Search

International audience; The main objective of this study is to combine the statistical shape analysis (SSA) with a morphing procedure in order to generate shape-parametric finite element models of tissues and organs and to explore the reliability and the limitations of this approach when applied to databases of real medical images. As classical statistical shape models are not always adapted to the morphing procedure, a new registration method was developed in order to maximize the morphing efficiency. The method was compared to the traditional iterative thin plate spline (iTPS). Two data sets of 33 proximal femora shapes and 385 liver shapes were used for the comparison. The principal component analysis (PCA) was used to get the principal morphing modes. In terms of anatomical shape reconstruction (evaluated through the criteria of generalization, compact-ness and specificity), our approach compared fairly well to the iTPS method, while performing remarkably better in terms of mesh quality, since it was less prone to generate invalid meshes in the interior. This was particularly true in the liver case. Such methodology offers a potential application for the generation of automated finite element (FE) models from medical images. Parametrized anatomical models can also be used to assess the influence of inter-patient variability on the biomechanical response of the tissues. Indeed, thanks to the shape parametrization the user would easily have access to a valid FE model for any shape belonging to the parameters subspace.

International audience; Micro-injection moulding is frequently used for the fabrication of devices in many different fields such as micro-medical technologies, micro-optics and micro-mechanics thanks to its effectiveness for mass production. This work focuses mainly on offering numerical methodology to model the injection into textured moulds. Such approach can predict the different filling scenarios of the micro-details and consequently can provide optimal operating conditions (mould and melt temperatures, flow rate) according to the desired final part quality. In fact, numerical simulations made with industrial software can only describe the injection process at the macroscopic scale where the micro details are not detected. Although the melt temperature and front evolution are tracked throughout time, neither the micro details nor the local heat transfer are properly represented. Since the latter impacts the local viscosity and solidification, simulation of both mould and cavity temperature evolutions is primordial to insure a complete and accurate representation of textured mould filling. The present computations are made at both macro- and micro- scales by using a full Eulerian approach in which the three phases (melt, mould and air) are described by level-set functions. Our numerical approach is checked to the replication of a textured mould for which two dimensional computations are relevant. This replication is properly modelled by taking into account viscosity dependence with temperature in the thermal boundary layer at the melt/mould interface. In particular the expected solidification below a specific temperature is taken into account by either increasing drastically the viscosity or by imposing a vanishing velocity by penalty method. The influence of flow rate and mould temperature are also analysed whereas it is shown that the surface tension can be neglected during injection stage.

In this paper we show the use of the focal underdetermined system solver to recover sparse empirical quadrature rules for parametrized integrals from existing data, consisting of the values of given parametric functions sampled on a discrete set of points. This algorithm, originally proposed for image and signal reconstruction, relies on an approximated $\ell^p$-quasi-norm minimization. The choice of $0, Comment: 27 pages, 10 figures

Flow of fiber suspensions is a major factor in the manufacturing process of discontinuous fiber composites, and which determines the characteristics of the resulting parts. To the present date, studying such problematic presents a challenge. In this thesis, we propose to use high performance computing tools in order to establish numerical simulation protocols allowing a better understanding of some critical aspects related to the issue. First, we present an Octree optimized numerical method to generate virtual isotropic and oriented discontinuous fibers microstructure. This has been achieved by developing a modified RSA algorithm based on no collisions and using particles of cylindrical shape. As a result, samples containing millions of fibers are quickly generated. Once this is done, flow through those microstructures is simulated using a stabilized finite element method associated with a multi-domain formulation. The computational domain is constituted of a unique anisotropic adapted mesh that encloses the different phases implicitly described by level-set functions. Two mains studies are carried: considering firstly a static fibrous architecture and secondly a dynamic fibers evolution. For the static case, an averaging method is applied, and permeability is determined by Darcy’s law. For the dynamic case, we present the evolution of a set of fibers within a Newtonian shear flow. Two approaches are tested and compared, a first one with weak coupling and a second one with strong coupling.; L'écoulement des suspensions de fibres est un facteur important dans le processus de fabrication des composites à fibres discontinues et qui détermine les caractéristiques des pièces obtenues. Dans cette thèse, nous proposons d'exploiter les moyens de calcul haute performance pour mettre en place des protocoles de simulations numériques permettant de mieux comprendre certains aspects critiques relatifs à cette question. Nous présentons tout d'abord un algorithme optimisé de génération de microstructures isotropes ou orientées. L’algorithme adopté est un algorithme de type adsorption séquentielle aléatoire (ASA) permettant de placer des fibres cylindriques sans collisions. Cet algorithme a été implémenté en séquentiel dans un premier temps, un algorithme de type Octree lui a été associé dans un deuxième temps, et finalement, il a été parallélisé. Par conséquent, une accélération importante est obtenue et des microstructures contenant des millions de fibres sont générées. Par la suite, l'écoulement à travers ces structures est simulé en utilisant une méthode d'éléments finis stabilisés associée à une formulation multi-domaine. Le domaine de calcul est constitué d’un maillage unique adapté autour des différentes phases implicitement décrites par des fonctions caractéristiques. Deux études principales sont menées: en considérant d'abord une architecture fibreuse statique et ensuite, une évolution dynamique des fibres. Pour le cas statique, une méthode d’homogénéisation est appliquée et la perméabilité est déterminée par la loi de Darcy. Pour le cas dynamique, nous présentons l'évolution d'un ensemble de fibres au sein d'un écoulement Newtonien de couette. Deux approches sont testées et comparées, une première avec couplage faible et une deuxième avec couplage fort.

Computer simulation is acknowledged as the third branch of Science. From the seminal work of Turner et al. (1956) [on Finite Elements, impressive improvements have been made in terms of software and hardware, so that, nowadays, there is no engineering device (in the broad sense of the word) that is not subjected to any kind of simulation. However, in the same way as there is a gap between theory and practice, at an industrial level there are still problems where, at the moment, numerical simulations are not used and instead, a hand-craft approach is applied. The mitigation of distortion in large aluminium forgings is one of these problems. Post-machining distortion is an open problem that affects every single large thickwalled aluminium forging assembled on an aircraft. The origin of distortion is the presence of residual stresses (RS) developed along the manufacturing chain, especially after the heat treatment of quenching. When machining takes places, it causes a redistribution at an internal level as the previous equilibrium state is broken by the material removal action. At a theoretical level, if the RS in a part are known in advance, a proper machining sequence could be planned with the aim to mitigate or counteract a warped geometry. This strategy is already implemented for parts machined from rolled plates, where RS can be considered as constant along the longitudinal direction. However, for forgings, RS are a function of the geometry and, as a result, a complex three-dimensional stress field is present. Important research efforts are done in order to predict RS numerically for forgings but still, the deterministic nature of numerical simulations are not able to capture the variable behaviour of distortions. At the moment, the current research direction looks at the distortion problem as something to avoid upwards in the manufacturing chain, it means, focusing the efforts in the steps before or during machining at latest. In the present thesis, we opted to follow the opposite direction, which means, how to proceed and handle distortion once it has arisen. To perform this task, the problem was first studied by conventional Finite Element Method (FEM), and then, by applying a non-intrusive Model Order Reduction (ROM) technique called Sparse Subspace Learning (SSL). The content of this thesis is structured as follows. In chapter 1 we introduce the distortion problem, followed by the definition and interconnection of the three main actors: residual stresses, distortion and reshaping. Then, a review of the available reshaping techniques is provided and finally, the challenges and perspectives for reshaping simulation are discussed. Chapter 2 presents two numerical models devoted to determine the residual stresses after quenching and plastic bending, respectively as the heat treatment is considered as the main source of residual stresses in aluminium forgings and the latter corresponds to the selected reshaping operation to be studied in this thesis. After its validation, both models are applied in the following chapters and they provide the reference solution to our problem. In chapter 3, we introduce the reshaping diagrams as a tool to assist the bending straightening operation. In addition, the residual stress free hypothesis is presented as an alternative to study the reshaping problem. This approach uses the distorted geometry as the main input to simulate the reshaping step by considering the part without residual stresses. Then, in chapter 4, a multiparametric study of bending straightening is provided with the aid of the SSL, so that the reshaping diagrams can be generalized for a previously defined set of parameters. Finally, as reshaping is an iterative and sequential procedure, in chapter 5, two consecutive bending straightening operations are simulated. Different reshaping strategies are studied and a methodology is provided to tackle in a more systematic way the open problem of reshaping. Las distorsiones después del mecanizado de grandes piezas de aluminio son un problema recurrente para la industria aeronáutica. Estas desviaciones de la geometría de diseño se deben a la presencia de tensiones residuales, que se desarrollan a lo largo de la cadena de fabricación, especialmente después del tratamiento térmico de temple. Para restablecer la geometría nominal, es necesario realizar una serie de operaciones de remodelación muy manuales y que requieren mucho tiempo. El presente trabajo de investigación se centra en el desarrollo de herramientas eficaces de simulación numérica para ayudar a los operadores en el enderezamiento por flexión, que es una de las operaciones de remodelación más comunes. Para ello, se desarrolla un modelo de simulación de elementos finitos representativo de la cadena de fabricación, incluyendo el temple, el mecanizado y la remodelación, que permite predecir las tensiones y distorsiones residuales en piezas forjadas de aluminio de paredes gruesas. El modelo se valida con los datos experimentales que se encuentran en la literatura. A continuación, se introduce el concepto de diagramas de remodelación, una herramienta que permite seleccionar una carga de flexión casi óptima para minimizar la distorsión. Se muestra que el diagrama de remodelación no necesita tener en cuenta el campo de tensión residual, ya que su único efecto es desfasar horizontalmente el diagrama de remodelación por una cierta distancia. Por lo tanto, el comportamiento general que incluye un campo de tensión residual tridimensional real en una pieza forjada puede recuperarse desplazando el diagrama de remodelación libre de tensión residual por el desfase apropiado. Por último, se propone una estrategia para identificar el desfase sobre la marcha durante la operación de remodelación utilizando medidas sencillas de fuerza-desplazamiento. A continuación, se explora el uso de nuevas técnicas numéricas, especialmente la reducción del orden del modelo (MOR), con un doble propósito: i) acelerar el cálculo de los diagramas de remodelación; y ii) tener en cuenta varios parámetros del proceso, como la distorsión inicial o la configuración de la remodelación. Para ello, nos basamos en el método de Sparse Subspace Learning (SSL), un método MOR no intrusivo que permite reconstruir el espacio de solución directamente a partir de los resultados del modelo de elementos finitos. Con la solución paramétrica a mano, se puede encontrar la configuración óptima de remodelación en tiempo real, para minimizar la distorsión antes de lanzar la operación de remodelación real. Por último, se propone los primeros pasos hacia la ampliación de la metodología anterior, que combina los diagramas de remodelación y los métodos MOR, a un entorno multietapa en el que se realizan varias operaciones de corrección de la forma de manera secuencial. La simulation numérique est reconnue comme étant la troisième branche de la science. À partir des travaux fondateurs de Turner et al. (1956) sur les éléments finis, des améliorations impressionnantes ont été apportées en termes de software et de hardware, de sorte qu’aujourd’hui, il n’existe plus aucun dispositif d’ingénierie (au sens large du terme) qui ne soit pas transcrit par une quelconque simulation.Cependant, tout comme il existe un fossé entre théorie et pratique, il existe encore des problèmes au niveau industriel où, pour le moment, les simulations numériques n’ont pas encore pris la place des approches artisanales. L’atténuation de la distorsion dans les grandes pièces forgées en aluminium est l’un des exemples.La distorsion post-usinage est un problème ouvert qui affecte chaque grande pièce forgée en aluminium à paroi épaisse assemblée sur un avion. Cette distorsion provient de la présence de contraintes résiduelles (RS) développées tout au long de la chaine de fabrication, en particulier après traitement thermique par trempe.Lorsque l’usinage a lieu, il provoque une redistribution à un niveau interne car l´état d’équilibre précédent est rompu par l’action d’enlèvement de matière. Au niveau théorique, si les RS d’une pièce sont connues à l’avance, une séquence d’usinage appropriée pourrait être planifiée dans le but d’atténuer ou de contrecarrer une géométrie déformée. Cette stratégie est déjà mise en œuvre pour les pièces usinées à partir de tôles laminées, où la RS peut être considérée comme constante dans la direction longitudinale. Cependant, pour les pièces forgées, les RS sont fonction de la géométrie et, par conséquent, un champ de contrainte tridimensionnel complexe est présent. D’importants efforts de recherche sont réalisés afin de prédire numériquement les RS pour les pièces forgées, mais la nature déterministe des simulations numériques ne permet toujours pas de saisir le comportement variable des déformations. Pour l’instant, l’orientation actuelle de la recherche considère le problème des distorsions comme quelque chose à éviter depuis le début de la chaine de fabrication, c’est-à-dire en concentrant les efforts dans les étapes précédentes, où au plus tard pendant l’usinage. Dans la présente thèse, nous avons choisi de suivre la direction opposée, c’est-à-dire comment procéder et gérer la distorsion une fois qu’elle est apparue. Pour réaliser cette tâche, le problème a d’abord été étudié par la méthode classique des éléments finis (FEM), et par la suite en appliquant une technique non intrusive de réduction de l’ordre des modèles (ROM) appelée ”Sparse Subspace Learning” (SSL).Le contenu de cette thèse est structuré comme suit. Dans le chapitre 1 le problème de la distorsion sera introduit, suivi de la définition et de l’interconnexion des trois acteurs principaux : les contraintes résiduelles, la distorsion et le redressage. Les techniques de redressage seront ensuite passées en revue pour finalement examiner les défis et les perspectives de la simulation du redressage. Le chapitre 2 présente deux modèles numériques consacres à la détermination des contraintes résiduelles après la trempe et le pliage plastique, le traitement thermique étant considéré comme la principale source de contraintes résiduelles dans les pièces forgées en aluminium. C’est dans ce cadre (origine majoritairement thermique des contraintes résiduelles) que sera étudiée l’opération de redressage sélectionnée dans cette thèse.Après leurs validations, les deux modèles sont appliqués dans les chapitres suivants où ils constitueront la solution de référence du problème. Dans le chapitre 3, les diagrammes de mise en forme sont présentés comme un outil d’aide à l’opération de redressement par flexion. En outre, l’hypothèse reste sans contrainte résiduelle est présentée comme une alternative pour étudier le problème de redressage. Cette approche utilise la géométrie déformée comme entrée principale permettant de simuler l’étape de redressage en considérant la pièce sans contraintes résiduelles. Le chapitre 4 montrera une étude multiparamétrique du redressement par flexion à l’aide du SSL.Les diagrammes de redressage seront généralisés pour un ensemble de paramètres préalablement définis. Le redressage étant une procédure itérative et séquentielle, le chapitre 5 explicitera la simulation de deux opérations consécutives de redressement par flexion. Différentes stratégies de redressage seront étudiées, et une méthodologie sera fournie pour aborder de manière plus systématique le problème ouvert du redressage. Erasmus Mundus en simulació en enginyeria i desenvolupament de l'emprenedoria

International audience; Over recent decades, tremendous advances in the field of scalable numerical tools and mesh immersion techniques have been achieved to improve numerical efficiency while preserving a good quality of the obtained results. In this context, an octree-optimized microstructure generation and domain reconstruction with adaptative meshing is presented and illustrated through a flow simulation example applied to permeability computation of micrometric fibrous materials. Thanks to the octree implementation, the numerous distance calculations in these processes are decreased, thus the computational complexity is reduced. Using the parallel environment of the ICI-tech library as a mesher and a solver, a large scale case study is performed. The study is applied to the computation of the full permeability tensor of a three-dimensional microstructure containing 10,000 fibers. The considered flow is a Stokes flow and it is solved with a stabilized finite element formulation and a monolithic approach.

The final publication is available at Springer via http://dx.doi.org/10.1007/s00170-020-05856-z Large and thick-walled aluminium forgings exhibit shape distortions induced by residual stresses. To restore the nominal geometry, a series of highly manual and time-consuming reshaping operations need to be carried out. In this paper, we are concerned with the development of efficient computer simulation tools to assist operators in bending straightening, which is one of the most common reshaping operations. Our approach is based on the computation of reshaping diagrams, a tool that allows selecting a nearly optimal bending load to be applied in order to minimize distortion. Most importantly, we show that the reshaping diagram needs not to account for the residual stress field, as its only effect is to shift of the reshaping diagram by some offset. That is, the overall behaviour including a realistic 3D residual stress field in a forged part can be retrieved by shifting the residual stress free reshaping diagram by the appropriate offset. Finally, we propose a strategy in order to identify the offset on-the-fly during the reshaping operation using simple force-displacement measures. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement no. 675919.

International audience

The simulation of Floating Offshore Wind Turbines (FOWTs) is a tool to help this technology reach an industrial scale. Nowadays, low-precision numerical methods are used for the dimensioning of the structures, as they involve a reduced computational effort. This PhD thesis focused on the development of highly-accurate numerical methods, with a potential to provide a thin description of the flows and efforts around FOWTs. The simulations presented in this thesis have been realized on the highly-parallelized software platform ICI-tech. A resolution of the Navier- Stokes equations in a Variational MultiScale formulation is performed using Stabilized Finite Elements. The representation of the different phases in the computational domain is achieved using immersed boundary methods. Several numerical tools have been implemented in ICItech towards an application to the simulation of FOWTs. A fluid-structure interaction paradigm has been set up, and a numerical wave tank has been defined. Verification and validation studies have been realized to assess the solver results for environmental conditions representative of those observed for operating FOWT. The accuracy achieved for both the aerodynamics at high Reynolds numbers and the propagation of wave fields has been disappointing. The influence of the anisotropic meshing on the results presented has been quantified. Several options aiming at increasing the accuracy of the simulations have been discussed.; Le calcul des performances et des efforts appliqués sur une éolienne offshore est actuellement réalisé à l'aide d’outils basés sur des approches quasi-statiques. Ces approches sont intéressantes pour leur vitesse de calcul, elles sont cependant perfectibles suivant la méthode de mise en oeuvre et suivant les cas de chargement étudiés. Une approche alternative consiste à utiliser la modélisation CFD. Cette thèse s’intéresse à des méthodes d’une haute précision, ayant le potentiel de fournir des écoulements et efforts précis. La plateforme logicielle hautement parallélisée ICI-tech est utilisée dans cette thèse. Elle se base sur une résolution des équations de Navier-Stokes dans une approche multi-échelle, effectuée à l’aide d’éléments finis stabilisés. La représentation des phases dans le domaine de calcul est réalisée grâce à une méthode frontières immergées. Des implémentations ont été réalisées dans ICI-tech afin de pouvoir simuler des éoliennes flottantes. L’interaction fluide-structure et un bassin de houle numérique ont notamment été considérés. Un processus de vérification et validation s’est intéressé au comportement du solveur dans des conditions reproduisant celles impactant des éoliennes flottantes. Le niveau de précision atteint par les écoulements à haut Reynolds et la propagation de champs de houle s’est avéré être décevant. L’influence du maillage anisotrope sur les résultats obtenus a été quantifiée. Plusieurs pistes visant à améliorer la précision des simulations ont été introduites.

International audience; This paper is concerned with the computation of the inverse impulse response of a parametrized structural dynamics problem using reduced-order modeling and randomized excitations. A two-stages approach is proposed, involving the solution of both direct and inverse problems. In the first stage, the parametrized structural dynamics problem is formulated in the frequency domain, and solved using a reduced-order modeling approach. As a result, the parametric transfer function of the structure is obtained, and then readily transformed into a parametric direct impulse response (DIR). In the second stage, the parametric inverse impulse response (IIR) is computed. We use randomized excitations to generate synthetic samples inexpensively from the parametric DIR. Based on these, the parametric IIR is computed by minimizing the mean square error between the estimate and the samples. Most importantly, we show that the randomized excitations can be generated by sampling the frequency domain only. Hence, the parametric domain does not need to be sampled, which makes the computation of the parametric IIR very efficient.

Multiphasic optical fibers are promising systems to develop new optical devices. The main issue for their optimization is the control of the structure of the phases. To improve the structuring capabilities, fiber drawing has been evidenced to modify the size and shape of the multiphasic structure of optical fibers. This possibility comes from the occurence of capillary effects during the flow of the material during the fiber drawing. To use the fiber drawing as a structure tailoring step, the main hindrance is the lack of information on the physical properties of the systems of interest. To that aim, this article presents the work done to measure these properties. Based on experimental results, the characterization of the flow of the fiber drawing of silica-based optical fibers containing nanoparticles is presented. A numerical model for the simulation of the flow of particles and its validation are detailed. Preliminary results of the deformation of particles of various properties in the flow of the fiber drawing are finally presented, indicating a possible non-newtonian behaviour of the particles.

International audience; Simulations of flows containing non-spherical particles (fibres or ellipsoids) rely on the knowledge of the equation governing the particle motion in the flow. Most models used nowadays are based on the pioneering work of Jeffery (1922), who obtained an equation for the motion of an ellipsoidal particle immersed in a Newtonian fluid, despite the fact that this model relies on strong assumptions: negligible inertia, unconfined flow, dilute regime, flow unperturbed by the presence of the suspended particle, etc. In this work, we propose a dumbbell-based model aimed to describe the motion of an inertial fibre or ellipsoid suspended in a Newtonian fluid. We then use this model to study the orientation kinematics of such particle in a linear shear flow and compare it to the inertialess case. In the case of fibres, we observe the appearance of periodic orbits (whereas inertialess fibres just align in the flow field). For spheroids, our model predicts an orbit drift towards the flow-gradient plane, either gradually (slight inertia) or by first rotating around a moving oblique axis (heavy particles). Multi-Particle Collision Dynamics (MPCD) simulations were carried out to assess the model predictions in the case of inertial fibres and revealed similar behaviours.

This is a post-peer-review, pre-copyedit version of an article published in Journal of scientific computing. The final authenticated version is available online at: http://dx.doi.org/10.1007/s10915-019-00917-2 Tensor representations allow compact storage and efficient manipulation of multi-dimensional data. Based on these, tensor methods build low-rank subspaces for the solution of multi-dimensional and multi-parametric models. However, tensor methods cannot always be implemented efficiently, specially when dealing with non-linear models. In this paper, we discuss the importance of achieving a tensor representation of the model itself for the efficiency of tensor-based algorithms. We investigate the adequacy of interpolation rather than projection-based approaches as a means to enforce such tensor representation, and propose the use of cross approximations for models in moderate dimension. Finally, linearization of tensor problems is analyzed and several strategies for the tensor subspace construction are proposed.

International audience; Many composite forming processes are based on the consolidation of preimpregnated preforms of different types, e.g., sheets, tapes, .... Composite plies are put in contact using different technologies and consolidation is performed by supplying heat and pressure, the first to promote molecular diffusion at the plies interface and both (heat and pressure) to facilitate the intimate contact by squeezing surface asperities. Optimal processing requires an intimate contact as large as possible between the surfaces put in contact, for different reasons: (i) first, a perfect contact becomes compulsory to make possible molecular diffusion at the interface level in order to ensure bulk properties at interfaces; (ii) second, imperfect contact conditions result in micro and meso pores located at the interface, weakening it from the mechanical point of view, where macro defects (cracks, plies delamination, etc.) are susceptible of appearing. As just indicated, the main process parameters are the applied heat and pressure, as well as the process time (associated with the laying head velocity). These parameters should be adjusted to ensure optimal consolidation, avoiding imperfect bonding or thermal degradation. However, experiments evidence that the consolidation degree is strongly dependent on the surface characteristics (roughness). The same process parameters applied to different surfaces produce very different degrees of intimate contact. The present study aims at identifying the main surface descriptors able to describe the evolution of the degree of intimate contact during processing. That knowledge is crucial for online process control in order to maximize both productivity and part quality.

The discrete ordinate method coupled with the finite element method is often used for the spatio-angular discretization of the radiative transfer equation. In this paper we attempt to improve upon such a discretization technique. Instead of using standard finite elements, we reformulate the radiative transfer equation using vectorial finite elements. In comparison to standard finite elements, this reformulation yields faster timings for the linear system assemblies, as well as for the solution phase when using scattering media. The proposed vectorial finite element discretization for solving the radiative transfer equation is cross-validated against a benchmark problem available in literature. In addition, we have used the method of manufactured solutions to verify the order of accuracy for our discretization technique within different absorbing, scattering, and emitting media. For solving large problems of radiation on parallel computers, the vectorial finite element method is parallelized using domain decomposition. The proposed domain decomposition method scales on large number of processes, and its performance is unaffected by the changes in optical thickness of the medium. Our parallel solver is used to solve a large scale radiative transfer problem of the Kelvin-cell radiation.

International audience; We discuss the use of hierarchical collocation to approximate the numerical solution of parametric models. With respect to traditional projection-based reduced order modeling, the use of a collocation enables non-intrusive approach based on sparse adaptive sampling of the parametric space. This allows to recover the low-dimensional structure of the parametric solution subspace while also learning the functional dependency from the parameters in explicit form. A sparse low-rank approximate tensor representation of the parametric solution can be built through an incremental strategy that only needs to have access to the output of a determin-istic solver. Non-intrusiveness makes this approach straightforwardly applicable to challenging problems characterized by nonlinearity or non affine weak forms. As we show in the various examples presented in the paper, the method can be interfaced with no particular effort to existing third party simulation software making the proposed approach particularly appealing and adapted to practical engineering problems of industrial interest.

PurposeThe purpose of this paper is to present a reduced order computational strategy for a multi-physics simulation involving a fluid flow, electromagnetism and heat transfer in a hot-wall chemical vapour deposition reactor. The main goal is to produce a multi-parametric solution for fast exploration of the design space to perform numerical prototyping and process optimisation.Design/methodology/approachDifferent reduced order techniques are applied. In particular, proper generalized decomposition is used to solve the parameterised heat transfer equation in a five-dimensional space.FindingsThe solution of the state problem is provided in a compact separated-variable format allowing a fast evaluation of the process-specific quantities of interest that are involved in the optimisation algorithm. This is completely decoupled from the solution of the underlying state problem. Therefore, once the whole parameterised solution is known, the evaluation of the objective function is done on-the-fly.Originality/valueReduced order modelling is applied to solve a multi-parametric multi-physics problem and generate a fast estimator needed for preliminary process optimisation. Different order reduction techniques are combined to treat the flow, heat transfer and electromagnetism problems in the framework of separated-variable representations.

International audience; Mesh adaptation has proven to be very efficient for simulating transient multiphase computational fluid dynamics applications. In this work, we present a new parallel anisotropic mesh adaptation technique relying on an edge based error estimator. It provides a high level of accuracy while substantially reducing the computational effort. This technique enables a good capture of physical phenomena, boundary layers, interfaces, free surfaces and even multiphase turbulent flows, and has a great potential to simulate a large variety of applications. Current investigations explore the performance of the new algorithm on massively parallel resources. In this paper, we show that the developed adaptive meshing works very well in a parallel environment involving topological mesh modifications and dynamic repartitioning of parallel slots. It is also shown that the proposed methodology provides an additional gain in terms of computational cost due the production of a non-uniform mesh size distribution. Runs performed on national and European supercomputers will show the scalability and pertinence of our developments.

This thesis investigates the use of model order reduction methods based on sparsity-related techniques for the development of real-time biophysical modeling. In particular, it focuses on the embedding of interactive biophysical simulation into patient-specific models of tissues and organs to enhance medical images and assist the clinician in the process of informed decision making. In this context, three fundamental bottlenecks arise. The first lies in the embedding of the shape parametrization into the parametric reduced order model to faithfully represent the patient’s anatomy. A non-intrusive approach relying on a sparse sampling of the space of anatomical features is introduced and validated. Then, we tackle the problem of data completion and image reconstruction from partial or incomplete datasets based on physical priors. The proposed solution has the potential to perform scene registration in the context of augmented reality for laparoscopy. Quasi-real-time computations are reached by using a new hyperreduction approach based on a sparsity promoting technique. Finally, the third challenge concerns the representation of biophysical systems under uncertainty of the underlying parameters. It is shown that traditional model order reduction approaches are not always successful in producing a low dimensional representation of a model, in particular in the case of electrosurgery simulation. An alternative is proposed using a metamodeling approach. To this end, we successfully extend the use of sparse regression methods to the case of systems with stochastic parameters.; Cette thèse a pour but d’évaluer l'utilisation des méthodes de réduction de modèles fondées sur des approches parcimonieuses pour atteindre des performances en temps réel dans la cadre de la chirurgie computationnelle. Elle se concentre notamment sur l’intégration de la simulation biophysique dans des modèles personnalisés de tissus et d'organes afin d'augmenter les images médicales et ainsi éclairer le clinicien dans sa prise de décision. Dans ce contexte, trois enjeux fondamentaux sont mis en évidence. Le premier réside dans l'intégration de la paramétrisation de la forme au sein du modèle réduit afin de représenter fidèlement l'anatomie du patient. Une approche non intrusive reposant sur un échantillonnage parcimonieux de l'espace des caractéristiques anatomiques est introduite et validée. Ensuite, nous abordons le problème de la complétion des données et de la reconstruction des images à partir de données partielles ou incomplètes via des à priori physiques. Nous explorons le potentiel de la solution proposée dans le cadre du recalage d’images pour la réalité augmentée en laparoscopie. Des performances proches du temps réel sont obtenues grâce à une nouvelle approche d'hyper-réduction fondée sur une technique de représentation parcimonieuse. Enfin, le troisième défi concerne la propagation des incertitudes dans le cadre de systèmes biophysiques. Il est démontré que les approches de réduction de modèles traditionnelles ne réussissent pas toujours à produire une représentation de faible rang, et ce, en particulier dans le cas de la simulation électrochirurgicale. Une alternative est alors proposée via la métamodélisation. Pour ce faire, nous étendons avec succès l'utilisation de méthodes de régression parcimonieuses aux cas des systèmes à paramètres stochastiques.

This thesis investigates the use of model order reduction methods based on sparsity-related techniques for the development of real-time biophysical modeling. In particular, it focuses on the embedding of interactive biophysical simulation into patient-specific models of tissues and organs to enhance medical images and assist the clinician in the process of informed decision making. In this context, three fundamental bottlenecks arise. The first lies in the embedding of the shape parametrization into the parametric reduced order model to faithfully represent the patient’s anatomy. A non-intrusive approach relying on a sparse sampling of the space of anatomical features is introduced and validated. Then, we tackle the problem of data completion and image reconstruction from partial or incomplete datasets based on physical priors. The proposed solution has the potential to perform scene registration in the context of augmented reality for laparoscopy. Quasi-real-time computations are reached by using a new hyperreduction approach based on a sparsity promoting technique. Finally, the third challenge concerns the representation of biophysical systems under uncertainty of the underlying parameters. It is shown that traditional model order reduction approaches are not always successful in producing a low dimensional representation of a model, in particular in the case of electrosurgery simulation. An alternative is proposed using a metamodeling approach. To this end, we successfully extend the use of sparse regression methods to the case of systems with stochastic parameters.; Cette thèse a pour but d’évaluer l'utilisation des méthodes de réduction de modèles fondées sur des approches parcimonieuses pour atteindre des performances en temps réel dans la cadre de la chirurgie computationnelle. Elle se concentre notamment sur l’intégration de la simulation biophysique dans des modèles personnalisés de tissus et d'organes afin d'augmenter les images médicales et ainsi éclairer le clinicien dans sa prise de décision. Dans ce contexte, trois enjeux fondamentaux sont mis en évidence. Le premier réside dans l'intégration de la paramétrisation de la forme au sein du modèle réduit afin de représenter fidèlement l'anatomie du patient. Une approche non intrusive reposant sur un échantillonnage parcimonieux de l'espace des caractéristiques anatomiques est introduite et validée. Ensuite, nous abordons le problème de la complétion des données et de la reconstruction des images à partir de données partielles ou incomplètes via des à priori physiques. Nous explorons le potentiel de la solution proposée dans le cadre du recalage d’images pour la réalité augmentée en laparoscopie. Des performances proches du temps réel sont obtenues grâce à une nouvelle approche d'hyper-réduction fondée sur une technique de représentation parcimonieuse. Enfin, le troisième défi concerne la propagation des incertitudes dans le cadre de systèmes biophysiques. Il est démontré que les approches de réduction de modèles traditionnelles ne réussissent pas toujours à produire une représentation de faible rang, et ce, en particulier dans le cas de la simulation électrochirurgicale. Une alternative est alors proposée via la métamodélisation. Pour ce faire, nous étendons avec succès l'utilisation de méthodes de régression parcimonieuses aux cas des systèmes à paramètres stochastiques.

Non-destructive testing (NDT) of materials and structures is a very important industrial issue in the fields of transport, aeronautics and space as well as in the medical domain. Active infrared thermography is an NDT method that consists of providing an external excitation to cause an elevation of the temperature field in the material, consequently allowing evaluation of the resulting temperature field at the surface. However, thermal exciters that are used (flash lamps, halogen, lasers) act only on the surface of the sample. On the other hand, several energy conversion systems can lead to the generation of volumetric sources, the phenomena of thermo-acoustics, thermo-induction, thermomechanics or thermochemistry can be cited. For instance, ultrasonic waves can generate volumetric heat sources if the material is viscoelastic or if there is a defect. The reconstruction of these sources is the initial process for the quantification of parameters responsible for the heating. Characterizing a heat source means reconstructing its geometry and the supplied power. Identification of volumetric heat sources from surface temperature fields is a mathematically ill-posed problem. The main cause of the issue is the diffusive nature of the temperature. In this work, 3D reconstruction of the volumetric heat sources from the resulting surface temperature field, measured by infrared thermography, is studied. An analysis of the physical problem enables specifying the limits of the reconstruction. In particular, a criterion on the achievable spatial resolution is defined, and a reconstruction limitation for in-depth sources is highlighted.

International audience; Compressed sensing is a signal compression technique with very remarkable properties. Among them, maybe the most salient one is its ability of overcoming the Shannon–Nyquist sampling theorem. In other words, it is able to reconstruct a signal at less than 2Q samplings per second, where Q stands for the highest frequency content of the signal. This property has, however, important applications in the field of computational mechanics, as we analyze in this paper. We consider a wide variety of applications, such as model order reduction, manifold learning, data-driven applications and nonlinear dimensionality reduction. Examples are provided for all of them that show the potentialities of compressed sensing in terms of CPU savings in the field of computational mechanics.

This paper concerns engineered composites integrating metallic particles to enhance thermal and electrical properties. However, these properties are strongly dependent on the forming process itself that determines the particle distribution and orientation. At the same time, the resulting enhanced thermal properties affect the reinforced resin viscosity whose flow is involved in the intimate contact evolution. Thus, a subtle and intricate coupling appears, and the process cannot be defined by ignoring it. In this paper, we analyze the effects of particle concentration and orientation on the process and processability. For this purpose, three main models are combined: (i) a multi-scale surface representation and its evolution, by using an appropriate numerical model, (ii) flow-induced orientation, and (iii) the impact of the orientation state on the homogenized thermal conductivity.

International audience; Offshore wind turbines are currently increasing the potential of wind energy, and numerical simulation is a way to help this industry to reach maturity. In the context of floating wind energy, predicting the loads applied on structures and their response is essential. Those data will enable an optimization of floaters dimensioning, necessary for CAPEX reduction. As the simulation of floating wind turbines requires the representation of both complex geometries and phenomena, several alternative techniques have been developed. The wake generated by the rotor can be modeled using methodologies inherited from onshore wind turbines simulation, and coupled with a hydrodynamic code. However those simplified methods have been primarily developed for wake study, and thus have varying precision for loads estimation. This work proposes a methodology for the simulation of a single or several turbines with an exact representation of the geometries involved, targeting an accurate evaluation of loads. The software library used is ICI-tech, developed at the High Performance Computing Institute (ICI) of Centrale Nantes. A monolithic approach is applied on a single computational mesh, where all the different phases are defined through level-set functions. The Navier-Stokes (NS) equations are solved in the Variational MultiScale (VMS) formalism using stabilized finite elements. This approach, coupled with an automatic and anisotropic adaptation procedure, guarantees the good representation of the geometries immersed. The automatic adaptation refines the mesh only in interest zones, allowing the simulation of phenomena with very different orders of magnitude, e.g. aerodynamics around blades and waves propagation. The reduction of the number of points in the mesh and the massive parallelization of the code are also necessary for wind turbine simulation.

International audience

Points clouds are mathematical objects that allows to describe discretely multivariable functions. They are mainly used in the statistical domain but also in geometrical manifolds. It is nowadays a real challenge to immerse the previous manifolds in finite element computation. Indeed, the immersion of those points clouds requires the reconstruction of the surface of the manifold and the generation of a surfacic mesh. As those operations are often based on an iterative process, they are extremely time-consuming as points clouds are usually massive. The method developed in this thesis allows to immerse points clouds in a meshed domain without the surface reconstruction and mesh generations steps. For that purpose, we use the Volume Immersion Method adapted to point clouds. We coupled this method with an adaped mesh generation technique. Then we are able to generate a monolithic anisotropic mesh, adapted around interest zones. We also use the variational multi-scale method to simulate fluid flow. This method is an extension of the classical finite element method and allows to simulate fluid flow. The last part of this thesis introduce some applications cases in the aerodynamic and urbans domains.; Les nuages de points sont des objets mathématiques permettant de décrire de manière discrète des fonctions à plusieurs variables. Ils sont principalement utilisés dans le domaine statistique mais on les retrouve également en géométrie afin de représenter des variétés géométriques complexes. Il est aujourd'hui difficile d'intégrer les objets représentés par ces nuages de points dans des calculs éléments finis car l'intégration de ces nuages de points requiert la reconstruction de la variété ainsi que la génération d'un maillage surfacique qu'il faut intégrer dans un maillage volumique. Ces opérations sont souvent basées sur des processus itératifs et sont extrêmement coûteuses en temps car les nuages de points utilisés sont de très grande taille. La méthodologie développée dans cette thèse permet d'immerger des nuages de points dans un domaine maillé sans passer par les étapes de reconstruction de surface et de génération de maillage. On utilise la technique d'immersion de volume adaptée aux nuages de points. Cette technique est couplée avec une méthode d'adaptation de maillage. Cela nous permettra de générer un maillage anisotropique adapté autour des zones d'intérêt. On utilise ensuite la méthode variationnelle multi-échelle afin de simuler des écoulements fluides. Cette technique est une extension de la méthode éléments finis classique permettant de simuler des écoulements à forte convection et à haut nombre de Reynolds. La dernière partie de ce manuscrit présente quelques cas d'application dans le domaine aérodynamique, hydrodynamique et urbains.

National audience; Grâce à une faible variation de la permittivité des polymères des hyperfréquences jusqu’à la fréquence optique d’une part, et au progrès dans la synthèse de chromophores de forte hyperpolarisabilité d’autre part, les polymères électro-optiques (EO) présentent un très fort potentiel pour la réalisation de composants opto-hyperfréquences de très large bande passante (110 GHz) et de faible tension de commande (< 1 V). Pour augmenter et concrétiser ce potentiel des polymères EO, des efforts sont à fournir pour améliorer leur effet EO et leurs propriétés fonctionnelles. Nous explorons une approche innovante qui consiste à incorporer des nanoparticules dans des polymères EO, en tirant profit de l’important effet de surface des nanoparticules sur les propriétés des polymères, comme cela a été démontré par une équipe de l’Université du Mans. La première étape de ce travail est la dispersion de nanoparticules et de chromophores dans une matrice polymère afin d’obtenir un mélange homogène et stable, condition indispensable à l’obtention de films, sans court-circuit ni craquelures, réalisés par spin-coating. Pour ce faire, nous avons associé le tensio-actif CTAB (bromure de cétrimonium) avec la sonication pour réaliser des films composites PMMA-DR1-TiO2, dont la résistivité est nettement améliorée grâce à une meilleure dispersion du chromophore DR1 (Red Disperse 1) et des nanoparticules TiO2 (dioxyde de titane) dans la matrice polymère PMMA (poly(méthacrylate de méthyle)).

International audience; A parallel multigrid (MG) method is developed to reduce the large computational costs involved by the finite element simulation of highly viscous fluid flows, especially those resulting from metal forming applications, which are characterized by using a mixed velocity/pressure implicit formulation, unstructured meshes of tetrahedra and frequent remeshings. The developed MG method follows a hybrid approach where the different levels of nonnested meshes are geometrically constructed by mesh coarsening, while the linear systems of the intermediate levels result from the Galerkin algebraic approach. A linear O(N) convergence rate is expected (with N the number of unknowns), while keeping software parallel efficiency. These objectives lead to selecting unusual MG smoothers (iterative solvers) for the upper grid levels and to developing parallel mesh coarsening algorithms along with parallel transfer operators between the different levels of partitioned meshes. Within the utilized PETSc library, the developed MG method is employed as a preconditioner for the usual Conjugate Residual algorithm because of the symetric undefinite matrix of the system to solve. It shows a convergence rate close to optimal, an excellent parallel efficiency, and the ability to handle the complex forming problems encountered in 3D hot forging, which involve large material deformations and frequent remeshings.

International audience; Describing the orientation state of the particles is often critical in fibre suspension applications. Macroscopic descriptors, the so-called second-order orientation tensor (or moment) leading the way, are often preferred due to their low computational cost. Closure problems however arise when evolution equations for the moments are derived from the orientation distribution functions and the impact of the chosen closure is often unpredictable. In this work, our aim is to provide macroscopic simulations of orientation that are cheap, accurate and closure-free. To this end, we propose an innovative data-based approach to the upscaling of orientation kinematics in the context of fibre suspensions. Since the physics at the microscopic scale can be modelled reasonably enough, the idea is to conduct accurate offline direct numerical simulations at that scale and to extract the corresponding macroscopic descriptors in order to build a database of scenarios. During the online stage, the macroscopic descriptors can then be updated quickly by combining adequately the items from the database instead of relying on an imprecise macroscopic model. This methodology is presented in the well-known case of dilute fibre suspensions (where it can be compared against closure-based macroscopic models) and in the case of suspensions of confined or electrically-charged fibres, for which state-of-the-art closures proved to be inadequate or simply do not exist.

Part of the Lecture Notes in Computer Science book series (LNCS, volume 10759)Also part of the Lecture Notes in Artificial Intelligence book sub series (LNAI, volume 10759); International audience; Learning from interpretation transition (LFIT) automatically constructs a model of the dynamics of a system from the observation of its state transitions. So far, the systems that LFIT handles are restricted to discrete variables or suppose a discretization of continuous data. However, when working with real data, the discretization choices are critical for the quality of the model learned by LFIT. In this paper, we focus on a method that learns the dynamics of the system directly from continuous time-series data. For this purpose, we propose a modelling of continuous dynamics by logic programs composed of rules whose conditions and conclusions represent continuums of values.

International audience; The present paper extends in-plane-out-of-plane separated representations successfully used for addressing fully 3D model solutions defined in plate-like domain, to dynamics. Common time integration are performed using explicit or implicit strategies. Even if the implementation of implicit integration schemes into a 3D in-plane-out-of-plane separated representation does not imply major difficulties, the use of explicit integration preferable in many applications becomes a tricky issue. In fact the mesh employed for discretizing the out-of-plane dimension (thickness) determines the maximum time-step ensuring stability. In this paper we introduce a new efficient hybrid explicit/implicit in-plane-out-of-plane separated representation for dynamic problems defined in plate-like domains that allows computing 3D solutions with the stability constraint exclusively determined by the coarser in-plane discretization.

This is a post-peer-review, pre-copyedit version of an article published in International journal of material forming. The final authenticated version is available online at: http://dx.doi.org/10.1007/s12289-018-1417-4 The numerical modelling of forming processes involving the flow of foams requires taking into account the different problem scales. Thus, in industrial applications a macroscopic approach is suitable, whereas the macroscopic flow parameters depend on the cellular structure: cell size, shape, orientation, etc. Moreover, the shape and orientation of the cells are induced by the flow. A fully microscopic description remains useful to understand the foam behaviour and the topological changes induced by the cell elongation or distortion, however, from an industrial point of view, microscopic simulations remain challenging to address practical applications involving flows in complex 3D geometries. In this paper, we propose a viscoelastic flow model where the foam microstructure is represented from suitable microstructure descriptors whose evolution is governed by the macroscopic flow kinematics.

International audience

International audience; An overview of various numerical methods developed for speeding-up computations is presented in the field of the bulk material forming under solid state, which is characterized by complex and evolving geometries requiring frequent remeshings and numerous time increments. These methods are oriented around the axis that constitutes the meshing problem. The multi-mesh method allows to optimally solve several physics involved on the same domain, according to its finite element discretization with several different meshes, for example in the cogging or cold pilgering processes. For quasi steady-state problems and problems with quite pronounced localization of deformation, such as Friction Stir Welding (FSW) or High Speed Machining, an Arbitrary Lagrangian or Eulerian formulation (ALE) with mesh adaptation shows to be imperative. When the problem is perfectly steady, as for the rolling of long products, the direct search for the stationary state allows huge accelerations. In the general case, where no process specificity can be used to solve the implicit equations, the multigrid method makes it possible to construct a much more efficient iterative solver, which is especially characterized by an almost linear asymptotic cost.

National audience

International audience

This thesis presents the study of the model order reduction for power grids and transmission networks. The specific focus has been the transient dynamics. A mathematical viewpoint has been adopted for model reduction. Power networks are huge and complex network, simulation for power grid analysis and design require large non-linearmodels to be solved. In the context of developing “SmartGrids” with the distributed generation of power, real time analysis of complex systems such as these needs fast,reliable and accurate models. In the current study we propose model order reduction methods both a-priori and aposteriori suitable for dynamic models of power grids.The model that describes the transient dynamics of the power grids is complex non-linear swing dynamics model. The non-linearity of the swing dynamics model necessitates special attention to achieve maximum benefit from the model order reduction techniques. In the current research, POD and LATIN methods were applied initially with varying degrees of success. The method of TPWL has been proved as the best-suited model reduction method for swing dynamics model ; this method combines POD with multiple linear approximations.For the transmission lines, a distributed parameters model infrequency-domain is used. PGD based reduced-order models are proposed for the DP model of transmission lines. A fully parametric problem with electrical parameters of transmission lines included as coordinates of the separated representation. The method was extended to present the solution of frequency-dependent parameters model for transmission lines.; Cette thèse présente l'étude de la réduction de modèles pour les réseaux électriques et les réseaux de transmission. Un point de vue mathématique a été adopté pour la réduction de modèles. Les réseaux électriques sont des réseaux immenses et complexes, dont l'analyse et la conception nécessite la simulation et la résolution de grands modèles non-linéaires. Dans le cadre du développement de réseaux électriques intelligents (smart grids) avec une génération distribuée de puissance, l'analyse en temps réel de systèmes complexes tels que ceux-ci nécessite des modèles rapides,fiables et précis. Dans la présente étude, nous proposons des méthodes de réduction de de modèles à la fois a priori et a posteriori, adaptées aux modèles dynamiques des réseaux électriques.Un accent particulier a été mis sur la dynamique transitoire des réseaux électriques, décrite par un modèle oscillant non linéaire et complexe. La non-linéarité de ce modèle nécessite une attention particulière pour bénéficier du maximum d'avantages des techniques de réduction de modèles.Initialement, des méthodes comme POD et LATIN ont été adoptées avec des degrés de succès divers. La méthode de TPWL, qui combine la POD avec des approximations linéaires multiples, a été prouvée comme étant la méthode de réduction de modèles la mieux adaptée pour le modèle dynamique oscillant.Pour les lignes de transmission, un modèle de paramètres distribués en domaine fréquentiel est utilisé. Des modèles réduits de type PGD sont proposés pour le modèle DP des lignes de transmission. Un problème multidimensionnel entièrement paramétrique a été formulé, avec les paramètres électriques des lignes de transmission inclus comme coordonnées additionnelles de la représentation séparée. La méthode a été étendue pour étudier la solution du modèle des lignes de transmission pour laquelle les paramètres dépendent de la fréquence.

International audience; Composites manufacturing processes usually involve multiscale models in both space and time, highly non-linear and anisotropic behaviors, strongly coupled multiphysics and complex geometries. In this framework, the use of simulation for real-time decision making directly in the manufacturing facility is still precluded nowadays, in spite of the impressive progresses reached in numerical analysis and computer science during the last decade. In this paper, a process-specific simulation tool based on reduced order modeling is introduced, the Simulation App. This concept is presented through a practical case involving a multi-physics and coupled problem describing the manufacturing process of a composite outlet guide vane. We show that several manufacturing settings can be simulated in few seconds with the Simulation App, thus enabling fast process optimization. Finally, the advantages over general-purpose simulation software, in the context of process simulation, are discussed.

This thesis presents the study of the model order reduction for power grids and transmission networks. The specific focus has been the transient dynamics. A mathematical viewpoint has been adopted for model reduction. Power networks are huge and complex network, simulation for power grid analysis and design require large non-linear models to be solved. In the context of developing "Smart Grids" with the distributed generation of power, real time analysis of complex systems such as these needs fast, reliable and accurate models. In the current study we propose model order reduction methods both a-priori and a-posteriori suitable for dynamic models of power grids. The model that describes the transient dynamics of the power grids is complex non-linear swing dynamics model. The non-linearity of the swing dynamics model necessitates special attention to achieve maximum benefit from the model order reduction techniques. In the current research, POD and LATIN methods were applied initially with varying degrees of success. The method of TPWL has been proved as the best-suited model reduction method for swing dynamics model; this method combines POD with multiple linear approximations. For the transmission lines, a distributed parameters model in frequency-domain is used. PGD based reduced-order models are proposed for the DP model of transmission lines. A fully parametric problem with electrical parameters of transmission lines included as coordinates of the separated representation. The method was extended to present the solution of frequency-dependent parameters model for transmission lines., Cette these présente l'étude de la réduction de modeles pour les réseaux électriques et les réseaux de transmission. Un point de vue mathématique a été adopté pour la réduction de modeles. Les réseaux électriques sont des réseaux immenses et complexes, dont l'analyse et la conception nécessite la simulation et la résolution de grands modeles non-linéaires. Dans le cadre du développement de réseaux électriques intelligents (smart grids) avec une génération distribuée de puissance, l'analyse en temps réel de systemes complexes tels que ceux-ci nécessite des modeles rapides, fiables et précis. Dans la présente étude, nous proposons des méthodes de réduction de de modeles a la fois a priori et a posteriori, adaptées aux modeles dynamiques des réseaux électriques. Un accent particulier a été mis sur la dynamique transitoire des réseaux électriques, décrite par un modele oscillant non­linéaire et complexe. La non-linéarité de ce modele nécessite une attention particuliere pour bénéficier du maximum d'avantages des techniques de réduction de modeles. lnitialement, des méthodes comme POD et LATIN ont été adoptées avec des degrés de succes divers. La méthode de TPWL, qui combine la POD avec des approximations linéaires multiples, a été prouvée comme étant la méthode de réduction de modeles la mieux adaptée pour le modele dynamique oscillant. Pour les lignes de transmission, un modele de parametres distribués en domaine fréquentiel est utilisé. Des modeles réduits de type PGD sont proposés pour le modele DP des lignes de transmission. Un probleme multidimensionnel entierement paramétrique a été formulé, avec les parametres électriques des lignes de transmission inclus comme coordonnées additionnelles de la représentation séparée. La méthode a été étendue pour étudier la solution du modele des lignes de transmission pour laquelle les parametres dépendent de la fréquence., Esta tesis presenta un estudio de la reducción de modelos (MOR) para redes de transmisión y distribución de electricidad. El enfoque principal utilizado ha sido la dinámica transitoria y para la reducción de modelos se ha adoptado un punto de vista matemático. Las redes eléctricas son complejas y tienen un tamaño importante. Por lo tanto, el análisis y diseño de este tipo de redes mediante la simulación numérica, requiere la resolución de modelos no-lineales complejos. En el contexto del desarrollo de redes inteligentes, el objetivo es un análisis en tiempo real de sistemas complejos, por lo que son necesarios modelos rápidos, fiables y precisos. En el presente estudio se proponen diferentes métodos de reducción de modelos, tanto a priori como a posteriori, adecuados para modelos dinámicos de redes eléctricas. La dinámica transitoria de redes eléctricas, se describe mediante modelos dinámicos oscilatorios no-lineales. Esta no-linearidad del modelo necesita ser bien tratada para obtener el máximo beneficio de las técnicas de reducción de modelos. Métodos como la POD y la LATIN han sido inicialmente utilizados en esta problemática con diferentes grados de éxito. El método de TPWL, que combina la POD con múltiples aproximaciones lineales, ha resultado ser el mas adecuado para sistemas dinámicos oscilatorios. En el caso de las redes de transmisión eléctrica, se utiliza un modelo de parámetros distribuidos en el dominio de la frecuencia. Se propone reducir este modelo basándose en la PGD, donde los parámetros eléctricos de la red de transmisión son incluidos como coordenadas de la representación separada del modelo paramétrico. Este método es ampliado para representar la solución de modelos con parámetros dependientes de la frecuencia para las redes de transmisión eléctrica

International audience; Several studies showed that thin-plies composite laminates apparently exhibit higher strength than its counterpart using thicker plies. In this work, a high-resolution numerical discretization based on the use of in-plane-out-of-plane separated representations within the Proper Generalized Decomposition PGD framework is performed in different composites laminates for determining the effect of ply-thickness on the laminate stiffness. The results reveal that the global stiffness increases with the ply-thickness reduction. The analysis also reveals that this mechanical enhancement is due to structural effects and not to the mechanical confinement initially advanced.

International audience; Liquid composite molding (LCM) includes all composite-manufacturing methods, where the liquid state resin is forced into the dry preformed reinforcement. In this study, numerical simulation of the resin infusion is presented based on a coupled approach involving Boundary Element Method (BEM) and Level Set Method. The method developed can handle stationary and transient flows by solving the Stokes equations. The numerical results on a square packed set of fibers show excellent agreement with the analytical model. The comparison between experimental and simulation results of flow front patterns revealed a fair accordance.

International audience; The properties of short fibre-reinforced polymer composites depend on the distribution and the orientation of fibres which drastically changes during the forming of composites. During this stage, these materials behave as fibre suspensions and usually flow in confined geometries. To analyse their flow-induced fibrous microstructures, we previously conducted 3D real-time in situ observations of the compression of non-Newtonian dilute fibre suspensions using fast X-ray microtomography [T. Laurencin et al., Compos Sci Technol 134 (2016)]. Here, we successfully simulated these experiments with a multi-domain Finite Element code and compared them with the predictions of Jeffery's model. Often, the Jeffery's equations agree with the experimental and numerical data. However, for fibres closed to compression platens, important deviations were observed with faster simulated and experimental fibre rotation. Adopting the dumbbell approach and revisiting the recent work of Perez et al. [J non-Newtonian Fluid Mech 233 (2016)], an extension of the Jeffery's model is proposed to account both for the non-Newtonian rheology of the suspending fluid and confinement effects. Despite its simplicity, the new model allows a good description of simulation and experimental results.

Collective motions, deserts of mobile dunes and flows of giant micellles share in common the fact that the local injection of energy leads to complex collective dynamics. At a microscopic level, interactions may remain unknown or they reach a such level of complexity that it is necessary to simplify the elementary ingredients. Models allow to understand the weight of each ingredients on the global dynamics. We then get an understandable picture. This is the main goal of minimal models.But the underlying ideas on universality and minimal models have a narrower and a more accurate meaning in the framework of at-equilibrium statistical physics. Such concepts are linked to the existence of continuous transition. Similar theoretical results do not exist for driven systems. Then the data analysis of numerical simulations are usually done following analogies with critical phenomena.Here, we present three cases at three different steps of study. For collective motions, we show that analogies with ferromagnetic materials lead to wrong conclusions. A long careful study of numerical simulations reveals a discontinuous phase transition. An instability leads to a non-linear dynamical pattern which gets similar characteristics to solitary waves. Other recent studies make analogies with smectic phases.Models of deserts of dunes allow to understand the effects of the different dunes interactions. Thus we explained how deserts could self-organise in time and in space. When models are used far from the geophysical hypotheses, we get behaviours which have already been observed in other out-of-equilibrium physical systems: percolation, reaction-diffusion, mass transfer. However we show that none of those analogies are fully conclusive in regard to our results.Last, in considering flows of solutions of giant micelles, we propose a minimal model in the aim to give a better understanding of the mechanisms of shear banding.; Les mouvements collectifs d'animaux, les déserts de dunes mobiles etles écoulements de micelles géantes ont ceci de commun que l'injection d'énergie au niveau local conduit à une dynamique collective complexe. Les interactions au niveau microscopique peuvent être inconnues, ou alors sont tellement complexes qu'il est nécessaire de simplifier les ingrédients élémentaires. La modélisation permet de comprendre le poids de chacun des ingrédients sur la dynamique globale. On en obtient ainsi un tableau causal intelligible. C'est le premier intérêt des modèles minimaux.Mais les concepts d'universalité et de modèles minimaux ont une signification bien établie et plus restreinte dans le cadre de la physique statistique des systèmes à l'équilibre. Ils sont attachés à l'existence de transitions continues. Un cadre théorique équivalent à celui des phénomènes critiques n'existe pas lorsque le système est maintenu loin de l'équilibre. L'analyse des données issues des simulations numériques est habituellement réalisée par analogie en suivant les résultats analytiques obtenus à l'équilibre.Nous présentons trois cas à différentes étapes du projet de recherche. Dans le cas des mouvements collectifs, nous montrons que les analogies avec les matériaux ferromagnétiques ont mené à des conclusions erronées. Une longue étude critique des simulations numériques a montré que la transition est discontinue. Une instabilité dans les assemblées en mouvement produit un motif spatio-temporel similaire à une onde solitaire. D'autres études récentes proposent une nouvelle analogie avec les phases smectiques.Les modèles de déserts de dunes permettent d'ordonner les effets des différentes interactions entre dunes. Ainsi, nous avons donné une explication à l'auto-organisation des déserts. Lorsque les modèles sont étudiés sans prendre en compte leur dimension géophysique, nous obtenons des comportements déjà observés dans d'autres modèles de physique statistique hors d'équilibre~: percolation, réaction-diffusion, transfert de masse. Cependant nous montrons qu'aucune analogie ne permet d'expliquer de manière convainquante nos résultats.Enfin, considérant les écoulements de solutions de micelles géantes, nous proposons un modèle minimal permettant de mieux comprendre les mécanismes à l'oeuvre dans les écoulements en bande de cisaillement.

Collective motions, deserts of mobile dunes and flows of giant micellles share in common the fact that the local injection of energy leads to complex collective dynamics. At a microscopic level, interactions may remain unknown or they reach a such level of complexity that it is necessary to simplify the elementary ingredients. Models allow to understand the weight of each ingredients on the global dynamics. We then get an understandable picture. This is the main goal of minimal models.But the underlying ideas on universality and minimal models have a narrower and a more accurate meaning in the framework of at-equilibrium statistical physics. Such concepts are linked to the existence of continuous transition. Similar theoretical results do not exist for driven systems. Then the data analysis of numerical simulations are usually done following analogies with critical phenomena.Here, we present three cases at three different steps of study. For collective motions, we show that analogies with ferromagnetic materials lead to wrong conclusions. A long careful study of numerical simulations reveals a discontinuous phase transition. An instability leads to a non-linear dynamical pattern which gets similar characteristics to solitary waves. Other recent studies make analogies with smectic phases.Models of deserts of dunes allow to understand the effects of the different dunes interactions. Thus we explained how deserts could self-organise in time and in space. When models are used far from the geophysical hypotheses, we get behaviours which have already been observed in other out-of-equilibrium physical systems: percolation, reaction-diffusion, mass transfer. However we show that none of those analogies are fully conclusive in regard to our results.Last, in considering flows of solutions of giant micelles, we propose a minimal model in the aim to give a better understanding of the mechanisms of shear banding.; Les mouvements collectifs d'animaux, les déserts de dunes mobiles etles écoulements de micelles géantes ont ceci de commun que l'injection d'énergie au niveau local conduit à une dynamique collective complexe. Les interactions au niveau microscopique peuvent être inconnues, ou alors sont tellement complexes qu'il est nécessaire de simplifier les ingrédients élémentaires. La modélisation permet de comprendre le poids de chacun des ingrédients sur la dynamique globale. On en obtient ainsi un tableau causal intelligible. C'est le premier intérêt des modèles minimaux.Mais les concepts d'universalité et de modèles minimaux ont une signification bien établie et plus restreinte dans le cadre de la physique statistique des systèmes à l'équilibre. Ils sont attachés à l'existence de transitions continues. Un cadre théorique équivalent à celui des phénomènes critiques n'existe pas lorsque le système est maintenu loin de l'équilibre. L'analyse des données issues des simulations numériques est habituellement réalisée par analogie en suivant les résultats analytiques obtenus à l'équilibre.Nous présentons trois cas à différentes étapes du projet de recherche. Dans le cas des mouvements collectifs, nous montrons que les analogies avec les matériaux ferromagnétiques ont mené à des conclusions erronées. Une longue étude critique des simulations numériques a montré que la transition est discontinue. Une instabilité dans les assemblées en mouvement produit un motif spatio-temporel similaire à une onde solitaire. D'autres études récentes proposent une nouvelle analogie avec les phases smectiques.Les modèles de déserts de dunes permettent d'ordonner les effets des différentes interactions entre dunes. Ainsi, nous avons donné une explication à l'auto-organisation des déserts. Lorsque les modèles sont étudiés sans prendre en compte leur dimension géophysique, nous obtenons des comportements déjà observés dans d'autres modèles de physique statistique hors d'équilibre~: percolation, réaction-diffusion, transfert de masse. Cependant nous montrons qu'aucune analogie ne permet d'expliquer de manière convainquante nos résultats.Enfin, considérant les écoulements de solutions de micelles géantes, nous proposons un modèle minimal permettant de mieux comprendre les mécanismes à l'oeuvre dans les écoulements en bande de cisaillement.

International audience; La simulation en mécanique des fluides numérique nécessite dans de nombreux cas la réalisation manuelle de modèles3D. Cette étape est fastidieuse et nécessite des compétences spécifiques. Nous proposons une méthode pourréaliser directement des simulations d’écoulements sur des modèles 3D numérisés. A la différence des chaînes detraitement classiques, notre méthode permet de construire un maillage volumique tétraédrique anisotrope adaptéautour d’une surface échantillonnée par points, sans passer par une étape de reconstruction de surface. La chaînede traitement que nous présentons permet ainsi d’automatiser la simulation d’écoulements à partir de nuages depoints. Elle permet également d’obtenir un meilleur contrôle sur la précision géométrique proche de la surfacetout en gardant un nombre de noeuds de calcul limité, ce qui représente un enjeu crucial en mécanique de fluides.Computational fluid dynamics (CFD) requires in many cases designing 3D models manually, which is a tedioustask that requires specific skills. In this paper, we present a novel method to perform CFD directly on scanned3D models. Unlike the other classic workflows, ours allows to build an anisotropic volumetric tetrahedral meshadapted around a point-sampled surface, without surface reconstruction step. The workflow we present allows usto compute flows around point sampled geometries automatically. It gives us also a better control on precisionaround the surface with a limited number of computational nodes, which is a critical issue in CFD.

International audience; The exploration of the phase diagram of a minimal model for barchan fields leads to the description of three distinct phases for the system: stationary, percolable and unstable. In the stationary phase the system always reaches an out of equilibrium, fluctuating, stationary state, independent of its initial conditions. This state has a large and continuous range of dynamics, from dilute – where dunes do not interact – to dense, where the system exhibits both spatial structuring and collective behavior leading to the selection of a particular size for the dunes. In the percolable phase, the system presents a percolation threshold when the initial density increases. This percolation is unusual, as it happens on a continuous space for moving, interacting, finite lifetime dunes. For extreme parameters, the system exhibits a sub-critical instability, where some of the dunes in the field grow without bound. We discuss the nature of the asymptotic states and their relations to well-known models of statistical physics.

International audience; A transverse isotropic viscous model accounting for the anisotropy exhibited in fiber-reinforced composite is integrated in the numerical platform of the software Rem3D®. Simulations under various mechanical loading are tested for volume fiber concentrations of 3.5% and 14.7%. Equivalent stresses and equivalent strain rate deformations given by the software were compared to the ones predicted by the model, finding very good agreements. As a second point developed on this paper, we comment on the slip condition between Die/Punch tool with the composite under compression. We noticed that the variation of the viscosity value on a small layer between the Die/Punch tooland the composite affects the nature of the contact. A viscous friction is then formulated as a technique to set slip/no-slip contact condition. We found that the slip condition is recovered at lower values of the viscosity in the interface Die/Punch with the reinforced composite, whereas the no slip condition stated for higher viscosity values.

International audience; Implicit boundary means that the boundaries and/or interfaces between domains are not anymore defined by an explicit boundary mesh but rather by an implicit function. It is the case with embedded boundary methods or immersed boundary methods. Here we consider a filtered level set methods and meshing is then performed using an anisotropic mesh adaptation framework applied to the level sel interpolation. The interpolation error estimate is driving the adaptive process giving rise to a new way of boundary recovery. The accuracy of the recovery process depends then on the user given parameter, an arbitrary thickness of the interface. The thickness is normally related to the mesh size, but it is shown that adaptive meshing enables to reverse this condition: fixing the thickness parameter and accounting for the adaptation process to fulfill the mesh size condition. Several examples are given to demonstrate the potential of this approach.

International audience; We present a new immersed method for Computational Fluid Dynamics applications. It is based on the use of Non Uniform Rational B-Splines (NURBS). The distance function to an immersed solid is computed directly from its Computer Aided Design (CAD) description. This allows to bypass the generation of surface meshes and to obtain accurate levelset functions for complex geometries. Combined with a metric based anisotropic mesh adaptation and stabilized Finite Elements Method (FEM), it allows a novel, efficient and flexible approach to deal with a wide range of fluid structure interaction problems. The metric field is computed directly at the node of the mesh using the length distribution tensor and an edge based error analysis. Several 2D and 3D numerical examples will demonstrate the applicability of the proposed method.

International audience