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    Hyperelastic nature of Hoek-Brown criterion

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    We propose a nonlinear elasto-plastic model, for which a specific class of hyperbolic elasticity arises as a straight consequence of the yield criterion invariance on the plasticity level. We superimpose this nonlinear elastic (or hyperelastic) behavior with plasticity obeying the associated flow rule. Interestingly, we find that a linear yield criterion on the thermodynamical force associated with plasticity results in a quadratic yield criterion in the stress space. This suggests a specific hyperelastic connection between Mohr–Coulomb and Hoek–Brown (or alternatively between Drucker–Prager and Pan–Hudson) yield criteria. We compare the elasto-plastic responses of standard tests for the Drucker–Prager yield criterion using either linear or the suggested hyperbolic elasticity. Notably, the nonlinear case stands out due to dilatancy saturation observed during cyclic loading in the triaxial compression test. We conclude this study with structural finite element simulations that clearly demonstrate the numerical applicability of the proposed model

    Global solution of Quadratic Problems by Interval Methods and Convex Relaxations

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    International audienceInterval branch-and-bound solvers provide reliable algorithms for handling non-convex optimization problems by ensuring the feasibility and the optimality of the computed solutions, i.e. independently from the floating-point rounding errors. Moreover, these solvers deal with a wide variety of mathematical operators. However, these solvers are not dedicated to quadratic optimization and do not exploit nonlinear convex relaxations in their framework. We present an interval branch-andbound method that can efficiently solve quadratic optimization problems. At each node explored by the algorithm, our solver uses a quadratic convex relaxation which is as strong as a semi-definite programming relaxation, and a variable selection strategy dedicated to quadratic problems. The interval features can then propagate efficiently this information for contracting all variable domains. We also propose to make our algorithm rigorous by certifying firstly the convexity of the objective function of our relaxation, and secondly the validity of the lower bound calculated at each node. In the non-rigorous case, our experiments show significant speedups on general integer quadratic instances, and when reliability is required, our first results show that we are able to handle medium-sized instances in a reasonable running time

    Contributions aux méthodologies et outils de conception des System-on-Chip : capture applicative, architecture et sécurité

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    Ce manuscrit présente une synthèse de mes activités de recherche, en grande partie réalisées à l’ENSTA Bretagne (désormais ENSTA) et au sein du laboratoire Lab-STICC (UMR6285) depuis 2009. Cette activité s’est nourrie d’une expérience industrielle préalable d’une dizaine d’années en tant qu’ingénieur de la société Thomson R&D France, acteur mondial de la compression vidéo. J’ai ainsi eu la chance de participer activement à la conception de circuits intégrés de grandes dimensions : les System-on-Chip (SoC). A travers ce domaine de la compression, j’ai ainsi pu me plonger au coeur de la problématique des SoCs en général : comment, à partir de comportements réputés complexes, faire émerger une structure matérielle performante qui réalise ces calculs ? Une grande partie de la réponse à cette question repose sur les capacités des outils logiciels utilisés lors de la conception. Après mon activité d’architecte et concepteur, où j’utilisais de tels outils, mon activité de recherche s’est donc logiquement recentrée sur l’étude et le prototypage de ces outils.Cette recherche s’est déroulée à la fois dans le domaine académique mais également par le montage d’une startup (Modaë Technologies) dans ce même domaine de l’ESL (Electronic System Level). Cet historique assez long m’amène à en couvrir, dans ce mémoire, plusieurs aspects : création de langages spécialisés (DSL domain specfic languages), techniques de compilation vers le matériel, ainsi que des propositions liées à la sécurité de ces "puces", désormais cibles de différentes attaques de type "cyber"

    Two-phase Trajectory Planning Method for Robust Planetary Landing in a Sensor-equipped Area

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    International audienceThis article addresses the planetary landing problem by considering uncertainties and leveraging the presence of a detection area where precise measurements are available. The flight consists of two distinct phases: the first phase, subject to a high level of uncertainties, and the second phase, during which the vehicle is feedback controlled to ensure precise landing. We propose a method to compute the optimal control for the initial phase, aiming to minimize fuel consumption for the entire trajectory while satisfying a probabilistic constraint that ensures the vehicle reaches the detection zone with a specified threshold.</div

    A Novel Approach to Guidance and Control of USVs Combining Flatness-Based and Model-Free Controllers

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    International audienceThis work presents a new approach to the guidance and control of marine craft by combining Flatness-Based and Model-Free controllers. Its goal is to develop a general regulator for Unmanned Surface Vehicles (USV). To do so, the well-known USV maneuvering model is simplified and proven to be flat. A flatness-based controller is derived for the simplified USV model and the loop is closed via an intelligent proportional derivative (iPD) regulator derived from model-free control. We thus associate the well-documented natural robustness of flatness-based control and adaptivity of iPDs. The controller is applied in simulation to two surface vessels, one meeting the simplifying hypotheses, the other one being a generic USV of the literature, and is shown to stabilize both systems even in the presence of unmodeled environmental disturbances

    Mechanisms of transverse cracking induced by adjacent ply matrix cracks in composite laminates

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    International audienceCracking in composite laminates containing θ-plies adjacent to 90 deg. plies is studied experimentally and numerically using the coupled criterion. Experimental observations of the composite edge evidence θ-ply cracking i) at an imposed strain level much larger than first transverse cracking in 90 deg. ply for a sufficiently large orientation mismatch between adjacent plies or ii) at a similar imposed strain level if the mismatch angle between two adjacent plies is small. The latter phenomenon may be mitigated by the presence of a 0 deg. ply between the 90 deg. and the θ-plies. These conclusions are supported by numerical simulation of the experimentally observed damage mechanisms, which also highlight that debonding between adjacent plies may occur as it becomes more favorable that adjacent ply crack re-initiation for sufficiently large adjacent ply mismatch angle.Cracking in composite laminates containing θ-plies adjacent to 90°plies is studied experimentally and numerically using the coupled criterion and finite element calculations. Different damage mechanisms are considered, namely transverse cracking in 90°, cracking in θ-plies, or debonding between adjacent misoriented plies. The influence of the stacking sequence on the damage mechanism sequence is investigated. Experimental observations of the composite edge under tensile loading evidence θ-ply cracking (i) at an imposed strain level much larger than first transverse cracking in 90°ply for a sufficiently large orientation mismatch between adjacent plies or (ii) at a similar imposed strain level if the mismatch angle between two adjacent plies is small. The latter phenomenon may be mitigated by the presence of a 0°ply between the 90°a nd the θ-plies.These conclusions are supported by numerical simulation of the experimentally observed damage mechanisms, evidencing a change in the damage mechanism sequence depending on the θ-ply misorientation. The numerical simulations also highlight that debonding between adjacent plies may occur as it becomes more favorable that adjacent ply crack re-initiation for sufficiently large adjacent ply mismatch angle.Résumé. La fissuration dans les stratifiés composites, contenant des plis orientés à θ°de la direction de chargement adjacents à des plis à 90°, est étudiée expérimentalement et numériquement à l'aide du critère couplé et de calculs par éléments finis. Différents mécanismes d'endommagement sont pris en compte : la fissuration transverse dans le pli à 90°, la fissuration dans les plis à θ°, ou la décohésion entre des plis adjacents d'orientation différente. L'influence de la séquence d'empilement sur la séquence des mécanismes d'endommagement est analysée. Les observations expérimentales effectuées sur des stratifiés sollicités en traction mettent en évidence une fissuration dans les plis à θ : (i) à un niveau de déformation imposé beaucoup plus élevé que celui de la première fissuration transverse dans les plis à 90°pour une désorientation suffisamment grand entre les plis adjacents, ou (ii) à un niveau de déformation imposé similaire si l'angle de</div

    Examples of non-scattering inhomogeneities

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    International audienceWe consider the scattering of waves by a penetrable inclusion embedded in some reference medium. We exhibit examples of materials and geometries for which non-scattering frequencies exist, i.e. for which at some frequencies there are incident fields which produce null scattered fields outside of the inhomogeneity. We show in particular that certain domains with corners or even cusps can support non-scattering frequencies. We relate the latter, for some inclusions, to resonance frequencies for Dirichlet or Neumann cavities. We also find situations where incident non-scattering fields solve the Helmholtz equation in a neighbourhood of the inhomogeneity and not in the whole space. In relation with invisibility, we give examples of inclusions of anisotropic materials which are non-scattering for all real frequencies. We prove that corresponding material indices must have a special structure on the boundary

    Experimental and Numerical Study of an Oscillating Foil Near the Free Surface

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    International audienceThis work presents experimental and numerical results to study the performances of an actively pitching and heaving NACA0015 hydrofoil near the free surface, as a biomimetic propulsion system for ships. The experiments are carried out in the IFREMER current and wave tank at Boulogne-sur-Mer for several heave and pitch amplitudes. The influence of the phase lag between the pitch and heave motions is also investigated, as well as the hydrofoil performances in regular waves. The experiments consists of forces measurements and they are compared with numerical predictions of the hydrodynamic forces using the potential flow code PUFFIn in its latest unsteady version. Comparisons with Reynolds Averaged Navier-Stokes (RANS) calculations are presented for cases where the discrepancies between the potential code and experimental results are significant. Overall, the mean numerical forces exhibit similar trends to the experimental averages, validating the use of the potential flow code to optimize foil kinematics and design in ship propulsion applications

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