Publications

2018

• Experimental characterization of Magneto-Rheological Elastomers for constitutive model parameters identification
  
  • Bodelot L
  • Voropaieff J.-P
  , 2018.
• A new multiaxial specimen for determining dynamic properties of adhesive joints
  
  • Janin A.
  • Constantinescu Andrei
  • Weisz-Patrault Daniel
  • Neviere R.
  • Stackler M.
  • Albouy W.
  Experimental Mechanics, Society for Experimental Mechanics, 2018. Adhesive joints are increasingly introduced in industrial structures for bonding critical parts. Their mechanical characterization is a key element for design and is, therefore, necessary. A significant work has been done for the characterization under quasi-static conditions, but techniques are rather limited for dynamic conditions. Indeed, existing dynamic studies characterize adhesive assemblies and not the adhesive joint alone, and do not investigate multiaxial loadings. Thus, this paper proposes an innovative experimental technique for the characterization of adhesive joints under dynamic multiaxial loadings. The experimental method relies on three main components: i) a conventional Split Hopkinson Pressure Bar (SHPB) apparatus, ii) a novel specimen named as DODECA enabling to test three distinct multiaxial loadings with the same methodology and iii) local strain and stress measurements performed by Digital Image Correlation (DIC). The paper exhibits all steps of the experimental procedure as well as underlying preparation and measuring methods. Stress and strain in the adhesive joint are estimated from experimental data directly both during loading and at the failure point. Finally, the dynamic material behavior of the adhesive joint is identified from the data. (10.1007/s11340-018-0402-7)
  DOI : 10.1007/s11340-018-0402-7
• La simulation médicale comme outil dans la formation des professionnels de la périnatalité
  
  • Tosello B.
  • Blanc J.
  • Kelway C.
  • Pellegrin V.
  • Quarello E.
  • Comte F.
  • Zakarian C.
  • d'Ercole C.
  • D’ercole C.
  Gynécologie Obstétrique Fertilité & Sénologie, Elsevier, 2018, 46 (6), pp.530-539. Though technology plays an increasingly important role in modern health systems, human performance remains a major determinant of safety, effectiveness and efficiency of patient care. This is especially true in the delivery room. Thus, the training of professionals must aim not only for the acquisition of theory and practical skills on an individual basis, but also for the learning of teamwork systematically. Training health professionals with simulation enhances their theoretical knowledge and meets formal requirements in literacy, technical skills and communication. Therefore, we intend to explore how, in perinatal care, training with simulation is actually a key teaching tool in initial education and in perpetuation of knowledge. We will approach three main aspects: individual, collective (team) and the impact of simulation in medical practice. The choice of this educational strategy improves the clinical skills that are required for optimal performance in complex, unpredictable and high-stake environments such as the delivery room. Nonetheless, the long term clinical impact of simulation and whether it's modalities, technical or not, are beneficial to the mother and the newborn are areas still to be explored. (10.1016/j.gofs.2018.04.003)
  DOI : 10.1016/j.gofs.2018.04.003
• A Hybrid High-Order method for Kirchhoff–Love plate bending problems
  
  • Bonaldi Francesco
  • Di Pietro Daniele Antonio
  • Geymonat Giuseppe
  • Krasucki Françoise
  ESAIM: Mathematical Modelling and Numerical Analysis, Société de Mathématiques Appliquées et Industrielles (SMAI) / EDP, 2018, 52 (2), pp.393-421. We present a novel Hybrid High-Order (HHO) discretization of fourth-order elliptic problems arising from the mechanical modeling of the bending behavior of Kirchhoff--Love plates, including the biharmonic equation as a particular case. The proposed HHO method supports arbitrary approximation orders on general polygonal meshes, and reproduces the key mechanical equilibrium relations locally inside each element. When polynomials of degree $k\ge 1$ are used as unknowns, we prove convergence in $h^{k+1}$ (with $h$ denoting, as usual, the meshsize) in an energy-like norm. A key ingredient in the proof are novel approximation results for the energy projector on local polynomial spaces. Under biharmonic regularity assumptions, a sharp estimate in $h^{k+3}$ is also derived for the $L^2$-norm of the error on the deflection. The theoretical results are supported by numerical experiments, which additionally show the robustness of the method with respect to the choice of the stabilization. (10.1051/m2an/2017065)
  DOI : 10.1051/m2an/2017065
• Low Cycle Fatigue of a Lost Foam Cast Al-Si-Cu alloy: study of the damage mechanisms with X-ray tomography and Digital Volume Correlation
  
  • Limodin Nathalie
  • Wang Long
  • Dahdah Nora
  • El Bartali Ahmed
  • Witz Jean-Francois
  • Seghir Rian
  • Charkaluk Eric
  • Buffiere Jean-Yves
  , 2018.
• Iterative observer-based state and parameter estimation for linear systems
  
  • Aalto Atte
  ESAIM: Control, Optimisation and Calculus of Variations, EDP Sciences, 2018, 24 (1), pp.265-288. We propose an iterative method for joint state and parameter estimation using measurements on a time interval [0,T] for systems that are backward output stabilizable. Since this time interval is fixed, errors in initial state may have a big impact on the parameter estimate. We propose to use the back and forth nudging (BFN) method for estimating the system's initial state and a Gauss–Newton step between BFN iterations for estimating the system parameters. Taking advantage of results on the optimality of the BFN method, we show that for systems with skew-adjoint generators, the initial state and parameter estimate minimizing an output error cost functional is an attractive fixed point for the proposed method. We treat both linear source estimation and bilinear parameter estimation problems. (10.1051/cocv/2017005)
  DOI : 10.1051/cocv/2017005
• A time integration algorithm for a 3D constitutive model for SMAs including permanent inelasticity and degradation effects
  
  • Peigney Michaël
  • Scalet Giulia
  • Auricchio Ferdinando
  International Journal for Numerical Methods in Engineering, Wiley, 2018. Components based on shape-memory alloys are often subjected to several loading cycles that result in substantial alteration of material behavior. In such a framework, accurate models as well as robust and efficient numerical approaches become essential to allow for the simulation of complex devices. The present paper focuses on the numerical simulation of quasi-static problems involving shape memory alloy (SMA) structures or components subjected to multiple loading-unloading cycles. A novel state-update procedure for a three-dimensional phenomenological model able to describe the saturation of permanent inelasticity, including degradation effects, is here proposed. The algorithm, being of the predictor-corrector type and relying on an incremental energy minimization approach, is based on elastic checks, closed-form solutions of polynomial equations, and nonlinear scalar equations solved through a combination of Newton-Raphson and bisection methods. This allows for an easy implementation of model equations and to avoid the use of regularization parameters for the treatment of non-smooth functions. Numerical results assess the good performances of the proposed approach in predicting both pseudoelastic and shape-memory material behavior under cyclic loading as well as algorithm robustness. (10.1002/nme.5835)
  DOI : 10.1002/nme.5835
• Asymptotic derivation of a linear plate model for soft ferromagnetic materials
  
  • Geymonat Giuseppe
  • Krasucki Françoise
  • Serpilli Michele
  Chinese Annals of Mathematics - Series B, Springer Verlag, 2018, 39 (3), pp.451-460. We apply the asymptotic expansion method by P.G. Ciarlet to obtain a Kirchhoff-Love-type plate model for a linear soft ferromagnetic material. We also give a mathematical justification of the obtained model by means of a strong convergence result . (10.1007/s11401-018-0077-5)
  DOI : 10.1007/s11401-018-0077-5
• DESIGN OF MULTI-LAYER MATERIALS USING INVERSE HOMOGENIZATION AND A LEVEL SET METHOD
  
  • Nika Grigor
  • Constantinescu Andrei
  , 2018. This work is concerned with the micro-architecture of multi-layer material that globally exhibits desired mechanical properties, for instance a negative apparent Poisson ratio. We use inverse homogenization, the level set method, and the shape derivative in the sense of Hadamard to identify material regions and track boundary changes within the context of the smoothed interface. The level set method and the shape derivative obtained in the smoothed interface context allows to capture, within the unit cell, the optimal micro-geometry. We test the algorithm by computing several multi-layer auxetic micro-structures. The multi-layer approach has the added benefit that contact during movement of adjacent " branches " of the micro-structure can be avoided in order to increase its capacity to withstand larger stresses.
• Uniaxial compression of calcite single crystals at low temperature: insights into twinning activation and development
  
  • Parlangeau Camille
  • Dimanov Alexandre
  • Lacombe Olivier
  • Daniel Jean-Marc
  , 2018. E-twinning is a common plastic deformation mechanism in calcite. Previous experiments have shown that temperature, strain rate and confining pressure have negligible effects on twinning activation, the latter being mainly dependent on differential stresses. Temperature is however reported to control the aspect of twin lamellae, with thickness exceeding 2-5 µm mostly at temperature above 200 °C. The critical resolved shear stress (CRSS) required for activation of twinning has been shown to be dependent on grain size and to be subjected to strain hardening: its value increases with the amount of strain accommodated and decreases with increasing grain size. This CRSS value may obey the Hall-Petch relation, but due to sparse experimental data the actual evolution of the CRSS with grain size and strain still remains a matter of debate. Numerous experiments were carried out at high temperature to investigate gliding systems in calcite, but just few data are available on the plastic behavior of calcite crystals at low temperature, despite the fact that the latter may help understand deformation processes of carbonate rocks in sedimentary basins. New mechanical tests were carried out at room temperature on unconfined single crystals of calcite, with different sizes and crystallographic orientations. Uniaxial deformation was performed at controlled displacement rate, meanwhile the sample surface was monitored using optical microscopy (reflected light) and high resolution CCD camera. The retrieved macroscopic stress-strain behavior of the crystals was correlated with the surface observations of the deformation process.
• A cyclic plasticity study by coupling Digital Image Correlation and Finite Elements methods
  
  • Hosdez Jerome
  • Langlois Médéric
  • Witz Jean-Francois
  • Limodin Nathalie
  • Najjar Denis
  • Charkaluk Eric
  , 2018.
• Schémas ALE multi-matériaux totalement conservatifs pour l'hydrodynamique
  
  • Marboeuf Alexis
  , 2018. Ce sujet de thèse s’inscrit dans le cadre des études actuellement menées au CEA/DAM concernant des schémas numériques ALE (Arbitrary-Lagrangian-Eulerian)de type « Lagrange + Projection », dans le contexte des simulations hydrodynamiques mutli-matériaux en grandes déformations. Ces schémas doivent respecter les équations de conservation de la masse, de la quantité de mouvement et de l’énergie totale.Les schémas décalés en temps et en espace sont très utilisés dans les codes industriels. Ils sont robustes et permettent une bonne approximation des comportements complexes, mais sont connus pour ne pas conserver exactement l’énergie totale. Cela pose un problème dans le traitement des chocs, sur maillages raffinés ou dans la simulation des milieux réactifs.En 2016, des travaux originaux on été proposés par A. Llor et. al. pour rendre conservatif ce type de schéma dans un contexte lagrangien (sans projection), notamment en proposant une correction pour retrouver la conservation de l’énergie totale.Le travail de cette thèse a été d’étendre ce schéma lagrangien dans un contexte ALE multi-matériaux (avec interface), en garantissant la conservation de toutes les quantités, le respect du second principe de la thermodynamique et la robustesse. De nombreux cas tests ont été menés (en 2D plan et en 2D axisymétrique) et comparés aux méthodes existantes afin de montrer la pertinence de cette approche.
• HOMOGENIZATION FOR A MULTI-SCALE MODEL OF MAGNETORHEOLOGICAL SUSPENSION
  
  • Nika Grigor
  • Vernescu Bogdan
  , 2018. Using the homogenization method we obtain a model describing the behavior of the suspension of solid magnetizable particles in a viscous non-conducting fluid in the presence of an externally applied magnetic field. We use the quasi-static Maxwell equations coupled with the Stokes equations to capture the magnetorheological (MR) effect. The model generalizes the one introduced by Neuringer and Rosensweig [14], for quasistatic phenomena. The macroscopic constitutive properties are given explicitly in terms of the solutions of the local problems. We determine the homogenized constitutive parameters for an aqueous MR fluid with magnetite particles using the finite element method. The Poiseuille flow, for the solution of our homogenized coupled system, approaches the Bingham flow profile for large values of the magnetic field. The stress–strain curves obtained for the Couette flow exhibit a yield stress close to the one determined experimentally.
• Modelling resonant arrays of the Helmholtz type in the time domain
  
  • Maurel Agnès
  • Marigo Jean-Jacques
  • Mercier Jean-François
  • Pham Kim
  Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Royal Society, The, 2018, 474 (2210), pp.20170894. We present a model based on a two-scale asymptotic analysis for resonant arrays of the Helmholtz type, with resonators open at a single extremity (standard resonators) or open at both extremities (double-sided resonators). The effective behaviour of such arrays is that of a homogeneous anisotropic slab replacing the cavity region, associated with transmission, or jump, conditions for the acoustic pressure and for the normal velocity across the region of the necks. The coefficients entering in the effective wave equation are simply related to the fraction of air in the periodic cell of the array. Those entering in the jump conditions are related to near field effects in the vicinity of the necks and they encapsulate the effects of their geometry. The effective problem, which accounts for the coupling of the resonators with the surrounding air, is written in the time domain which allows us to question the equation of energy conservation. This is of practical importance if the numerical implementations of the effective problem in the time domain is sought. (10.1098/rspa.2017.0894)
  DOI : 10.1098/rspa.2017.0894
• Experimental investigation of the coupled magneto-mechanical response in magnetorheological elastomers
  
  • Bodelot Laurence
  • Voropaieff Jean-Pierre
  • Pössinger Tobias
  Experimental Mechanics, Society for Experimental Mechanics, 2018, 58 (2), pp.207–221. (10.1007/s11340-017-0334-7)
  DOI : 10.1007/s11340-017-0334-7
• Characterization of oxide scales formed on alloy 82 in nominal PWR primary water at 340 °C and in hydrogenated steam at 400 °C
  
  • Duhamel Cecilie
  • Sennour Mohamed
  • Georgi Frédéric
  • Guerre Catherine
  • Chaumun Elizabeth
  • Crépin Jérôme
  • Héripré Eva
  • Curières Ian De
  Corrosion Science, Elsevier, 2018, 131, pp.386-403. Alloy 82, used as weld metal in Pressurized Water Reactor (PWR), was exposed to hydrogenated steam at 400 °C and to simulated primary water at 340 °C. A comparative study of the oxide layer formed on the alloy surface in both environments was performed to confirm that steam conditions were representative of accelerated primary water conditions. For this purpose, the oxidation products were investigated at a nanometer scale using Scanning Electron Microscopy (SEM), X-ray Photoelectron Spectrometry (XPS) and Transmission Electron Microscopy (TEM). Results obtained in both conditions are compared and the influences of heat treatment, test duration and surface preparation are studied. (10.1016/j.corsci.2017.11.029)
  DOI : 10.1016/j.corsci.2017.11.029
• La mécanique des biofilms à la surface de liquides
  
  • Douarche Carine
  • Bailleux Virginie
  • Even Catherine
  • Allain Jean-Marc
  • Regeard Christophe
  • Raspaud Eric
  Reflets de la Physique, EDP sciences, 2018, 56, pp.20-24. Les micro-organismes peuvent coloniser les surfaces environnantes et s'organiser en un film de plusieurs centaines de microns d'épaisseur, appelé « biofilm ». Ils sécrètent une matrice extracellulaire polymérique qui assure une véritable cohésion et protection physique de la colonie, avec des effets qui peuvent être aussi bien bénéfiques que mortels pour son environnement. Nous nous sommes intéressés aux forces mécaniques structurant cette matière vivante solide et contribuant à maintenir son intégrité. Nous avons travaillé sur des biofilms de bactéries flottant à la surface d'un liquide. Nous montrons que ces systèmes ont des propriétés mécaniques originales et remarquables, du fait de leur capacité à croître et proliférer. (10.1051/refdp/201856020)
  DOI : 10.1051/refdp/201856020
• Influence du vieillissement en atmosphère confinée sur la prédiction de la durée de vie des joints adhésifs
  
  • Jouan Alexandre, Alain
  , 2018. L’industrie pétrolière s’intéresse aujourd’hui à la possibilité de remplacer certaines brasures par des joints adhésifs rendus conducteurs par leur fort taux de charges conductrices dans les outils électroniques. Ces outils évoluent aujourd’hui à des hauts niveaux de température et de pression pendant leur vie en service. L’utilisation de joints adhésifs pose donc automatiquement la question de leur fiabilité à long terme. L’étude de leur tenue en fatigue, et de l’influence du vieillissement sur cette tenue en fatigue devient nécessaire pour le déploiement final de ces joints. Cette thèse se propose de répondre à une double question : la prédiction de la durée de vie de deux colles commerciales dans les outils électroniques et l’influence du vieillissement de ces colles sur cette prédiction. Deux vieillissements différents ont été mis en œuvre : un vieillissement à l’air libre et un vieillissement inerte (sous argon) confiné.Dans un premier temps, une caractérisation expérimentale du comportement viscoélastique des colles a été menée. Elle met en particulier l’accent sur les non-linéarités induites par les deux paramètres de chargements retenus que sont le cisaillement et la pression hydrostatique.Dans un deuxième temps, une étude plus fine de la microstructure a été effectuée numériquement. Une série d’hypothèses de modélisation a été faite. Les résultats de ces calculs - plutôt qualitatifs - permettent de dégager les tendances sur l’influence de la présence des charges conductrices sur la réponse macroscopique du joint adhésif.Enfin, la tenue en fatigue des joints et sa dépendance à leur vieillissement a été abordée expérimentalement. L’influence de l’atmosphère et du confinement pendant le vieillissement sur l’évolution de la tenue en fatigue a été mise en évidence pour les deux colles étudiées dans cette thèse. Les résultats obtenus ont permis de proposer des lois de fatigue dont certains paramètres dépendent du vieillissement.
• Exploring kinetic energy as a new marker of cardiac function in the single ventricle circulation
  
  • Wong James
  • Chabiniok Radomir
  • Tibby Shane M
  • Pushparajah Kuberan
  • Sammut Eva
  • Celermajer David
  • Giese Daniel
  • Hussain Tarique
  • Greil Gerald F
  • Schaeffter Tobias
  • Razavi Reza
  Journal of Applied Physiology, American Physiological Society, 2018, 125, pp.889-900. Ventricular volumetric ejection fraction (VV EF) is often normal in patients with single ventricle circulations despite them experiencing symptoms related to circulatory failure. We sought to determine if kinetic energy (KE) could be a better marker of ventricular performance. KE was prospectively quantified using 4D flow MRI in 41 patients with a single ventricle circulation (aged 0.5 - 28 years) and compared to 43 healthy volunteers (aged 1.5 - 62 years) and 14 patients with left ventricular (LV) dysfunction (aged 28 - 79 years). Intraventricular end-diastolic blood was tracked through systole and divided into ejected and residual blood components. Two ejection fraction (EF) metrics were devised based on the KE of the ejected component over the total of both the ejected and residual components using: (1) instantaneous peak KE to assess KE EF or; (2) summating individual peak particle energy (PE) to assess PE EF. KE EF and PE EF had a smaller range than VV EF in healthy subjects (97.9 {plus minus} 0.8% vs. 97.3 {plus minus} 0.8% vs. 60.1 {plus minus} 5.2%). LV dysfunction caused a fall in KE EF (p =0.01) and PE EF (p =0.0001). VV EF in healthy LVs and single ventricle hearts was equivalent however KE EF and PE EF were lower (p <0.001) with a wider range indicating a spectrum of severity. Those reporting the greatest symptomatic impairment (NYHA II) had lower PE EF than asymptomatic subjects (p =0.0067). KE metrics are markers of healthy cardiac function. PE EF may be useful in grading dysfunction. (10.1152/japplphysiol.00580.2017)
  DOI : 10.1152/japplphysiol.00580.2017
• Caractérisation du rayonnement acoustique d'un haut-parleur monté sur une enceinte parallélépipédique allongée. Application a une barre de son.
  
  • Roggerone Vincent
  , 2018. Le rayonnement d'un haut-parleur monté sur une enceinte est généralement caractérisé par des mesures ou une simulation par la méthode des éléments finis. Cependant, ces méthodes de référence restent très coûteuses et ne permettent pas une interprétation physique des résultats. Dans ce manuscrit, nous proposons deux modèles analytiques pour prédire ce rayonnement, dans le cadre d'une application à une barre de son. Le premier modèle consiste à assimiler la géométrie de la barre de son à un sphéroïde. De cette manière, les variables sont séparées et on peut trouver une solution analytique sous la forme d'une somme d’harmoniques sphéroïdales. On décrira chaque étape de la méthode, ainsi que la comparaison des résultats à ceux des méthodes de référence. On développera particulièrement le calcul pour un haut-parleur circulaire sur le sphéroïde et la mise en place d'un critère de troncature des harmoniques. Ce modèle fonctionne bien en basse-fréquence, mais ne peut pas rendre compte de tous les phénomènes de diffraction par l'enceinte en haute fréquence. Pour celles-ci, la diffraction du champ sonore par les arêtes de l'enceinte devient non négligeable. Nous avons donc développé un second modèle analytique, basé sur une formulation intégrale de cette diffraction. Celle-ci est vue comme un ensemble de sources secondaires localisées sur les arêtes. On montrera comment établir ce modèle et on donnera des détails sur son implémentation. L'application de ce modèle permet d'interpréter physiquement le rayonnement d'une barre de son, et donc de conclure sur la validité du modèle sphéroïdal. On montre également comment les arêtes du baffle d'une enceinte entraînent des effets d'interférences constructives, qui peuvent induire un gain allant jusqu’à 3 dB. Ces effets entraînent également un phénomène contre-intuitif : si le haut-parleur n'est pas centré sur le baffle, la direction du maximum d'intensité du rayonnement tend à se décaler vers le côté opposé au décalage du haut-parleur sur le baffle.
• GLISSEMENT AUX JOINTS DE GRAINS DANS LES MATÉRIAUX MÉTALLIQUES : ÉTUDE PAR ESSAIS IN-SITU MEB ET CARACTÉRISATION PAR CIN
  
  • El Sabbagh Alexandre
  • Raphanel Jean
  • Bornert Michel
  • Dimanov Alexandre
  , 2018. Le but de cette étude est de caractériser les mécanismes de déformation plastiques à moyennes et hautes températures (>0.4 T m) dans les métaux, en se concentrant sur l'observation du glissement aux joints de grain (GBS pour "Grain Boundary Sliding"). Nous avons mené des essais de compression uniaxiale sur des échantillons d'aluminium à vitesse de déplacement constante dans un microscope électronique à balayage (MEB). L'outil de corrélation d'images numériques (CIN) a été utilisé pour quantifier les champs de déformations locales aux échelles micro et mésoscopiques, grâce à la réalisation de motifs multi-échelles par micro-lithographie MEB sur la surface l'échantillon. Nous observons que depuis l'entrée en plasticité et tout au long de la déformation, la plasticité cristalline et le GBS coexistent et coopèrent. Nous recherchons la part de GBS dans la déformation totale, ainsi que les conditions de chargement (température et vitesse de déformation) et la microstructure (configurations locales des grains voisins) favorisant ce dernier.
• Mathematical and numerical methods for modeling and computing the cyclic steady states in non-linear mechanics
  
  • Khristenko Ustim
  , 2018. This work is focused on fast techniques for computing the steady cyclic states of evolution problems in non-linear mechanics with space and time periodicity conditions. This kind of problems can be faced, for instance, in the beating heart modeling. Another example concerns the rolling of a tyre with periodic sculptures, where the cyclic state satisfies "rolling" periodicity condition, including shifts both in time and space. More precisely, the state at any point is the same that at the corresponding point observed at the next sculpture one time period ago.Direct solvers for such problems are not very convenient, since they require inversion of very large matrices. In industrial applications, in order to avoid this, such a cyclic solution is usually computed as an asymptotic limit of the associated initial value problem with arbitrary initial data. However, when the relaxation time is high, convergence to the limit cycle can be very slow. In such cases nonetheless, one is not interested in the transient solution, but only in a fast access to the limit cycle. Thus, developing methods accelerating convergence to this limit is of high interest. This work is devoted to study and comparison of two techniques for fast calculation of the space-time periodic solution.The first is the well-known Newton-Krylov shooting method, looking for the initial state, which provides the space-time periodic solution. It considers the space-time periodicity condition as a non-linear equation on the unknown initial state, which is solved using Newton-Raphson technique. Since the associated Jacobian can not be expressed explicitly, the method uses one of the matrix-free Krylov iterative solvers. Using information stored while computing the residual to solve the linear system makes its calculation time negligible with respect to the residual calculation time. On the one hand, the algorithm is a shooting method, on the other side, it can be considered as an observer-controller method, correcting the transient solution after each cycle and accelerating convergence to the space-time periodic state.The second method, considered in this work, is an observer-controller type modification of the standard evolution to the limit cycle by introducing a feedback control term, based on the periodicity error. The time-delayed feedback control is a well-known powerful tool widely used for stabilization of unstable periodic orbits in deterministic chaotic systems. In this work the time-delayed feedback technique is applied to an a priori stable system in order to accelerate its convergence to the limit cycle. Moreover, given the space-time periodicity, along with the time-delay, the feedback term includes also a shift in space. One must then construct the gain operator, applied to the periodicity error in the control term. Our main result is to propose and to construct the optimal form of the gain operator for a very general class of linear evolution problems, providing the fastest convergence to the cyclic solution. The associated control term can be mechanically interpreted.Efficiency of the method increases with the problem's relaxation time. The method is presented in a simple predictor-corrector form, where correction is explicit and numerically cheap. In this later form, the feedback control has been also adapted and tested for a nonlinear problem.The discussed methods have been studied using academic applications and they also have been implemented into the Michelin industrial code, applied to a full 3D tyre model with periodic sculpture in presence of slip-stick frictional contact with the soil, and then compared to the standard asymptotic convergence.
• Effective rigidity of ribbed plates revealed by spatial spectra analysis
  
  • Lefebvre Gautier
  • Filoche Marcel
  • Boutillon Xavier
  , 2018.
• Mechanosensitivity of cancer cells in contact with soft substrates using AFM
  
  • Abidine Yara
  • Constantinescu Andrei
  • Laurent Valérie M.
  • Sundar Rajan Vinoth
  • Michel Richard
  • Laplaud Valentin
  • Duperray Alain
  • Verdier Claude
  Biophysical Journal, Biophysical Society, 2018, 114 (5), pp.1165-1175. Cancer cells are usually found to be softer than normal cells. But their stiffness changes when they are in contact with different environments, due to mechanosensitivity. For example, they adhere to a given substrate by tuning their cytoskeleton, thus affecting their rheological properties. This mechanism could become efficient when cancer cells invade the surrounding tissues, and they have to remodel their cytoskeleton in order to achieve particular deformations. Here we use an atomic force microscope (AFM) in force modulation mode to study how local rheological properties of cancer cells are affected by a change of the environment. Cancer cells are plated on functionalized polyacrylamide substrates of different stiffnesses, as well as on an endothelium substrate. A new correction of Hertz model is developed because measurements require to account for the precise properties of the layered, thin viscoelastic substrates. The main results show the influence of local cell rheology (nucleus, perinuclear, edge locations), and the role of invasiveness. A general mechanosensitive trend is found where the cell elastic modulus and transition frequency increase with substrate elasticity, but this tendency breaks down with a real endothelium substrate. These effects are investigated further during cell transmigration, when the actin cytoskeleton undergoes a rapid reorganization process necessary to push through the endothelial gap, in agreement with the local viscoelastic changes measured by AFM. Taken together, these results introduce a paradigm for a new possible extravasation mechanism. (10.1016/j.bpj.2018.01.005)
  DOI : 10.1016/j.bpj.2018.01.005
• A Discrete-time Optimal Filtering Approach for Non-linear Systems as a Stable Discretization of the Mortensen Observer
  
  • Moireau Philippe
  ESAIM: Control, Optimisation and Calculus of Variations, EDP Sciences, 2018, 24 (4), pp.1815 - 1847. In this work, we seek exact formulations of the optimal estimator and filter for a non-linear framework, as the Kalman filter is for a linear framework. The solution is well established with the Mortensen filter in a continuous-time setting, but we seek here its counterpart in a discrete-time context. We demonstrate that it is possible to pursue at the discrete-time level an exact dynamic programming strategy and we find an optimal estimator combining a prediction step using the model and a correction step using the data. This optimal estimator reduces to the discrete-time Kalman estimator when the operators are in fact linear. Furthermore, the strategy that consists of discretizing the least square criterion and then finding the exact estimator at the discrete level allows to determine a new time-scheme for the Mortensen filter which is proven to be consistent and unconditionally stable, with also a consistent and stable discretization of the underlying Hamilton-Jacobi-Bellman equation. (10.1051/cocv/2017077)
  DOI : 10.1051/cocv/2017077