A mathematical framework for finite strain elastoplastic consolidation. Part 1: Balance laws, variational formulation, and linearization

A mathematical formulation for finite strain elasto plastic consolidation of fully saturated soil media is presented. Strong and weak forms of the boundary-value problem are derived using both the material and spatial descriptions. The algorithmic treatment of finite strain elastoplasticity for the solid phase is based on multiplicative decomposition and is coupled with the algorithm for fluid flow via the Kirchhoff pore water pressure. Balance laws are written for the soil-water mixture following the motion of the soil matrix alone. It is shown that the motion of the fluid phase only affects the Jacobian of the solid phase motion, and therefore can be characterized completely by the motion of the soil matrix. Furthermore, it is shown from energy balance consideration that the effective, or intergranular, stress is the appropriate measure of stress for describing the constitutive response of the soil skeleton since it absorbs all the strain energy generated in the saturated soil-water mixture. Finally, it is shown that the mathematical model is amenable to consistent linearization, and that explicit expressions for the consistent tangent operators can be derived for use in numerical solutions such as those based on the finite element method.

Coupled model of initiation and propagation of corrosion in reinforced concrete

Corrosion of reinforcing steel in concrete due to chloride ingress is one of the main causes of the deterioration of reinforced concrete structures. Structures most affected by such a corrosion are marine zone buildings and structures exposed to de-icing salts like highways and bridges. Such process is accompanied by an increase in volume of the corrosión products on the rebarsconcrete interface. Depending on the level of oxidation, iron can expand as much as six times its original volume. This increase in volume exerts tensile stresses in the surrounding concrete which result in cracking and spalling of the concrete cover if the concrete tensile strength is exceeded. The mechanism by which steel embedded in concrete corrodes in presence of chloride is the local breakdown of the passive layer formed in the highly alkaline condition of the concrete. It is assumed that corrosion initiates when a critical chloride content reaches the rebar surface. The mathematical formulation idealized the corrosion sequence as a two-stage process: an initiation stage, during which chloride ions penetrate to the reinforcing steel surface and depassivate it, and a propagation stage, in which active corrosion takes place until cracking of the concrete cover has occurred. The aim of this research is to develop computer tools to evaluate the duration of the service life of reinforced concrete structures, considering both the initiation and propagation periods. Such tools must offer a friendly interface to facilitate its use by the researchers even though their background is not in numerical simulation. For the evaluation of the initiation period different tools have been developed: Program TavProbabilidade: provides means to carry out a probability analysis of a chloride ingress model. Such a tool is necessary due to the lack of data and general uncertainties associated with the phenomenon of the chloride diffusion. It differs from the deterministic approach because it computes not just a chloride profile at a certain age, but a range of chloride profiles for each probability or occurrence. Program TavProbabilidade_Fiabilidade: carries out reliability analyses of the initiation period. It takes into account the critical value of the chloride concentration on the steel that causes breakdown of the passive layer and the beginning of the propagation stage. It differs from the deterministic analysis in that it does not predict if the corrosion is going to begin or not, but to quantifies the probability of corrosion initiation. Program TavDif_1D: was created to do a one dimension deterministic analysis of the chloride diffusion process by the finite element method (FEM) which numerically solves Fick’second Law. Despite of the different FEM solver already developed in one dimension, the decision to create a new code (TavDif_1D) was taken because of the need to have a solver with friendly interface for pre- and post-process according to the need of IETCC. An innovative tool was also developed with a systematic method devised to compare the ability of the different 1D models to predict the actual evolution of chloride ingress based on experimental measurements, and also to quantify the degree of agreement of the models with each others. For the evaluation of the entire service life of the structure: a computer program has been developed using finite elements method to do the coupling of both service life periods: initiation and propagation. The program for 2D (TavDif_2D) allows the complementary use of two external programs in a unique friendly interface: • GMSH - an finite element mesh generator and post-processing viewer • OOFEM – a finite element solver. This program (TavDif_2D) is responsible to decide in each time step when and where to start applying the boundary conditions of fracture mechanics module in function of the amount of chloride concentration and corrosion parameters (Icorr, etc). This program is also responsible to verify the presence and the degree of fracture in each element to send the Information of diffusion coefficient variation with the crack width. • GMSH - an finite element mesh generator and post-processing viewer • OOFEM – a finite element solver. The advantages of the FEM with the interface provided by the tool are: • the flexibility to input the data such as material property and boundary conditions as time dependent function. • the flexibility to predict the chloride concentration profile for different geometries. • the possibility to couple chloride diffusion (initiation stage) with chemical and mechanical behavior (propagation stage). The OOFEM code had to be modified to accept temperature, humidity and the time dependent values for the material properties, which is necessary to adequately describe the environmental variations. A 3-D simulation has been performed to simulate the behavior of the beam on both, action of the external load and the internal load caused by the corrosion products, using elements of imbedded fracture in order to plot the curve of the deflection of the central region of the beam versus the external load to compare with the experimental data.

Análisis de la influencia de distintos diseños de paraguas de micropilotes, pantalla de micropilotes, paraguas de jet grouting y pantallas de jet grouting en los asientos en superficie durante la ejecución de túneles perforados superficialmente

Ya en el informe acerca del estado de la tecnología en la excavación profunda y en la construcción de túneles en terreno duro presentado en la 7ª Conferencia en Mecánica de Suelos e Ingeniería de la Cimentación, Peck (1969) introdujo los tres temas a ser tenidos en cuenta para el diseño de túneles en terrenos blandos: o Estabilidad de la cavidad durante la construcción, con particular atención a la estabilidad del frente del túnel; o Evaluación de los movimientos del terreno inducidos por la construcción del túnel y de la incidencia de los trabajos subterráneos a poca profundidad sobre los asentamientos en superficie; o Diseño del sistema de sostenimiento del túnel a instalar para asegurar la estabilidad de la estructura a corto y largo plazo. Esta Tesis se centra en los problemas señalados en el segundo de los puntos, analizando distintas soluciones habitualmente proyectadas para reducir los movimientos inducidos por la excavación de los túneles. El objeto de la Tesis es el análisis de la influencia de distintos diseños de paraguas de micropilotes, pantalla de micropilotes, paraguas de jet grouting y pantallas de jet grouting en los asientos en superficie durante la ejecución de túneles ejecutados a poca profundidad, con objeto de buscar el diseño que optimice los medios empleados para una determinada reducción de asientos. Para ello se establecen unas premisas para los proyectistas con objeto de conocer a priori cuales son los tratamientos más eficientes (de los propuestos en la Tesis) para la reducción de asientos en superficie cuando se ha de proyectar un túnel, de tal manera que pueda tener datos cualitativos y algunos cuantitativos sobre los diseños más óptimos, utilizando para ello un programa de elementos finitos de última generación que permite realizara la simulación tensodeformación del terreno mediante el modelo de suelo con endurecimiento (Hardening Soil Small model), que es una variante elastoplástica del modelo hiperbólico, similar al Hardening Soil Model. Además, este modelo incorpora una relación entre deformación y el modulo de rigidez, simulando el diferente comportamiento del suelo para pequeñas deformaciones (por ejemplo vibraciones con deformaciones por debajo de 10-5 y grandes deformaciones (deformaciones > 10-3). Para la realización de la Tesis se han elegido cinco secciones de túnel, dos correspondiente a secciones tipo de túnel ejecutado con tuneladora y tres secciones ejecutados mediante convencionales (dos correspondientes a secciones que han utilizado el método Belga y una que ha utilizado el NATM). Para conseguir los objetivos marcados, primeramente se ha analizado mediante una correlación entre modelos tridimensionales y bidimensionales el valor de relajación usado en estos últimos, y ver su variación al cambio de parámetros como la sección del túnel, la cobertera, el procedimiento constructivo, longitud de pase (métodos convencionales) o presión del frente (tuneladora) y las características geotécnicas de los materiales donde se ejecuta el túnel. Posteriormente se ha analizado que diseño de pantalla de protección tiene mejor eficacia respecto a la reducción de asientos, variando distintos parámetros de las características de la misma, como son el empotramiento, el tipo de micropilotes o pilote, la influencia del arriostramiento de las pantallas de protección en cabeza, la inclinación de la pantalla, la separación de la pantalla al eje del túnel y la disposición en doble fila de la pantalla de pantalla proyectada. Para finalizar el estudio de la efectividad de pantalla de protección para la reducción de asiento, se estudiará la influencia de la sobrecarga cercanas (simulación de edificios) tiene en la efectividad de la pantalla proyectada (desde el punto de vista de reducción de movimientos en superficie). Con objeto de poder comparar la efectividad de la pantalla de micropilotes respecto a la ejecución de un paraguas de micropilotes se ha analizado distintos diseños de paraguas, comparando el movimiento obtenido con el obtenido para el caso de pantalla de micropilotes, comparando ambos resultados con los medidos en obras ya ejecutadas. En otro apartado se ha realizado una comparación entre tratamientos similar, comparándolos en este caso con un paraguas de jet grouting y pantallas de jet grouting. Los resultados obtenidos se han con valores de asientos medidos en distintas obras ya ejecutadas y cuyas secciones se corresponden a los empleados en los modelos numéricos. Since the report on the state of technology in deep excavation and tunnelling in hard ground presented at the 7th Conference on Soil Mechanics and Foundation Engineering, Peck (1969) introduced the three issues to be taken into account for the design of tunnels in soft ground: o Cavity Stability during construction, with particular attention to the stability of the tunnel face; o Evaluation of ground movements induced by tunnelling and the effect of shallow underground workings on surface settlement; o Design of the tunnel support system to be installed to ensure short and long term stability of the structure. This thesis focuses on the issues identified in the second point, usually analysing different solutions designed to reduce the movements induced by tunnelling. The aim of the thesis is to analyse the influence of different micropile forepole umbrellas, micropile walls, jet grouting umbrellas and jet grouting wall designs on surface settlements during near surface tunnelling in order to use the most optimal technique to achieve a determined reduction in settlement. This will establish some criteria for designers to know a priori which methods are most effective (of those proposed in the thesis) to reduce surface settlements in tunnel design, so that it is possible to have qualitative and some quantitative data on the optimal designs, using the latest finite element modelling software that allows simulation of the ground’s infinitesimal strain behaviour using the Hardening Soil Small Model, which is a variation on the elasto-plastic hyperbolic model, similar to Hardening Soil model. In addition, this model incorporates a relationship between strain and the rigidity modulus, simulating different soil behaviour for small deformations (eg deformation vibrations below 10-5 and large deformations (deformations > 10-3). For the purpose of this thesis five tunnel sections have been chosen, two sections corresponding to TBM tunnels and three sections undertaken by conventional means (two sections corresponding to the Belgian method and one corresponding to the NATM). To achieve the objectives outlined, a correlation analysis of the relaxation values used in the 2D and 3D models was undertaken to verify them against parameters such as the tunnel cross-section, the depth of the tunnel, the construction method, the length of step (conventional method) or face pressure (TBM) and the geotechnical characteristics of the ground where the tunnel is constructed. Following this, the diaphragm wall design with the greatest efficiency regarding settlement reduction was analysed, varying parameters such as the toe depth, type of micropiles or piles, the influence of bracing of the head protection diaphragm walls, the inclination of the diaphragm wall, the separation between the diaphragm wall and the tunnel axis and the double diaphragm wall design arrangement. In order to complete the study into the effectiveness of protective diaphragm walls ofn the reduction of settlements, the influence of nearby imposed loads (simulating buildings) on the effectiveness of the designed diaphragm walls (from the point of view of reducing surface movements) will be studied. In order to compare the effectiveness of micropile diaphragm walls regarding the installation of micropile forepole umbrellas, different designs of these forepole umbrellas have been analysed comparing the movement obtained with that obtained for micropiled diaphragm walls, comparing both results with those measured from similar completed projects. In another section, a comparison between similar treatments has been completed, comparing the treatments with a forepole umbrella by jet grouting and jet grouting walls. The results obtained compared with settlement values measured in various projects already completed and whose sections correspond to those used in the numerical models.

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.

Combining a Similar Coefficient Identification Algorithm with the Boundary Element Method

The boundary element method (BEM) has been applied successfully to many engineering problems during the last decades. Compared with domain type methods like the finite element method (FEM) or the finite difference method (FDM) the BEM can handle problems where the medium extends to infinity much easier than domain type methods as there is no need to develop special boundary conditions (quiet or absorbing boundaries) or infinite elements at the boundaries introduced to limit the domain studied. The determination of the dynamic stiffness of arbitrarily shaped footings is just one of these fields where the BEM has been the method of choice, especially in the 1980s. With the continuous development of computer technology and the available hardware equipment the size of the problems under study grew and, as the flop count for solving the resulting linear system of equations grows with the third power of the number of equations, there was a need for the development of iterative methods with better performance. In [1] the GMRES algorithm was presented which is now widely used for implementations of the collocation BEM. While the FEM results in sparsely populated coefficient matrices, the BEM leads, in general, to fully or densely populated ones, depending on the number of subregions, posing a serious memory problem even for todays computers. If the geometry of the problem permits the surface of the domain to be meshed with equally shaped elements a lot of the resulting coefficients will be calculated and stored repeatedly. The present paper shows how these unnecessary operations can be avoided reducing the calculation time as well as the storage requirement. To this end a similar coefficient identification algorithm (SCIA), has been developed and implemented in a program written in Fortran 90. The vertical dynamic stiffness of a single pile in layered soil has been chosen to test the performance of the implementation. The results obtained with the 3-d model may be compared with those obtained with an axisymmetric formulation which are considered to be the reference values as the mesh quality is much better. The entire 3D model comprises more than 35000 dofs being a soil region with 21168 dofs the biggest single region. Note that the memory necessary to store all coefficients of this single region is about 6.8 GB, an amount which is usually not available with personal computers. In the problem under study the interface zone between the two adjacent soil regions as well as the surface of the top layer may be meshed with equally sized elements. In this case the application of the SCIA leads to an important reduction in memory requirements. The maximum memory used during the calculation has been reduced to 1.2 GB. The application of the SCIA thus permits problems to be solved on personal computers which otherwise would require much more powerful hardware.

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.

Análisis del acoplamiento vibro-acústico en resonadores de membrana

El presente Trabajo Fin de Máster pretende llevar a cabo el análisis del comportamiento vibratorio de resonadores de membrana, consistentes en un panel delgado y ligero montado a cierta distancia de un elemento constructivo rígido y pesado. Este tipo de sistemas resonantes son empleados habitualmente como absorbentes de media-baja frecuencia en aplicaciones de acondicionamiento acústico de salas. El análisis hará especial hincapié en la influencia del acoplamiento mecánico-acústico entre la placa vibrante (estructura) y el colchón de aire (fluido) encerrado entre la misma y la pared rígida. En primer lugar, realizaremos el análisis modal experimental del resonador objeto de ensayo a partir de las mediciones de su respuesta vibratoria, con el fin de caracterizar su comportamiento en base a sus primeros modos propios acoplados de flexión. El análisis de las señales vibratorias en el dominio de la frecuencia para la identificación de dicho modos se realizará en el entorno de programación MATLAB, haciendo uso de una herramienta propia que implementa los métodos de cálculo y los algoritmos necesarios para tal fin. Asimismo, simularemos el comportamiento del resonador mediante el método de elementos finitos (FEM), utilizando las aplicaciones ANSYS y SYSNOISE, considerando diferentes condiciones frontera en el modelo generado. Los resultados aquí obtenidos serán de utilidad para complementar aquellos obtenidos de forma experimental a la hora de extraer conclusiones prácticas del análisis realizado. SUMMARY. This Master's Thesis intends to carry out the analysis of the vibratory behaviour of resonance absorbers, consisting of a thin and lightweight panel mounted at a distance from a rigid wall. Such systems are commonly used as sound absorption systems for mid-low frequency in room acoustics applications. The analysis will emphasize the influence of mechanical-acoustic coupling between the vibrating plate (structure) and the air cushion (acoustic element) enclosed behind it. First of all, we are performing the experimental modal analysis of the resonance absorber under test from the vibrational response measurements, in order to characterize its behaviour based on its first bending coupled-modes. The analysis of vibration signals in the frequency domain for the identification of such modes will be made in MATLAB programming environment, using a proprietary tool that implements the calculation methods and algorithms needed for this purpose. Furthermore, we are simulating the behaviour of the resonance absorber applying the Finite Element Method (FEM) – using ANSYS and SYSNOISE applications - considering different boundary conditions in the model created. The results from the simulation will be useful to complement those obtained experimentally when drawing practical conclusions from this analysis.

Seismic performance case study of bridge pile cap foundation

The purpose of this report is to build a model that represents, as best as possible, the seismic behavior of a pile cap bridge foundation by a nonlinear static (analysis) procedure. It will consist of a reproduction of a specimen already built in the laboratory. This model will carry out a pseudo static lateral and horizontal pushover test that will be applied onto the pile cap until the failure of the structure, the formation of a plastic hinge in the piles due to the horizontal deformation, occurs. The pushover test consists of increasing the horizontal load over the pile cap until the horizontal displacement wanted at the height of the pile cap is reached. The output of this model will be a Skeleton curve that will plot the lateral load (kN) over the displacement (m), so that the maximum movement the pile cap foundation can reach before its failure can be calculated. This failure will be achieved when the load at that specific shift is equal to 85% of the maximum. The pile cap foundation finite element model was based on pile cap built for a laboratory experiment already carried out by the Master student Deming Zhang at Tongji University. Two different pile caps were tested with a difference in height above the ground level. While one has 0:3m, the other rises 0:8m above the ground level. The computer model was calibrated using the experimental results. The pile cap foundation will be programmed in a finite element environment called OpenSees (Open System for Earthquake Engineering Simulation [28]). This environment is a free software developed by Berkeley University specialized, as it name says, in the study of earthquakes and its effects on structures. This specialization is the main reason why it is being used for building this model as it makes it possible to build any finite element model, and perform several analysis in order to get the results wanted. The development of OpenSees is sponsored by the Pacific Earthquake Engineering Research Center through the National Science Foundation engineering and education centers program. OpenSees uses Tcl language to program it, which is a language similar to C++.

Latent hardening size effect in small-scale plasticity

We aim at understanding the multislip behaviour of metals subject to irreversible deformations at small-scales. By focusing on the simple shear of a constrained single-crystal strip, we show that discrete Dislocation Dynamics (DD) simulations predict a strong latent hardening size effect, with smaller being stronger in the range [1.5 µm, 6 µm] for the strip height. We attempt to represent the DD pseudo-experimental results by developing a flow theory of Strain Gradient Crystal Plasticity (SGCP), involving both energetic and dissipative higher-order terms and, as a main novelty, a strain gradient extension of the conventional latent hardening. In order to discuss the capability of the SGCP theory proposed, we implement it into a Finite Element (FE) code and set its material parameters on the basis of the DD results. The SGCP FE code is specifically developed for the boundary value problem under study so that we can implement a fully implicit (Backward Euler) consistent algorithm. Special emphasis is placed on the discussion of the role of the material length scales involved in the SGCP model, from both the mechanical and numerical points of view.

High-accuracy adaptive simulations of a Petri dish exposed to electromagnetic radiation

This paper analyses numerically the electric field distribution of a liquid contained in a Petri dish when exposed to electromagnetic waves excited in a rectangular waveguide. Solutions exhibit high-gradients due to the presence of the dielectric liquid contained in the dish. Furthermore, electromagnetic fields within the dielectric have a dramatically lower value than on the remaining part of the domain, which difficults its simulation. Additionally, various singularities of different intensity appear along the boundary of the Petri dish. To properly reproduce and numerically study those effects, we employ a highly-accurate hp-adaptive finite element method. Results of this study demonstrate that the electric field generated within the circular Petri dish is non-homogeneous, and thus, a better shape, size, or location of the dish is needed to achieve an equally distributed radiation enabling the uniform growth of cell cultives.

Estudio de las propiedades mecánicas de obleas de silicio

En esta tesis se propone un procedimiento para evaluar la resistencia mecánica de obleas de silicio cristalino y se aplica en diferentes casos válidos para la industria. En el sector de la industria fotovoltaica predomina la tecnología basada en paneles de silicio cristalino. Estos paneles están compuestos por células solares conectadas en serie y estas células se forman a partir de obleas de silicio. Con el objetivo de disminuir el coste del panel, en los últimos años se ha observado una clara tendencia a la reducción del espesor de las obleas. Esta reducción del espesor modifica la rigidez de las obleas por lo que ha sido necesario modificar la manera tradicional de manipularlas con el objetivo de mantener un bajo ratio de rotura. Para ello, es necesario conocer la resistencia mecánica de las obleas. En la primera parte del trabajo se describen las obleas de silicio, desde su proceso de formación hasta sus propiedades mecánicas. Se muestra la influencia de la estructura cristalográfica en la resistencia y en el comportamiento ya que el cristal de silicio es anisótropo. Se propone también el método de caracterización de la resistencia. Se utiliza un criterio probabilista basado en los métodos de dimensionamiento de materiales frágiles en el que la resistencia queda determinada por los parámetros de la ley de Weibull triparamétrica. Se propone el procedimiento para obtener estos parámetros a partir de campañas de ensayos, modelización numérica por elementos finitos y un algoritmo iterativo de ajuste de los resultados. En la segunda parte de la tesis se describen los diferentes tipos de ensayos que se suelen llevar a cabo con este material. Se muestra además, para cada uno de los ensayos descritos, un estudio comparativo de diferentes modelos de elementos finitos simulando los ensayos. Se comparan tanto los resultados aportados por cada modelo como los tiempos de cálculo. Por último, se presentan tres aplicaciones diferentes donde se ha aplicado este procedimiento de estudio. La primera aplicación consiste en la comparación de la resistencia mecánica de obleas de silicio en función del método de crecimiento del lingote. La resistencia de las tradicionales obleas monocristalinas obtenidas por el método Czochralski y obleas multicristalinas es comparada con las novedosas obleas quasi-monocristalinas obtenidas por métodos de fundición. En la segunda aplicación se evalúa la profundidad de las grietas generadas en el proceso de corte del lingote en obleas. Este estudio se realiza de manera indirecta: caracterizando la resistencia de grupos de obleas sometidas a baños químicos de diferente duración. El baño químico reduce el espesor de las obleas eliminando las capas más dañadas. La resistencia de cada grupo es analizada y la comparación permite obtener la profundidad de las grietas generadas en el proceso de corte. Por último, se aplica este procedimiento a un grupo de obleas con características muy especiales: obleas preparadas para formar células de contacto posterior EWT. Estas obleas presentan miles de agujeros que las debilitan considerablemente. Se aplica el procedimiento de estudio propuesto con un grupo de estas obleas y se compara la resistencia obtenida con un grupo de referencia. Además, se propone un método simplificado de estudio basado en la aplicación de una superficie de intensificación de tensiones. ABSTRACT In this thesis, a procedure to evaluate the mechanical strength of crystalline silicon wafers is proposed and applied in different studies. The photovoltaic industry is mainly based on crystalline silicon modules. These modules are composed of solar cells which are based on silicon wafers. Regarding the cost reduction of solar modules, a clear tendency to use thinner wafers has been observed during last years. Since the stiffness varies with thickness, the manipulation techniques need to be modified in order to guarantee a low breakage rate. To this end, the mechanical strength has to be characterized correctly. In the first part of the thesis, silicon wafers are described including the different ways to produce them and the mechanical properties of interest. The influence of the crystallographic structure in the strength and the behaviour (the anisotropy of the silicon crystal) is shown. In addition, a method to characterize the mechanical strength is proposed. This probabilistic procedure is based on methods to characterize brittle materials. The strength is characterized by the values of the three parameters of the Weibull cumulative distribution function (cdf). The proposed method requires carrying out several tests, to simulate them through Finite Element models and an iterative algorithm in order to estimate the parameters of the Weibull cdf. In the second part of the thesis, the different types of test that are usually employed with these samples are described. Moreover, different Finite Element models for the simulation of each test are compared regarding the information supplied by each model and the calculation times. Finally, the method of characterization is applied to three examples of practical applications. The first application consists in the comparison of the mechanical strength of silicon wafers depending on the ingot growth method. The conventional monocrystalline wafers based on the Czochralski method and the multicrystalline ones are compared with the new quasi-monocrystalline substrates. The second application is related to the estimation of the crack length caused by the drilling process. An indirect way is used to this end: several sets of silicon wafers are subjected to chemical etchings of different duration. The etching procedure reduces the thickness of the wafers removing the most damaged layers. The strength of each set is obtained by means of the proposed method and the comparison permits to estimate the crack length. At last, the procedure is applied to determine the strength of wafers used for the design of back-contact cells of type ETW. These samples are drilled in a first step resulting in silicon wafers with thousands of tiny holes. The strength of the drilled wafers is obtained and compared with the one of a standard set without holes. Moreover, a simplified approach based on a stress intensification surface is proposed.

Cover cracking of the reinforced concrete due to rebar corrosion induced by chloride penetration

Este artículo estudia el proceso de fisuración del hormigón por corrosión de la armadura. Se presenta un modelo de transporte de cloruros en el hormigón, que contempla la no-linealidad de los coeficientes de difusión, las isotermas de absorción y el fenómeno de convección. A partir de los resultados de penetración de cloruros, se establece la corrosión de la armadura con la consiguiente expansión radial. La fisuración del hormigón se estudia con un modelo de fisura embebida. Los dos modelos (iniciación y propagación) se incorporan en un programa de elementos finitos. El modelo se contrasta con resultados experimentales, obteniéndose un buen ajuste. Una de las dificultades es establecer el umbral de concentración de cloruros que da lugar al inicio de la corrosión de la armadura.This paper is focused on the chloride-induced corrosion of the rebar in RC. A comprehensive model for the chloride ingress into concrete is presented, with special attention to non-linear diffusion coefficients, chloride binding isotherms and convection phenomena. Based on the results of chloride diffusion, subsequent active corrosion is assumed and the radial expansion of the corroded reinforcement reproduced. For cracking simulation, the Strong Discontinuity Approach is applied. Both models (initiation and propagation corrosion stages) are incorporated in the same finite element program and chained. Comparisons with experimental results are carried out, with reasonably good agreements being obtained, especially for cracking patterns. Major limitations refer to difficulties to establish precise levels of basic data such as the chloride ion content at concrete surface, the chloride threshold concentration that triggers active corrosion, the rate of oxide production or the rust mechanical properties.

Experimental and numerical analysis of concrete Slabs subjected to Blast

This paper summarizes the research activities focused on the behaviour of concrete and concrete structures subjected to blast loading carried out by the Department of Materials Science of the Technical University of Madrid (PUM). These activities comprise the design and construction of a test bench that allows for testing up to four planar concrete specimens with one single explosion, the study of the performance of different protection concepts for concrete structures and, finally, the development of a numerical model for the simulation of concrete structural elements subjected to blast. Up to date 6 different types of concrete have been studied, from plain normal strength concrete, to high strength concrete, including also fibre reinforced concretes with different types of fibres. The numerical model is based on the Cohesive Crack Model approach, and has been developed for the LSDYNA finite element code through a user programmed subroutine. Despite its simplicity, the model is able to predict the failure patterns of the concrete slabs tested with a high level of accuracy

Cover cracking of reinforced concrete due to rebar corrosión induced by chloride penetration

Este artículo estudia el proceso de fisuración del hormigón por corrosión de la armadura. Se presenta un modelo de transporte de cloruros en el hormigón, que contempla la no-linealidad de los coeficientes de difusión, las isotermas de absorción y el fenómeno de convección. A partir de los resultados de penetración de cloruros, se establece la corrosión de la armadura con la consiguiente expansión radial. La fisuración del hormigón se estudia con un modelo de fisura embebida. Los dos modelos (iniciación y propagación) se incorporan en un programa de elementos finitos. El modelo se contrasta con resultados experimentales, obteniéndose un buen ajuste. Una de las dificultades es establecer el umbral de concentración de cloruros que da lugar al inicio de la corrosión de la armadura.This paper is focused on the chloride-induced corrosion of the rebar in RC. A comprehensive model for the chloride ingress into concrete is presented, with special attention to non-linear diffusion coefficients, chloride binding isotherms and convection phenomena. Based on the results of chloride diffusion, subsequent active corrosion is assumed and the radial expansion of the corroded reinforcement reproduced. For cracking simulation, the Strong Discontinuity Approach is applied. Both models (initiation and propagation corrosion stages) are incorporated in the same finite element program and chained. Comparisons with experimental results are carried out, with reasonably good agreements being obtained, especially for cracking patterns. Major limitations refer to difficulties to establish precise levels of basic data such as the chloride ion content at concrete surface, the chloride threshold concentration that triggers active corrosion, the rate of oxide production or the rust mechanical properties.