Thesis--Zurich. / Vita.

Thesis--Zurich. / Vita.

Le travail de cette thèse consiste en l’investigation de techniques de caractérisation et de contrôle électromagnétique de pièces en matériaux composites, en particulier les composites unidirectionnels à fibres de carbone (CFRP : Carbon Fibers Reinforced Polymer). Deux modèles sont alors développés. Le premier modèle qui est destiné à la caractérisation de la conductivité électrique transverse du CFRP est basé sur la percolation par réseau de résistances. Les grandeurs physiques de ce réseau sont établies à partir d’approches stochastiques (chaînes de Markov). Outre la prédiction de la conductivité électrique transverse du composite, le modèle permet d’appréhender les principaux paramètres qui influencent la conductivité. Le deuxième modèle traite du contrôle non destructif par courants de Foucault de ces matériaux en adoptant une approche de résolutions parallèle des problèmes micro et macro par la méthode dite d’éléments finis hétérogènes multi échelles (FE-HMM).Ce modèle est relativement plus précis que l’approche classique qui se base sur les techniques d’homogénéisation, ce qui permet notamment de caractériser des défauts microscopiques. / The work of this thesis consists in the investigation of characterization techniques and electromagnetic testing of composite materials, particularly the unidirectional CFRP ones (Carbon Fibers Reinforced Polymer). Two models are then developed. The first model that is intended for the characterization of the transverse electric conductivity of CFRP is based on percolation through resistor network. The physical parameters of the network make use of stochastic approaches (Markov chains). Besides predicting the transverse electrical conductivity of the material, the model allows us to understand the main parameters that influence the conductivity. The second model deals with the eddy current non-destructive testing of these materials by adopting an approach of parallel resolutions of micro and macro problems using the finite element heterogeneous multiscale method (FE-HMM). This model is relatively more accurate than the classical approach based on the homogenization techniques, and notably allows to characterize microscopic defects

Les travaux présentés dans cette thèse portent sur l’identification des propriétés électriques anisotropes de matériaux composites complexes. Ils visent à contribuer à une meilleure maîtrise de l’impact des paramètres des procédés de fabrications des différentes architectures, des formulations et du pourcentage de renforts, etc., sur le comportement électrique de ces composites. Ils s’inscrivent dans le cadre du projet de recherche FUI ACCEA (Amélioration des Conductivités des Composites pour Équipements Aéronautiques) financé en partie par la région Pays de la Loire. Ce projet a pour but de concevoir un matériau composite multi-fonctionnel d’un nouveau genre à matrice thermoplastique chargée en graphite de carbone qui verrait ses propriétés électriques et thermiques améliorées sans dégrader ses propriétés mécaniques. Dès lors l’une des principales difficultés du concepteur est donc de trouver des outils innovants de mise en oeuvre, pour améliorer les propriétés thermique et électrique de ces composites de manière non intrusive et nondestructive pour leurs propriétés mécaniques avec un moindre coût. C’est dans cette logique que nous proposons dans ce travail de thèse, une approche modélisation et une approche de mesure expérimentale du tenseur de conductivité électrique de ses composites, afin de fournir un outil d’aide à la décision sur le choix de la matrice, de l’armure, du procédé de mise en oeuvre, etc. Une confrontation entre les résultats de simulations et les mesures expérimentales a permis de valider le modèle développé. / The works presented in this thesis focuses on the identification of anisotropic electrical properties of complex composite materials. They aim to contribute to a better control of the impact of manufacturing process parameters, different architectures, formulations and fibres filling rate, etc., on the electrical behaviour of these composite materials. They inscribe themselves in the frame of the FUI ACCEA research project funded in part by the region Pays de la Loire. This project aims to produce a multi-functional composite material of a new type of thermoplastic matrix loaded with carbon graphite which would see its electrical and thermal properties improved without degrading the mechanical properties. From then one of the main difficulties of the designer is to find innovative implementation tools, to improve the thermal and electrical properties of these composites non-intrusive and non-destructive to their mechanical properties with less cost. It is in this logic that this PhD work is interested in modelling and experimental measurement of the electrical conductivity tensor of this composites to provide an help to the decision on the choice of matrix, of the weave, the implemented method, etc. The comparison between the simulation and experimental results gives a good concordance.

Algorithms are presented for the computationally efficient manipulation of graphs. These are subsequently used as the basis of a Monte Carlo method for sampling from the microcanonical ensemble of lattice configurations of a percolation model within a neighbourhood of the critical point. This new method arbitrarily increments and decrements the number of occupied lattice sites, and is shown to be a generalisation of several earlier, purely incremental, methods. As demonstrations of capability, the method was used to construct a phase diagram for exciton transport on a disordered surface, and to study finite size effects upon the incipient spanning cluster. Application of the method to the classical site percolation model on the two-dimensional square lattice resulted in an exceptionally precise estimate of the critical threshold. Although this estimate is not in agreement with earlier results, its accuracy was established through an application specific test of randomness, which is also introduced here. The same test suggests that many earlier results have been systematically biased due to the use of deficient pseudorandom number generators. The estimate made here has since been independently confirmed.

Algorithms are presented for the computationally efficient manipulation of graphs. These are subsequently used as the basis of a Monte Carlo method for sampling from the microcanonical ensemble of lattice configurations of a percolation model within a neighbourhood of the critical point. This new method arbitrarily increments and decrements the number of occupied lattice sites, and is shown to be a generalisation of several earlier, purely incremental, methods. As demonstrations of capability, the method was used to construct a phase diagram for exciton transport on a disordered surface, and to study finite size effects upon the incipient spanning cluster. Application of the method to the classical site percolation model on the two-dimensional square lattice resulted in an exceptionally precise estimate of the critical threshold. Although this estimate is not in agreement with earlier results, its accuracy was established through an application specific test of randomness, which is also introduced here. The same test suggests that many earlier results have been systematically biased due to the use of deficient pseudorandom number generators. The estimate made here has since been independently confirmed.

Thesis (Ph. D.)--Oregon State University, 1969. / Typescript. Includes bibliographical references (leaves 66-69). Also available on the World Wide Web.

Laboratory tests were performed to investigate the possibilities of using a modified form of Steinbrenner’s apparatus to estimate the intrinsic permeabilities of four different soils. Readings were taken on soils at the same moisture content but different void ratios; and on soils at the same void ratio but different moisture contents. Straight line graphs of positive slopes were obtained when the logarithm of intrinsic permeability was plotted against void ratio for peat, a sandy loam and synthetic soils. Results were extremely variable in the case of a clay soil. An attempt was made to relate the permeability estimated with the apparatus and using air as the permeant to the permeability estimated with water on core samples. Some correlation was observed between the two types of tests on the sandy loam and synthetic soils; but there was no correlation in the case of the peat and clay soils. Results, in general, were variable. / Land and Food Systems, Faculty of / Graduate

Cette thèse est consacrée à l'étude des grands clusters en percolation et se compose de quatre articles distincts. Les différents modèles étudiés sont la percolation Bernoulli, la percolation FK et la percolation orientée. Les idées clés sont la renormalisation, les grandes déviations, les inégalités FKG et BK, les proprietés de mélange. Nous prouvons un principe de grandes déviations pour les clusters en régime sous-critique de la percolation Bernoulli. Nous utilisons l'inégalité FKG pour démontrer la borne inférieure du PGD. La borne supérieure est obtenue à l'aide de l'inégalité BK combinée avec des squelettes, les squelettes étant des sortes de lignes brisées approximant les clusters. Concernant la FK percolation en régime sur-critique, nous établissons des estimés d'ordre surfacique pour la densité du cluster maximal dans une boîte en dimension deux. Nous utilisons la renormalisation et comparons un processus sur des blocs avec un processus de percolation par site dont le paramètre de rétention est proche de un. Pour toutes les dimensions, nous prouvons que les grands clusters finis de la percolation FK sont distribués dans l'espace comme un processus de Poisson. La preuve repose sur la méthode Chen-Stein et fait appel à des propriétés de mélange comme la ratio weak mixing property. Nous établissons un principe de grandes déviations surfaciques dans le régime sur-critique du modèle orienté. Le schéma de la preuve est similaire à celui du cas non-orienté, mais des difficultés surgissent malgré l'aspect Markovien du réseau orienté. De nouveaux estimés blocs sont donnés, qui décrivent le comportement du processus orienté. Nous obtenons également la décroissance exponentielle des connectivités en dehors du cône de percolation, qui représente la forme typique d'un cluster infini.

The thesis provides the discussion of three last passage percolation models. In particular, we focus on three aspects of probability theory: the law of large numbers, the order of the variance and large deviation estimates. In Chapter 1, we give a brief introduction to the percolation models in general and we present some important results for this topic which are heavily used in the following proofs. In Chapter 2, we prove a strong law of large numbers for directed last passage times in an independent but inhomogeneous exponential environment. Rates for the exponential random variables are obtained from a discretisation of a speed function that may be discontinuous on a locally finite set of discontinuity curves. The limiting shape is cast as a variational formula that maximises a certain functional over a set of weakly increasing curves. Using this result, we present two examples that allow for partial analytical tractability and show that the shape function may not be strictly concave, and it may exhibit points of non-differentiability, at segments, and non-uniqueness of the optimisers of the variational formula. Finally, in a specific example, we analyse further the macroscopic optimisers and uncover a phase transition for their behaviour. In Chapter 3, we discuss the order of the variance on a lattice analogue of the Hammersley process with boundaries, for which the environment on each site has independent, Bernoulli distributed values. The last passage time is the maximum number of Bernoulli points that can be collected on a piecewise linear path, where each segment has strictly positive but finite slope. We show that along characteristic directions the order of the variance of the last passage time is of order N2=3 in the model with boundary. These characteristic directions are restricted in a cone starting at the origin, and along any direction outside the cone, the order of the variance changes to O(N) in the boundary model and to O(1) for the non-boundary model. This behavior is the result of the two at edges of the shape function. In Chapter 4, we prove a large deviation principle and give an expression for the rate function, for the last passage time in a Bernoulli environment. The model is exactly solvable and its invariant version satisfies a Burke-type property. Finally, we compute explicit limiting logarithmic moment generating functions for both the classical and the invariant models. The shape function of this model exhibits a flat edge in certain directions, and we also discuss the rate function and limiting log-moment generating functions in those directions.