamiento mecánico-resistente. Para ello se diseñó una campaña de ensayos en modo mixto sobre probetas de diferente tamaño. Se han realizado ensayos de flexión en tres puntos en modo mixto de unas probetas entalladas, geométricamente similares y de diferente tamaño, obteniéndose las curvas carga-desplazamiento y cargaabertura de la boca de la entalla. Para simular numéricamente el comportamiento en fractura del panel en modo mixto se ha utilizado un modelo de elementos finitos con fisura embebida basado en la fisura cohesiva en el que se introducen como entrada los parámetros obtenidos a partir de la experimentación de trabajos anteriores, obteniéndose un buen ajuste. En función de estos resultados se analiza el efecto del tamaño en los paneles. Sandwich panels of laminated gypsum and rockwool have an abundant pathology of cracking due to excessive slabs deflection. Therefore, it is necessary to progress in the simulation and prediction of behaviour under tensile and shear load of such panels, although in typical applications have no structural responsability. The behaviour of this material may be considered quasi-brittle and, based on this idea, in this work has been studied using a cohesive crack model that has been applied to other quasi-brittle materials, such as concrete, and has provided very satisfactory results. This communication presents the work carried out to study the size effect of the specimen of plasterboard and rockwool in its mechanical and resistant behaviour. The authors designed an experimental campaign under mixed mode composed by testing specimens of different sizes. Assymetrical three-point bending tests have been performed on notched specimens, geometrically similar and of different size, to obtain load-displacement and load-crack moutn opening displacement curves. To numerically simulate the mixed-mode fracture behaviour of the panels we have used a finite element model with embedded crack, based on the cohesive crack model, using as input the experimental parameters obtained in previous work, obtaining a good adjustment. Based on these results we analyze the size effect of the panels.

Study of the Edge and Surface Cracks Influence in the Mechanical Strength of Silicon Wafers

The objective of the present study is the estimation of the depth to which the wire sawing process causes damage to the wafer surfaces. Previous analyses were carried out by means of the four line bending test. The characteristic of this test implied that the failure could be due to surface cracks located in the central zone of the wafer or near the edges. In order to evaluate the influence of the edge or surface cracks a new study has been carried out using the ball/ring on ring test. Description and results of the tests are presented. The preliminary analysis of the failure stress using analytical methods confirms the expected results. A Finite Element model developed to get more information of the test results is also presented.

Simulación de la rotura de barras de acero perlítico sometidas a tracción mediante un modelo de fisura cohesiva. Validación experimental

Las probetas cilíndricas fabricadas con materiales metálicos de elevada ductilidad, como el aluminio o el cobre, sometidas a tracción suelen presentar una rotura comúnmente denominada rotura en copa y cono, debido a su geometría. Este tipo de rotura se reproduce numéricamente con éxito mediante el modelo de Gurson-Tvergaard- Needleman, cuya formulación matemática se basa en el fenómeno físico de nucleación, crecimiento y coalescencia de microhuecos. A diferencia de dichos materiales, las barras de acero perlítico, material con una ductilidad apreciable, presentan un frente de rotura plano que no puede simularse correctamente con los modelos antes mencionados, apareciendo una región interior de daño que, en principio, también puede atribuirse a un fenómeno de nucleación y crecimiento de microhuecos, mientras que en el exterior aparece una zona cuya micrografía permite asociar su rotura a un mecanismo de clivaje. En trabajos anteriores los autores han presentado un elemento de intercara cohesivo dependiente de la triaxialidad de tensiones que, incorporado a un código de elementos finitos, permite reproducir de forma razonable el daño que se desarrolla en la región interior mencionada. En este trabajo se presentan los resultados de una campaña experimental que permite validar el modelo desarrollado. Para ello, se ensayan probetas de diferentes diámetros y se comparan los resultados con los obtenidos numéricamente, empleando tres bases extensométricas diferentes en cada uno de los diámetros. Los resultados numéricos se ajustan razonablemente bien a los obtenidos experimentalmente.The cylindrical specimens made of high-ductility metallic materials, such as aluminium and copper, usually fail showing a fracture surface commonly known as cup-cone fracture because of its shape. This type of fracture is successfully reproduced using the Gurson-Tvergaard-Needleman model, which is based on the physical process of nucleation, growth and coalescence of microvoids. Unlike these materials, pearlitic steel bars, which are considerably ductile, show a flat fracture surface that cannot be correctly reproduced with the aforementioned models. In this flat fracture surface, a dark region can be observed in the centre of the specimen, which is the result of a process of nucleation and growth of microvoids, while in the rest of the fracture surface a different region can be identified, which a micrographic study reveals to be the result of a process of cleavage. In previous works, the authors presented a triaxiality-dependent cohesive interface element that, implemented in a finite element code, can reproduce in a reasonably accurate manner the damage that takes place in the dark region mentioned before. The results of an experimental campaign designed to validate the model are presented in this paper. For it, different diameter specimens are tested and these results are compared to those obtained with the numerical models, using three different initial lengths for the strain. Numerical results agree reasonably well with those obtained experimentally.

Simulación de la rotura de barras de acero perlítico sometidas a tracción mediante un modelo de fisura cohesiva. Validación experimental

Las probetas cilíndricas fabricadas con materiales metálicos de elevada ductilidad, como el aluminio o el cobre, sometidas a tracción suelen presentar una rotura comúnmente denominada rotura en copa y cono, debido a su geometría. Este tipo de rotura se reproduce numéricamente con éxito mediante el modelo de Gurson-Tvergaard- Needleman, cuya formulación matemática se basa en el fenómeno físico de nucleación, crecimiento y coalescencia de microhuecos. A diferencia de dichos materiales, las barras de acero perlítico, material con una ductilidad apreciable, presentan un frente de rotura plano que no puede simularse correctamente con los modelos antes mencionados, apareciendo una región interior de daño que, en principio, también puede atribuirse a un fenómeno de nucleación y crecimiento de microhuecos, mientras que en el exterior aparece una zona cuya micrografía permite asociar su rotura a un mecanismo de clivaje. En trabajos anteriores los autores han presentado un elemento de intercara cohesivo dependiente de la triaxialidad de tensiones que, incorporado a un código de elementos finitos, permite reproducir de forma razonable el daño que se desarrolla en la región interior mencionada. En este trabajo se presentan los resultados de una campaña experimental que permite validar el modelo desarrollado. Para ello, se ensayan probetas de diferentes diámetros y se comparan los resultados con los obtenidos numéricamente, empleando tres bases extensométricas diferentes en cada uno de los diámetros. Los resultados numéricos se ajustan razonablemente bien a los obtenidos experimentalmente.The cylindrical specimens made of high-ductility metallic materials, such as aluminium and copper, usually fail showing a fracture surface commonly known as cup-cone fracture because of its shape. This type of fracture is successfully reproduced using the Gurson-Tvergaard-Needleman model, which is based on the physical process of nucleation, growth and coalescence of microvoids. Unlike these materials, pearlitic steel bars, which are considerably ductile, show a flat fracture surface that cannot be correctly reproduced with the aforementioned models. In this flat fracture surface, a dark region can be observed in the centre of the specimen, which is the result of a process of nucleation and growth of microvoids, while in the rest of the fracture surface a different region can be identified, which a micrographic study reveals to be the result of a process of cleavage. In previous works, the authors presented a triaxiality-dependent cohesive interface element that, implemented in a finite element code, can reproduce in a reasonably accurate manner the damage that takes place in the dark region mentioned before. The results of an experimental campaign designed to validate the model are presented in this paper. For it, different diameter specimens are tested and these results are compared to those obtained with the numerical models, using three different initial lengths for the strain. Numerical results agree reasonably well with those obtained experimentally.

New concepts and techniques for the development of high-efficiency concentrating photovoltaic modules

El interés por los sistemas fotovoltaicos de concentración (CPV) ha resurgido en los últimos años amparado por el desarrollo de células multiunión de muy alta eficiencia basadas en semiconductores de los grupos III-V. Estas células han permitido obtener módulos de concentración con eficiencias que prácticamente duplican las del panel plano y que llegan al 35% en los módulos récord. Esta tesis está dedicada al diseño y la implementación experimental de nuevos conceptos que permitan obtener módulos CPV que no sólo alcancen una eficiencia alta en condiciones estándar sino que, además, sean lo suficientemente tolerantes a errores de montaje, seguimiento, temperatura y variaciones espectrales para que la energía que producen a lo largo del año sea máxima. Una de las primeras cuestiones que se abordan es el diseño de elementos ópticos secundarios para sistemas cuyo primario es una lente de Fresnel y que permiten, para una concentración fija, aumentar el ángulo de aceptancia y la tolerancia del sistema. Varios secundarios reflexivos y refractivos han sido diseñados y analizados mediante trazado de rayos. En particular, utilizando óptica anidólica y basándose en el diseño de una sola etapa conocido como ‘concentrador dieléctrico que funciona por reflexión total interna‘, se ha diseñado, fabricado y caracterizado un secundario con salida cuadrada que, usado junto con una lente de Fresnel, permite alcanzar simultáneamente una elevada eficiencia, concentración y aceptancia. Además, se ha propuesto y prototipado un método alternativo de fabricación para otro de los secundarios, denominado domo, consistente en el sobremoldeo de silicona sobre células solares. Una de las características que impregna todo el trabajo realizado en esta tesis es la aproximación holística en el diseño de módulos CPV, es decir, se ha prestado especial atención al diseño conjunto de la célula y la óptica para garantizar que el sistema total alcance la mayor eficiencia posible. En este sentido muchos sistemas ópticos desarrollados en esta tesis han sido diseñados, caracterizados y optimizados teniendo en cuenta que el ajuste de corriente entre las distintas subcélulas que comprenden la célula multiunión bajo el concentrador sea muy próximo a uno. La capa antirreflectante sobre la célula funciona, en cierto modo, como interfaz entre la óptica y la célula, por lo que se ha diseñado un método de optimización de capas antirreflectantes que considera no sólo el amplio rango de longitudes de onda para el que las células multiunión son sensibles sino también la distribución angular de intensidad sobre la célula creada por la óptica de concentración. Además, la cuestión de la falta de uniformidad también se ha abordado mediante la comparación de las distribuciones espectrales y espaciales de irradiancia que crean diferentes ópticas (simuladas mediante trazado de rayos y fotografiadas) y las pérdidas de eficiencia que experimentan las células iluminadas por dichas ópticas de concentración medidas experimentalmente. El efecto de la temperatura en la óptica de concentración también ha sido objeto de estudio de esta tesis. En particular, mediante simulaciones de elementos finitos se han dado los primeros pasos para el análisis de las deformaciones que sufren los dientes de las lentes de Fresnel híbridas (vidrio-silicona), así como el cambio de índice de refracción con la temperatura y la influencia de ambos efectos sobre el funcionamiento de los sistemas. Se ha implementado un modelo que tiene por objeto considerar las variaciones ambientales, principalmente temperatura y contenido espectral de la radiación directa, así como las sensibilidades térmica y espectral de los sistemas CPV, con el fin de maximizar la energía producida por un módulo de concentración a lo largo de un año en un emplazamiento determinado. Los capítulos 5 y 6 de este libro están dedicados al diseño, fabricación y caracterización de un nuevo concepto de módulo fotovoltaico denominado FluidReflex y basado en una única etapa reflexiva con dieléctrico fluido. En este nuevo concepto la presencia del fluido aporta algunas ventajas significativas como son: un aumento del producto concentración por aceptancia (CAP, en sus siglas en inglés) alcanzable al rodear la célula con un medio cuyo índice de refracción es mayor que uno, una mejora de la eficiencia óptica al disminuir las pérdidas por reflexión de Fresnel en varias interfaces, una mejora de la disipación térmica ya que el calor que se concentra junto a la célula se trasmite por convección natural y conducción en el fluido y un aislamiento eléctrico mejorado. Mediante la construcción y medida de varios prototipos de unidad elemental se ha demostrado que no existe ninguna razón fundamental que impida la implementación práctica del concepto teórico alcanzando una elevada eficiencia. Se ha realizado un análisis de fluidos candidatos probando la existencia de al menos dos de ellos que cumplen todos los requisitos (en particular el de estabilidad bajo condiciones de luz concentrada) para formar parte del sistema de concentración FluidReflex. Por ´ultimo, se han diseñado, fabricado y caracterizado varios prototipos preindustriales de módulos FluidReflex para lo cual ha sido necesario optimizar el proceso de fabricación de la óptica multicavidad a fin de mantener el buen comportamiento óptico obtenido en la fabricación de la unidad elemental. Los distintos prototipos han sido medidos, tanto en el laboratorio como bajo el sol real, analizando el ajuste de corriente de la célula iluminada por el concentrador FluidReflex bajo diferentes distribuciones espectrales de la radiación incidente así como el excelente comportamiento térmico del módulo. ABSTRACT A renewed interest in concentrating photovoltaic (CPV) systems has emerged in recent years encouraged by the development of high-efficiency multijunction solar cells based in IIIV semiconductors that have led to CPV module efficiencies which practically double that of flat panel PV and which reach 35% for record modules. This thesis is devoted to the design and experimental implementation of new concepts for obtaining CPV modules that not only achieve high efficiency under standard conditions but also have such a wide tolerance to assembly errors, tracking, temperature and spectral variations, that the energy generated by them throughout the year is maximized. One of the first addressed issues is the design of secondary optical elements whose primary optics is a Fresnel lens and which, for a fixed concentration, allow an increased acceptance angle and tolerance of the system. Several reflective and refractive secondaries have been designed and analyzed using ray tracing. In particular, using nonimaging optics and based on the single-stage design known as ‘dielectric totally internally reflecting concentrator’, a secondary with square output has been designed, fabricated and characterized. Used together with a Fresnel lens, the secondary can simultaneously achieve high efficiency, concentration and acceptance. Furthermore, an alternative method has been proposed and prototyped for the fabrication of the secondary named dome. The optics is manufactured by direct overmolding of silicone over the solar cells. One characteristic that permeates all the work done in this thesis is the holistic approach in the design of CPV modules, meaning that special attention has been paid to the joint design of the solar cell and the optics to ensure that the total system achieves the highest attainable efficiency. In this regard, many optical systems developed in the thesis have been designed, characterized and optimized considering that the current matching among the subcells within the multijunction solar cell beneath the optics must be close to one. Antireflective coating over the cell acts, somehow, as an interface between the optics and the cell. Consequently, a method has been designed to optimize antireflective coatings that takes into account not only the broad wavelength range that multijunction solar cells are sensitive to but also the angular intensity distribution created by the concentrating optics. In addition, the issue of non-uniformity has also been addressed by comparing the spectral and spatial distributions of irradiance created by different optics (simulated by ray tracing and photographed) and the efficiency losses experienced by cells illuminated by those concentrating optics experimentally determined. The effect of temperature on the concentrating optics has also been studied in this thesis. In particular, finite element simulations have been use to analyze the deformations experienced by the facets of hybrid (silicon-glass) Fresnel lenses, the change of refractive index with temperature and the influence of both effects on the system performance. A model has been implemented which take into consideration atmospheric variations, mainly temperature and spectral content of the direct normal irradiance, as well as thermal and spectral sensitivities of systems, with the aim of maximizing the energy harvested by a CPV module throughout the year in a particular location. Chapters 5 and 6 of this book are devoted to the design, fabrication, and characterization of a new concentrator concept named FluidReflex and based on a single-stage reflective optics with fluid dielectric. In this new concept, the presence of the fluid provides some significant advantages such as: an increased concentration acceptance angle product (CAP) achievable by surrounding the cell with a medium whose refractive index is greater than one, an improvement of the optical efficiency by reducing losses due to Fresnel reflection at several interfaces, an improvement in heat dissipation as the heat concentrated near the cell is transmitted by natural convection and conduction in the fluid, and an improved electrical insulation. By fabricating and characterizing several elementary-unit prototypes it was shown that there is no fundamental reason that prevents the practical implementation of this theoretical concept reaching high efficiency. Several fluid candidates were investigated proving the existence of at least to fluids that meet all the requirements (including the stability under concentrated light) to become part of the FluidReflex concentrator. Finally, several pre-industrial FluidReflex module prototypes have been designed and fabricated. An optimization process for the manufacturing of the multicavity optics was necessary to attain such an optics quality as the one achieved by the single unit. The module prototypes have been measured, both indoors and outdoors, analyzing the current matching of the solar cells beneath the concentrator for different spectral distribution of the incident irradiance. Additionally, the module showed an excellent thermal performance.