Publications

2016

• Coupled S-P wave propagation in nonlinear regularized micromorphic media
  
  • Rapti Ioanna
  • Modaressi-Farahmand Razavi Arézou
  • Foucault Alexandre
  • Lopez-Caballero Fernando
  • Voldoire François
  Computers and Geotechnics, Elsevier, 2016, 77 (1), pp.106 - 114. (10.1016/j.compgeo.2016.04.012)
  DOI : 10.1016/j.compgeo.2016.04.012
• Phenomenological model for predicting stationary and non-stationary spectra of wave turbulence in vibrating plates
  
  • Humbert Thomas
  • Josserand Christophe
  • Touzé Cyril
  • Cadot Olivier
  Physica D: Nonlinear Phenomena, Elsevier, 2016, 316, pp.34-42. A phenomenological model describing the time-frequency dependence of the power spectrum of thin plates vibrating in a wave turbulence regime, is introduced. The model equation contains as basic solutions the Rayleigh-Jeans equipartition of energy, as well as the Kolmogorov-Zakharov spectrum of wave turbulence. In the Wave Turbulence Theory framework, the model is used to investigate the self-similar, non-stationary solutions of forced and free turbulent vibrations. Frequency-dependent damping laws can easily be accounted for. Their effects on the characteristics of the stationary spectra of turbulence are then investigated. Thanks to this analysis, self-similar universal solutions are given, relating the power spectrum to both the injected power and the damping law. (10.1016/j.physd.2015.11.006)
  DOI : 10.1016/j.physd.2015.11.006
• 3D crack propagation with cohesive elements in the extended finite element method
  
  • Ferté Guilhem
  • Massin Patrick
  • Moes Nicolas
  Computer Methods in Applied Mechanics and Engineering, Elsevier, 2016, 300, pp.347-374. A model is presented that accurately describes brittle failure in the presence of cohesive forces, with a particular focus on the prediction of non planar crack paths. In comparison with earlier literature, the originality of the procedure lies in the a posteriori computation of the crack advance from the equilibrium, instead of a most common determination beforehand from the stress state ahead of the front. To this aim, a robust way of introducing brittle non-smooth cohesive laws in the X-FEM is presented. Then the a posteriori update algorithm of the crack front is detailed. The crack deflection angle is computed from cohesive quantities exclusively, by introducing equivalent stress intensity factors. The procedure shows good accordance with experiments from the literature. (10.1016/j.cma.2015.11.018)
  DOI : 10.1016/j.cma.2015.11.018
• Condensed SFEs for nonlinear mechanical problems
  
  • Llau Antoine
  • Baroth Julien
  • Jason Ludovic
  • Dufour Frédéric
  Computer Methods in Applied Mechanics and Engineering, Elsevier, 2016, 309, pp.434-452. This paper introduces a coupled approach between stochastic finite element methods and an adaptive condensation technique for the analysis of nonlinear mechanical problems under uncertainties. This coupling reduces the size of each individual nonlinear problem solved in SFE by the use of an adaptive condensation method. The reduced stiffnesses and other quantities necessary for the condensation technique are approximated using a second, low-order, polynomial expansion, thus taking advantage of the coupling with SFE. This approach also features a semi-analytical technique to compute accurately distributions of structural quantities of interest. This method is applied on an elasto-plastic steel bar with a small defect, and on a damaged beam under 4-point bending. In both cases it predicts the random behavior of the structure quite accurately, and is able to provide higher-order models than a state-of-the-art stochastic collocation method, for a reduced computation time. (10.1016/j.cma.2016.06.014)
  DOI : 10.1016/j.cma.2016.06.014
• Wave turbulence in vibrating plates
  
  • Cadot Olivier
  • Ducceschi Michele
  • Humbert Thomas
  • Miquel Benjamin
  • Mordant Nicolas
  • Josserand Christophe
  • Touzé Cyril
  , 2016. Turbulence is a general term used for describing the erratic motions displayed by nonlinear systems that are driven far from their equilibrium position and thus display complicated motions involving different time and length scales. Wave turbulence (WT) share many common ideas with turbulence, in particular as being a statistical theory for out-of-equilibrium systems. A main difference resides in the fact that the persistence of waves is assumed. The application of WT to vibrating plates started with the theoretical derivation of the kinetic equation from the dynamical von Karman equations that describe large-amplitude motions of thin plates. Since this date, numerous papers have been published covering experimental, theoretical and numerical materials. In fact, it appears that the vibrating plate is a perfect candidate for a thorough comparison of experiments with theoretical predictions. As compared to other physical systems such as capillary or gravity waves for example, an experimental set-up with a fine control of energy injection and a confortable range of wavelength is not too difficult to put in place. Secondly, the available measurement techniques allow one to get a complete and precise picture of the dynamics through the scales, both in the space and frequency domains. Finally, numerical codes with good accuracy have been developed so that all the underlying assumptions of the theory as well as its predictions have been tested, both on the experimental and the numerical levels. (10.1201/b20232-21)
  DOI : 10.1201/b20232-21
• Finite element modelling of 1D steel components in reinforced and prestressed concrete structures
  
  • Llau Antoine
  • Jason Ludovic
  • Dufour Frédéric
  • Baroth Julien
  Engineering Structures, Elsevier, 2016, 127, pp.769-783. This paper introduces a new approach for FE modelling of 1D steel inclusions within a 3D concrete domain. Reinforcements modelled with 1D meshes, when included in 3D domains, are indeed responsible for pathological effects like stress concentration at the local scale. The alternative solution of an explicit 3D mesh of the steel elements requires a large amount of work, and a relatively fine conform mesh (and therefore, additional computation cost). It is thus hardly applicable to large-scale structures. The approach proposed in this contribution, called “1D-3D”, generates an equivalent volume from a 1D mesh of the reinforcements. Associated stresses and stiffnesses, which can be condensed on the boundaries of the newly created volume, are then applied to concrete 3D elements using kinematic relations. This approach is validated on two representative cases of civil engineering applications, including active and passive steel reinforcements. It provides results similar to an explicit 3D approach, without its meshing complexity. It thus combines the advantages of 1D and 3D approaches in a single modelling. (10.1016/j.engstruct.2016.09.023)
  DOI : 10.1016/j.engstruct.2016.09.023
• Synchronized switch harvesting applied to piezoelectric flags
  
  • Pineirua Miguel
  • Michelin Sébastien
  • Vasic Dejan
  • Doaré Olivier
  Smart Materials and Structures, IOP Publishing, 2016. In this article the energy transfer between a flow and a fluttering piezoelectric plate is investigated. In particular, the benefits of the use of a synchronized switch harvesting on inductor (SSHI) circuit are studied. Both wind tunnel experiments and numerical simulations are conducted in order to analyze the influence of the switching process on the dynamics and the efficiency of the system. Numerical simulations consist of a weakly nonlinear model of a plate in axial flow equipped with a single pair of piezoelectric patches, discretized using a Galerkin method where basis functions are the modes of the plate in vacuum. The discretized model is then integrated in time. The results presented in this paper show that a significant improvement of the harvested energy can be obtained using SSHI circuits compared to basic resistive circuits. It is also shown that for strongly coupled systems, the switching process inherent to he SSHI circuit has a significant impact on the dynamics of the flag, which tends to decrease the relative efficiency gain Q1 . (10.1088/0964-1726/25/8/085004)
  DOI : 10.1088/0964-1726/25/8/085004
• On the computation of the Baer–Nunziato model using ALE formulation with HLL- and HLLC-type solvers towards fluid–structure interactions
  
  • Daude Frédéric
  • Galon Pascal
  Journal of Computational Physics, Elsevier, 2016, 304, pp.189-230. Computation of compressible two-phase flows with the unsteady compressible Baer–Nunziato model in conjunction with the moving grid approach is discussed in this paper. Both HLL- and HLLC-type Finite-Volume methods are presented and implemented in the context of Arbitrary Lagrangian–Eulerian formulation in a multidimensional framework. The construction of suitable numerical methods is linked to proper approximations of the non-conservative terms on moving grids. The HLL discretization follows global conservation properties such as free-stream preservation and uniform pressure and velocity profiles preservation on moving grids. The HLLC solver initially proposed by Tokareva and Toro [1] for the Baer–Nunziato model is based on an approximate solution of local Riemann problems containing all the characteristic fields present in the exact solution. Both “subsonic” and “supersonic” configurations are considered in the construction of the present HLLC solver. In addition, an adaptive 6-wave HLLC scheme is also proposed for computational efficiency. The methods are first assessed on a variety of 1-D Riemann problems including both fixed and moving grids applications. The methods are finally tested on 2-D and 3-D applications: 2-D Riemann problems, a 2-D shock–bubble interaction and finally a 3-D fluid–structure interaction problem with a good agreement with the experiments. (10.1016/j.jcp.2015.09.056)
  DOI : 10.1016/j.jcp.2015.09.056
• Amortissement de vibrations de poutres par effet Trou Noir : caractérisation expérimentale et modèles numériques
  
  • Denis Vivien
  • Pelat Adrien
  • Gautier François
  • Touzé Cyril
  Acoustique et Techniques : trimestriel d'information des professionnels de l'acoustique, Neuilly-sur-Seine : Centre d'information et de documentation sur le bruit, 2016 (83), pp.5-11. L'effet Trou Noir Acoustique (TN) est une technique passive d'amortissement de vibrations sans ajout de masse fondée sur les propriétés des ondes de flexion dans des structures minces d'épaisseur variable. La mise en oeuvre habituelle consiste en une plaque avec une extrémité profilée selon une loi exponentielle, recouverte d'un film viscoélastique. L'inhomogénéité de la structure conduit à une baisse de la célérité et une augmentation de l'amplitude des ondes de flexion, ce qui a pour conséquence une dissipation d'énergie efficace quand un film amortissant est placé dans la zone de faible épaisseur. Lorsqu'un tel profil est placé à l'extrémité d'une poutre, des caractérisations expérimentales sont possibles à l'aide du coefficient de réflexion ou du recouvrement modal. Des modèles numériques d'une telle structure existent et peuvent aider à comprendre le rôle de la variation d'épaisseur, les effets d'imperfections de fabrication ou encore les effets non-linéaires dus aux faibles épaisseurs.
• HLLC-type Riemann solver with approximated two-phase contact for the computation of the Baer-Nunziato two-fluid model
  
  • Lochon Hippolyte
  • Daude Frédéric
  • Galon Pascal
  • Hérard Jean-Marc
  Journal of Computational Physics, Elsevier, 2016. The computation of compressible two-phase flows with the Baer-Nunziato model is addressed. Only the convective part of the model that exhibits non-conservative products is considered and the source terms of the model that represent the exchange between phases are neglected. Based on the solver proposed by Tokareva & Toro [42], a new HLLC-type Riemann solver is built. The key idea of this new solver lies in an approximation of the two-phase contact discontinuity of the model. Thus the Riemann invariants of the wave are approximated in the " subsonic " case. A major consequence of this approximation is that the resulting solver can deal with any Equation of State. It also allows to bypass the resolution of a non-linear equation based on those Riemann invariants. We assess the solver and compare it with others on 1D Riemann problems including grid convergence and efficiency studies. The ability of the proposed solver to deal with complex Equations Of State is also investigated. Finally, the different solvers have been compared on challenging 2D test-cases due to the presence of both material interfaces and shock waves: a shock-bubble interaction and underwater explosions. When compared with others, the present solver appears to be accurate, efficient and robust. (10.1016/j.jcp.2016.09.015)
  DOI : 10.1016/j.jcp.2016.09.015
• Limited memory preconditioners for symmetric indefinite problems with application to structural mechanics
  
  • Gratton Serge
  • Mercier Sylvain
  • Tardieu Nicolas
  • Vasseur Xavier
  Numerical Linear Algebra with Applications, Wiley, 2016, 23 (5), pp.865--887. This paper presents a class of limited memory preconditioners (LMP) for solving linear systems of equations with symmetric indefinite matrices and multiple right-hand sides. These preconditioners based on limited memory quasi-Newton formulas require a small number k of linearly independent vectors and may be used to improve an existing first-level preconditioner. The contributions of the paper are threefold. First, we derive a formula to characterize the spectrum of the preconditioned operator. A spectral analysis of the preconditioned matrix shows that the eigenvalues are all real and that the LMP class is able to cluster at least k eigenvalues at 1. Secondly, we show that the eigenvalues of the preconditioned matrix enjoy interlacing properties with respect to the eigenvalues of the original matrix provided that the k linearly independent vectors have been prior projected onto the invariant subspaces associated with the eigenvalues of the original matrix in the open right and left half-plane, respectively. Third, we focus on theoretical properties of the Ritz-LMP variant, where Ritz information is used to determine the k vectors. Finally, we illustrate the numerical behaviour of the Ritz limited memory preconditioners on realistic applications in structural mechanics that require the solution of sequences of large-scale symmetric saddle-point systems. Numerical experiments show the relevance of the proposed preconditioner leading to a significant decrease in terms of computational operations when solving such sequences of linear systems. A saving of up to 43% in terms of computational effort is obtained on one of these applications. (10.1002/nla.2058)
  DOI : 10.1002/nla.2058
• Idiophones à plaques et coques. Partie II. Instruments fortement non linéaires : cymbales, tam-tams et plaques tonnerre
  
  • Touzé Cyril
  • Thomas Olivier
  Musique & Technique, ITEMM, 2016, 6, pp.51-63. Dans cet article nous nous intéressons aux idio-phones à plaques et coques dont le comportement est fortement non linéaire. Nous traiterons du cas des cymbales, des gongs – et plus particulièrement des tam-tams – ainsi que de la plaque tonnerre. Ces instruments sont distingués des précédents, dits « à faible non-linéarité », car la physique vibratoire mise en jeu est radicalement différente, beaucoup plus complexe et très fortement non linéaire. Au niveau perceptif, cette distinction est immédiatement notable à l'oreille car les instruments que nous considérons dans cet article n'ont pas de hauteur définie. Leur son caractéristique est décrit comme très brillant : le contenu fréquentiel est tellement riche qu'on ne peut leur attribuer une hauteur précise, on observe plutôt un continuum de fréquences.
• Synchronized flutter of two slender flags
  
  • Mougel Jérôme
  • Doaré Olivier
  • Michelin Sébastien
  Journal of Fluid Mechanics, Cambridge University Press (CUP), 2016, 801, pp.652-669. The interactions and synchronization of two parallel and slender flags in a uniform axial flow are studied in the present paper by generalizing Lighthill's Elongated Body Theory (EBT) and Lighthill's Large Amplitude Elongated Body Theory (LAEBT) to account for the hydrodynamic coupling between flags. The proposed method consists in two successive steps, namely the reconstruction of the flow created by a flapping flag within the LAEBT framework and the computation of the fluid force generated by this nonuniform flow on the second flag. In the limit of slender flags in close proximity, we show that the effect of the wakes have little influence on the long time coupled-dynamics and can be neglected in the modeling. This provides a simplified framework extending LAEBT to the coupled dynamics of two flags. Using this simplified model, both linear and large amplitude results are reported to explore the selection of the flapping regime as well as the dynamical properties of two side-by-side slender flags. Hydrodynamic coupling of the two flags is observed to destabilize the flags for most parameters, and to induce a long-term synchronization of the flags, either in-phase or out-of-phase. (10.1017/jfm.2016.451)
  DOI : 10.1017/jfm.2016.451
• Idiophones à plaque et à coque. Partie I. Instruments linéaires et faiblement non linéaires: entre cloches et steelpans
  
  • Thomas Olivier
  • Monteil Mélodie
  • Touzé Cyril
  Musique & Technique, ITEMM, 2016, 6, pp.34-50. Dans cet article, ainsi que le suivant, on s'intéresse aux idiophones à plaque et à coque. Cette famille englobe des instruments aussi divers que la cloche d'église, le bol tibétain, les divers types de gongs, les cymbales ou encore les plaques tonnerre, dont le corps sonore à la forme d'une plaque, plus ou mois épaisse et plus ou moins incurvée. L'ensemble des idiophones étudiés dans ces deux articles a été séparé en deux familles, sur des critère de physique vibratoire, en distinguant les instruments dits faiblement non linéaires, pour lesquels la non linéarité, bien que produisant des effets déjà audibles, est faiblement mise en jeu, des instruments fortement non linéaires, pour lesquels la physique vibratoire est beaucoup plus complexe. Le présent article se focalise sur les instruments de la première famille, dont le timbre, influencé par les non-linéarités, produit tout de même un son de hauteur tonale parfaitement perceptible. On y regroupe, entre autres, les grands gongs de Gamelan, dont le son présente des battements qui s'expliquent par des phénomènes non linéaires, les gongs d'opéra chinois, dont le timbre est caractérisé par des glissements fréquentiels, montant ou descendant selon la taille de l'instrument considéré, ou encore les steelpans, instruments de percussion mélodiques de Tri-nidad et Tobago, dont la brillance particulière du timbre est là encore d'origine non linéaire.
• Wind Turbine Noise Modeling Based on Amiet's Theory: Effects of Wind Shear and Atmospheric Turbulence
  
  • Tian Yuan
  • Cotté Benjamin
  Acta Acustica united with Acustica, Hirzel Verlag, 2016, 102 (4), pp.626-639. Broadband noise generated aerodynamically is the dominant source for a modern wind turbine. In this paper, trailing edge noise and turbulent inflow noise are modeled using Amiet’s theory to predict wind turbine noise spectra, directivity and amplitude modulation. First, by comparing model predictions with wind tunnel experiments from the literature, we show that a wall pressure spectral model that includes the effect of an adverse pressure gradient is needed to correctly predict trailing edge noise spectra. Then, we adapt the model to rotating blades and compare sound power level spectra of trailing edge noise with field measurements, assuming a constant wind speed profile. A good agreement is found at frequencies higher than approximately 1000 Hz, but the levels are underestimated at lower frequencies. Finally, we account for wind shear and atmospheric turbulence effects using the Monin-Obukhov similarity theory. On the one hand, we show that angle of attack variations due to wind shear can produce a significant change in the wall pressure spectra of some blade sections, especially in stable atmospheric conditions, even though this effect is not clearly seen on the trailing edge noise spectra at the receiver. On the other hand, turbulent inflow noise does vary with atmospheric conditions, and contributes significantly to the noise radiated by a wind turbine at low frequencies. When both mechanisms are considered, the predicted sound power level spectra are in good agreement with measurements. (10.3813/AAA.918979)
  DOI : 10.3813/AAA.918979
• Stochastic fluid structure interaction of three dimensional plates facing a uniform flow
  
  • Cadot Olivier
  Journal of Fluid Mechanics, Cambridge University Press (CUP), 2016, 794 (R1). An experiment of a flat rectangular plate facing a uniform flow at Re= 264000 shows the importance on the base pressure loading of the asymmetric static modes of the turbulent wake. The plate is free to rotate around its small symmetry axis. For plates with aspect ratio κ < 6, the angular position exhibits strong random discontinuities between steady states of non zero angles. The steady states have long time durations, more than one order of magnitude larger than the convective timescale. The discontinuities, comparable to rare and violent events are due to strong fluid forces associated with the drastic global change of the three dimensional wake, mainly the switching between the static asym-metric modes. A clear transition occurs at κ = 6 for which the angular fluctuations are minimum leading for κ > 6 to a classical fluid structure interaction with periodic fluctuations. The transition is supported by a recent global stability analysis of rectangular fixed plates in the laminar regime. (10.1017/jfm.2016.187)
  DOI : 10.1017/jfm.2016.187
• Comparison of two-fluid models on steam-water transients
  
  • Lochon Hippolyte
  • Daude Frédéric
  • Galon Pascal
  • Hérard Jean-Marc
  ESAIM: Mathematical Modelling and Numerical Analysis, Société de Mathématiques Appliquées et Industrielles (SMAI) / EDP, 2016. This paper is devoted to the comparison of three two-fluid models in steam-water applications involving phase transition and shock waves. The three models are presented in a common formalism that helps to underline their shared properties. A numerical method based on previous work is extended to all models and to more complex Equations Of State. Particular attention is paid to the verification of every step of the method so that convergence studies can be carried out. Afterwards, models are compared with each other and with experimental data in two different cases of steam-water transients. The first one is Simpson water-hammer experiment and the second one is a rapid depressurization with flashing studied in Canon experiment. (10.1051/m2an/2016001)
  DOI : 10.1051/m2an/2016001
• Design of a Magnetic Vibration Absorber with Tunable Stiffnesses
  
  • Benacchio Simon
  • Malher Arnaud
  • Boisson Jean
  • Touzé Cyril
  Nonlinear Dynamics, Springer Verlag, 2016, 85 (2), pp.893-911. The design and characterisation of a magnetic vibration absorber (MVA), completely relying on magnetic forces, is addressed. A distinctive feature of the absorber is the ability of tuning the linear stiffness together with the nonlinear cubic and quintic stiffnesses by means of repulsive magnets located in the axis of the main vibrating magnetic mass, together with a set of corrective magnets located off the main axis. The tuning methodology is passive and relies only on three geometrical parameters. Consequently the MVA can be adjusted to design either a nonlinear tuned vibration absorber (NLTVA), a nonlinear energy sink (NES), or a bi-stable absorber with negative linear stiffness. The expressions of the stiffnesses are given from a multipole expansion of the magnetic fields of repulsive and corrective magnets. A complete static and dynamic characterisation is performed, showing the robustness of the modelling together with the ability of the MVA to work properly in different vibratory regimes, thus making it a suitable candidate for passive vibration mitigation in a wide variety of contexts. (10.1007/s11071-016-2731-3)
  DOI : 10.1007/s11071-016-2731-3
• Using a mixed DEM/FEM approach to model advanced damage of reinforced concrete under impact
  
  • Potapov S.
  • Masurel A.
  • Daudeville L.
  • Marin Philippe Maurice
  International Journal of Computational Methods and Experimental Measurements, WIT Press, 2016, 4 (3), pp.258-268. Advanced damage behaviour of reinforced concrete is modelled using a mixed modelling approach, in which concrete is represented through the spherical-type discrete element model, whereas steel reinforcement is modelled by using beam-type finite elements. An original steel-concrete bond model developed and calibrated on pull-out tests is used to ensure transfer of forces between steel and concrete. The proposed approach is applied to simulate soft and hard-type impacts on RC beams within a very complete modelling framework, thus allowing validating by comparison with experimental data the overall numerical approach developed (10.2495/CMEM-V4-N3-258-268)
  DOI : 10.2495/CMEM-V4-N3-258-268
• A biorthogonal decomposition for the identification and simulation of non-stationary and non-Gaussian random fields
  
  • Zenter I.
  • Ferré G.
  • Poirion F.
  • Benoit Michel
  Journal of Computational Physics, Elsevier, 2016, 314, pp.1-13. In this paper, a new method for the identification and simulation of non-Gaussian and non-stationary stochastic fields given a database is proposed. It is based on two successive biorthogonal decompositions aiming at representing spatio-temporal stochastic fields. The proposed double expansion allows to build the model even in the case of large-size problems by separating the time, space and random parts of the field. A Gaussian kernel estimator is used to simulate the high dimensional set of random variables appearing in the decomposition. The capability of the method to reproduce the non-stationary and non-Gaussian features of random phenomena is illustrated by applications to earthquakes (seismic ground motion) and sea states (wave heights). (10.1016/j.jcp.2016.02.067)
  DOI : 10.1016/j.jcp.2016.02.067