[pt] Este trabalho dá continuidade ao desenvolvimento de uma metodologia para extensão e configuração de aplicações gráficas interativas utilizadas em simulações baseadas no método dos elementos finitos (MEF). Novos atributos requisitados pelos módulos de análise podem ser facilmente incluídos nos pré- e pós-processadores. Os atributos são definidos, através de uma linguagem de extensão interpretada relativamente simples, em um arquivo de configuração. A configuração e extensão é feita a partir da criação de classes e métodos, no contexto da programação orientada a objetos, de atributos da simulação. Esta metodologia foi implementada no desenvolvimento de um sistema integrado para simulações numéricas de problemas bidimensionais em geotecnia pelo MEF. A tese apresenta, inicialmente, uma discussão sobre a evolução dos sistemas utilizados para simulações numéricas na mecânica computacional, desenvolvidos no Departamento de Engenharia Civil da PUC-Rio, indicando os problemas existentes. A seguir, é apresentada uma extensão da arquitetura do módulo utilizado para o gerenciamento e extensão configurável dos atributos (ESAM), que, originalmente, considerava uma abordagem onde atributos só podiam ser aplicados a entidades geométricas. A nova arquitetura permite que atributos também possam ser aplicados diretamente em nós e elementos de uma malha de elementos finitos. O sistema implementado através da integração dos módulos utilizados para pré-processamento, análise numérica e pós- processamento com o módulo de gerenciamento de atributos resultou em um sistema bastante flexível, podendo ser estendido por um usuário configurador para diversos outros tipos de simulação. As fases envolvidas em um processo de simulação na mecânica computacional (definição da geometria, especificação dos atributos, geração da malha de elementos finitos, análise numérica e visualização dos resultados) são ilustradas em um exemplo de aplicação do sistema proposto. / [en] This work continues the development of a methodology for extension and configuration of interactive graphics applications utilized on a finite element simulations. New attributes necessary for the analysis modules can be easily included in pre- and post-processor modules. The attributes are defined, through a relatively simple interpreted extension language, in a configuration file. The extension and configuration is performed through the creation of classes and methods, in the context of object oriented programming, of simulation attributes. This methodology was implemented in development of an integrated system for two- dimensional numerical simulation of geotechnical problems by the finite element method. The dissertation presents, initially, a discussion on the evolution of the systems used for numerical simulations in computational mechanics, developed in Department of Civil Engineering of PUC-Rio, pointing the existing problems. In the sequence, it is presented an extension of architecture of module that manager extension the simulation attributes (ESAM), that, originally, considerated only an approach where attributes could be applied in geometrical entities. The new architecture permits that attributes may also be applied directly to nodes and elements of a finite element mesh. The system implemented through the integration of the pre- processing, numerical analysis and post-processing modules, with the attribute management module resulted in a very flexible system, that can be extended for several other types of simulations. The phases involved in a simulations of a computational mechanics process (geometry defined, attributes specification, automatic mesh generation, numerical analysis and visualization of results) are illustrated in an application example of the proposed system. / [es] Este trabajo da continuidad al desarrollo de una metodología para extensión y configuración de aplicaciones gráficas interactivas utilizadas en simulaciones que tiene como base el método de los elementos finitos (MEF). Los nuevos atributos que requieran los módulos de análisis pueden ser facilmente incluidos en los pre y pos procesadores. Los atributos son definidos, a través de un lenguaje de extensión interpretada relativamente simple, en un archivo de configuración. La configuración y extensión se realiza a partir de la creación de clases y métodos, en el contexto de la programación orientada a objetos, de atributos de la simulación. Esta metodología fue implementada en el desarrollo de un sistema integrado para simulaciones numéricas de problemas bidimensionales en geotecnía por el MEF. La tesis presenta, inicialmente, una discusión sobre la evolución de los sistemas utilizados para simulaciones numéricas en la mecánica computacional, desarrollados por el Departamento de Ingeniería Cívil de la PUC-Rio, indicando los problemas existentes. A seguir, se presenta una extensión de la arquitectura del módulo utilizado para el gerenciamiento y extensión configurable de los atributos (ESAM) que, originalmente, consideraba una abordaje donde los atributos solo podían ser aplicados a entidades geométricas. La nueva arquitectura permite que los atributos también puedan ser aplicados directamente en nodos y elementos de una malla de elementos finitos. El sistema implementado a través de la integración de los módulos utilizados para preprocesamiento, análisis numérico y posprocesamiento con el módulo de gerenciamento de atributos tuvo como resultado un sistema bastante flexible, que puede ser extendido por un usuario configurador para diversos otros tipos de simulación. Las fases involucradas en un proceso de simulación en la mecánica computacional (definición de la geometría, especificación de los atributos, generación de la malla de elementos finitos, análisis numérico y visualización de los resultados) son ilustradas en un ejemplo.

Cette thèse présente un modèle générique d'écrans de filets pare-blocs sous sollicitations dynamiques de type impacts. Ces ouvrages pare-blocs sont décrits comme un assemblage abstrait de leurs principaux constituants. Le modèle développé permet ainsi de représenter la plupart des technologies existantes. Un code de calcul en C++ utilisant une Méthode aux Éléments Discrets est développé afin de réaliser les simulations numériques d'impacts. La description générique des ouvrages est mise en œuvre au niveau du code de calcul grâce à une structuration des données et une programmation orientée objet correspondantes. Le modèle générique est complété par deux modèles mécaniques de constituants. Dans un premier temps, un modèle mécanique de filet à anneaux à 4 contacts est développé. Ce modèle est calibré et validé par une campagne expérimentale réalisée sur des anneaux en acier utilisés dans les écrans de filets. Dans un second temps, un modèle général de câble glissant est développé pour modéliser le phénomène d'effet rideau. Ce modèle démontre de fortes capacités de description des phénomènes de glissement et de très bonnes performances de calcul. Enfin, des essais d'impact en vraie grandeur sur deux écrans de filets de technologies différentes sont utilisés afin de valider le modèle générique. Les simulations numériques de ces essais sur ouvrages réels mettent en évidence la pertinence du modèle développé. Les résultats numériques sont en très bon accord avec les expérimentations et le modèle présente des capacités prédictives pertinentes dans la perspective d'usage en ingénierie. Les déformations, les temps de chargement et l'intensité des efforts sont obtenus avec des erreurs inférieures à 10 %. Des simulations complexes d'impacts répétés sont réalisées pour la première fois et le comportement lors de l'impact et pendant la phase de retour élastique après impact est bien appréhendé par le modèle. / This thesis introduces a generic model of rockfall barriers under impact loading. The structures are described as an abstract assembly of their main components. The developed model thereby enables the consideration of most of the existing technologies. A C++ code based on the Discrete Element Method is developed in order to perform the numerical simulations of impacts. The generic description of the barriers is implemented at the code level using a corresponding data structure and object-oriented programming. The generic model is completed by the mechanical models of two components. First, a mechanical model of 4-contact interlaced ring nets is developed. An experimental campaign is carried out to calibrate and validate the model against steel wire rings used in rockfall restraining nets. Second, a general sliding cable model is developed to account for the curtain effect. This model demonstrates great capabilities in describing sliding phenomena and a low computational cost. Finally, full-scale impact tests performed on two barriers of different technologies are used to validate the generic model. Numerical simulations of the full-scale tests highlight the relevance of the developed model. Numerical results agree finely with experiments and the model exhibits compelling predictive capacities for engineering applications. Deformations, loading time and forces magnitude are all predicted within 10 % relative error. Complex and unprecedented simulations of repeated impacts are carried out and the model is able to reproduce the barrier behavior both during the impact phase and after springback.

O presente trabalho trata da análise numérica de cascas abatidas com o uso do método dos elementos de contorno (MEC). A formulação é desenvolvida a partir do acoplamento entre as equações integrais para flexão de placas delgadas e para estado plano de tensão. No esquema implementado, os termos sobre o contorno são avaliados a partir de processos analíticos e numéricos de integração. No caso das integrais de domínio, aplica-se um procedimento semi-analítico de cálculo sobre células discretas. A validação do modelo computacional desenvolvido é feita com base em resultados da literatura, obtidos com uso do método dos elementos finitos e dos elementos de contorno, além de soluções analíticas. / The present work deals with the numerical analysis of shallow shells using boundary element method (BEM). The formulation is developed by coupling integral equations of plate bending and plane stress elasticity. In the implemented scheme, the boundary terms are evaluated with analytical and numerical processes of integration. In the case of domain integrals, a semi-analytical calculation procedure is applied on discrete cells. The validation of developed computational model is made with results from other works, obtained by use of BEM or finite element method, besides analytical solutions.

[pt] A modelagem de problemas relacionados a geomecânica do reservatório é tradicionalmente realizada por elementos finitos. Para utilizar esse método é preciso que o modelo englobe uma região consideravelmente superior a região em que o reservatório está inserido, além de necessitar imposição condições de contorno. Pensando em reduzir a necessidade de discretização de grandes regiões do maciço rochoso é proposto o método das funções de Green para análise geomecânica. Este método é baseado no uso de soluções analíticas clássicas (solução fundamental de Kelvin, solução fundamental de Melan, por exemplo) como soluções auxiliares para resolver problemas elasticamente heterogêneo e não lineares em meios saturados de fluidos. A não linearidade do material pode ser devido a deformações irreversíveis ou resposta de elasticidade não linear típica da análise 4D. O procedimento de solução geral depende de um método de colocação discreta e uma abordagem iterativa de ponto fixo para construir o campo de deslocamento. Esse método teve sua convergência verificada através de modelos simplificados que possuem solução analítica. Visando o avanço do desempenho computacional do método das funções de Green, foram feitas duas modificações independentes utilizando inteligência artificial. A primeira modificação é baseada na integração de dois conceitos principais: o teorema da reciprocidade e a capacidade de generalização das redes neurais artificiais. O teorema da reciprocidade é usado para formular a expressão matemática que rege o problema geomecânico, que é então discretizado no espaço em elementos inteligentes. O comportamento do campo de deformação dentro desses novos elementos é previsto usando uma rede neural artificial. Para fazer essas previsões, a rede neural usa condições de contorno de deslocamento, propriedades do material e a forma geométrica do elemento como dados de entrada. A segunda modificação consiste na utilização de soluções auxiliares que considerem a heterogeneidade de maciços estratificados. Essas soluções são obtidas através do treinamento de redes neurais artificiais que tem como dado de saída o deslocamento em um determinado ponto do maciço estratificado devido a aplicação de uma força pontual em um ponto no interior desse maciço. Para isso, as redes neurais de deslocamentos necessitam das propriedades elásticas e da espessura de cada camada do maciço bem como das coordenadas de aplicação da força pontual e do ponto onde será avaliado o deslocamento. Ao se utilizar essas soluções fundamentais baseadas em inteligência artificial é possível se obter todo o campo de deslocamentos de um problema heterogêneo e elástico de geomecânica do reservatório bastando apenas discretizar o reservatório. Cada uma das modificações do método da função de Green foi avaliada individualmente e observou-se um ganho de pelo menos 5 vezes no tempo de processo, utilizando o mesmo recurso computacional, quando se compara ao método clássico da função de Green. / [en] The analysis and simulation of problems associated with reservoir geomechanics are traditionally performed using the finite element method. However, to perform this analysis, it is necessary to consider a region much larger than the region in which the reservoir is inserted. This is done so that boundary conditions can be applied in an attempt to mimic the effect of the infinite media surrounding the reservoir. With the aim of reducing the need for discretization of large regions of the massif, a Green s functions approach was proposed for reservoir geomechanical analysis. This method is based on the use of classical analytical solutions (Kelvin s fundamental solution, Melan s fundamental solution, for example) as auxiliary solutions to solve elastically heterogeneous and nonlinear problems in fluid-saturated media. The non-linearity of the material can be due to irreversible deformations or non-linear elasticity response typical of 4D analysis. The general solution procedure relies on a discrete collocation method and an iterative fixed-point approach to build the displacement field. This method´s convergence was verified through simplified models that have analytical solutions. As the reduction in processing time is crucial for decision-makers to act in field applications, two improvements were proposed using artificial intelligence (AI) to reduce processing time of the Green s function approach. The first improvement is based on the generalization ability of artificial neural networks (ANN). Due to this characteristic, it was proposed to discretize the model with a coarse mesh of intelligent elements instead of refined mesh of traditional elements based on polynomials. The behavior of the strain field within these new elements is predicted using an ANN. To make these predictions, the neural network uses displacement boundary conditions, material properties and the geometric shape of the element as input data. The examples comparing the intelligent element approach and the traditional method were performed on a computer with 12 threads of 2,6GHz and 32GB RAM. This comparison showed reductions between five and ten times in CPU time, while maintaining the accuracy of the results. The second improvement consists in the use of auxiliary solutions that consider the heterogeneity of stratified massifs. These solutions are obtained through the training of artificial neural networks that have as output the displacement in a certain point of the stratified massif due to the application of a point load inside the massif. This ANN uses as input data elastic properties and the thickness of each layer of the massif, and of the semi-infinite media, as well as the coordinates of the point load and of the point where the displacement is to be evaluated. The use of the developed ANN-based Green’s function approach only demands the discretization of the reservoir itself, thus avoiding the discretization of other regions of the massif. Furthermore, it is possible to obtain the displacement at any point of the massif due to a pore pressure variation within the reservoir without having to solve for the other points in the massif. These two characteristics increase the efficient of the method in relation to traditional methods, such as the finite element method. A numerical example was performed on a computer with 12 threads of 2,6GHz and 32GB RAM to compare the ANN-based Green’s function approach with the traditional approach. The CPU time to obtain the solution using the ANN-based Green’s function approach was five times smaller than the that required by the traditional approach.

[pt] A Análise Isogeométrica (IGA) é um método de análise numérica de estruturas que surge com a proposta de unificação entre projeto e simulação, permitindo a criação de modelos computacionais que preservam a geometria exata do problema. Essa abordagem é possível por meio de uma classe de funções matemáticas denominadas NURBS (Non-Uniform Rational B-Splines), amplamente utilizadas em sistemas CAD (Computer-Aided Design) para modelagem de curvas e superfícies. Na análise isogeométrica, as mesmas funções que representam a geometria aproximam as variáveis de campo. Neste contexto, foi desenvolvido este trabalho que tem como objetivo fornecer uma ferramenta no âmbito da mecânica computacional para análise isogeométrica bidimensional de problemas de elasticidade linear, incluindo as etapas de modelagem, análise e visualização de resultados. O sistema é composto por dois softwares: FEMEP (Finite Element Method Educational Computer Program), desenvolvido em Python e responsável pela etapa de modelagem geométrica, e FEMOOLab (Finite Element Method Object-Oriented Laboratory), software MATLAB para análise e exibição de resultados. A ferramenta proposta apresenta uma interface gráfica de usuário (GUI) que permite a visualização e manipulação intuitiva de curvas NURBS com recursos avançados de modelagem, como interseção de curvas e recursos de reconhecimento de região que agilizam e simplificam o processo. Uma contribuição significativa deste trabalho reside na capacidade de gerar malhas isogeométricas não estruturadas, utilizando T-Splines baseadas em um algoritmo de decomposição de domínio. O sistema de código aberto permite a colaboração e o desenvolvimento contínuo pela comunidade de usuários e desenvolvedores. / [en] Isogeometric Analysis (IGA) is a numerical analysis method for structures that arises with the proposal of unification between design and simulation, allowing the creation of computational models that preserve the exact geometry of the problem. This approach is possible by a class of mathematical functions called NURBS (Non-Uniform Rational B-Splines), widely used in CAD (Computer-Aided Design) systems for modeling curves and surfaces. In isogeometric analysis, the same functions representing the geometry approximate the field variables. In this context, this work was developed to provide a tool within the scope of computational mechanics for two-dimensional isogeometric analysis of linear elasticity problems, including the steps of modeling, analysis, and visualization of results. The system consists of two software programs: FEMEP (Finite Element Method Educational Computer Program), developed in Python and responsible for the geometric modeling stage, and FEMOOLab (Finite Element Method Object-Oriented Laboratory), a MATLAB software for analysis and display of results. The proposed tool features a graphical user interface (GUI) that allows intuitive visualization and manipulation of NURBS curves with advanced modeling features such as curve intersection and region recognition features that streamline and simplify the process. A significant contribution of this work lies in the ability to generate non-structured isogeometric meshes, using T-Splines based on a domain decomposition algorithm. The open-source system allows collaboration and continuous development by the community of users and developers.

Diese Dissertation verallgemeinert die nichtkonformen Finite-Elemente-Methoden (FEMn) nach Morley und Crouzeix und Raviart durch neue gemischte Formulierungen für das Poisson-Problem, die Stokes-Gleichungen, die Navier-Lamé-Gleichungen der linearen Elastizität und m-Laplace-Gleichungen der Form $(-1)^m\Delta^m u=f$ für beliebiges m=1,2,3,... Diese Formulierungen beruhen auf Helmholtz-Zerlegungen. Die neuen Formulierungen gestatten die Verwendung von Ansatzräumen beliebigen Polynomgrades und ihre Diskretisierungen stimmen für den niedrigsten Polynomgrad mit den genannten nicht-konformen FEMn überein. Auch für höhere Polynomgrade ergeben sich robuste Diskretisierungen für fast-inkompressible Materialien und Approximationen für die Lösungen der Stokes-Gleichungen, die punktweise die Masse erhalten. Dieser Ansatz erlaubt außerdem eine Verallgemeinerung der nichtkonformen FEMn von der Poisson- und der biharmonischen Gleichung auf m-Laplace-Gleichungen für beliebiges m>2. Ermöglicht wird dies durch eine neue Helmholtz-Zerlegung für tensorwertige Funktionen. Die neuen Diskretisierungen lassen sich nicht nur für beliebiges m einheitlich implementieren, sondern sie erlauben auch Ansatzräume niedrigster Ordnung, z.B. stückweise affine Polynome für beliebiges m. Hat eine Lösung der betrachteten Probleme Singularitäten, so beeinträchtigt dies in der Regel die Konvergenz so stark, dass höhere Polynomgrade in den Ansatzräumen auf uniformen Gittern dieselbe Konvergenzrate zeigen wie niedrigere Polynomgrade. Deshalb sind gerade für höhere Polynomgrade in den Ansatzräumen adaptiv generierte Gitter unabdingbar. Neben der A-priori- und der A-posteriori-Analysis werden in dieser Dissertation optimale Konvergenzraten für adaptive Algorithmen für die neuen Diskretisierungen des Poisson-Problems, der Stokes-Gleichungen und der m-Laplace-Gleichung bewiesen. Diese werden auch in den numerischen Beispielen dieser Dissertation empirisch nachgewiesen. / This thesis generalizes the non-conforming finite element methods (FEMs) of Morley and Crouzeix and Raviart by novel mixed formulations for the Poisson problem, the Stokes equations, the Navier-Lamé equations of linear elasticity, and mth-Laplace equations of the form $(-1)^m\Delta^m u=f$ for arbitrary m=1,2,3,... These formulations are based on Helmholtz decompositions. The new formulations allow for ansatz spaces of arbitrary polynomial degree and its discretizations coincide with the mentioned non-conforming FEMs for the lowest polynomial degree. Also for higher polynomial degrees, this results in robust discretizations for almost incompressible materials and approximations of the solution of the Stokes equations with pointwise mass conservation. Furthermore this approach also allows for a generalization of the non-conforming FEMs for the Poisson problem and the biharmonic equation to mth-Laplace equations for arbitrary m>2. A new Helmholtz decomposition for tensor-valued functions enables this. The new discretizations allow not only for a uniform implementation for arbitrary m, but they also allow for lowest-order ansatz spaces, e.g., piecewise affine polynomials for arbitrary m. The presence of singularities usually affects the convergence such that higher polynomial degrees in the ansatz spaces show the same convergence rate on uniform meshes as lower polynomial degrees. Therefore adaptive mesh-generation is indispensable especially for ansatz spaces of higher polynomial degree. Besides the a priori and a posteriori analysis, this thesis proves optimal convergence rates for adaptive algorithms for the new discretizations of the Poisson problem, the Stokes equations, and mth-Laplace equations. This is also demonstrated in the numerical experiments of this thesis.

[pt] O objetivo deste estudo foi ampliar o conhecimento em mecânica de rochas evaporíticas e aplicar a mecânica computacional na modelagem numérica do comportamento estrutural de poços de petróleo em zonas de sal. Amostras de rochas evaporíticas de anidrita, halita, carnalita e taquidrita pertencentes à sequência evaporítica Ibura da Formação Muribeca, testemunhadas em poços de petróleo, foram submetidas a ensaios laboratoriais de mecânicas de rochas, em especial a ensaios triaxiais de fluência sob diferentes condições de estado de tensões e temperaturas. Nas mesmas condições de ensaio triaxial de fluência a taquidrita desenvolveu deformação axial específica de cerca de 107 vezes maior que a halita e 2,7 vezes maior que a carnalita, sendo que a anidrita permanece essencialmente indeformável. Para os ensaios triaxiais de fluência com a halita na temperatura de 86 graus Celsius foi possível definir o mecanismo duplo de deformação por fluência, enquanto que para a carnalita e a taquidrita isto ocorreu nas temperaturas de 130 e 86 graus Celsius, respectivamente. A taxa de deformação por fluência em regime permanente obtida por simulação numérica reproduziu fielmente os resultados experimentais dos ensaios triaxias de fluência, com erro relativo inferior a 1 por cento. Através dos ensaios laboratoriais foram obtidos os parâmetros geomecânicos de fluência das rochas ensaiadas e a seguir aplicados nos modelos numéricos de simulação, construídos para avaliar a influência de diversos parâmetros nos estudos de estabilidade de poços e integridade de revestimentos. A desconsideração da interação geomecânica entre estruturas salíferas e o maciço hospedeiro pode conduzir a falhas na perfuração de poços próximos a tais estruturas devido ao processo de halocinése do sal que altera o estado de tensões gravitacional. / [en] The aim of this study was to increase knowledge of evaporitic rock mechanics and apply computational mechanics in numerical modeling of structural behavior of oil wells in areas of salt. Evaporitic rock samples of anhydrite, halite, carnallite e tachyhydrite and belonging to the evaporitic sequence Ibura from the Muribeca formation, coring in oil wells, were subjected to laboratory tests of rock mechanics, especially the triaxial creep under different states of stress and temperature. Under the same conditions of triaxial creep tachyhydrite developed specific axial strain rate about 107 times that of halite and 2.7 times that of carnallite, and anhydrite remains essentially undeformed. For the triaxial creep of halite in the temperature of 86 degrees Celsius it was possible to define the double mechanism creep law, while for carnallite and tachyhydrite this occurred at temperatures of 130 and 86 degrees Celsius, respectively. The creep rate in steady state condition obtained by numerical simulation accurately reproduced the experimental results of the triaxial creep tests, with a relative error less than 1 percent. Through laboratory tests geomechanical creep parameters of the tested rocks were obtained and then applied in numerical simulation models, designed to evaluate the influence of various parameters in the well stability and casing design. The lack of consideration of the geomechanical interaction between the salt structures and the host rock can lead to drilling failures in wells near such structures due to the salt halokinesis process that changes the gravitational stress state.

Response of flexible structures — such as cable-supported bridges and aircraft wings — is associated with a number of uncertainties in structural and flow parameters. This thesis is aimed at efficient uncertainty quantification in a few such flow and flow-induced structural response problems. First, the uncertainty quantification in the lift force exerted on a submerged body in a potential flow is considered. To this end, a new method — termed here as semi-intrusive stochastic perturbation (SISP) — is proposed. A sensitivity analysis is also performed, where for the global sensitivity analysis (GSA) the Sobol’ indices are used. The polynomial chaos expansion (PCE) is used for estimating these indices. Next, two stability problems —divergence and flutter — in the aeroelasticity are studied in the context of reliability based design optimization (RBDO). Two modifications are proposed to an existing PCE-based metamodel to reduce the computational cost, where the chaos coefficients are estimated using Gauss quadrature to gain computational speed and GSA is used to create nonuniform grid to reduce the cost even further. The proposed method is applied on a rectangular unswept cantilever wing model. Next, reliability computation in limit cycle oscillations (LCOs) is considered. While the metamodel performs poorly in this case due to bimodality in the distribution, a new simulation-based scheme proposed to this end. Accordingly, first a reduced-order model (ROM) is used to identify the critical region in the random parameter space. Then the full-scale expensive model is run only over a this critical region. This is applied to the rectangular unswept cantilever wing with cubic and fifth order stiffness terms in its equation of motion. Next, the wind speed is modeled as a spatio-temporal process, and accordingly new representations of spatio-temporal random processes are proposed based on tensor decompositions of the covariance kernel. These are applied to three problems: a heat equation, a vibration, and a readily available covariance model for wind speed. Finally, to assimilate available field measurement data on wind speed and to predict based on this assimilation, a new framework based on the tensor decompositions is proposed. The framework is successfully applied to a set of measured data on wind speed in Ireland, where the prediction based on simulation is found to be consistent with the observed data.

Articular cartilage covers the articulating ends of diarthrodial joints. It plays a vital role in the function of the musculoskeletal system by allowing almost frictionless motion to occur between the articular surfaces of a diarthrodial joint. Study of cartilage contact behavior will help to understand the intrinsic biomechanical properties related to cartilage degeneration and related pathology. In order to study the mechanical behavior of the cartilage a FEM based computational model of the knee-joint was developed from MRI data. A heuristic algorithm was developed based on Image processing techniques using Evolve2D toolbox and edge detection. An indigenous path following algorithm to capture minute details of bone and soft tissue curvature was developed using Image Processing Toolbox of Matlab. Parts including femur, tibia, femoral and tibial cartilages, lateral & medial menisci were extracted as a point cloud from each of the slices and rendered into a 3D model using GUI driven CAD package RHINOCEROS 4.0. Commercial FE software HYPERMESH 9.0 was used to develop FE model from geometric model. Cartilage and Menisci were modeled using eight node hexahedral elements and bones were modeled using four node quadrilateral elements. Bones were assumed to be rigid. Cartilage and menisci were assumed to be linearly elastic, isotropic and homogenous. The knee joint was subjected to a uniaxial compressive load with tibia remaining fixed and femur subjected to two primary boundary conditions: 1.Flexion - extension and Varus - Valgus rotation constrained; 2.Only Varus - Valgus rotation constrained. Parameters such as contact area, contact pressure, contact force, centre of contact pressure, mises stress distribution; maximum and minimum principal stresses were studied at maximum compressive load condition and also in intermittent steps. This model considered both geometric and contact non-linearity. From the FE analysis, it was observed that peak contact deformation and contact area on both femoral and tibial medial cartilage was found to be greater than the lateral side under full extension condition. More than 50% of the load transmission was through the medial side - which could be an indication of cartilage degeneration. Deformation of lateral meniscus was more than the medial meniscus under angular constrained conditions. Loading history during intermittent steps suggested that contact area on lateral tibial cartilage increased with load, indicating joint asymmetry. These results indicate the importance of the rotational constraints (boundary conditions) and represent more accurate physiological behavior of knee joint. Role of menisci in this study was analyzed, which indicated that consideration of menisci is essential in biomechanical estimation of load transmission. In conclusion, detailed segmentation to develop geometric model, precise boundary conditions & time dependent behavior of cartilage and menisci helped in understanding knee joint load bearing capacity to a better accuracy and can potentially give rise to designing better cartilage implants.

A research study has been conducted to simulate liquefaction in saturated sandy soil induced by nearby controlled blasts. The purpose of the study is to help quantify soil characteristics under multiple and consecutive high-magnitude shock environments similar to those produced by large earthquakes. The simulation procedure involved the modeling of a three-dimensional half-space soil region with pre-defined, embedded, and strategically located explosive charges to be detonated at specific time intervals. LS-DYNA, a commercially available finite element hydrocode, was the solver used to simulate the event. A new geo-material model developed under the direction of the U.S. Federal Highway Administration was applied to evaluate the liquefaction potential of saturated sandy soil subjected to sequential blast environments. Additional procedural enhancements were integrated into the analysis process to represent volumetric effects of the saturated soil's transition from solid to liquid during the liquefaction process. Explosive charge detonation and pressure development characteristics were modeled using proven and accepted modeling techniques. As explosive charges were detonated in a pre-defined order, development of pore water pressure, volumetric (compressive) strains, shear strains, and particle accelerations were carefully computed and monitored using custom developed MathCad and C/C++ routines. Results of the study were compared against blast-test data gathered at the Fraser River Delta region of Vancouver, British Columbia in May of 2005 to validate and verify the modeling procedure's ability to simulate and predict blast-induced liquefaction events. Reasonable correlations between predicted and measured data were observed from the study.