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.
• Rapid Depresurizations: Can they lead to irreversible damage?
  
  • Berest Pierre
  • Djakeun-Djizanne Hippolyte
  • Brouard Benoît
  • Hévin Grégoire
  , 2012, pp.63-86. Rapid gas depressurization leads to gas cooling that is followed by slow gas warming when the cavern is kept idle. The decrease in the temperature of gas depends upon the relative withdrawal rate (in %/day), and cavern size and shape. Gas cooling may result in the onset of tensile stresses at cavern walls and roofs that may generate fractures or cracks. However, in most cases, the depth of penetration of these fractures is small, and they are perpendicular to the cavern wall. The distance between two parallel fractures becomes larger when fractures penetrate deeper into the rock mass, as some fractures stop growing. Fractures form a polygonal pattern. Salt slabs are created, with boundaries formed by the opened fractures. As long as the depth of penetration of the fracture remains small, these slabs remain strongly bonded to the rock mass, and it is believed that, in many cases, their weights are not large enough to allow them to break off the cavern wall.
• 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.
• 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.
• 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.
• 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.
• 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
• 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
• 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
• 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.
• 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.
• Apparent and effective mechanical properties of linear matrix-inclusion random composites: Improved bounds for the effective behavior
  
  • Salmi Moncef
  • Auslender François
  • Bornert Michel
  • Fogli Michel
  International Journal of Solids and Structures, Elsevier, 2012, 49 (10), pp.1195-1211. This paper is devoted to the derivation of improved bounds for the effective behavior of linear elastic matrix-inclusion composites based on a strategy which is inspired by both the works of Huet (1990) and Danielsson et al. (2007). As shown by the former author, the effective properties of random linear composites can be bounded by ensemble averages of their apparent elastic moduli defined on square (or cubic) volume elements (VEs) and computed with either affine displacement Boundary Conditions (BC) or uniform traction BC. However, in the case of a large contrast of the constituents, the discrepancy between the upper and lower bounds remains significant, even for large values of the VE size. This occurs because the contribution to the total potential (or complementary) energy of the particles (or pores) which intersect the edges of the VE becomes unphysically very large when uniform BC are directly applied to the particles. To avoid such limitations, we considerer non-square (or non-cubic) VEs consisting in simply connex assemblages of cells, each cell being composed of an inclusion surrounded by the matrix, thus forbidding any direct application of BC to the particles. Such VEs are generated by extending the scheme proposed by Danielsson et al. (2007) in the context of periodic random microstructures to fully random microstructures. By applying the classical energy bounding theorems to the non-square VEs, new bounds for the effective behavior are derived. Their application to a two-phase composite composed of an isotropic matrix and aligned identical fibers randomly distributed in the transverse plane leads to sharper bounds which converge quickly with the VE size, even for infinite contrasts. © 2012 Elsevier Ltd. All rights reserved. (10.1016/j.ijsolstr.2012.01.018)
  DOI : 10.1016/j.ijsolstr.2012.01.018
• Solving dynamic contact problems with local refinement in space and time
  
  • Hager Corinna I
  • Hauret Patrice
  • Le Tallec Patrick
  • Wohlmuth Barbara I
  Computer Methods in Applied Mechanics and Engineering, Elsevier, 2012, 201, pp.25 - 41. Frictional dynamic contact problems with complex geometries are a challenging task from the compu tational as well as from the analytical point of view since they generally involve space and time multi scale aspects. To be able to reduce the complexity of this kind of contact problem, we employ a non conforming domain decomposition method in space, consisting of a coarse global mesh not resolving the local struc ture and an overlapping fine patch for the contact computation. This leads to several benefits: First, we resolve the details of the surface only where it is needed, i.e., in the vicinity of the actual contact zone. Second, the subproblems can be discretized independently of each other which enables us to choose a much finer time scale on the contact zone than on the coarse domain. Here, we propose a set of interface conditions that yield optimal a priori error estimates on the fine meshed subdomain without any artificial dissipation. Further, we develop an efficient iterative solution scheme for the coupled problem that is robust with respect to jumps in the material parameters. Several complex numerical examples illustrate the performance of the new scheme. (10.1016/j.cma.2011.09.006)
  DOI : 10.1016/j.cma.2011.09.006
• An adaptive algorithm for cohesive zone model and arbitrary crack propagation
  
  • Chiaruttini Vincent
  • Geoffroy Dominique
  • Riolo Vincent
  • Bonnet Marc
  Revue Européenne de Mécanique Numérique/European Journal of Computational Mechanics, Hermès / Paris : Lavoisier, 2012, 21, pp.208-218. This paper presents an approach to the numerical simulation of crack propagation with cohesive models for the case of structures subjected to mixed mode loadings. The evolution of the crack path is followed by using an adaptive method: with the help of a macroscopic branching criterion based on the calculation of an energetic integral, the evolving crack path is remeshed as the crack evolves in the simulation. Special attention is paid to the unknown fields transfer approach that is crucial for the success of the computational treatment. This approach has been implemented in the finite element code Z-Set (jointly developed by Onera and Ecole des Mines) and is tested on two examples, one featuring a straight crack path and the other involving a complex crack propagation under critical monotonous loading monotonous. (10.1080/17797179.2012.744544)
  DOI : 10.1080/17797179.2012.744544