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An implicit–explicit time discretization for elastic wave propagation problems in plates
No full textInternational audienceWe propose a new implicit–explicit scheme to address the challenge of modeling wave propagation within thin structures using the time‐domain finite element method. Compared to standard explicit schemes, our approach renders a time marching algorithm with a time step independent of the plate thickness and its associated discretization parameters (mesh step and order of approximation). Relying on the standard three dimensional elastodynamics equations, our strategy can be applied to any type of material, either isotropic or anisotropic, with or without discontinuities in the thickness direction. Upon the assumption of an extruded mesh of the plate‐like geometry, we show that the linear system to be solved at each time step is partially lumped thus efficiently treated. We provide numerical evidence of an adequate convergence behavior, similar to a reference solution obtained using the well‐known leapfrog scheme. Further numerical investigations show significant speed up factors compared to the same reference scheme, proving the efficiency of our approach for the configurations of interest
Negative refraction in a single-phase flexural metamaterial with hyperbolic dispersion
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Incorporating interface permeability into the diffusion MRI signal representation while using impermeable Laplace eigenfunctions
No full textInternational audienceAbstract Objective . The complex-valued transverse magnetization due to diffusion-encoding magnetic field gradients acting on a permeable medium can be modeled by the Bloch–Torrey partial differential equation. The diffusion magnetic resonance imaging (MRI) signal has a representation in the basis of the Laplace eigenfunctions of the medium. However, in order to estimate the permeability coefficient from diffusion MRI data, it is desirable that the forward solution can be calculated efficiently for many values of permeability. Approach . In this paper we propose a new formulation of the permeable diffusion MRI signal representation in the basis of the Laplace eigenfunctions of the same medium where the interfaces are made impermeable. Main results. We proved the theoretical equivalence between our new formulation and the original formulation in the case that the full eigendecomposition is used. We validated our method numerically and showed promising numerical results when a partial eigendecomposition is used. Two diffusion MRI sequences were used to illustrate the numerical validity of our new method. Significance. Our approach means that the same basis (the impermeable set) can be used for all permeability values, which reduces the computational time significantly, enabling the study of the effects of the permeability coefficient on the diffusion MRI signal in the future
Influence of Heat-treatment on Fatigue Properties of Super Duplex 2507 Stainless Steel produced by Directed Energy Deposition Process
No full textInternational audienceSuper duplex 2507 (2507 SDSS) is a two-phase austeno-ferritic stainless steel known for its good mechanical properties, especially for fatigue as well as corrosion resistance, due to its mixed microstructure. Metal additive manufacturing, and in particular the Directed Energy Deposition (DED) process, allows the construction or repair of structures for more complex geometries than conventional processes. DED process uses powder that is projected by an argon flow and melted by a laser in the printing area to form the material. This manufacturing protocol however results in different microstructures (grain sizes and orientation, phases repartition) from those observed in conventional processes and particularly forging.The objectives of the study are first to carefully analyse the microstructure of DED-manufactured 2507 SDSS and the effect of different heat treatments on it. Effects on the ratio between austenite and ferrite is particularly discussed. Then, the fatigue limit of this new "material-process" combination is investigated both with Staircase protocols and self-heating tests campaigns. A same grade forged steel is used as reference material.Fatigue limit modelling of DED-manufactured 2507 SDSS is finally performed on the basis of self-heating tests and a dedicated plastic constitutive model
Développement d’un macro-élément de fondations sous charge dynamique : Application au cas des sols renforcés par inclusions rigides
No full textThe dynamic response of a rigid inclusion-reinforced foundation represents a complex Soil-Structure Interaction (SSI) problem. Considering the limited existing studies, there is a clear necessity to explore the SSI phenomena involved in the response of such foundations under seismic conditions and to enhance the corresponding design methodologies.Building upon insights gained from a limited number of dynamic experimental and numerical studies, this research focuses on the dynamic soil-structure interaction phenomena of foundations reinforced by rigid inclusions. The study aims to provide a better understanding of the seismic behaviour of such foundations using several complementary approaches, including various numerical models, resolution strategies, and analytical analyses. The effects of inertial and kinematic interaction phenomena on the response of both the overall foundation and individual elements within the system (e.g., rigid inclusions, load transfer platform, etc.) are examined in detail.The seismic bearing capacity of foundations reinforced by rigid inclusions is further investigated, using the kinematic exterior approach within the framework of yield design theory. A multi-subsystem analytical approach based on the kinematic exterior approach is introduced and validated through FEM analyses. The evolution of the reduction factors associated with load eccentricity, load inclination, and soil inertia is also explored for several configurations of the reinforcement in terms of coverage area ratio.A novel macro-element for rigid inclusion-reinforced foundations under seismic loading is developed and numerically validated. It allows the modelling of both the linear and non-linear response of the foundation, including uplift, sliding and loss of bearing capacity mechanisms. The validated macro-element model is used to perform a parametric study using a lumped mass model and the Incremental Dynamic Analysis (gls{IDA}) of a 22-storey building, demonstrating the effectiveness and usefulness of the proposed approach in a performance-based design approach.This research is conducted within the framework of the French National project ASIRI+ and French National Research (ANR) project ASIRIplus_SDS.La réponse dynamique d'une fondation renforcée par inclusions rigides représente un problème complexe d'interaction sol-structure (ISS). Cependant, le nombre d’études s’intéressant à ce type de fondations reste encore limité, et il est nécessaire d’explorer davantage les phénomènes d’ISS impliqués dans leur réponse sous l’action des séismes et d’améliorer les méthodes d’analyse correspondantes.Sur la base des connaissances acquises à partir des études expérimentaux et numériques disponibles à ce jour, ce travail de recherche s’intéresse aux phénomènes d’interaction sol-structure dynamique des fondations renforcées par inclusions rigides. L'étude vise à fournir une meilleure compréhension du comportement sismique de ce type de fondation en utilisant plusieurs approches complémentaires comprenant dives modèles numériques, stratégies de résolution et approches analytiques. Les effets des phénomènes d’interaction inertiel et cinématique à la fois sur la réponse globale de la fondation et sur la réponse des différents éléments du système (i.e., inclusions rigides, matelas de répartition, etc.) sont examinés en détail.La capacité portante sismique des fondations renforcées par inclusions rigides est étudiée en utilisant l'approche cinématique par l'extérieur dans le cadre de la théorie du calcul à la rupture. Une approche analytique permettant d’explorer plusieurs mécanismes de rupture de la fondation est proposée et validée par des analyses numériques en éléments finis.L'évolution des facteurs de réduction associés à l'excentrement et l’inclinaison de la charge ainsi qu’à l'inertie du sol est également explorée pour plusieurs configurations de renforcement en termes du taux de substitution.Un nouveau macro-élément pour les fondations renforcées par inclusions rigides sous chargement sismique est développé et validé numériquement. Il permet la modélisation de la réponse linéaire et non-linéaire de la fondation, incluant les mécanismes de décollement, de glissement et de perte de la capacité portante. Ce modèle est ensuite utilisé pour conduire une étude paramétrique à l'aide d'un modèle de structure simplifiée et l'analyse dynamique incrémentale d'une tour R+22, démontrant l'efficacité et l'utilité de l'approche proposée dans une démarche de conception parasismique basée sur la performance.Cette recherche est menée dans le cadre du Projet National français ASIRI+ et du projet ANR ASIRIplus_SDS
Study of the evolution of stresses and associated mechanisms in zirconia growing at high temperature on Zircaloy-4 by use of synchrotron radiation
No full textInternational audienceHigh temperature (> 700°C) steam oxidation of zirconium alloys occurs during some hypothesized accidental conditions in pressurized water reactor (PWR). This oxidation affects the mechanical properties of the material. Moreover, the oxide layer develops internal stresses which may play a role on the oxidation kinetics of zirconium alloys at high temperature. Thus, it is important to determine the strain and stress fields associated to the growth of the oxide film especially above 700°C due to very little data in the literature!The present work studied the evolution of stresses and associated mechanisms in the zirconia layer formed during the oxidation of Zircaloy-4 under a He/O2 mixture, at temperatures of 700°C, 800°C and 900°C. Measurements by X-ray diffraction are performed in-situ under synchrotron radiation during oxidation to determine the evolutions of phases and stresses in the oxide layer with time. The results show that the zirconia formed contains a mixture of monoclinic and tetragonal phases. The proportion of the tetragonal phase depends on the oxidation temperature and decreases during oxidation. In order to better understand the influence of this evolution and localize the tetragonal phase, measurements by Raman spectroscopy have also been performed. These two phases are subjected to compressive stresses in directions perpendicular to the oxide layer growth direction. These stresses depend on temperature and decrease during oxidation. Two mechanical models either considering the zirconia phases independently or considering an equivalent homogeneous oxide are proposed to describe the evolution of these stresses, considering that it is due to oxide viscoplasticity. The model parameters are analysed to discuss the mechanisms of viscoplastic flow in the oxide. Numerical values for the viscoplastic parameters of the model as well as for the corresponding activation energy are therefore provided
Numerical analysis of cross‐sectional effects during the magnetic pulse disassembly of laminate structures
No full textInternational audienceTo improve performances of engineered systems, laminate composite structures are widely used as they offer the best strength‐to‐weight ratio. However, maintenance and recycling of these structures still remain a challenge. One solution could be to disassemble the layers, without damaging them, so that they can be repaired, re‐used or recycled. To do so, impulsive source such as high pulsed powers are considered. In the present work, the influence of transverse or cross‐sectional effects on the wave propagation within the laminate and on its disassembly conditions is studied by the means of two‐dimensional numerical simulations performed on a model assembly using the finite element method. The specimen considered is an aluminium/steel assembly joined along a stripe. Two different modelings of the loading applied to the laminate of increasing complexity are successively considered. First, linear elastodynamic simulations show that transverse effects reduce by around 12% the maximum achievable interfacial tensile stress ratio compared with that predicted by the 1D reference model. Then, weakly coupled eddy current‐linear elastodynamic numerical analyses clarify the latter result with an estimation of about 16% with respect to the 1D analytical solution. These results permit the design of experiments serving as a proof of concept of the proposed process. This article is protected by copyright. All rights reserved
Effet de la relaxation des contraintes sur la cristallisation induite mécaniquement dans le caoutchouc naturel
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Charles David, Millet Claude, Dictionnaire Victor Hugo
No full text52 notices: Actes et Paroles, Anonymat , Anthropométrie de VH, Assemblée Nationale, Auverney (Vicomte d’) V. Pseudonyme , Barbe, Berryer, Blanc (Louis), Chambre des députés, Chambre des Pairs, Clemenceau Georges, Éloquence , Emploi du temps, Esclavage, Falloux (Frédéric Albert de), Gambetta (Léon) , Gide André , Girardin Émile de, Goton (Marguerite Martin-Chopine dite), Grandiloquence, Habillement, Hugolâtrie, Hugophobie,, Hygiène, Ledru-Rollin, Loisirs, Mirabeau, Mondanités, Moniteur universel (Le) , Montalembert comte de, Nefftzer, Opportunisme, Orateur, Palmerston (lord), Pamphlet, Parisis, Patrimoine de VH, Postérité, Presse (Hugo et la), Procès, Propriété littéraire, Pseudonyme, Radicalisme, Revenus, Saint-Valry, Santé, Tribune, Vallès Jules, Voix (timbre, hauteur, intensité), Brown (John), Alice
Deterministic optimal control on Riemannian manifolds under probability knowledge of the initial condition
No full textInternational audienceIn this article, we study an optimal control problem on a compact Riemannian manifold M with imperfect information on the initial state of the system. The lack of information is modelled by a Borel probability measure along which the initial state is distributed. The state space of this problem is the space of Borel probability measures over M. We define a notion of viscosity in this space by taking as test functions a subset of the set of functions that can be written as a difference of two semi-convex functions. With this choice of test functions, we extend the notion of viscosity solution to Hamilton-Jacobi-Bellman equations in Wasserstein space, we also establish that the value function of the control problem with imperfect information is the unique viscosity solution of a Hamilton-Jacobi-Bellman equation in the space of Borel probability measures