Publications

2016

• 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
• 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
• Gradient damage modeling of brittle fracture in an explicit dynamics context
  
  • Li Tianyi
  • Marigo Jean-Jacques
  • Guilbaud Daniel
  • Potapov Serguei
  International Journal for Numerical Methods in Engineering, Wiley, 2016. In this contribution we propose a dynamic gradient damage model as a phase-field approach for studying brutal fracture phenomena in quasi-brittle materials under impact-type loading conditions. Several existing approaches to account for the tension-compression asymmetry of fracture behavior of materials are reviewed. A better understanding of these models is provided through a uniaxial traction experiment. We then give an efficient numerical implementation of the model in an explicit dynamics context. Simulations results obtained with parallel computing are discussed both from a computational and physical point of view. Different damage constitutive laws and tension-compression asymmetry formulations are compared with respect to their aptitude to approximate brittle fracture. (10.1002/nme.5262)
  DOI : 10.1002/nme.5262
• Feedback control of bimodal wake dynamics
  
  • Li Ruying
  • Barros Diogo
  • Borée Jacques
  • Cadot Olivier
  • Noack Bernd R.
  • Cordier Laurent
  Experiments in Fluids, Springer Verlag (Germany), 2016, 57, pp.158. Feedback control is applied to symmetrize the bimodal dynamics of a turbulent blunt body wake. The flow is actuated with two lateral slit jets and monitored with pressure sensors at the rear surface. The physics-based controller is inferred from preliminary open-loop tests and is capable of symmetrizing the wake. A slight pressure recovery is achieved due to the net balance between the favourable effect of wake symmetrization and adverse effect of shear layer mixing and vortex shedding amplification (10.1007/s00348-016-2245-2)
  DOI : 10.1007/s00348-016-2245-2
• Gradient damage models and their use in brittle fracture
  
  • Marigo Jean-Jacques
  • Maurini Corrado
  • Pham Kim
  , 2016. The paper is devoted to gradient damage models which allow us to describe all the process of degradation of a body including the nucleation of cracks and their propagation. The construction of such model follows the variational approach to fracture and proceeds into two stages: (i) definition of the energy; (ii) formulation of the damage evolution problem. The total energy of the body is defined in terms of the state variables which are the displacement field and the damage field in the case of quasi-brittle materials. That energy contains in particular gradient damage terms in order to avoid too strong damage localizations. The formulation of the damage evolution problem is then based on the concepts of irreversibility, stability and energy balance. That allows us to construct homogeneous as well as localized damage solutions in a closed form and to illustrate the concepts of loss of stability, of scale effects, of damage localization, and of structural failure. Moreover, the variational formulation leads to a natural numerical method based on an alternate minimization algorithm. Several numerical examples illustrate the ability of this approach to account for all the process of fracture including a 3D thermal shock problem where the crack evolution is very complex.
• A simple turbulent two-fluid model
  
  • Hérard Jean-Marc
  • Lochon Hippolyte
  Comptes Rendus. Mécanique, Académie des sciences (Paris), 2016, 344 (11-12), pp.776-783. We present in this paper a simple turbulent two-phase flow model using the two-fluid approach. The model, that relies on the classical ensemble averaging, allows the computation of unsteady flows including shock waves, rarefaction waves and contact discontinuities. It requires the definition of adequate source terms and interfacial quantities. The hyperbolic turbulent two-fluid model is such that unique jump conditions hold within each field. Closure laws for the interfacial velocity and the interfacial pressure comply with a physically relevant entropy inequality. Moreover, source terms that account for mass, momentum and energy in-terfacial transfer are in agreement with the entropy inequality. Particular attention is also given to the jump conditions when assuming a perfect gas equation of state within each phase ; this enables to recover expected bounds on the mean density through shock waves. (10.1016/j.crme.2016.10.010)
  DOI : 10.1016/j.crme.2016.10.010
• Experimental database with full field measurements for mixed-mode crack propagation in concrete: comparison between experimental and numerical results
  
  • Carpiuc Andreea
  • Jailin Clément
  • Poncelet M.
  • Kyrylo K.
  • Hild François
  , 2016. no abstract
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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.
• 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
• 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