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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

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.

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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.

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.

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; 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.

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.

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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.

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 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.

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