Publications

2012

• From vibration to perception: using Large Multi-Actuator Panels (LaMAPs) to create coherent audio-visual environments
  
  • Rébillat Marc
  • Corteel Etienne
  • Katz Brian F.G.
  • Boutillon Xavier
  , 2012. Virtual reality aims at providing users with audio-visual worlds where they will behave and learn as if they were in the real world. In this context, specific acoustic transducers are needed to fulfill simultaneous spatial requirements on visual and audio rendering in order to make them coherent. Large multi-actuator panels (LaMAPs) allow for the combined construction of a projection screen and loudspeaker array, and thus allows for the coherent creation of an audio and visual virtual world. They thus constitute an attractive alternative to electro-dynamical loudspeakers and multi-actuator panels previously used. In this paper, the vibroacoustic behavior of LaMAPs is studied and it is shown that LaMAPs can be used as secondary sources for wave field synthesis (WFS). The auditory virtual environment created by LaMAPs driven by WFS is then perceptually assessed in an experiment where users estimate the egocentric distance of an audio virtual object by means of triangulation. Vibro-acoustic and perceptual results indicate that LaMAPs driven by WFS can be confidently used for the creation of auditory virtual worlds.
• Estimations of non-linearities in structural vibrations of string musical instruments
  
  • Ege Kerem
  • Rébillat Marc
  • Boutillon Xavier
  , 2012, pp.[N° 470], 1211-1216. Under the excitation of strings, the wooden structure of string instruments is generally assumed to undergo linear vibrations. As an alternative to the direct measurement of the distortion rate at several vibration levels and frequencies, we characterise weak non-linearities by a signal-model approach based on cascade of Hammerstein models. In this approach, in a chain of two non-linear systems, two measurements are sufficient to estimate the non-linear contribution of the second (sub-)system which cannot be directly linearly driven, as a function of the exciting frequency. The experiment consists in exciting the instrument acoustically. The linear and non-linear contributions to the response of (a) the loudspeaker coupled to the room, (b) the instrument can be separated. Some methodological issues will be discussed. Findings pertaining to several instruments - one piano, two guitars, one violin - will be presented.
• Comparison of the vibroacoustical characteristics of different pianos
  
  • Boutillon Xavier
  • Ege Kerem
  • Paulello Stephen
  , 2012, pp.[N° 522], 2743-2748. On the basis of a recently proposed vibro-acoustical model of the piano soundboard (X. Boutillon and K. Ege, Vibroacoustics of the piano soundboard: reduced models, mobility synthesis, and acoustical radiation regime. \emph{submitted to the Journal of Sound and Vibration}, 2011.), we present several models for the coupling between the bridge and the ribbed plate of the soundboard. The models predict the modal density and the characteristic impedance at the bridge as a function of the frequency. Without parameter adjustment, the sub-structure model turns out to fit the experimental data with an excellent precision. The influence of the elastic parameters of wood is discussed. The model predictions are compared for pianos of different sizes and types.
• Very slow creep tests on rock samples
  
  • Berest Pierre
  • Béraud Jean François
  • Bourcier Mathieu
  • Dimanov Alexandre
  • Gharbi Hakim
  • Brouard Benoît
  • Devries Kerry
  • Tribout Daniel
  , 2012, pp.81-88. Twelve years ago, creep tests at very low deviatoric stress were performed on an Etrez salt sample in the Varangéville Mine. Recently, a new testing campaign was performed on various salt samples to gain further insight on salt behavior. Creep tests are performed under a 0.1 MPa uniaxial loading on rock-salt samples from the Varangéville and Avery Island Mines and under a 0.24 MPa uniaxial loading on a crushed-salt sample. To minimize the effects of temperature variations, testing devices were placed in an underground mine room, where temperature fluctuations are of the order of one-hundredth of a degree Celsius. The me-chanical loading is provided by dead weights. The deformations were measured through special displacement sensors with a resolution of 1/80 µm. A typical steady-state strain rate reached after 6 months is -2.4 × 10-12 s-1. The influence of air hygrometry, which is approximately 74%RH in the mine, is smaller than expected.
• Mechanical stability of a salt cavern submitted to high-frequency cycles
  
  • Brouard Benoit
  • Berest Pierre
  • Djizanne Hippolyte
  • Frangi Attilio
  , 2012, pp.381-390. Storage of natural gas in salt caverns had been developed mainly for seasonal storage, resulting in a small number of yearly pressure cycles and moderate gas-production rates. The needs of energy traders are changing toward more aggressive operational modes. Gas temperature changes and additional stresses generated by high-frequency cycling in a storage cavern are discussed. It is proved that when fast pressure changes or short-period gas pressure cycles are considered, the thickness of the thermally disturbed zone at the cavern wall is relatively small. Refined meshes of the disturbed zone are required when performing numerical computations.
• Dynamic back-calculation of the collapse of the Saint-Maximilien mining field during mining on rock salt in Varangéville (1873)
  
  • Berest Pierre
  • Wolfgang Minkley
  • J.P. Schleinig
  • Farkas F.
  • Böttge V.
  , 2012, pp.241-252.
• Development and optimization of a formable sandwich sheet
  
  • Besse Camille
  , 2012. This thesis investigates the mechanical behavior of a new type of formable all-metal bi-directionally corrugated sandwich sheet material. Unlike conventional flat sandwich panel materials, this type of sandwich sheet material can be formed into three-dimensional shapes using traditional sheet metal forming techniques. In a first step, the core structure geometry is optimized such as to offer the highest shear stiffness-to-weight ratio. The post yielding behavior of the "optimal" sandwich structure is investigated using finite elements simulations of multi-axial experiments. A phenomenological constitutive model is proposed using an associative flow rule and distortional hardening. An inverse procedure is outlined to describe the sandwich material model parameter identification based on uniaxial tension and four-point bending experiments. In addition, simulations of a draw bending experiment are performed using a detailed finite element model as a well as a computationally-efficient composite shell element model. Good agreement of both simulations is observed for different forming tool geometries which is seen as a partial validation of the proposed constitutive model.
• A NON-ITERATIVE SAMPLING APPROACH USING NOISE SUBSPACE PROJECTION FOR EIT
  
  • Bellis Cédric
  • Constantinescu Andrei
  • Lechleiter Armin
  , 2012.
• Mechanical Behaviour of Salt VII
  
  • Berest Pierre
  • Ghoreychi Mehdi
  • Hadj Hassen Faouzi
  • Tijani Michel
  , 2012, pp.492.
• Homogenized Interface Model Describing Inhomogeneities Located on a Surface
  
  • David Martin
  • Pideri Catherine
  • Marigo Jean-Jacques
  Journal of Elasticity, Springer Verlag, 2012, 109 (2), pp.153--187. We study the influence of heterogeneities located near a planar surface on the elastic response of a three-dimensional elastic medium. These heterogeneities can be either reinforcements, like steel reinforce- ments in concrete, or defects, like micro-cracks periodically distributed. We prove that their influence is of the second order from an energetic viewpoint. Then, we propose an "up to second order effective model" in which the influence of the heterogeneities is given by a surface energy contribution involving both the jump of displacement across the surface and the tangential strain components on the surface. The effective coefficients entering in the definition of the surface energy are obtained by solving "elementary" elastic problems formulated on an infinite representative cell containing the defects. We analyze this model, in particular the properties of the effective surface coefficients, and establish its coherence with limit models previously described in the literature for stiff or soft interfaces. This approach is finally applied to several kinds of heterogeneities. (10.1007/s10659-012-9382-5)
  DOI : 10.1007/s10659-012-9382-5
• Influence of the Lode parameter and the stress triaxiality on the failure of elasto-plastic porous materials
  
  • Danas Kostas
  • Ponte Castañeda Pedro
  International Journal of Solids and Structures, Elsevier, 2012, 49, pp.1325-1342. This work makes use of a recently developed ''second-order'' homogenization model to investigate failure in porous elasto-plastic solids under general triaxial loading conditions. The model incorporates dependence on the porosity and average pore shape, whose evolution is sensitive to the stress triaxiality and Lode parameter L. For positive triaxiality (with overall tensile hydrostatic stress), two different macroscopic failure mechanisms are possible, depending on the level of the triaxiality. At high triaxiality, void growth induces softening of the material, which overtakes the intrinsic strain hardening of the matrix phase, leading to a maximum in the effective stress-strain relation for the porous material, followed by loss of ellipticity by means of dilatant shear localization bands. In this regime, the ductility decreases with increasing triaxiality and is weakly dependent on the Lode parameter, in agreement with earlier theoretical analyses and experimental observations. At low triaxiality, however, a new mechanism comes into play consisting in the abrupt collapse of the voids along a compressive direction (with small, but finite porosity), which can dramatically soften the response of the porous material, leading to a sudden drop in its load-carrying capacity, and to loss of ellipticity of its incremental constitutive relation through localization of deformation. This low-triaxiality failure mechanism leads to a reduction in the ductility of the material as the triaxiality decreases to zero, and is highly dependent on the value of the Lode parameter. Thus, while no void collapse is observed at low triaxiality for axisymmetric tension (L=-1), the ductility of the material drops sharply with decreasing values of the Lode parameter, and is smallest for biaxial tension with axisymmetric compression (L=+1). In addition, the model predicts a sharp transition from the low-triaxiality regime, with increasing ductility, to the high-triaxiality regime, with decreasing ductility, as the failure mechanism switches from void collapse to void growth, and is in qualitative agreement with recent experimental work.
• Inverse Analysis of Multiple Indentation Unloading Curves for Thin Film Young's Modulus Evaluation
  
  • Prou Joris
  • Kishimoto Kikuo
  • Inaba Kazuaki
  • Constantinescu Andrei
  Theoretical and Applied Mechanics, 2012, 60, pp.249-261. The Oliver and Pharr method is the prevailing process for thin films Young's modulus evaluation. Introduced initially for homogeneous materials, this method does not account for the substrate and can consequently lead to significant error, especially at large indentation depths. We suggest here possible methods to improve the accuracy by making use of inverse analysis and finite element computations of the one layer elastic indentation problem. (10.11345/nctam.60.249)
  DOI : 10.11345/nctam.60.249
• Magnetorheological Elastomers
  
  • Triantafyllidis Nicolas
  • Danas Kostas
  , 2012. Magnetorheological elastomers (MREs) are ferromagnetic particle impregnated rubbers whose mechanical properties are altered by the application of external magnetic fields. Due to their coupled magnetoelastic response, MREs are finding an increasing number of engineering applications. In this work, we present a combined experimental and theoretical study of the macroscopic response of a particular MRE consisting of a rubber matrix phase with spherical carbonyl iron particles. The MRE specimens used in this work are cured in the presence of strong magnetic fields leading to the formation of particle chain structures and thus to an overall transversely isotropic composite. The MRE samples are tested experimentally under uniaxial stresses as well as under simple shear in the absence or in the presence of magnetic fields and for different initial orientations of their particle chains with respect to the mechanical and magnetic loading direction. Using the theoretical framework for finitely strained MREs introduced earlier by the author, we propose a transversely isotropic energy density function that is able to reproduce the experimentally measured magnetization, magnetostriction and simple shear curves under different prestresses, initial particle chain orientations and magnetic fields. Microscopic mechanisms are also proposed to explain i) the counterintuitive effect of dilation under zero or compressive applied mechanical loads for the magnetostriction experiments and ii) the importance of a finite strain constitutive formulation even at small magnetostrictive strains. The model gives an excellent agreement with experiments for relatively moderate magnetic fields but has also been satisfactorily extended to include magnetic fields near saturation.
• Mécanique et vibro-acoustique du piano
  
  • Boutillon Xavier
  , 2012, pp.http://savoirsenmultimedia.ens.fr/expose.php?id=521. Le piano est constitué de deux ensembles pratiquement découplés. D'une part, le clavier propulse les marteaux vers les cordes et donne au pianiste une information haptique sur son jeu. D'autre part, l'ensemble cordes-table d'harmonie est mis en vibration par le bref choc du marteau sur les cordes et émet le son que nous entendons. Le fonctionnement mécanique du clavier et l'interaction du marteau avec les cordes sont fortement non-linéaires tandis que la vibro-acoustique de l'ensemble d'harmonie est pratiquement linéaire. Les recherches en cours sur le clavier et son interaction avec le pianiste seront brièvement évoquées. La table d'harmonie est une structure complexe et ses fréquences propres s'avèrent suivre une distribution statistique apparemment non-standard ; l'irrégularité de l'espacement inter-raidisseurs semble localiser les modes propres en haute fréquence. Un modèle vibro-acoustique assez complet de la table d'harmonie sera présenté, en relation avec quelques questions relatives à la facture du piano.
• Numerical modeling of elasto-plastic porous materials with void shape effects at finite deformations
  
  • Danas Kostas
  • Aravas N.
  Composites Part B: Engineering, Elsevier, 2012, 43, pp.2544-2559. A new constitutive model for elasto-plastic (rate-independent) porous materials subjected to general three-dimensional finite deformations is presented. The new model results from simple modifications of an earlier model of Kailasam and Ponte Castañeda (1997, 1998) [40,41] so that it reproduces the exact spherical and cylindrical shell solution (composite sphere and composite cylinder assemblage) under purely hydrostatic loadings, while predicting (by calibration) accurately the void shape evolution according to the recent ''second-order'' model of Danas and Ponte Castañeda [17]. Furthermore, the present model is based on a rigorous homogenization method which is capable of predicting both the constitutive behavior and the microstructure evolution of porous materials. The microstructure is described by voids of arbitrary ellipsoidal shapes and orientations and as a result the material exhibits deformation-induced (or morphological) anisotropy at finite deformations. This is in contrast with the well-known Gurson [32] model which assumes that the voids remain spherical during the deformation process and thus the material remains always isotropic. The present model is implemented numerically in a finite element program where a three-dimensional thin-sheet (butterfly) specimen is subjected to a combination of shear and traction loading conditions in order to examine the effect of stress triaxiality and shearing upon material failure. The ability of the present model to take into account the nontrivial evolution of the microstructure and especially void shape effects leads to the prediction of material failure even at low stress triaxialities and small porosities without the use of additional phenomenological damage criteria. At high stress triaxialities, the present model gives similar predictions as the Gurson model. (10.1016/j.compositesb.2011.12.011)
  DOI : 10.1016/j.compositesb.2011.12.011
• TMF-LCF life assessment of a Lost Foam Casting A319 aluminum alloy
  
  • Tabibian Shadan
  • Charkaluk Eric
  • Constantinescu Andrei
  • Szmytka Fabien
  • Oudin Alexis
  International Journal of Fatigue, Elsevier, 2012. The LFC (Lost Foam Casting) process affects the microstructure, the mechanical properties, the damage mechanisms and the fatigue failure of the materials. The first purpose of this paper is to study the cyclic mechanical behaviors, damage and lifetime of the A319 aluminum alloy manufactured by the LFC process used in the automotive industry under TMF (Thermo-Mechanical Fatigue) and LCF (Low Cycle Fatigue) conditions. A second objective is to select an effective fatigue criterion which should be easy to apply for the design of structures submitted to complex multiaxial thermo-mechanical loadings. In this way, several energy-based criteria are used to predict fatigue failure. Good agreement between predicted fatigue lifetimes and experimental results was obtained for different TMF and LCF loading conditions. (10.1016/j.ijfatigue.2012.01.012)
  DOI : 10.1016/j.ijfatigue.2012.01.012
• A new duality approach to elasticity
  
  • Ciarlet Philippe G.
  • Geymonat Giuseppe
  • Krasucki Françoise
  Mathematical Models and Methods in Applied Sciences, World Scientific Publishing, 2012, Vol. 22, (1), pp.1-21. The displacement-traction problem of three-dimensional linearized elasticity can be posed as three different minimization problems, depending on whether the displacement vector field, or the stress tensor field, or the strain tensor field, is the unknown. The objective of this paper is to put these three different formulations of the same problem in a new perspective, by means of Legendre-Fenchel duality theory. More specifically, we show that both the displacement and strain formulations can be viewed as Legendre-Fenchel dual problems to the stress formulation. We also show that each corresponding Lagrangian has a saddle-point, thus fully justifying this new duality approach to elasticity. (10.1142/S0218202512005861)
  DOI : 10.1142/S0218202512005861
• Mathematical and numerical modelling of piezoelectric sensors
  
  • Imperiale Sébastien
  • Joly Patrick
  ESAIM: Mathematical Modelling and Numerical Analysis, Société de Mathématiques Appliquées et Industrielles (SMAI) / EDP, 2012. The present work aims at proposing a rigorous analysis of the mathematical and numerical modelling of ultrasonic piezoelectric sensors. This includes the well-posedness of the final model, the rigorous justification of the underlying approximation and the design and analysis of numerical methods. More precisely, we first justify mathematically the classical quasi-static approximation that reduces the electric unknowns to a scalar electric potential. We next justify the reduction of the computation of this electric potential to the piezoelectric domains only. Particular attention is devoted to the different boundary conditions used to model the emission and reception regimes of the sensor. Finally, an energy preserving finite element / finite difference numerical scheme is developed; its stability is analyzed and numerical results are presented.
• Fast multipole method applied to Symmetric Galerkin boundary element method for 3D elasticity and fracture problems
  
  • Pham Anh Duc
  • Mouhoubi Saida
  • Bonnet Marc
  • Chazallon Cyrille
  Engineering Analysis with Boundary Elements, Elsevier, 2012, 36, pp.1838-1847. The solution of three-dimensional elastostatic problems using the Symmetric Galerkin Boundary Element Method (SGBEM) gives rise to fully-populated (albeit symmetric) matrix equations, entailing high solution times for large models. This article is concerned with the formulation and implementation of a multi-level fast multipole SGBEM (FM-SGBEM) for elastic solid with cracks. Arbitrary geometries and boundary conditions may be considered. Numerical results on test problems involving a cube, single or multiple cracks in an unbounded medium, and a cracked cylindrical solid are presented. BEM models involving up to $10^{6}$ BEM unknowns are considered, and the desirable predicted trends of the elastostatic FM-SGBEM, such as a $O(N)$ complexity per iteration, are verified. (10.1016/j.enganabound.2012.07.004)
  DOI : 10.1016/j.enganabound.2012.07.004
• Optimization of the Effective Shear Properties of a Bidirectionally Corrugated Sandwich Core Structure
  
  • Besse C.
  • Mohr Dirk
  Journal of Applied Mechanics, American Society of Mechanical Engineers, 2012, pp.011012.
• Damage localization and rupture with gradient damage models
  
  • Pham Kim
  • Marigo Jean-Jacques
  Frattura ed Integrità Strutturale = Fracture and Structural Integrity, Università degli Studi di Cassino, 2012, 19, pp.pages 5-19. We propose a method of construction of non homogeneous solutions to the problem of traction of a bar made of an elastic-damaging material whose softening behavior is regularized by a gradient damage model. We show that, for sufficiently long bars, localization arises on sets whose length is proportional to the material internal length and with a profile which is also characteristic of the material. The rupture of the bar occurs at the center of the localization zone when the damage reaches there the critical value corresponding to the loss of rigidity of the material. The dissipated energy during all the damage process up to rupture is a quantity c G which can be expressed in terms of the material parameters. Accordingly, Gc can be considered as the usual surface energy density appearing in the Griffith theory of brittle fracture. All these theoretical considerations are illustrated by numerical examples.
• Dependence of elastic properties of argillaceous rocks on moisture content investigated with optical full-field strain measurement techniques
  
  • Yang Diansen
  • Bornert Michel
  • Chanchole Serge
  • Gharbi Hakim
  • Valli Pierre
  • Gatmiri Behrouz
  International Journal of Rock Mechanics and Mining Sciences, Pergamon and Elsevier, 2012, 53, pp.45-55. The mechanical behaviour of the argillaceous rock considered in France as a potential host rock for nuclear waste repository strongly depends on water content. In order to quantify the dependence of the mechanical properties on humidity, an experimental setup that combines hydromechanical loadings with optical observations and digital image correlation (DIC) has been developed. It allows investigation of the hydromechanical behaviour of a material from the sample scale (cm) down to micrometric scale (100 mu m). Using this system, the shrinkage and swelling properties of the argillaceous rock at various constant uniaxial stresses, and the linear mechanical behaviour of the material at different moisture levels, were experimentally studied. A quasi-linear relation between the relative humidity, ranging from 39% to 85%, and the deformation during dehydration and rehydration is found at both the sample scale (cm), and a mesoscopic scale of a few hundred micrometres. This relation depends on the applied stress with much less swelling at higher axial compressive stress. In addition, a linear decrease of the axial Young's modulus (normal to bedding plane) with an increase of the relative humidity is observed. (10.1016/j.ijrmms.2012.04.004)
  DOI : 10.1016/j.ijrmms.2012.04.004
• On the role of kinetic energy during unstable propagation in a heterogeneous peeling test
  
  • Lazzaroni Giuliano
  • Bargellini R.
  • Dumouchel P.E.
  • Marigo Jean-Jacques
  International Journal of Fracture, Springer Verlag, 2012, 175, pp.127-150. We study the dynamic debonding of a one-dimensional inextensible film, subject to a monotonic loading and under the hypothesis that the toughness of the glue can take only two values. We first consider the case of a single defect of small length in the glue where the toughness is lower than in the remaining part. The dynamic solution is obtained in a closed form and we prove that it does not converge to the expected quasi-static one when the loading speed tends to zero. The gap is due to a kinetic energy which appears when the debonding propagates across the defect at a velocity which is of the same order as the sound velocity. The kinetic energy becomes negligible again only when the debonding has reached a critical distance beyond the defect. The case of many defects is then considered and solved using an exact numerical solution of the wave equation and the Griffith law of propagation. The numerical results highlight the effects of the time evolution of the kinetic energy which induce alternate phases of rapid and slow debonding, these oscillations depending essentially on the volume fraction of the greater toughness. (10.1007/s10704-012-9708-0)
  DOI : 10.1007/s10704-012-9708-0
• Variational convergences of dual energy functionals for elastic materials with a ε thin strong inclusion
  
  • Bessoud Anne-Laure
  • Geymonat Giuseppe
  • Krasucki Francoise
  • Michaille Gérard
  Journal of Elasticity, Springer Verlag, 2012, 109, pp.51-65. We give a new derivation, based on the complementary energy formulation, of a simplified model for a multi-structure made up of two anisotropic hyper-elastic bodies connected by a thin strong material layer. The model is obtained by identifying the Mosco limit of the stored complementary energy functional when the thickness is of order ε and the stiffness of order 1/ε where ε is a positive real adimensional parameter. In order to prove the existence of the displacement associated with the stress we use a suitable weak version of the Saint-Venant compatibility condition also known as Donati's theorem. (10.1007/s10659-011-9368-8)
  DOI : 10.1007/s10659-011-9368-8
• Boiling Crisis as a Critical Phenomenon
  
  • Lloveras Pol
  • Salvat-Pujol Frederick
  • Truskinovsky Lev
  • Vives Eduard
  Physical Review Letters, American Physical Society, 2012, pp.215701. We present the first experimental study of intermittency and avalanche distribution during a boiling crisis. To understand the emergence of power law statistics we propose a simple spin model capturing the measured critical exponent. The model suggests that behind the critical heat flux is a percolation phenomenon involving drying-rewetting competition close to the hot surface. (10.1103/PhysRevLett.108.215701)
  DOI : 10.1103/PhysRevLett.108.215701