Publications

2010

• A New Formulation of Dynamic Problems in Zener Type Viscoelasticity
  
  • Bui Huy Duong
  • Chaillat Stéphanie
  , 2010, pp.1-6. The dynamic response of a Zener viscoelastic medium in the frequency domain is addressed. It is shown that, for low frequency, the elastic-viscoelastic correspondence allows a simple solution to Neumann boundary value problems for viscoelasticity. The dynamic solution is derived by an Indirect method of Boundary Integral Equations. For low frequency, the indirect BIE is established as a regular perturbation of the static BIE which has been studied by Pham (1967). Pham's solution is then extended to the dynamic case by perturbation arguments. A review of applications to inverse problems is addressed for the dynamic identification of a planar crack as well as an inclusion in a viscoelastic body. The method of solutions is based on the use of the reciprocity gap functional.
• Remplacement de la table d'harmonie du violon par un sandwich balsa/fibre de lin
  
  • Ege Kerem
  • Caron Jean-François
  • Marcadet Stéphane
  • Martin Hugo
  , 2010. Le remplacement des tables d'harmonie d'instruments à cordes par des structures en matériau composite est un sujet qui passionne les luthiers et les facteurs de piano. Le principal défi est de trouver un matériau qui puisse reproduire les remarquables propriétés vibratoires du bois et en particulier de l'épicéa : une forte rigidité longitudinale pour une très faible densité, et de faibles facteurs de pertes viscoélastiques. Nous présentons dans cette communication une étude concrète effectuée sur le violon. Ce travail a été mené dans le cadre d'un module expérimental (mécanique / matériaux composites) de l'École Polytechnique. L'originalité de ce travail repose dans la recherche d'une même densité modale asymptotique (à surface donnée) entre la table de substitution en matériau composite et la table d'harmonie d'origine en épicéa, tout en conservant au mieux la position des premières fréquences propres. Par ailleurs la structure doit vérifier certains critères vibro-acoustiques : un coefficient de rayonnement élevé et des facteurs de pertes viscoélastiques comparables à ceux de l'épicéa. Nous avons opté pour une structure sandwich dont l'âme est en balsa et dont les peaux sont formées chacune d'un empilement de couches de fibre de lin pré-imprégnées (résine époxy). Plus légère que la fibre de carbone ou la fibre de verre et possédant des caractéristiques d'amortissement plus importantes (études sur raquette de tennis), qui plus est d'origine naturelle, les fibres végétales nous ont parus constituer une alternative intéressante aux matériaux composites habituellement utilisés dans la facture instrumentale. L'épaisseur de l'âme, le nombre de couches de fibre de lin et l'angle d'orientation des fibres ont été déterminés par un calcul d'optimisation sous contraintes dont les objectifs sont le coefficient de rayonnement, l'espacement intermodal moyen et la première fréquence de torsion de la table en épicéa. Ces valeurs ont étés mesurées sur la table en épicéa après détablage et retrait de la barre de table. La table en composite est conforme aux attentes : les premières fréquences propres et les densités modales asymptotiques des deux tables sont particulièrement proches. La table en composite est par ailleurs plus fine et plus légère que l'originale (d'environ 20%). Les luthiers ayant joué sur l'instrument rapportent que la qualité du son est bonne : le son est doux, plaisant, agréable, le violon est facile à jouer. L'instrument sonne comme un violon mais comparé à un instrument de bonne qualité il ne porte pas assez, ne projette pas assez ; le son est dedans, comme un peu trop étouffé. L'énergie vibratoire perdue dans la table en composite est trop importante (trop d'amortissement) ; des mesures vibro-acoustiques sur l'instrument en composites en situation de jeu confirment les remarques des luthiers. Une solution serait par exemple de coupler la fibre de lin à la fibre de carbone qui possède des facteurs de pertes très inférieurs.
• Gradient Thermodynamics & Heat Equations
  
  • Nguyen Quoc Son
  Comptes Rendus. Mécanique, Académie des sciences (Paris), 2010, 338 (6), pp.321-326. In this paper, a thermodynamic description is proposed to include the gradient of the temperature in the set of state variables. It is based upon an original expression of the entropy and of the internal energy taking account of the presence of the temperature gradient by Legendre transform with respect to the variable (T, grad T ). The proposed description can be justified in a homogenization process. In particular, the associated heat equations is derived and discussed in comparison with the existing results of the literature. It is shown that this equation removes the paradox of instantaneous propagation. (10.1016/j.Crme.2010.07.010)
  DOI : 10.1016/j.Crme.2010.07.010
• Thermodynamical description of running discontinuties: application to friction and wear
  
  • Stolz Claude
  Entropy, MDPI, 2010, 12, pp.1418-1439. The friction and wear phenomena appear due to contact and relative motion between two solids. The evolution of contact conditions depends on loading conditions and mechanical behaviours. The wear phenomena are essentially characterized by a matter loss. Wear and friction are in interaction due to the fact that particles are detached from the solids. A complex medium appears as an interface having a strong effect on the friction condition. The purpose of this paper is to describe such phenomena taking account of different scales of modelization in order to derive some macroscopic laws. A thermodynamical approach is proposed and models of wear are analysed in this framework where the separation between the dissipation due to friction and that due to wear is made. Applications on different cases are presented. (10.3390/e12061418)
  DOI : 10.3390/e12061418
• Polygonization as low energy dislocation structure
  
  • Le Khanh-Chau
  • Nguyen Quoc Son
  Continuum Mech. Thermodyn., 2010, 22, pp.291-298. Within continuum dislocation theory, one-dimensional energy functional of a bent beam, made of a single crystal, is derived. By relaxing the continuously differentiable minimizer of this energy functional, we construct a sequence of piecewise smooth deflections and piecewise constant plastic distortions reducing the energy and exhibiting polygonization. The number of polygons can be estimated by comparing the surface energy of small angle tilt boundaries with the contribution of the gradient terms from the weak minimizer in the bulk energy. (10.1007/s00161-010-0137-x)
  DOI : 10.1007/s00161-010-0137-x
• 2-D non-periodic homogenization of the elastic wave equation: SH case
  
  • Guillot Laurent
  • Capdeville Yann
  • Marigo Jean-Jacques
  Geophysical Journal International, Oxford University Press (OUP), 2010, 182 (2), pp.1438-1454. In the Earth, seismic waves propagate through 3-D heterogeneities characterized by a large variety of scales, some of them much smaller than their minimum wavelength. The costs of computing the wavefield in such media using purely numerical methods, are very high. To lower them, and also to obtain a better geodynamical interpretation of tomographic images, we aim at calculating appropriate effective properties of heterogeneous and discontinuous media, by deriving convenient upscaling rules for the material properties and for the wave equation. To progress towards this goal we extend our successful work from 1-D to 2-D. We first apply the so-called homogenization method (based on a two-scale asymptotic expansion of the field variables) to model antiplane wave propagation in 2-D periodic media. These latter are characterized by short-scale variations of elastic properties, compared to the smallest wavelength of the wavefield. Seismograms are obtained using the 0th-order term of this asymptotic expansion, plus a partial first-order correction. Away from boundaries, they are in excellent agreement with solutions calculated at a much higher computational cost, using spectral elements simulations in the reference media. We then extend the homogenization of the wave equation, to 2-D non-periodic, deterministic media. (10.1111/j.1365-246X.2010.04688.x)
  DOI : 10.1111/j.1365-246X.2010.04688.x
• Prediction of harmonic distortion generated by electro-dynamic loudspeakers using cascade of Hammerstein models
  
  • Rébillat Marc
  • Hennequin Romain
  • Corteel Etienne
  • Katz Brian F.G.
  , 2010, pp.7993. Audio rendering systems are always slightly nonlinear. Their non-linearities must be modeled and mea- sured for quality evaluation and control purposes. Cascade of Hammerstein models describes a large class of non-linearities. To identify the elements of such a model, a method based on a phase property of exponential sine sweeps is proposed. A complete model of non-linearities is identified from a single mea- surement. Cascade of Hammerstein models corresponding to an electro-dynamic loudspeaker are identified this way. Harmonic distortion is afterward predicted using the identified models. Comparisons with clas- sical measurements techniques show that harmonic distortion is accurately predicted by the identified models over the entire audio frequency range for any desired input amplitude.
• A thermodynamical analysis of wear
  
  • Stolz Claude
  , 2010.
• A level set approach for brittle damage
  
  • Chevaugeon Nicolas
  • Moes Nicolas
  • Stolz Claude
  • Bernard Paul Emile
  , 2010. We propose a new approach of the propagation of damage based on level set description.
• A thermodynamic analysis of wear
  
  • Stolz Claude
  , 2010. We propose a description of the wear process through a description of moving boundaries.
• Direct cyclic methods for structures under thermomechanical loading
  
  • Maitournam Habibou
  • Pommier Benjamin
  • Comte François
  • Nguyen-Tajan Thi Mac-Lan
  , 2010. A great number of structures are subjected to thermomechanical cyclic loading. For instance, it is the case of automotive engine: components such as cylinder heads or exhaust manifolds experience cyclic thermal loading. It is also the case of rails: in curve, gauge corners are subjected to high rolling contact stresses inducing cyclic plasticity or even ratchetting. The estimation of the lifetime of such structures under cyclic thermomechanical loading requires, on the one hand, the determination of the response until an asymptotic state is reached, and on the other hand, the use of an appropriate damage criterion. The computation of the whole loading history leads to lenghty and expensive incremental calculations, especially for structures with large number of degrees of freedom. Therefore, it is very useful to develop computational approaches for straightforward calculations of the possible stabilized state under repeated thermomechanical loading. Direct Cyclic Methods offer this alternative. The paper is devoted to Direct Cyclic Methods we propose. These numerical strategies, derived from the Large Time Increment Method are alternative to classical incremental methods or cycle jump techniques. Direct Cyclic Methods permit the direct determination of the asymptotic response of inelastic structures subjected to cyclic thermomechanical loadings.The different versions of the Direct Cyclic Method are presented. They differ from the solution of the global stage which is consuming the most CPU time. The first version of the Direct Cyclic Method uses a classical finite element method to compute the SA and KA response and has been used to studying cyclic response of structures subjected to small oscillatory contact displacements for fretting fatigue applications. The second version uses Fourier expansion in solving the global equations. It is this version which is in Abaqus Sofware. The third version adopts a decomposition in a wavelet basis and the SKA solutions are estimated using only the largest coefficients.
• A thick level set approach to model evolving damage and transition to fracture
  
  • Bernard Paul Emile
  • Moes Nicolas
  • Stolz Claude
  • Chevaugeon Nicolas
  , 2010. Local damage models are known to suffer from spurious localization and present therefore a high sensitivity to the mesh. Several damage models were proposed in the literature to avoid these issues [1], as for instance non-local damage models [2, 3] or higher order gradients models [4, 5]. We proposed a new approach for damage growth modeling in solids [6], using level set functions to represent the damaged zones. The damage front is then located on the iso-zero of the level set. Its propagation can be described in terms of the energy along the front while its curvature is used to introduce a characteristic length in the model.
• Asymptotic behaviour of structures subjected to thermomechanical cyclic loadings: application to exhaust manifolds
  
  • Benoit Aurélie
  • Maitournam Habibou
  • Rémy Luc
  • Oger Frédéric
  , 2010. Under cyclic loadings, structures can show different types of asymptotic behaviour: elastic shakedown when the asymptotic answer is purely elastic, cyclic plasticity when plastic deformations become periodic and ratchetting, plastic deformations will then accumulate and lead to the ruin of the structure. For industrial components, elastic shakedown is related to high cycle fatigue, while cyclic plasticity and ratchetting mean low cycle fatigue, but ratchetting must be prevented since it could drastically limits the lifetime of the structure. In the automotive industry, cold parts like suspension systems often present elastic shakedown whereas hot parts like exhaust systems and cylinder heads are subjected to thermomechanical loadings and often exhibit cyclic plasticity. To evaluate the lifetime of components, one can follow the evolution of a damage variable or use a fatigue criterion that assesses the lifetime of a structure from macroscopic thermomechanical quantities evaluated on the stabilized cycle. Ambrico and Begley suggested a method to identify the different types of asymptotic behaviour in the case of fretting. In this study, we propose slightly different definitions of the cyclic part and of the ratchetting part of the deformation. The ratchetting part of the deformation er(t) is built for all instants t, taking account of the whole evolution of the plastic deformation during the cycle. Then a new definition of the amplitude of the cyclic plastic deformation during cycle k, Dec(k) is given. This definition takes into account multiaxial loadings and corresponds to the difference between two deformation states really reached during the cycle. This method is adapted to thermo-mechanical loadings with a material which mechanical characteristics depend on temperature. Finally, an application example is given on an exhaust manifold subjected to a classical thermomechanical fatigue test
• Parabolic reciprocity gap for heat source identification
  
  • Auffray Nicolas
  • Bonnet Marc
  • Pagano Stéphane
  , 2010. The deformation of solid materials is nearly always accompanied with temperature variations. These variations, governed by the heat diffusion equation stemming from the first and second laws of thermodynamics, are induced by intrinsic dissipation of energy and thermomechanical coupling. Infrared thermography techniques provide an experimental means for measuring thermal fields on specimen boundaries. But even if thermal fields are related to the material behavior they are not intrinsic to it as they also depend on external factors such as boundary conditions. Inverting boundary thermal fields is thus needed to obtain valid insight into the specimen thermomechanical behavior. Such an operation belongs to the class of source inverse problem. Inverse source problems are known to be ill-posed in the sense of Hadamard: their solution does not depend continuously on the data, and is not unique for a general source distribution when using only boundary measurements. Modeling hypotheses on the sought sources are thus needed to properly retrieve information.
• Multi-level fast multipole bem for the complex-wavenumber formulation of 3-d viscoelastodynamics
  
  • Grasso Eva
  • Bost Régis
  • Chaillat Stéphanie
  • Semblat Jean-François
  • Bonnet Marc
  , 2010.
• Improved bounds for linear elastic composites
  
  • Salmi M.
  • Auslender F.
  • Bornert Michel
  • Fogli Michel
  , 2010.
• Biophysical Modelling To Predict Acute Hemodynamic Response To Cardiac Resynchronization Therapy In Human
  
  • Rinaldi Aldo C.
  • Lambiase P.D.
  • Sermesant Maxime
  • Chinchapatnam Phani
  • Rhode Kawal S.
  • Duckett Simon B.
  • Shetty Anoop
  • Chabiniok Radomir
  • Mansi Tommaso
  • Billet Florence
  • Peyrat Jean-Marc
  • Delingette Hervé
  • Moireau Philippe
  • Sorine Michel
  • Chapelle Dominique
  • Ayache Nicholas
  • Ginks Matthew
  • Razavi Reza
  , 2010.
• Caractérisation par thermographie infrarouge du comportement d'éprouvettes en acier sollicitées en fatigue
  
  • Fraux David
  • Pron Hervé
  • Laloue Peggy
  • Bissieux Christian
  • Maitournam Habibou
  • Rota Laurent
  Revue de Métallurgie, EDP Sciences, 2010, 107, pp.69-74. A thermal model was developed to identify the heat sources accompanying the micro-plastic strains during a cyclic fatigue test. In the first minute of each loading sequence, an infinite bar model allows to defer the consideration of the conductive losses at the jaws. Sources are identified for increasing loading levels, however avoiding to reach the macroscopic plasticity domain. (10.1051/metal/2010012)
  DOI : 10.1051/metal/2010012
• The SMART-I²: A new approach for the design of immersive audio-visual environments
  
  • Rébillat Marc
  • Corteel Etienne
  • Katz Brian F.G.
  , 2010. The SMART-I² aims at creating a precise and coherent virtual environment by providing users with both audio and visual accurate localization cues. Wave field synthesis, for audio rendering, and tracked passive stereoscopy, for visual rendering, individually permit high quality spatial immersion within an extended space. The proposed system combines these two rendering approaches through the use of large multi-actuator panels used as both loudspeaker arrays and as projection screens, providing a more perceptually consistent rendering.
• Encadrements améliorés des propriétés effectives d'un composite linéaire à fort contraste
  
  • Salmi M.
  • Auslender F.
  • Bornert Michel
  • Fogli Michel
  , 2010.
• Deformation mechanisms in synthetic halite samples : observations and full field measurements in a scanning electron microscope and comparison with crystalline plasticity computations
  
  • Bourcier Mathieu
  • Bornert Michel
  • Dimanov Alexandre
  • Héripré Eva
  • Raphanel Jean
  , 2010. Halite is an important analog material as well as a geological material of choice for underground storage cavities. We present the initial part of an extensive study which aims at characterizing the deformation mechanisms of halite with surface and volume observations and to model them with special attention to the mechanisms of grain boundary sliding which complements or acts in parallel with the more classic crystalline plasticity. In this first part, we limit ourselves to surface observations of samples of synthetic halite deformed in uniaxial compression inside a scanning electron microscope (SEM). The sample are prepared by HIP (Hot Isostactic Pressure) and after annealing, a rather homogeneous and compact structure is achieved with grain sizes ranging from 250 to 500 micrometers. Digital image correlation (DIC) is used in order to record the local deformation and compute the components of the strain tensor. Electron back scattering diffraction (EBSD) provides the local crystal orientations (local textures) at an initial stage and intermediate steps of the mechanical test. Traces of slip planes and DIC computed local strains are markers of intra-crystalline plasticity but also for the latter of potential grain boundary sliding. The first computations use a 3D finite element scheme, which considers a few grains of known geometry and orientation. Applying proper boundary conditions to reproduce the local ones, one computes through a crystal plasticity based model which slip systems are active and how do the different parts of the grains reorient themselves. Comparisons are made between experimental data et computations in order to test the validity of the model. First attempts are made to account for grain boundary sliding in the computations. Computations are an important complement to experiments, since they can provide estimates of local stress magnitudes, while the experiments are limited to the kinematics of the deformation. In the next stage of the project, we shall attempt to integrate 3D experimental data into our approach and to have a better physically based model of grain boundary sliding.
• Discrete and Continuum analysis of localised deformation in sand using X-ray CT and Volumetric Digital Image Correlation
  
  • Hall S.A.
  • Bornert Michel
  • Desrues Jacques
  • Pannier Yannick
  • Lenoir Nicolas
  • Viggiani Gioacchino Cinno
  • Bésuelle Pierre
  Geotechnique, Thomas Telford, 2010, 60 (5), pp.315-322. The objective of this work was to observe and quantify the onset and evolution of localised deformation processes in sand with grain-scale resolution. The key element of the proposed approach is combining state-of-the-art X-ray micro tomography imaging with three-dimensional volumetric digital image correlation techniques. This allows not only the grain-scale details of a deforming sand specimen to be viewed, but also, and more importantly, the evolving three-dimensional displacement and strain fields throughout loading to be assessed. X-ray imaging and digital image correlation have been in the past applied individually to study sand deformation, but the combination of these two methods to study the kinematics of shear band formation at the grain scale is the first novel aspect of this work. Moreover, the authors have developed a completely original grain-scale volumetric digital image correlation method that permits the characterisation of the full kinematics (i.e. three-dimensional displacements and rotations) of all the individual sand grains in a specimen. The results obtained using the discrete volumetric digital image correlation confirm the importance of grain rotations associated with strain localisation. (10.1680/geot.2010.60.5.315)
  DOI : 10.1680/geot.2010.60.5.315
• 3D shear-mode fatigue crack growth in maraging steel and Ti-6Al-4V
  
  • Doquet Véronique
  • Bui Quang-Hien
  • Bertolino Graciela
  • Mehry Elias
  • Alves Lysandra
  International Journal of Fracture, Springer Verlag, 2010, 165 (1), pp.61 - 76. Fatigue crack growth tests in mixed-mode II + III were performed on maraging steel and Ti-6Al- 4V. The 3D evolutions of the crack fronts -measured by SEM after interrupted tests- were analyzed, taking into account the reduction in effective crack driving force by the interlocking and friction of the asperities of the crack surface. Under small-scale yielding conditions, the mixed-mode crack growth rates were found to correlate best with Keff2 II + 1.2Keff2 III in maraging steel, while for Ti-6Al-4V, Keff2 II + 0.9Keff2 III appeared suitable. For extended plasticity, a crack growth prediction method is proposed and validated for Ti-6Al-4V. This method is based on elastic-plastic F.E. computations and application, ahead of each node of the crack front, of a shear-dominated fatigue criterion. (10.1007/s10704-010-9504-7)
  DOI : 10.1007/s10704-010-9504-7
• 2-D non-periodic homogenization to upscale elastic media for P-SV waves
  
  • Capdeville Yann
  • Guillot Laurent
  • Marigo Jean-Jacques
  Geophysical Journal International, Oxford University Press (OUP), 2010, 182 (2), pp.903-922. The pur pose of this paper is to give an upscaling tool valid for the wave equation in general elastic media. This paper is focused on P–SV wave propagation in 2-D, but the methodology can be extended without any theoretical difficulty to the general 3-D case. No assumption on the heterogeneity spectrum is made and the medium can show rapid variations of its elastic properties in all spatial directions. The method used is based on the two-scale homogenization expansion, but extended to the non-periodic case. The scale separation is made using a spatial low-pass filter. The ratio of the filter wavelength cut-off and the minimum wavelength of the propagating wavefield defines a parameter ε0 with which the wavefield propagating in the homogenized medium converges to the reference wavefield. In the general case, this non- periodic extension of the homogenization technique is only valid up to the leading order and for the so-called first-order cor rector. We apply this non-periodic homogenization procedure to two kinds of heterogeneous media: a randomly generated, highly heterogeneous medium and the Marmousi2 geological model. The method is tested with the Spectral Element Method as a solver to the wave equation. Comparing computations in the homogenized media with those obtained in the original ones shows that convergence with ε0 is even better than expected. The effects of the leading order cor rection to the source and first cor rection at the receivers' location are shown. (10.1111/j.1365-246X.2010.04636.x)
  DOI : 10.1111/j.1365-246X.2010.04636.x
• Cyclic behavior of short glass fiber reinforced polyamide for fatigue life prediction of automotive components
  
  • Launay Antoine
  • Marco Yann
  • Maitournam Habibou
  • Raoult Ida
  • Szmytka Fabien
  Procedia Engineering, Elsevier, 2010, 2 (1), pp.901-910. Fatigue life prediction of polymer matrix composites requires the investigation of the cyclic behavior. This paper deals with the experimental study conducted on a polyamide 66 reinforced with 35 wt% of short glass fibers (PA66 GF35), at room temperature. The material was tested dry-as-molded or at the equilibrium with an air containing 50% of relative humidity. The dynamic mechanical analysis leads us to focus on the material conditioned at RH=50%, which appears to exhibit the most complex mechanical effects, and is yet representative of the actual service life. An exhaustive experimental campaign in tensile mode has been carried out, including various strain or stress rates, complex mechanical histories and local thermo-mechanical recording. The material has thus been tested in static tension at stress rates ranging over four decades (from 2.5 to 2500 MPa/s), and also in cyclic tension with loading histories combining creep, stress relaxation or strain recovery steps at different strain/stress levels. Such an extended database allowed us to highlight several mechanical phenomena: at least two characteristic viscous times co-exist, and are independent of any irreversible mechanism. Residual strain appears above a stress threshold, and a kinematic hardening law is suggested to explain tension-relaxation-recovery tests. Eventually, hints of a non-linear viscous flow law and of a cyclic damage law are pointed out. (10.1016/j.proeng.2010.03.097)
  DOI : 10.1016/j.proeng.2010.03.097