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• High-performance model reduction procedures in multiscale simulations

  J. Hernández, J. Oliver, A. Huespe, M. Caicedo

  Monograph CIMNE (2012). M127

  
  

  Abstract

  Technological progress and discovery and mastery of increasingly sophisticated structural materials have been inexorably tied together since the dawn of history. In the present era — the so-called Space Age —-, the prevailing trend is to design and create new materials, or improved existing ones, by meticulously altering and controlling structural features that span across all types of length scales: the ultimate aim is to achieve macroscopic proper- ties (yield strength, ductility, toughness, fatigue limit . . . ) tailored to given practical applications. Research efforts in this aspect range in complexity from the creation of structures at the scale of single atoms and molecules — the realm of nanotechnology —, to the more mundane, to the average civil and mechanical engineers, development of structural materials by changing the composition, distribution, size and topology of their constituents at the microscopic/mesoscopic level (composite materials and porous metals, for instance).

  Abstract
  Technological progress and discovery and mastery of increasingly sophisticated structural materials have been inexorably tied together since the dawn of history. In the [...]

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• Evaluación del daño por impacto en laminados de material compuesto mediante la respuesta dinámica

  M. Pérez, L. Gil, S. Oller

  Monograph CIMNE (2012). M128

  
  

  Abstract

  La presente monografía está basada en el texto de la tesis doctoral homónima defendida en la Universitat Politècnica de Catalunya el 6 de febrero de 2012, en el marco del programa de doctorado de Análisis Estructural del Departament de Resistència de Materials i Estructures a l’Enginyeria. En este estudio se analiza la viabilidad del uso de las técnicas experimentales y numéricas basadas en la respuesta dinámica, para la detección y localización del daño inducido, la cuantificación del grado de severidad y la predicción de las propiedades mecánicas residuales de laminados de material compuesto tras ser sometidos a un impacto a baja velocidad. El trabajo de investigación comprende un enfoque mixto experimental y numérico. Por un lado constituye un riguroso estudio experimental que incluye la evaluación de la resistencia a impacto, la caracterización del daño inducido, la cuantificación de los efectos en la respuesta dinámica y la evaluación de la capacidad portante residual. El estudio experimental se completa con un minucioso análisis del efecto inducido por deslaminaciones artificiales en la respuesta dinámica y en la capacidad portante residual de los laminados. Por otro lado, se ha simulado el fenómeno estimando principalmente la iniciación y la propagación del daño interlaminar e igualmente los efectos inducidos en la respuesta dinámica. En el enfoque numérico se trata el material compuesto como un sistema microestructural, en el cual los fallos surgen en la interacción entre los materiales constituyentes. Para reproducir la degradación se emplea una estrategia de reducción localizada de la rigidez elástica del material que no demanda una intervención durante el preproceso. Los resultados empíricos aportan conclusiones relevantes en relación al grado de sensibilidad y a la adecuación de los diferentes criterios de correlación modal para la identificación del daño inducido por un impacto. Los nuevos criterios de correlación definidos y el análisis conjunto de las propiedades estáticas y dinámicas residuales, han permitido acotar el intervalo de incertidumbre y reducir la limitación actual en relación a la deformación máxima admisible a compresión de los laminados. La herramienta de cálculo desarrollada permite simular el comportamiento vibratorio de laminados compuestos definiendo el material y su estado de degradación en la microescala. Los resultados corroboran la viabilidad del enfoque microestructural para la simulación del fenómeno.

  Abstract
  La presente monografía está basada en el texto de la tesis doctoral homónima defendida en la Universitat Politècnica de Catalunya el 6 de febrero [...]

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• Movimiento plano de barras gruesas rectas y curvas de sección uniforme no homogénea

  C. Filipich

  Monograph CIMNE (2012). M129

  
  

  Abstract

  El divulgado uso estructural de barras gruesas tanto rectas como curvas gruesas en las distintas aplicaciones de las diversas ingenierías, hace que conocer su comportamiento dinámico frente a solicitaciones arbitrarias, constituya una finalidad que todo avance tecnológico requiere. El presente trabajo abarca y extiende, dentro del marco de la Resistencia de Materiales (RM) y de materiales no homogéneos (materiales funcionales y/o compuestos), uno previo del autor que consiste en la teoría general de movimiento de piezas curvas gruesas homogéneas y que está desarrollado en el Capítulo primero de su Tesis Doctoral [1]. En éste se toman en consideración la totalidad de los aportes energéticos para hallar el sistema diferencial gobernante de vibración forzada. En el desarrollo general que presentaremos y que incluye entre otros a los temas nombrados, se aborda la posibilidad de que el módulo de elasticidad, el módulo de elasticidad transversal y la densidad puedan variar independiente y arbitrariamente en el dominio de la sección transversal (aunque de forma simétrica respecto del eje de simetría de la misma ya que estudiamos el movimiento plano de piezas gruesas). La teoría presentada incluye a la teoría clásica de barras delgadas rectas y curvas homogéneas (Bernoulli-Euler y barras de gran curvatura sometidas a flexión compuesta [2] [3] [4]) y como caso especial cuando tratamos barras rectas pero también homogéneas, a la denominada Teoría de Vigas Timoshenko [5]. Se desarrollan y se justifican teóricamente temas fundamentales tales como las expresiones que ligan constitutivamente al esfuerzo de corte con el régimen de deformación; la expresión general del factor de corte a través de la vía energética dependiendo de la distribución de las dos componentes de la tensión tangencial –una según el eje de simetría de la sección y perpendicular al mismo la otra– actuantes en elementos de área del plano de cada sección de la barra y debidas a un esfuerzo de corte Q. Una conclusión, que presentamos como “Resullttado Fundamenttall”, permite obtener el régimen de tensiones tangenciales para barras curvas gruesas no homogéneas, por medio de barras rectas ficticias. Es decir, se manejan unas barras rectas (curvatura infinita) en las cuales modificando algunos parámetros físico– geométricos, pueden hallarse las tensiones tangenciales y con ellas el factor de corte de barras curvas. Todavía el trabajo aporta la conclusión más importante en cuanto a la distribución de las tensiones tangenciales y con ésta el cálculo del ffacttor de cortte, que desarrollamos en la PARTE SEGUNDA denominándolo como TEOREMA GENERAL. Afirma que una vez hallada la distribución tangencial en algún tipo de barra gruesa –recta, curva o ficticia– un cálculo directo, con apropiados intercambios de parámetros físico–geométricos que dependen del tipo de barra y de la distribución de las no homogeneidades y forma de la sección transversal de la barra, permite conocer la distribución de las tensiones tangenciales en los otros dos tipos de barra con la misma sección. Se incluyen otros dos resultados originales que se denominan métodos I y II de superposición –para los tres tipos de barras gruesas que el trabajo aborda– que, cuando las secciones de las barras modifican “a saltos” sus propiedades elásticas y de densidad, puede hallarse el régimen tensional combinando linealmente regímenes conocidos de secciones homogéneas. Esto simplifica notablemente el trabajo de búsqueda para estos tipos de sección no homogénea bajo estudio. Se encuentra también un acople flexo–axial del movimiento y se trabaja y se generaliza el concepto del corrimiento del eje neutro, imposición clásica en barras homogéneas de gran curvatura que permite no sólo simplificar el proceso algebraico sino que extiende naturalmente la definición de eje neutro que se utiliza tradicionalmente en barras rectas homogéneas. Al desarrollar el ítem de vibraciones naturales de las barras gruesas partiendo de las ecuaciones de movimiento, tanto rectas como curvas, se encuentran las condiciones de ortogonalidad entre formas modales (extensión ad-hoc del tradicional modelo de Sturm– Liouville [6]) para ser utilizadas en una eventual superposición modal clásica en problemas lineales y separables, para hallar la respuesta dinámica del sistema (Vibración Forzada). Algunos Apéndices y varios Ejemplos resueltos analítica y numéricamente completan el trabajo que permite inferir que los resultados encontrados coinciden con muy buena precisión con los hallados con otras metodologías aproximadas como son las de elementos finitos en 2D y 3D pero por medio de un encuadre mucho más directo, sencillo y abarcativo. Cabe todavía agregar que la propuesta para llegar al régimen de tensiones tangenciales de las secciones de formas arbitrarias constitutivamente no homogéneas, y aún múltiplemente conexas, reemplaza a las utilizadas comúnmente para barras rectas homogéneas y que son conocidas como de Collignon o de Jourawsky. Por otro lado estas metodologías tradicionales serían prácticamente inadecuadas de utilizar para ciertos casos dentro del espectro de aplicaciones que presentamos. Fundamentalmente, lo dicho permite hallar el factor de corte de las secciones de barras gruesas y entonces completar los coeficientes del sistema diferencial que gobierna el movimiento de estos tipos estructurales. Por último entendemos que el Resullttado Fundamenttall, el TEOREMA GENERAL, los Métodos de Superposición, las Ecuaciones de Movimiento y las Condiciones de Ortogonalidad presentadas, son resultados originales dentro de la bibliografía afín.  

  Abstract
  El divulgado uso estructural de barras gruesas tanto rectas como curvas gruesas en las distintas aplicaciones de las diversas ingenierías, hace que conocer su comportamiento [...]

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• Stabilized finite element methods for convection-diffusion-reaction, Helmholtz and Stokes problems

  P. Nadukandi, E. Oñate, J. García-Espinosa

  Monograph CIMNE (2012). M130

  
  

  Abstract

  We present three new stabilized finite element (FE) based Petrov–Galerkin methods for the convection–diffusion–reaction (CDR), the Helmholtz and the Stokes problems, respectively. The work embarks upon a priori analysis of some consistency recovery procedures for some stabilization methods belonging to the Petrov–Galerkin framework. It was found that the use of some standard practices (e. g.M-Matrices theory) for the design of essentially non-oscillatory numerical methods is not appropriate when consistency recovery methods are employed. Hence, with respect to convective stabilization, such recovery methods are not preferred. Next, we present the design of a high-resolution Petrov–Galerkin (HRPG) method for the CDR problem. The structure of the method in 1d is identical to the consistent approximate upwind (CAU) Petrov–Galerkin method [68] except for the definitions of the stabilization parameters. Such a structure may also be attained via the Finite Calculus (FIC) procedure [141] by an appropriate definition of the characteristic length. The prefix high-resolution is used here in the sense popularized by Harten, i. e.second order accuracy for smooth/regular regimes and good shock-capturing in non-regular regimes. The design procedure in 1d embarks on the problem of circumventing the Gibbs phenomenon observed in L2 projections. Next, we study the conditions on the stabilization parameters to circumvent the global oscillations due to the convective term. A conjuncture of the two results is made to deal with the problem at hand that is usually plagued by Gibbs, global and dispersive oscillations in the numerical solution. A multi dimensional extension of the HRPG method using multi-linear block finite elements is also presented. Next, we propose a higher-order compact scheme (involving two parameters) on structured meshes for the Helmholtz equation. Making the parameters equal, we recover the alpha-interpolation of the Galerkin finite element method (FEM) and the classical central finite difference method. In 1d this scheme is identical to the alphainterpolation method [140] and in 2d choosing the value 0.5 for both the parameters, we recover the generalized fourth-order compact Padé approximation [81, 168] (therein using the parameter gamma = 2). We follow [10] for the analysis of this scheme and its performance on square meshes is compared with that of the quasi-stabilized FEM [10]. Generic expressions for the parameters are given that guarantees a dispersion accuracy of sixth-order should the parameters be distinct and fourth-order should they be equal. In the later case, an expression for the parameter is given that minimizes the maximum relative phase error in 2d. A Petrov–Galerkin formulation that yields the aforesaid scheme on structured meshes is also presented. Convergence studies of the error in the L2 norm, the H1 semi-norm and the l1 Euclidean norm is done and the pollution effect is found to be small. Finally, we present a collection of stabilized FE methods derived via first-order and second-order FIC procedures for the Stokes problem. It is shown that several well known existing stabilized FE methods such as the penalty technique, the Galerkin Least Square (GLS) method [93], the Pressure Gradient Projection (PGP) method [35] and the orthogonal sub-scales (OSS) method [34] are recovered from the general iii residual-based FIC stabilized form. A new family of Pressure Laplacian Stabilization (PLS) FE methods with consistent nonlinear forms of the stabilization parameters are derived. The distinct feature of the family of PLS methods is that they are nonlinear and residual-based, i. e.the stabilization terms depend on the discrete residuals of the momentum and/or the incompressibility equations. The advantages and disadvantages of these stabilization techniques are discussed and several examples of application are presented.

  Abstract
  We present three new stabilized finite element (FE) based Petrov–Galerkin methods for the convection–diffusion–reaction (CDR), the Helmholtz and the Stokes [...]

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• Clasificadores basados en máquinas de soporte vertical para el diagnóstico y predicción de la enfermedad de Alzheimer

  G. Gavidia, E. Soudah, E. Oñate

  Monograph CIMNE (2012). M131

  
  

  Abstract

  En este trabajo, se estableció una metodología de soporte al diagnostico de AD, principalmente en sus etapas MCI ocasionado por AD y demencia ocasionada por AD. Para este fin fueron obtenidos casos clínicos de dos proyectos de investigación en demencia del tipo AD de reconocida trayectoria: las bases de datos Alzheimer's Disease Neuroimaging Initiative (ADNI) (www.loni.ucla.edu/ADNI) y la base de datos The Open Access Series of Imaging Studies (OASIS) (http://www.oasis-brains.org/). Asimismo, fueron establecidas dos tareas principales: la selección de variables predictoras de AD y la construcción de modelos de clasificacion basados en máquinas de soporte vectorial (SVM), entrenados a partir de las variables seleccionadas. Las variables predictoras seleccionadas estuvieron conformadas por biomarcadores morfométricos y características socio-demográficas y neuropsicológicas. Estas variables deberan ser útiles para la discriminación de casos clínicos en tres estados: (1) Estado normal (generalmente personas mayores sanas); (2) Estado MCI ocasionado por AD; y (3) Etapa de demencia ocasionada por AD. Por otro lado, los modelos SVM estarán enfocados a dos tareas principales: (1) Diagnóstico de AD mediante la discriminación entre sujetos sanos y sujetos con AD; y (2) Predicción de AD, orientada a la discriminación de sujetos MCI con riesgo de convertirse a AD y sujetos MCI sin riesgo de conversión. Asimismo, estos modelos deberán garantizar resultados aceptables, respecto a la sensibilidad y especificidad de las tareas de clasificación. Los resultados obtenidos en esta investigación son prometedores. Por un lado, el subconjunto de variables seleccionadas como relevantes para el diagnóstico de AD, tienen correlación con los resultados de investigaciones previas. Asimismo, en la etapa de testeo, los resultados demostraron que los modelos SVM son de gran utilidad para el soporte diagnóstico clínico de esta enfermedad, siendo capaces de discriminar sujetos con AD de sujetos sanos (diagnóstico) con una exactitud mayor al 99% y distinguir a los sujetos MCI con riesgo de conversión a AD de los sujetos MCI sin riego de conversión (predicción) con una exactitud superior al 94%.

  Abstract
  En este trabajo, se estableció una metodología de soporte al diagnostico de AD, principalmente en sus etapas MCI ocasionado por AD y demencia ocasionada por [...]

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• A coupled Eulerian-Pfem model for the simulation of overtropping in rockfill dams

  A. Larese, E. Oñate, R. Rossi

  Monograph CIMNE (2012). M133

  
  

  Abstract

  Rockfill dams are nowadays often preferred over concrete dams because of their economic advantages, their flexible and thank to the great advance achieved in geosciences and geomechanics. Unfortunately their behavior in case of overtopping is still an open issue. In fact very little is known on this phenomenon that in most cases leads to the complete finite failure o the structure with catastrophic consequences in term of loss of lives and economic damage. The principal aim of the present work is the development of a computational method to simulate the overtopping and the beginning of failure of the downstream shoulder of a rockfill dam. The whole phenomenon is treated in a continuous framework. The fluid free surface problem outside and inside the rockfill slop e is treated using a unique Eulerian fixed mesh formulation. A level set technique is employed to track the evolution of the free surface. The traditional Navier-Stokes equations are modified in order to automatically detect the presence of the porous media. The non-linear seepage is evaluated using a quadratic form of the resistance law for which the Ergun's coefficients have been chosen.  

  Abstract
  Rockfill dams are nowadays often preferred over concrete dams because of their economic advantages, their flexible and thank to the great advance achieved in geosciences and [...]

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• Strain injection techniques in numerical modeling of propagating material failure

  I. Dias, J. Oliver, A. Huespe

  Monograph CIMNE (2012). M134

  
  

  Abstract

  The methodology proposed in this research work explores the use of the strain injection concept in a combination of classical strain localization methods and embedded strong discontinuities, to remove the flaws (stress locking and mesh bias dependence) of the former, and simultaneously abdicate of the global tracking algorithms usually required by the later. The basic idea is to use, after the bifurcation instant, i.e. after the time that elements are amenable to develop discontinuities, a mixed continuous displacements - discontinuous constant strains condensable finite element formulation (Q1/e0 ) for quadrilaterals in 2D. This formulation provides improved behavior results, specially, in avoiding mesh bias dependence. In a first, very short, stage after the bifurcation the concept of strong discontinuity is then left aside, and the apparent displacement jump is captured across the finite element length (smeared) like in classical strain localization settings. Immediately after, in a second stage, the kinematics of those finite elements that have developed deep enough strain localization is enriched with the injection of a weak/strong discontinuity mode that minimizes the stress locking defects. The necessary data to inject the discontinuity (the discontinuity direction and its position inside the finite element) is obtained by a post process of the strain-like internal variable field obtained in the first stage, this giving rise to a local (elemental based) tracking algorithm (the crack propagation problem) that can be locally and straightforwardly implemented in a finite element code in a non invasive manner. The obtained approach enjoys the benefits of embedded strong discontinuity methods (stress locking free, mesh bias independence and low computational cost), at a complexity similar to the classical, and simpler, though less accurate, strain localization methods. Moreover, the methodology is applicable to any constitutive model (damage, elasto-plasticity, etc.) without apparent limitations. Representative numerical simulations validate the proposed approach.

  Abstract
  The methodology proposed in this research work explores the use of the strain injection concept in a combination of classical strain localization methods and embedded strong [...]

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• A comparative study on homogenization strategies for multi-scale analysis of materials

  J. Ortolano, J. Hernández, J. Oliver

  Monograph CIMNE (2013). M135

  
  

  Abstract

  One of the most important engineering tasks over the years has been the design and manufacture of increasingly sophisticated structural materials as a result of the requirements related to the technological progress. In the last decades, the growing needs for improved properties of products have been partially solved through the development of composite materials. A key to the success of many modern structural components is the tailored behavior of the material to given applications. Therefore, research efforts in material science engineering have been focused in the design of new materials either through the creation of new structures at the scale of single atoms and molecules or through the development of structural materials by changing the composition, size, arrangement and topology of the constituents at larger scales: the microscopic/mesoscopic level. The development of new materials has been linked to the development of a new theoretical field within the mechanics of solids. This branch of the mechanical, known as Continuum Micromechanics, introduces a series of new concepts that are key to the definition of the macroscopic properties of composite materials on the basis of the definition of the characteristics of its components. Starting from the premise of separation of scales and the concept of Representative Volume Element, defined the so-called homogenization methods, whose number has been increasing as the Micromechanics is gone extend over the years. Such methods are many and varied, although especially there have been two that have been used and developed by the majority of authors: the so-called Mean-Homogenization techniques and the multi-scale based on Finite Element Approaches. Mean-fifieeld homogenization schemes are an efficient way to predict the behavior of heterogeneous materials. They range from the simplest hypotheses of the stress or strain sharing among the phases which do not require analytical solution on the associated boundary-value problem to more involved geometric models based on the solution of a boundary-value problem involving a single or composite inclusion embedded in an equivalent homogenized medium whose elastic module become part of the solution procedure. In general, they are based on analytical solutions of the boundary value problem defined in the microstructure level of the inhomogeneous material and provide good predictions for the mean values over the RVE. Although originally designed for elastic materials, some approaches to deal with elastoplastic materials and even with viscoplastic materials have been developed over the years and compared with the results obtained using Finite Element Approaches. The comparison between different methods of homogenization allows the definition of a range of validity between the different methods, which helps to discover the limitations of the various methods and aspects to take into account for future developments and research. The main goal of this work is, firstly, to present a general overview of the different techniques that have been developed in the last years in order to obtain a prediction of the behavior of elastoplastic composites by taking into account geometrical and mechanical aspects. Secondly, a comparison between the different approaches is carried out through a numerical implementation of such techniques. Both objectives will be carried out through eight different chapters. The first chapter serves as an introduction and historical review of the advances that have been made in the field of micromechanics. On the other hand, the second chapter deals with some important theoretical background that is important in the field of Continuum Micromechanics, as well as a short introduction of the different approaches that traditionally have been considered to solve the problem. One group of methods, based on analytical solutions { the so-called Mean Field Analysis { will be commented in chapter 3. Chapter 4 is devoted to the implementation and validation of a numerical tool that solves the mean-field homogenization using analytical schemes for elastoplastic materials. Subsequent chapters are devoted to the comparison of the results with the results given by the Finite Element Method. The general formulation of such method { applied to multi-scale problems { is presented in chapter 5 from a theoretical point of view, as well as the corresponding numerical examples. Finally, last chapter will be dedicated to enumerate some conclusions extracted from the present work, including some aspects that can be object of future works or improvements. The current work presents some important aspects about the theoretical concepts and the numerical implementation of some key approaches for solving the mechanical problem regarding composite materials. There exist a large number of possibilities to approximate the response of such complex materials, based in different assumptions. This document shows the general efficiency of the so-called mean-field homogenization schemes to capture correctly the macroscopic behavior of composites. Although these techniques show some limitations, like the incapability to provide results for the distribution of the different variables over the microgeometry or the low accuracy in the case of complex microgeometries (like porous materials), they represent an efficient way to predict the main general behavior of a composite material spending low computational effort. They are specially indicated to be used in the previous steps of an analysis or as a tool to validate the results with more involved approaches.

  Abstract
  One of the most important engineering tasks over the years has been the design and manufacture of increasingly sophisticated structural materials as a result of the requirements [...]

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• Algoritmos de pre y postproceso para métodos numéricos de puntos, métodos de partículas y libres de mallas

  H. Yervilla, L. González, C. Recarey

  Monograph CIMNE (2013). M136

  
  

  Abstract

  In computational mechanics, scientific visualization provides researchers and engineers with tools for studying numerical data. The basis of each of these tools is comprised by scientific visualization techniques. This thesis deals with the necessary changes to conventional scientific visualization techniques in order to visualize the results obtained from the application of particle based methods and mesh-less methods. This is done taking into account the large amount of data that results from the application of these methods and the presence or absence of contour information. Moreover, it is developed a visualization technique for representing micro-cracks and discontinuities, which are the beginning of chains of structural failures. A mesh generation method is selected, given its provided facilities, and it is adapted to generate point clouds for representing volumes and surfaces. For each proposed technique we study the advantages of the data structures used, and show its contributions to computer graphics and to data analysis.

  Abstract
  In computational mechanics, scientific visualization provides researchers and engineers with tools for studying numerical data. The basis of each of these tools is comprised [...]

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• Mechanistic and pathological study of the genesis, growth and rupture of abdominal aortic aneurysms

  E. Soudah, M. Bordone, E. Kwee, T. Loong, C. Tan, P. Uei, N. Sriram

  Monograph CIMNE (2013). M137

  
  

  Abstract

  The aim of this document is to report the study process and the work carried on by CIMNE, in order that NTU and TTSH can validate the AAA results obtained during this analysis. The structure of this numerical analysis will be used for the following cases.

  Abstract
  The aim of this document is to report the study process and the work carried on by CIMNE, in order that NTU and TTSH can validate the AAA results obtained during this analysis. [...]

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