Sur la théorie des méconnaissances en mécanique des structures

International audienceToday, the validation of complex structural models – i.e. the assessment of their quality compared to an experimental reference – remains a major issue. Strictly speaking, the validation problem consists in comparing the response of the numerical model (whether deterministic or stochastic) with complete reality. A first answer to this problem, using Lack-Of-Knowledge (LOK) theory, was introduced at LMT-Cachan. This theory is an attempt to “model the unknown” by taking all the sources of uncertainties, including modeling errors, into account through the concept of basic LOKs. In this article, we introduce basic LOKs associated with both the amplitudes and directions of excitations. These basic LOKs are propagated rigorously throughout the mechanical model in order to determine intervals (with stochastic bounds) within which lies a given quantity of interest (stress or displacement). Then, we introduce a strategy for the reduction of lack of knowledge, which we illustrate through an academic example.La validation de modèles structuraux complexes – c'est-à-dire la vérification de leur qualité vis-à-vis d'une référence expérimentale – demeure un verrou scientifique fort. Le véritable problème de validation consiste à comparer la réponse du modèle numérique, qu'il soit déterministe ou pas, avec la réponse de toutes les structures réelles, dans tous les environnements possible. Un premier élément de réponse à ce problème a été introduit via la théorie des méconnaissances au LMT-Cachan. Afin de « modéliser l'inconnu », cette théorie prend en compte toutes les incertitudes, en incluant les erreurs de modèles, à travers le concept de méconnaissances de base. Dans le cet article, on introduit des méconnaissances de base sur les excitations (amplitude et direction). Ces méconnaissances de base sont ensuite propagées à travers le modèle mécanique afin de déterminer des intervalles dont les bornes sont probabilistes, contenant une quantité d'intérêt (contrainte ou déplacement). Ensuite une stratégie de réduction des méconnaissances de base par apport d'information expérimentale est présentée sur un exemple académique

Elastocapillary network model of inhalation

The seemingly simple process of inhalation relies on a complex interplay between muscular contraction in the thorax, elasto-capillary interactions in individual lung branches, propagation of air between different connected branches, and overall air flow into the lungs. These processes occur over considerably different length and time scales; consequently, linking them to the biomechanical properties of the lungs, and quantifying how they together control the spatiotemporal features of inhalation, remains a challenge. We address this challenge by developing a computational model of the lungs as a hierarchical, branched network of connected liquid-lined flexible cylinders coupled to a viscoelastic thoracic cavity. Each branch opens at a rate and a pressure that is determined by input biomechanical parameters, enabling us to test the influence of changes in the mechanical properties of lung tissues and secretions on inhalation dynamics. By summing the dynamics of all the branches, we quantify the evolution of overall lung pressure and volume during inhalation, reproducing the shape of measured breathing curves. Using this model, we demonstrate how changes in lung muscle contraction, mucus viscosity and surface tension, and airway wall stiffness---characteristic of many respiratory diseases, including those arising from COVID-19, cystic fibrosis, chronic obstructive pulmonary disease, asthma, and emphysema---drastically alter inhaled lung capacity and breathing duration. Our work therefore helps to identify the key factors that control breathing dynamics, and provides a way to quantify how disease-induced changes in these factors lead to respiratory distress.Comment: In pres

Optimisation Géométrique d'une Machine à Commutation de Flux à Aimants Permanents en utilisant un Modèle Analytique Magnéto-Acoustique

Cet article présente les résultats d'une optimisation de la géométrie des Machines à Commutation de Flux à Aimants Permanents (MCF-AP) basée sur des critères multi-physiques magnéto-acoustiques en utilisant un modèle entièrement analytique visant à prédire le fonctionnement magnétique, mécanique et acoustique de ces structures. L'optimisation est réalisée sur une structure triphasée 12/10 et sur une structure pentaphasée 20/18 pour une alimentation et une vitesse donnés. Le modèle analytique, présenté et validé expérimentalement, permet un gain de temps non négligeable dans la prédiction des phénomènes magnéto-acoustiques en comparaison d'un modèle éléments finis et permet naturellement son implémentation dans un algorithme d'optimisation

Obstructed swelling and fracture of hydrogels

Obstructions influence the growth and expansion of bodies in a wide range of settings -- but isolating and understanding their impact can be difficult in complex environments. Here, we study obstructed growth/expansion in a model system accessible to experiments, simulations, and theory: hydrogels swelling around fixed cylindrical obstacles with varying geometries. When the obstacles are large and widely-spaced, hydrogels swell around them and remain intact. In contrast, our experiments reveal that when the obstacles are narrow and closely-spaced, hydrogels unexpectedly fracture as they swell. We use finite element simulations to map the magnitude and spatial distribution of stresses that build up during swelling at equilibrium, providing a route toward predicting when this phenomenon of self-fracturing is likely to arise. Applying lessons from indentation theory, poroelasticity, and nonlinear continuum mechanics, we also develop a theoretical framework for understanding how the maximum principal tensile and compressive stresses that develop during swelling are controlled by obstacle geometry and material parameters. These results thus help to shed light on the mechanical principles underlying growth/expansion in environments with obstructions.Comment: 12 pages, 5 figures; SI: 16 pages, 14 figure

Fast model updating coupling Bayesian inference and PGD model reduction

International audienceThe paper focuses on a coupled Bayesian-Proper Generalized Decomposition (PGD) approach for the real-time identification and updating of numerical models. The purpose is to use the most general case of Bayesian inference theory in order to address inverse problems and to deal with different sources of uncertainties (measurement and model errors, stochastic parameters). In order to do so with a reasonable CPU cost, the idea is to replace the direct model called for Monte-Carlo sampling by a PGD reduced model, and in some cases directly compute the probability density functions from the obtained analytical formulation. This procedure is first applied to a welding control example with the updating of a deterministic parameter. In the second application, the identification of a stochastic parameter is studied through a glued assembly example

Recalage de modèles de lanceur à partir d'essais en vol

La validation de modèle est une question centrale quant à la diminution des marges notamment dans le cas des lanceurs spatiaux. Les modèles sont de plus en plus performants, mais malgré tout, des méconnaissances fortes subsistent, quant aux excitations et aux paramètres structuraux de certaines liaisons complexes. La démarche de recalage développée a pour but de mettre à profit les mesures réalisées en phase de vol atmosphérique,  ce afin de réduire les méconnaissances

Microbial narrow-escape is facilitated by wall interactions

Cells have evolved efficient strategies to probe their surroundings and navigate through complex environments. From metastatic spread in the body to swimming cells in porous materials, escape through narrow constrictions - a key component of any structured environment connecting isolated microdomains - is one ubiquitous and crucial aspect of cell exploration. Here, using the model microalgae Chlamydomonas reinhardtii, we combine experiments and simulations to achieve a tractable realization of the classical Brownian narrow-escape problem in the context of active confined matter. Our results differ from those expected for Brownian particles or leaking chaotic billiards and demonstrate that cell-wall interactions substantially modify escape rates and, under generic conditions, expedite spread dynamics.</p

Recalage de structures légères par une approximation polynomiale en vue de leur contrôle actif

Le recalage de structures légères en vue du contrôle de leurs vibrations est une problématique importante. Un des outils mécaniques performant dans ce domaine est le recalage basé sur l'erreur en relation de comportement. Cet outil est adapté ici au contrôle actif en contexte incertain de telles structures grâce une description polynomiale de l'algorithme de calcul : les inconnues des polynômes sont la variabilité des paramètres (matériau ou conditions aux limites) qu'on souhaite recaler