Le contrôle de la qualité des calculs de structure suscite un intérêt croissant dans les processus de conception et de certification. Il repose sur l'utilisation d'estimateurs d'erreur, dont la mise en pratique entraîne un sur-coût numérique souvent prohibitif sur des calculs de grande taille. Le présent travail propose une nouvelle procédure permettant l'obtention d'une estimation garantie de l'erreur de discrétisation dans le cadre de problèmes linéaires élastiques résolus au moyen d'approches par décomposition de domaine. La méthode repose sur l'extension du concept d'erreur en relation de comportement au cadre des décompositions de domaine sans recouvrement, en s'appuyant sur la construction de champs admissibles aux interfaces. Son développement dans le cadre des approches FETI et BDD permet d'accéder à une mesure pertinente de l'erreur de discrétisation bien avant convergence du solveur lié à la décomposition de domaine. Une extension de la procédure d'estimation aux problèmes hétérogènes est également proposée. Le comportement de la méthode est illustré et discuté sur plusieurs exemples numériques en dimension 2. / The control of the quality of mechanical computations arouses a growing interest in both design and certification processes. It relies on error estimators the use of which leads to often prohibitive additional numerical costs on large computations. The present work puts forward a new procedure enabling to obtain a guaranteed estimation of discretization error in the setting of linear elastic problems solved by domain decomposition approaches. The method relies on the extension of the constitutive relation error concept to the framework of non-overlapping domain decomposition through the recovery of admissible interface fields. Its development within the framework of the FETI and BDD approaches allows to obtain a relevant estimation of discretization error well before the convergence of the solver linked to the domain decomposition. An extension of the estimation procedure to heterogeneous problems is also proposed. The behaviour of the method is illustrated and assessed on several numerical examples in 2 dimension.

[pt] A grande maioria das obras geotécnicas, tais como algumas fundações, aterros e escavações, apresentam uma configuração geométrica tipicamente tridimensional. No entanto, em função da complexidade da obtenção de soluções considerando os aspectos inerentes à condição de deformação e tensão tridimensionais, as análises destas obras têm sido comumente realizadas adotando-se as aproximações de deformação plana e/ou axissimétrica. Esta dissertação apresenta um modelo computacional baseado na formulação em deslocamento do método dos elementos finitos para a simulação de problemas mecânicos de equilíbrio estático de obras geotécnicas em condição tridimensional. São ressaltados os problemas de capacidade de carga de fundações superficiais e a simulação da construção de aterros. O solo é considerado como um material não linear elasto-plástico e os modelos não associados Mohr-Coulomb modificado e Lade-Kim são adotados para representar sua relação tensão-deformação resistência. As estratégias de solução não linear, tanto a nível global quanto em nível de ponto de Gauss, são apresentadas e discutidas. Os exemplos de capacidade de carga das fundações superficiais são comparados com os resultados da teoria do equilíbrio limite e da análise limite indicando bons resultados. O efeito da tensão intermediária na trajetória de tensão é apresentado e discutido nos exemplos de simulação da construção de aterros. / [en] The vast majority of geotechnical works, such as some foundations, embankments and excavations, show a typical three-dimensional geometric configuration. However, depending on the complexity of obtaining solutions considering the aspects inherent to the three-dimensional deformation and stress, the analysis of these works have been performed by adopting common approaches and plane strain or axisymmetric. This dissertation presents a computational model based on displacement formulation of finite element method for simulation of mechanical problems of static equilibrium condition of geotechnical works in three dimensions. It highlights the problems of load capacity of shallow foundations and the simulation of embankment construction. The soil is considered as material non-linear elastic-plastic models and non-associated Mohr- Coulomb and modified Lade-Kim are adopted to represent their relationship stress-strain-resistance. The nonlinear solution strategies, both overall and in the Gauss point level, are presented and discussed. Examples of load capacity of shallow foundations are compared with the results of the theory of limit equilibrium and limit analysis showing good results. The effect of tension in the intermediate stress path is presented and discussed in the simulation examples of the construction of embankments.

Les propriétés des polymères sont intéressantes pour des applications pneumatiques, de verres organiques, de joints, … Leurs propriétés mécaniques sont néanmoins mal comprises. Dans ce manuscrit, le comportement mécanique du PMMA et du CR39 est étudié en fonction du temps.Il en résulte des courbes maîtresses à partir d’expérience de relaxation de contrainte et de fluage d’indentation. D'autre part, le comportement mécanique au contact est analysé sur des expériences de fluage et recouvrance d’indentation et de rayures analysées pour la première fois dans cette thèse. Finalement, des lois de comportements sont construites, leurs précisions sont comparées grâce à des calculs par éléments finis aux expériences en contact. / Polymer's low weight, deformability and easy manufacturing make them attractive materials for tire, organic glasses, sealing applications … Their mechanical properties are nonetheless poorly understood. In particular, two fields are searched over this thesis: time dependency and contact behavior for two transparent polymer: PMMA and CR39. The mechanical behavior time dependency is observed by the construction of stress relaxation and contact master curves. The mechanical contact behavior is analyzed by indentation creep and recovery experiments. Moreover the immediate scratch recovery is measured in the thesis. Finally, the uniaxial data is used to build constitutive laws, which accuracy is compared by Finite Element Modeling to contact tests.

The research presented in this work addresses open questions regarding (i) the fundamental understanding of powder compaction, and (ii) the complex mechanical response of particle-binder composites under large deformations. This work thus benefits a broad range of industries, from the pharmaceutical industry and its recent efforts on continuous manufacturing of solid tablets, to the defense and energy industries and the recurrent need to predict the performance of energetic materials. Powder compacts and particle-binder composites are essentially confined particulate systems with significant heterogeneity at the meso (particle) scale. While particle mechanics strategies for modeling evolution of mesoscale microstructure during powder compaction depend on the employed contact formulation to accurately predict macroscopic quantities like punch and die wall pressures, modeling of highly nonlinear, strain-path dependent macroscopic response without a distinctive yield surface, typical of particle-binder composites, requires proper constitutive modeling of these complex deformation mechanisms. Moreover, continued loading of particle-binder composites over their operational life may introduce significant undesirable changes to their microstructure and mechanical properties. These challenges are addressed with a combined effort on theoretical, modeling and experimental fronts, namely, (a) novel contact formulations for elasto-plastic particles under high levels of confinement, (b) a multi-scale experimental procedure for assessing changes in microstructure and mechanical behavior of particle-binder composites due to cyclic loading and time-recovery, and (c) a finite strain nonlinear elastic, endochronic plastic constitutive formulation for particle-binder composites.

La presente tesis tiene como finalidad establecer criterios de influencia entre parámetros geotécnicos y profundidad de excavaciones en suelos gravosos, mediante la aplicación de un software de elementos finitos. Para ello, se tomó como referencia a 5 estudios geotécnicos desarrollados en Lima Metropolitana (Santa Anita, San Isidro, Miraflores y San Luis), en donde se emplearon diversos ensayos con el fin de obtener parámetros necesarios para su modelación. Por ejemplo, gracias a estos estudios, se determinaron rangos a los parámetros geotécnicos (Ángulo de fricción, Cohesión y Peso Específico) que serán considerados en la modelación de los casos de estudio. De acuerdo con estos estudios, el Ángulo de Fricción oscila entre 25° y 46°; la Cohesión entre 10 kPa y 84 kPa; mientras que el Peso Específico tiene un rango de 18 kN/m3 a 24 kN/m3. Las excavaciones que serán evaluadas durante la presente investigación serán de 8m, 12m y 16m de profundidad y contarán también con rangos para el Módulo de Elasticidad (E50) y el Coeficiente de carga y descarga (Eur) necesarios para analizar el comportamiento físico del suelo. Los resultados obtenidos luego de emplear el Modelo Constitutivo Hardening Soil, fue que conforme van incrementado los Ángulos de fricción del suelo y el Módulo de Elasticidad (E50), los desplazamientos van disminuyendo poco a poco (estamos hablando de una relación inversamente proporcional). Asimismo, existe una relación directamente proporcional entre la profundidad de excavación, el módulo de elasticidad y los desplazamientos del suelo considerando un sistema de reforzamiento anclado. / The purpose of this thesis is to establish criteria of influence between geotechnical parameters and depth of excavations in burdensome soils, through the application of finite element software. For this, 5 geotechnical studies developed in Metropolitan Lima (Santa Anita, San Isidro, Miraflores and San Luis) were taken as a reference, where various tests were used in order to obtain parameters necessary for their modeling. For example, thanks to these studies, ranges were determined for the geotechnical parameters (Angle of friction, Cohesion and Specific Weight) that will be considered in the modeling of the case studies. According to these studies, the Angle of Friction ranges from 25 ° to 46 °; Cohesion between 10 kPa and 84 kPa; while the Specific Weight has a range from 18 kN / m3 to 24 kN / m3. The excavations that will be evaluated during this investigation will be 8m, 12m and 16m deep and will also have ranges for the Modulus of Elasticity (E50) and the Coefficient of loading and unloading (Eur) necessary to analyze the physical behavior of the soil. The results obtained after using the Hardening Soil Constitutive Model were that as the friction Angles of the soil and the Modulus of Elasticity (E50) increase, the displacements gradually decrease (we are talking about an inversely proportional relationship). Likewise, there is a directly proportional relationship between excavation depth, modulus of elasticity and soil displacements considering an anchored reinforcement system. / Tesis

Choice of the constitutive model and determination of input parameters are necessary for a successful application of numerical methods in geotechnical engineering. Higher complexity of modern constitutive models results in an increase of the number of input parameters and time requirements for their calibration. Optimization methods are a possible solution for this problem. An application in which metaheuristic optimization method Particle swarm optimization (PSO) is involved is presented in this thesis. Critical review and testing of various PSO alternatives was performed in the first part of this thesis. The most efective PSO alternatives were chosen. In the second part connection between PSO algorithm and finite element solver was prepared. Automatization of determination of constitutive models input parameters was performed on three boundary value problems: laboratory test (oedometer), in-situ test (pressuremeter) and geotechical construction (retaining wall). Three types of constitutive models are used. Linear elastic-perfectly plastic Mohr-Coulomb model, elastoplastic non-linear Hardening soil model and Hardening soil - small strain model.

Die vorliegende Arbeit stellt eine mehrskalige Modellierungs-Strategie für die Beschreibung magnetorheologischer Elastomere (MRE) vor. Diese ermöglicht die Betrachtung von MRE sowohl auf der Mikroskala, wo die heterogene Mikrostruktur bestehend aus Partikeln und Matrix explizit aufgelöst ist, als auch auf der Makroskala, in welcher das MRE als homogener magnetisch aktiver Körper aufzufassen ist. Auf beiden Skalen kommt dabei eine Kontinuumsformulierung des gekoppelten magneto-mechanischen Feldproblems mit Gültigkeit für finite Deformationen zum Einsatz, wobei die Lösung des Systems partieller Differentialgleichungen mittels der Finite-Elemente-Methode erfolgt. Ausgehend von einer experimentellen Charakterisierung der Konstituenten werden Materialmodelle für die elastomere Matrix sowie Carbonyleisen- und Neodym-Eisen-Bor-Partikel formuliert und mittels dieser Daten kalibriert. Im nächsten Schritt erfolgt die Analyse des effektiven Verhaltens hart- und weichmagnetischer MRE auf Basis von numerischen Homogenisierungen verschiedener mikroskopischer Partikelverteilungen und den Materialmodellen für die Konstituenten. Um weiterhin die effiziente Simulation makroskopischer MRE-Proben und -Bauteile zu ermöglichen, ist daran anschließend die Entwicklung und Parametrisierung eines Makromodells ausgehend von mikroskopisch generierten Datensätzen beschrieben. Mit diesem für isotrope, weichmagnetische und elastische MRE gültigen Modell werden abschließend Simulationen des magnetostriktiven sowie des magnetorheologischen Effektes verschiedener Proben durchgeführt. / In this contribution, a strategy for the multiscale modeling of magnetorheological elastomers (MREs) is presented. It allows to consider these materials on the microscopic scale, where the heterogeneous microstructure consisting of an elastomer matrix and embedded magnetizable particles is explicitly resolved, as well as the macroscopic scale, where the MRE is considered to be a homogeneous magneto-active body. On both scales, a continuum formulation of the coupled magneto-mechanical boundary value problem valid for finite strains is applied. The solution of the system of partial differential equations is calculated by using the finite element method. Starting with an experimental characterization of the individual constituents, constitutive models for the elastomer matrix as well as carbonyl iron and neodymium-iron-boron particles are formulated and adjusted to experimental data. In a next step, basic effective properties of magnetically soft and hard MREs are analyzed by using a computational homogenization scheme, where different geometrical arrangements of the particles on the microscale are considered. In order to enable the efficient simulation of macroscopic MRE samples and components, the developement and parametrization of a macroscopic model based on a microscopically generated data basis is described. With this model which is applicable for isotropic, magnetically soft and elastic MREs, simulations of the magnetostrictive and magnetorheological effects of several sample geometries are performed.

In diesem Preprint werden grundlegende Gleichungen zur Behandlung von transversal isotropem Materialverhalten zusammengetragen. Wir betrachten ein transversal isotropes Materialgesetz mit linear elastischem Verhalten. Die angegebenen Materialgleichungen sind zur Beschreibung sowohl kleiner als auch großer Deformationen geeignet. Sie bilden eine wesentliche Grundlage zur Lösung statischer Probleme mit der Methode der finiten Elemente. Es werden Gleichungen für den ebenen Spannungszustand und den ebenen Verzerrungszustand hergeleitet.:1 Einführung 2 Energiefunktional 3 Umrechnung der Materialkonstanten 4 Elastizitätsmatrix 5 Eigenwerte 6 Ebener Verzerrungszustand 7 Ebener Spannungszustand 8 Anhang

In the first part of this thesis we are concerned with the constitutive the- ory for incompressible fluids characterized by a continuous monotone rela- tion between the velocity gradient and the Cauchy stress. We, in particular, investigate a class of activated fluids that behave as the Euler fluid prior activation, and as the Navier-Stokes or power-law fluid once the activation takes place. We develop a large-data existence analysis for both steady and unsteady three-dimensional flows of such fluids subject either to the no-slip boundary condition or to a range of slip-type boundary conditions, including free-slip, Navier's slip, and stick-slip. In the second part we show that the W−1,q norm is localizable provided that the functional in question vanishes on locally supported functions which constitute a partition of unity. This represents a key tool for establishing local a posteriori efficiency for partial differential equations in divergence form with residuals in W−1,q . In the third part we provide a novel analysis for the pressure convection- diffusion (PCD) preconditioner. We first develop a theory for the precon- ditioner considered as an operator in infinite-dimensional spaces. We then provide a methodology for constructing discrete PCD operators for a broad class of pressure discretizations. The...

1 Abstract: The diploma thesis focuses on study of sex chromosomes evolution and repetitive organized genes of chosen mygalomorph and araneomorph spiders. Spiders are characterized by complexicity of sex chromosome systems, their karyotypes contain multiple sex chromosomes X. Besides multiple X chromosomes they also contain a pair or two pairs of nondiferentiated sex chromosomes X and Y. The used methods include methods of classical cytogenetics (preparation of chromosome slides, C-banding) and methods of molecular cytogenetics (fluorescent in situ hybridization and comparative genome hybridization). Complex sex systems were discovered in the studied Theraphosidae spiders. In Theraphosidae spiders Atropothele socotrana and Poecilotheria vittata neo-sex chromosomes were found. Analysis of molecular differentiation of sex chromosomes suggests low differentiation of Y chromosome in neo-sex chromosomes and pair of nondifferentiated sex chromosomes XY. In haplogyne spider Kukulcania aff. hibernalis (X1X2Y), the Y chromosome was significantly differentiated, male specific signal covered the whole chromosome. Detection of 18S rDNA showed that karyotypes of majority of analysed Theraphosidae spiders and haplogyne spiders contain low number (1 or 2) of nucleolar organizing regions localized terminally, which...