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International audience; Early detection of damage and monitoring helps improving the safety and durability of structures. The ability to model and simulate this phenomenon, along with measurements, facilitates system control.Various sensor types have been used in the context of structural health monitoring. Among them, Distributed Optic Fiber Sensors grant certain benefits which make them a convenient option for real-time monitoring of structures. This work comprises of using distributed strain sensors, based on Rayleigh backscattering and OFDR technology, in samples that bear loading up to their failure point. The collected data are then post-processed in the framework of modified constitutive relation error (mCRE) to perform damage model updating and estimate the material condition. Several damage models are presented and compared, and the most suitable model is also selected using mCRE.; La détection précoce de l’endommagement et le suivi de sa progression contribuent à améliorer la sécurité et la durabilité des structures. La capacité à modéliser et simuler ce phénomène, en complément de mesures, facilite le contrôle du système. Différents types de capteurs ont été utilisés dans le cadre de la surveillance de l’état des structures. Parmi eux, les capteurs à fibre optique distribués offrent divers avantages qui en font une option pratique pour la surveillance en temps réel des structures. Ce travail consiste à utiliser des capteurs distribués de déformation, basés sur la rétrodiffusion de Rayleigh et la technologie OFDR, dans des échantillons qui supportent une charge jusqu’à leur point de rupture. Les données recueillies sont ensuite post-traitées dans le cadre de l’erreur en relation de comportement modifiée (mCRE) pour effectuer la mise à jour du modèle d’endommagement et estimer l’état du matériau.Plusieurs modèles d’endommagement sont présentés et comparés, et le modèle le plus adapté est aussi sélectionné au moyen de la mCRE.

International audience; La méthode isogéométrique présente des avantages quant à son lien avec la CAO. Afin de pouvoir utili- ser des codes préexistants donc généralement basés sur une structure élémentaire avec cette méthode, nous présentons une "réinterprétation " de l’extraction de Bézier. En effet à partir du maillage NURBS il est possible d’en extraire un maillage à structure élémentaire sur lequel des calculs éléments finis peuvent être lancés, en modifiant uniquement les fonctions de forme utilisées. Nous avons ensuite mis en place une projection entre les bases éléments finis et les bases NURBS afin de bien récupérer le résultats isogéométrique. Un exemple numérique permet de valider la performance de cette projection.

National audience; Despite the important progress in computer sciences, the cost associated with the resolution of multi- parametric problems can be extremely prohibitive. This is especially important when dealing with problems depending on numerous parameters, as encountered in optimization studies, which are becoming more and more mandatory for the design of new products. Reduced Order Modelling (ROM) is a convenient answer to circumvent this issue, usually called curse of dimensionality. However, a main drawback of ROM is the lack of robust a posteriori error estimators to measure the quality of the approximated solution, even if first advances have been performed [1,2].This paper extends the a posteriori verification procedure proposed in [3] that enables to control and certify PGD-based model reduction techniques, which are currently the subject of many research activities [4]. This procedure uses the concept of constitutive relation error allowing to get guaranteed global/goal-oriented error estimator taking both discretization and PGD truncation error into account. By splitting the errors sources, it also leads to a natural greedy adaptive strategy, which can be driven in order to optimize the accuracy of PGD approximation [5,6]. We extend it to the cases of geometrical parameters models and PGD separation of space variables [7].The focus of the talk is on two technical points: (i) construction of equilibrated fields required to compute guaranteed error bounds for those specific cases; (ii) error splitting and adaptive process when performing PGD-based model reduction.

International audience; In this work, we propose new bounding techniques that enable to derive accurate and strict error bounds on outputs of interest computed from numerical ap- proximation methods such as the finite element method. These techniques are based on Saint-Venant's principle and exploit specific homotheticity properties in order to im- prove the quality of the bounds computed from the classical bounding technique. The capabilities of the proposed approaches are illustrated through two-dimensional numerical experiments carried out on a linear elasticity problem.

International audience; Nowadays, a major interest in research activities concerns methods that aim at providing a reliable mean to control and assess the numerical quality of specific quanti- ties, i.e. strict and accurate local error bounds. A general method for robust goal-oriented error estimation relies on the concept of constitutive relation error (CRE), associated to admissible stress fields and classical extraction techniques. This paper first deals with the comparison between different techniques used for constructing admissible stress fields, which are usually required in methods providing for robust global/goal-oriented error estimation. In this work, a new hybrid technique, called the element equilibration + star-patch technique (EESPT), is compared with the two other main existing techniques, namely the element equilibration technique (EET), and the star-patch equilibration tech- nique (SPET) in terms of quality of associated error estimates, computational cost and simplicity of practical implementation into existing finite element codes. Besides, an en- hanced version of the EESPT method has been revisited and demonstrates its relevance to produce sharper estimators. In a second part, we analyze goal-oriented error estimators constructed from the CRE. Two- and three-dimensional numerical experiments are car- ried out to investigate the performance of each estimator for the calculation of guaranteed error bounds on specific quantities of interest.

National audience; See http://hal.archives-ouvertes.fr/docs/00/59/28/86/ANNEX/r_NZO1G1L1.pdf

International audience