Le travail présenté dans cette thèse vise à comprendre les vibrations de pièce mince durant l’usinage. De nombreux travaux proposent des modélisations de ce phénomène, mais des écarts persistent entre résultats de modélisation et réalité. Ce constat nous pousse à nous interroger sur l’emploi dans les modèles des modes propres de la pièce, sans y intégrer le contact de l’outil. Face à l’incapacité de vérifier la validité de cette hypothèse par mesures ponctuelles, la mesure de champ s’impose comme une alternative prometteuse. La deuxième partie du travail porte sur la mise au point d’un protocole expérimental novateur. Il inclut le relevé des déformées vibratoires d’une pièce mince en usinage par mesure de champs de déplacements. La stéréo corrélation d’images numériques se confronte à de nombreuses limitations dans ce contexte. Nous avons développé une méthode de réglage des capteurs permettant de contourner rapidement certaines difficultés. Cette méthode présentée sous forme graphique souligne la nécessité d’optimiser les paramètres de mesure dans un tel contexte. La troisième partie met en oeuvre le protocole de mesures. Le test des capteurs montre le fort intérêt de la mesure sans contact vis-à-vis de l’objectif recherché. Des essais d’usinage sont présentés en se basant sur une modélisation existante du broutement. Les déformées mesurées pendant l’usinage livrent des informations d’un type nouveau. Leur exploitation a impliqué la mise en place d’une procédure spécifique de traitement. La dernière partie présente les analyses de deux usinages. L’étude est effectuée au regard des états de surface obtenus, du comportement temporel, fréquentiel, et spatial. Cette approche souligne les subtilités de la génération d’état de surface en la présence de vibrations. L’examen des mesures de champs permet de relever des incohérences avec l’emploi des modes propres, classiquement utilisés en modélisation. / The work presented in this thesis aims at understanding thin part vibrations during machining. Many works propose modelings of this phenomenon but differencies still exist between modeling results and tests. This observation lead us to wonder about the employment of natural modes of the part in the models, without taking into account the tool presence. The fact that punctual measurements don’t enable to verify the validity of this hypothesis, field measurement prove to be a hopeful alternative. The second part focuses on adjusting a novel experimental protocol. It includes the recording of the thin part vibrating shapes by displacement field measurement. Digital Image Stereo Correlation is confronted to many limitations in this context. We developed a method to set sensors enabling the quick avoidance of difficulties. This method is presented in a graphical form, and underlines the need of optimising measurement parameters in such an environment. In the third part of the work, the measurement protocol is used. The sensors testing shows the high interest of contactless measurement for the aimed goal. Machininng tests are presented in connection with an existing model of chatter. The measured shapes during machining give a new sort of informations. So, their analyse implied the building of a specific processing procedure. The last part presents analyses of two machining tests. The study is done by parallely looking at the machined surface, and the behavior in temporal and frequency space as so as the part displacement fields. This approach underlines subtleties of surface generation under vibration conditions. The fields inspection enables to mark inconsistencies if employing the natural modes that are classically used in models.

The application of static shape control was investigated in this thesis particularly for a composite plate configuration using piezoelectric actuators. A new electro-mechanically coupled mathematical model was developed for the analysis and is based on a third order displacement field coupled with a layerwise electric potential concept. This formulation, TODL, is then implemented into a finite element program. The mathematical model represents an improvement over existing formulations used to model intelligent structures using piezoelectric materials as actuators and sensors. The reason is TODL does not only account for the electro-mechanical coupling within the adaptive material, it also accounts for the full structural coupling in the entire structure due to the piezoelectric material being attached to the host structure. The other significant improvement of TODL is that it is applicable to structures which are relatively thick whereas existing models are based on thin beam / plate theories. Consequently, transverse shearing effects are automatically accounted for in TODL and unlike first order shear deformation theories, shear correction factors are not required. The second major section of this thesis uses the TODL formulation in static shape control. Shape control is defined here as the determination of shape control parameters, including actuation voltage and actuator orientation configuration, such that the structure that is activated using these parameters will conform as close as possible to the desired shape. Several shape control strategies and consequently algorithms were developed here. Initial investigations in shape control has revealed many interesting issues which have been used in later investigations to improve shape controllability and also led to the development of improved algorithms. For instance, the use of discrete actuator patches has led to greater shape controllability and the use of slopes and curvatures as additional control criteria have resulted in significant reduction in internal stresses. The significance of optimizing actuator orientation and its relation to piezoelectric anisotropy in improving shape controllability has also been presented. Thus the major facets of shape control has been brought together and the algorithms developed here represent a comprehensive strategy to perform static shape control.

A new approach to the absolute measurement of two-dimensional optical path differences is presented in this thesis. The method, which incorporates a white light interferometer and a hyperspectral imaging system, is referred to as Hyperspectral Interferometry. A prototype of the Hyperspectral Interferometry (HSI) system has been designed, constructed and tested for two types of measurement: for surface profilometry and for depth-resolved displacement measurement, both of which have been implemented so as to achieve single shot data acquisition. The prototype has been shown to be capable of performing a single-shot 3-D shape measurement of an optically-flat step-height sample, with less than 5% difference from the result obtained by a standard optical (microscope) based method. The HSI prototype has been demonstrated to be able to perform single-shot measurement with an unambiguous 352 (m depth range and a rms measurement error of around 80 nm. The prototype has also been tested to perform measurements on optically rough surfaces. The rms error of these measurements was found to increase to around 4× that of the smooth surface. For the depth-resolved displacement field measurements, an experimental setup was designed and constructed in which a weakly-scattering sample underwent simple compression with a PZT actuator. Depth-resolved displacement fields were reconstructed from pairs of hyperspectral interferograms. However, the experimental results did not show the expected result of linear phase variation with depth. Analysis of several possible causes has been carried out with the most plausible reasons being excessive scattering particle density inside the sample and the possibility of insignificant deformation of the sample due to insufficient physical contact between the transducer and the sample.

The application of static shape control was investigated in this thesis particularly for a composite plate configuration using piezoelectric actuators. A new electro-mechanically coupled mathematical model was developed for the analysis and is based on a third order displacement field coupled with a layerwise electric potential concept. This formulation, TODL, is then implemented into a finite element program. The mathematical model represents an improvement over existing formulations used to model intelligent structures using piezoelectric materials as actuators and sensors. The reason is TODL does not only account for the electro-mechanical coupling within the adaptive material, it also accounts for the full structural coupling in the entire structure due to the piezoelectric material being attached to the host structure. The other significant improvement of TODL is that it is applicable to structures which are relatively thick whereas existing models are based on thin beam / plate theories. Consequently, transverse shearing effects are automatically accounted for in TODL and unlike first order shear deformation theories, shear correction factors are not required. The second major section of this thesis uses the TODL formulation in static shape control. Shape control is defined here as the determination of shape control parameters, including actuation voltage and actuator orientation configuration, such that the structure that is activated using these parameters will conform as close as possible to the desired shape. Several shape control strategies and consequently algorithms were developed here. Initial investigations in shape control has revealed many interesting issues which have been used in later investigations to improve shape controllability and also led to the development of improved algorithms. For instance, the use of discrete actuator patches has led to greater shape controllability and the use of slopes and curvatures as additional control criteria have resulted in significant reduction in internal stresses. The significance of optimizing actuator orientation and its relation to piezoelectric anisotropy in improving shape controllability has also been presented. Thus the major facets of shape control has been brought together and the algorithms developed here represent a comprehensive strategy to perform static shape control.

Au cours du développement du cancer, la migration des cellules cancéreuse en 3D joue un rôle essentiel dans le processus de dissémination des métastases. L’étude de la migration cellulaire dans des matrices 3D ainsi que les conséquences induites sur cette matrice sont actuellement étudiées par plusieurs équipes de recherche. Notamment, la réorganisation de la matrice extracellulaire et plus précisément les déplacements des fibres de la matrice induits par les forces que la cellule exerce sont des études en plein essor. Nous avons étudié comment les cellules cancéreuses migrent dans des gels 3D en utilisant du collagène et de la fibronectine pour mimer la matrice extracellulaire des tissus. Nous avons utilisé un microscope confocal afin de visualiser le cytosquelette d’actine des cellules en fluorescence et les fibres de collagène en réflexion. Dans ce travail,nous avons utilisé différentes concentrations de collagène et des lignées cellulaires d’invasivités différentes. A partir des films 3D obtenus en microscopie, nous avons déterminé la vitesse et la persistance des cellules cancéreuses en fonction de leur invasivité et de la concentration de collagène. La vitesse augmente avec l’invasivité cellulaire et diminue avec l’augmentation de la concentration en collagène. La persistance ne dépend que de la concentration en collagène et décroit avec celle-ci. Nous avons également calculé les champs de déplacement des fibres de collagène à l’aide d’un programme de corrélation de volume. Nous avons pu étudier ces champs de déplacement en fonction du type de migration de la cellule, de l’invasivité cellulaire et de la concentration en collagène des gels. Nous avons montré que les normes de vecteurs de déplacement augmentent avec l’invasivité cellulaire et diminuent avec l’augmentation de concentration en collagène. Enfin, ces champs de déplacement nous ont permis de déterminer les étapes des migrations mésenchymateuse et amiboïde en 3D. Nous avons découvert 5 étapes pour la migration mésenchymateuse correspondant au repos de la cellule, à la création d’une extension membranaire, à l’adhésion de la cellule aux fibres, au détachement de l’arrière du corps cellulaire afin de permettre à la cellule de migrer et à la dissolution de l’adhésion cellule/fibre. 4 étapes ont été déterminées pour la migration amiboïde et correspondent au repos de la cellule, à la création d’une extension membranaire, au déplacement de la cellule en poussant sur son environnement et à la rotation de la cellule. Ces étapes associées à des champs de déplacement sont en accord avec la littérature et nous avons pu mettre en évidence de nouvelles étapes comme la rotation de la cellule dans la migration amiboïde.Ces résultats permettent de mieux comprendre comment se déroule la migration des cellules cancéreuses dans une matrice extracellulaire. / 3D migration of cancer cells plays an essential role in the dissemination of cells during metastasisin cancer. The behavior of cancer cells migrating in a 3D extracellular matrix and its consequences on themicroenvironment are still currently under investigation. The study of the reorganization of the extracellular matrixfibers and more precisely how the fibers move due to the forces that the cell exerts just start to be investigating.We studied how cancer cells migrate in 3D gels using collagen and fibronectin to mimic the extracellularmatrix. We used confocal microscopy to image the actin cytoskeleton of cells in fluorescence and fibers in reflectionover time. In our studies, we used different collagen concentrations and cell lines with different invasivities. Fromthese 3D movies, we determined cancer cell velocities and persistence as a function of collagen gel concentration aswell as cell invasiveness. The cells velocities increase with invasiveness and decrease with collagen concentration.As for persistence, it decreases with collagen concentration but it do not change with cells invasiveness. We alsocalculated the displacement field of the collagen using a volume correlation program. Using this information, westudied the fibers displacement induced by the cell depending on its migration type, its invasivity and the collagenconcentration. We showed norms of fibers deplacement vectors increase with cell invasiveness and decrease withcollagen concentration. Finally, the displacement fields enabled us to determine the migration steps of mesenchymaland amiboid migrations. We discovered 5 steps in mesenchymal migration : cell rest, creation of extension, adhesionof the cell to the fibers, detachment of the cell rear and dissolution of cell/fibers adhesions. 4 steps have beencharacterized in amiboid migration : cell rest, creation of extension, displacement of the cell by pushing on fibersand rotation of the cell. These steps associated with displacement fields are in agreement with litterature and wehighlighted new steps as the rotation of the cell in amiboid migration.Taken together these results enable us to better understand how the migration of cancer cells takes place in a3D matrix.

Le travail présenté dans ce mémoire consiste à adapter la méthode de corrélation d'images numériques (CIN) pour la gestion des discontinuités du milieu et de la transformation. Le cadre d'utilisation des méthodes optiques de mesure i.e. celui de la mécanique des milieux continus, impose une continuité matérielle : i) du domaine et ii) de la transformation. Pour traiter les discontinuités en question, on peut reconsidérer la continuité (milieu et transformation) par morceaux. Dans le cadre de la CIN, cela se traduit par la possibilité d'adapter localement la forme et la taille des fenêtres de corrélation à la zone d'intérêt et à sa cinématique. Pour ce faire, il est possible d'utiliser des masques : un masque-objet pour traiter les discontinuités du milieu et un masque-discontinuité pour traiter les discontinuités de la transformation. Cependant, avant l'implémentation des masques dans la procédure de corrélation, plusieurs essais expérimentaux de déplacement sur des modèles comportant les deux types de discontinuité, ont été conduits. Ces essais ont permis de prouver l'influence des discontinuités sur la dégradation de la précision de mesure par CIN. Ensuite, des essais de traction ont été menés sur une éprouvette en polycarbonate conduisant à un mode I d'ouverture ou de fermeture de fissure. Après l'implémentation des masques dans le logiciel de corrélation Correla, le calcul des champs de déplacement et de déformation a été opéré avec succès à la surface de cette éprouvette, démontrant ainsi l'efficacité de la CIN adaptée. / The development of the digital image correlation method (DIC) for the management of discontinuities of the material and the transformation is discussed in this thesis. As we know, the framework for the use of the optical measurement methods i.e. of continuum mechanics requires a continuity of: i) domain and ii) transformation. To treat those discontinuities, we can consider a piecewise continuity (material and transformation). In the case of DIC method, this can be done by adapting locally the shape and size of the correlation subsets to the zone of interest and its kinematics. A novel way to do it, is by using masks: an object mask to process material discontinuities and a discontinuity mask to process transformation discontinuities. However before the implementation of masks in the correlation process, several experimental displacement tests on models reproducing the two types of discontinuity at small scale were performed. Those tests proved the influence of discontinuities on the degradation of the measurement accuracy by DIC. Then, tensile tests were conducted on a polycarbonate made specimen knowing a mode I opening or closing crack. After implementing masks in the correlation software Correla, the calculation of displacement and deformation fields was successfully performed on the surface of this specimen for all its edges, demonstrating the effectiveness of the adapted DIC.

No description available.

This study aims to investigate the behaviour of low-order beam and plate elements especially for their application to laminated structures. The merits and dements of the existing elements are brought out and new low-order elements with better interpolation polynomials are proposed. Two new beam elements are proposed for laminated composite beams that yield better representation of twist due to material coupling. Out of the two elements developed, one is based on the conventional formulation and the other on the coupled-field formulation, both capturing material induced coupling. The beam developed using coupled field formulation shows a novel way of obtaining a fully coupled interpolation function for field variables using the complete set of equilibrium equations for the composite beams. The element has shown a superior coarse mesh performance. These elements can practically capture plate behaviour in beam elements for a wide range of plate thickness. The locking problems in conventional 4-node quadrilateral elements, such as shear locking and geometric locking are studied. Various techniques available in literature to remedy these problems are also studied. A suite of QUAD4 with conventional techniques such as. Reduced Integration, Field Consistency, Mixed Interpolation of Tensorial strain Components, Assumed Natural Strain, Discrete Shear Gap, Incompatible modes Q6 and QM6 is developed. An effort is made to combine these techniques to develop new element that yields improved performance. The element is shown to exhibit improved performance for certain cases. Several four-node rectangular elements are developed based on the coupled-field techniques. First two new-coupled elements are formulated that employ Sabir's [101] plane bending formulation with drilling degree of freedom, and the plate bending rotations are generated using equilibrium equations. However, since Sabir's plane bending interpolation polynomials yielded inaccurate performance for composites, it led to development of elements with fully coupled field formulations. Finally, two new 4-node rectangular elements are developed using coupled-field formulations with six and seven dof freedom per node respectively. Here the interpolation polynomials are derived using the complete equilibrium equations. The elements are extensively tested for static deflection, dynamics and buckling of isotropic and laminated plates/beams. The elements show superior coarse mesh convergence. Several problems pertaining to vibration and buckling of composite plates/beams are solved using the elements developed in this work.

Les forces mécaniques, générées par la cellule jouent un rôle crucial dans l'adhésion cellulaire, qui est un processus commun à un grand nombre de lignées cellulaires. Afin de mesurer la champ des forces pendant l'adhérence cellulaire, nous utilisons la microscopie de force de traction, où la cellule adhère à la surface plane d'un substrat souple dans le plan. Les forces sont calculées à partir du champ de déplacement mesuré à l'intérieur du substrat sous la cellule. Nous avons construit le microscope, dans lequel nous utilisons des billes sphériques en polystyrène pour mesurer le champ de déplacement. Les positions des marqueurs sont obtenues en analysant I' image interférentielle des particules. Avec cette technique, nous atteignons une précision nanométrique sur le champ de déplacement des particules, ce qui nous permet d'améliorer la résolution en force de ce type de microscope. Les premières mesures ont été effectuées avec la lignée de cellules cancéreuses SW 480. / Mechanical forces, generated by the cell plays crucial role in cell adhesion - common process for different cell lines. ln order to measure the force map during cellular adhesion, we use Traction Force Microscopy (TFM), where cell adheres to the soft substrate in 20 plane, and the forces are calculated from measured displacement field inside the substrate underneath the cell. We built the microscope, where instead of using fluorescent markers, we use spherical polystyrene beads in order to measure the displacement field. Positions of the markers are obtained by analyzing the interference pattern caused by the beads in bright-field light. With this technique, we reach nanometer accuracy of the microsphere position determination, that, respectively, influence accuracy of the calculated force field. With the microscope first measurements were performed with cancer cell line SW 480.

The presented master’s thesis deals with the application of the gradient elasticity in fracture mechanics problems. Specifically, the displacement and stress field around the crack tip is a matter of interest. The influence of a material microstructure is considered. Introductory chapters are devoted to a brief historical overview of gradient models and definition of basic equations of dipolar gradient elasticity derived from Mindlin gradient theory form II. For comparison, relations of classical elasticity are introduced. Then a derivation of asymptotic displacement field using the Williams asymptotic technique follows. In the case of gradient elasticity, also the calculation of the J-integral is included. The mathematical formulation is reduced due to the singular nature of the problem to singular integral equations. The methods for solving integral equations in Cauchy principal value and Hadamard finite part sense are briefly introduced. For the evaluation of regular kernel, a Gauss-Chebyshev quadrature is used. There also mentioned approximate methods for solving systems of integral equations such as the weighted residual method, especially the least square method with collocation points. In the main part of the thesis the system of integral equations is derived using the Fourier transform for straight crack in an infinite body. This system is then solved numerically in the software Mathematica and the results are compared with the finite element model of ceramic foam.