Publications

2007

• Méthode multipôle rapide pour les éléments de frontière en élastodynamique tridimensionnelle : Application à la propagation d'ondes sismiques
  
  • Chaillat Stéphanie
  • Bonnet Marc
  • Semblat Jean-François
  , 2007, pp.615--620. La résolution des équations de l’élastodynamique par la méthode des éléments de frontière (BEM) conduit à un système linéaire plein. Faisant suite à des travaux sur les équa- tions de Helmholtz et Maxwell ayant établi la capacité de la méthode multipôle rapide (FM) à réduire la complexité de la BEM à $N \log 2 N$ par itération d’un solveur de type GMRES, cet article présente la transposition de l’approche FM-BEM à l’élastodynamique 3D dans le domaine fréquentiel. La précision et l’efficacité de la méthode sont illustrées sur des exemples numériques mobilisant jusqu’à $N = O(10^6)$ inconnues nodales.
• Vibrations non-linéaires des structures en situation de contact frottant : application aux crissements des freins à disque
  
  • Lorang Xavier
  • Son Nguyen Quoc
  , 2007, pp.383-388. The dynamics of an elastic disk in rotation between two elastic cylinders representing the pads of a simplified model of disk brake is considered. A numerical simulation of the transcient behaviour is discussed. The limit response at large time is analized in relation with the flutter modes of the steady sliding solution.
• A model for in situ grouting with account for particle filtration
  
  • Maghous S.
  • Saada Z.
  • Dormieux L.
  • Canou Jean
  • Dupla J.-C.
  Computers and Geotechnics, Elsevier, 2007, 34 (3), pp.164-174.
• Analyse de stabilité des évolutions quasi-statiques de systèmes standard dissipatifs
  
  • Abed-Meraim Farid
  • Nguyen Quoc Son
  , 2007, Tome II (Mécanique des Fluides), pp.193-195. Cette étude est consacrée à la stabilité de la réponse quasi-statique de systèmes standard dissipatifs (visco-élastiques, visco-plastiques ou élasto-plastiques). Dans le cas de solides visqueux (visco-élastiques ou visco-plastiques), pour lesquels la réponse à une sollicitation est en partie différée dans le temps, l’absence d’équilibre nous suggère naturellement d’étudier la stabilité de leurs évolutions quasi-statiques. Dans le cas de solides élasto-plastiques, cette approche est motivée par le fait que, bien souvent, nous sommes en présence d’une réponse quasi-statique pour un trajet de chargement donné ; même si cette évolution représente une succession d’états d’équilibres. Cette notion de stabilité au sens des trajectoires est donc plus générale que celle d’un équilibre, plus communément étudiée en mécanique. Elle généralise d’ailleurs l’étude de stabilité d’un état d’équilibre, qui peut être vu comme un cas particulier de trajectoires. La principale difficulté rencontrée dans l’analyse de stabilité de solutions non-stationnaires vient du caractère non autonome des équations différentielles gouvernant leur évolution. Quelques résultats partiels, mais beaucoup moins généraux que le théorème de stabilité de Lyapunov pour un équilibre, peuvent être trouvés pour des systèmes linéaires non autonomes. Ainsi, l’application de la méthode de linéarisation de Lyapunov ne donne qu’une réponse partielle, car elle ne s’applique que pour des systèmes suffisamment réguliers, d’une part, et conduit à des équations non autonomes, d’autre part. Pour les solides visco-élastiques, nous appliquons cette méthode de linéarisation qui nous donne une condition de stabilité asymptotique basée sur la définie positivité de la seconde variation de l’énergie. Pour des solides à potentiel de dissipation moins régulier, élasto-plastiques ou visco-plastiques, une approche par estimations directes est appliquée et nous donne une condition suffisante de stabilité basée sur la positivité de la seconde variation de l’énergie le long de la réponse considérée. Ce critère unifié représente une extension du critère de seconde variation, bien connu en théorie de stabilité élastique, au cas de stabilité d’évolutions quasi-statiques. Plus récemment, une version étendue de l’équation d’évolution de Biot a été considérée pour discuter la stabilité d’une réponse quasi-statique dans le cadre de matériaux standard généralisés. On montre également que pour les théories à gradients cette équation reste valide, puisque les gradients d’ordres supérieurs peuvent être introduits dans les expressions des deux potentiels (énergie libre et dissipation). Ainsi, l’étude de stabilité d’une évolution quasi-statique gouvernée par l’équation de Biot étendue a été discutée, nous permettant de faire une généralisation du critère de stabilité de seconde variation de l’énergie.
• Thermal effects in salt caverns
  
  • Berest Pierre
  • Bérest P.
  • Karimi-Jafari Mehdi
  • Brouard Benoît
  , 2007, pp.165-177.
• Pressure Build-up in a Sealed Cavern: Effect of a Gas Blanket
  
  • Berest Pierre
  • Karimi-Jafari Mehdi
  • Brouard Benoît
  • Durup Gérard
  , 2007, pp.179-188.
• Stress dependent permeabilities of sandstones : anisotropic response and end effects
  
  • Gland N.
  • Dautriat J.
  • Dimanov A.
  , 2007.
• Bifurcation of equilibrium solutions and defects nucleation
  
  • Stolz Claude
  , 2007.
• Modeling microstructures and microstructural effects on macroscopic and intragranular mechanical behavior
  
  • Bertolino Graciela
  • Bilger Nicolas
  • Crepin Jerome
  Computational Materials Science, Elsevier, 2007, 40, pp.408–416. The objective of the present paper is to study the influence of different microstructures on mechanical behavior at the intragranular and macroscopic scales. A new methodology that simulates a realistic 2D microstructure from statistical 2D experimental characterization (grain size distribution, grain shape, texture distribution) is presented and compared with the Voronoi simulation and the experimental microstructure. Finite element simulations using phenomenological constitutive law that takes into account crystallographic microstructure data and grain size effect are presented and results from both microstructure types are compared with the experimental macroscopic response, as well as the in-plane intragranular strain field and its distribution.
• EBSD : a major device for mechanical characterization of polycrystalline materials
  
  • Bertolino Graciela
  • Caldemaison Daniel
  • Crepin Jerome
  • Dexet Marie
  • Heripre Eva
  , 2007. This paper presents a coupling methodology between microstructure characterization, mechanical tests and numerical simulations for polycrystalline materials that has been developed in order to compare directly and simultaneously numerical results to experimental ones at different length scales. This methodology is based on Orientation Imaging Microscopy that is used to obtain a crystallographic orientations field (X, Y, & & &) of the zone of interest of the polycrystalline sample. Then these data can be analyzed to yield statistical information about the microstructure as the size of the Representative Volume Element, based on texture analysis, and also about the location of grain boundaries that is used to generate automatically a Finite Element mesh from a subsection of this investigated microstructure. Secondly, Digital Imaging Correlation technique, performed during mechanical test, is used to characterize the in plane strain field associated with the microstructure. This field quantifies the local in-plane strain heterogeneities and their spatial distribution with respect to the microstructure. From this intragranular in-plane field, different kinds of averages can be obtained as grain averages, phase averages (where a phase could be defined as the sum of grains with the same crystallographic orientation) and of course the macroscopic strain. Finally, a Finite Element simulation can be carried out on the mesh that was generated. This FE simulation uses crystallographic constitutive laws and the grain orientations as measured thanks to EBSD. The in-plane experimental displacements obtained by the DIC technique are then applied as boundary conditions at the mesh edges. This allows a comparison of the intragranular strain or displacement fields in the whole mesh without artefacts generated by homogeneous or periodic boundary conditions, as is typically the case in conventional approaches.
• M-shaped specimen for the high strain rate tensile testing using a Split Hopkinson bar apparatus
  
  • Mohr Dirk
  • Gary Gérard
  Experimental Mechanics, Society for Experimental Mechanics, 2007, 47 (5), pp.681-692. An experimental technique is proposed to determine the tensile stress-strain curve and strain to fracture of metals at high strain rates. An M-shaped specimen is designed which converts a compression loading at its boundaries into tensile loading of its gage section. The specimen can be used in a conventional split Hopkinson pressure bar apparatus, thereby circumventing experimental problems related to the gripping of tensile specimens under dynamic loading. The M-specimen achieves plane strain conditions within its gage section. This feature retards necking and allows for very short gage sections. This new technique has been validated both experimentally and numerically for true equivalent plastic strain rates of up to 4250/s. (10.1007/s11340-007-9035-y)
  DOI : 10.1007/s11340-007-9035-y
• Fast multipole method formulation for 3D elastodynamics in the frequency domain
  
  • Chaillat Stéphanie
  • Bonnet Marc
  • Semblat Jean-François
  , 2007.
• Coupling between experimental measurements and polycristal finte element calculations for micromechanical study of metallic materials
  
  • Heripre Eva
  • Dexet Marie
  • Crepin Jerome
  • Gélebart Lionel
  • Roos Arjen
  • Bornert Michel
  • Caldemaison Daniel
  International Journal of Plasticity, Elsevier, 2007, 23 (9), pp.1512-1539. This paper presents a methodology for multiscale coupling between the morphology and texture of a microstructure as has been characterised experimentally, and the results of mechanical strain field analysis. This methodology is based on a coupling between experimental characterisation of the microstructure, in-situ and/or ex-situ mechanical tests, local strain field measurements performed at the grain scale, and finite element simulations. First, with orientation imaging microscopy, a map of the microstructure is generated that can be meshed. Then, finite element calculations are carried out on this mesh, using a constitutive law which takes into account the crystallographic orientation of each grain, as has been determined by the orientation imaging itself. These numerical results are then compared to the experimental strain field as obtained by digital image correlation at the scale of the grains. After a review of the different aspects of the coupling, the paper characterises and analyses possible sources of error of the measurements, as well as the differences in the simulation results with respect to mesh refinement and boundary conditions. Then, a definition of a cost function is proposed in order to optimise the parameters of the crystallographic constitutive law. Finally, this method is applied to the studies of zirconium and titanium aluminide alloys in order to improve the understanding of their mechanical behaviour in relation with their microstructures, which is a key requirement for their use in the nuclear and aeronautic industries, respectively.
• Contribution à l'étude théorique de la localisation plastique dans les poreux
  
  • Willot François
  , 2007. Ce travail s'inscrit dans la thématique classique en mécanique théorique de l'homogénéisation de milieux hétérogènes, dans le cadre notoirement problématique d'un contraste infini entre deux phases en présence (l'une étant la porosité du milieu), et d'un comportement non-linéaire, celui de la phase solide plastique. Il traite de la question d'une prise en compte correcte du phénomène de localisation de la déformation plastique en présence de porosité dans la loi de comportement effective du milieu poreux, en particulier dans la limite non-triviale des porosités faibles. Cette question, importante pour la bonne compréhension de l'endommagement ductile, est examinée tant d'un point de vue numérique que théorique, dans le cadre restreint de systèmes bi-dimensionnels, dans une approche en déformation de la plasticité. L'approche numérique utilise des calculs quasi-exacts des champs de contrainte et de déformation par méthode de Transformée de Fourier Rapide sur des systèmes périodiques (réseau de pores) ou aléatoires (désordre sans corrélations spatiales), menée au moyen d'une fonction de Green particulière. L'approche théorique repose sur des calculs exacts, possibles dans certain cas, ainsi que sur l'exploitation de méthodes d'homogénéisation non-linéaires récentes, dites « de second ordre ». La qualité de l'homogénéisation non-linéaire du milieu poreux est évaluée en deux étapes, d'abord au moyen d'une étude de l'homogénéisation linéaire anisotrope qui la sous-tend, puis de la mise en oeuvre non-linéaire proprement dite. La nature et la signification des singularités qui apparaissent dans la théorie, dans la limite des faibles porosités, confirmée par les calculs numériques, sont élucidées en partie. Enfin, des observations originales sur la relation entre l'organisation de la plasticité dans un milieu poreux aléatoire, et certaines caractéristiques de la courbe de déformation macroscopique sont présentées.
• Resolution of linear viscoelastic equations in the frequency domain using real Helmholtz boundary integral equations
  
  • Chaillat Stéphanie
  • Bui Hui Duong
  Comptes Rendus. Mécanique, Académie des sciences (Paris), 2007, 335, pp.746-750. Boundary integral equations are well suitable for the analysis of seismic waves propagation in unbounded domains. Formulations in elastodynamics are well developed. In contrast, for the dynamic analysis of viscoelastic media, there are very seldom formulations by boundary integral equations. In this Note, we propose a new and simple formulation of time harmonic viscoelasticity with the Zener model, which reduces to classical elastodynamics if a compatibility condition is satisfied by boundary conditions. Intermediate variables which satisfy the classical elastodynamic equations are introduced. It makes it possible to utilize existing numerical tools of time harmonic elastodynamics.
• A numerical evaluation of various scale transition rules for uniform field models
  
  • Bouteleux Simon
  • Gérard Céline
  • Bacroix Brigitte
  • Bornert Michel
  • Brenner Renald
  • Cailletaud Georges
  • Crépin Jérôme
  • Leclercq Sylvain
  , 2007.
• A Fast Multipole Method formulation for 3D elastodynamics in the frequency domain
  
  • Chaillat Stéphanie
  • Bonnet Marc
  • Semblat J. F.
  Comptes Rendus. Mécanique, Académie des sciences (Paris), 2007, 335, pp.709-714. The solution of the elastodynamic equations using boundary element methods (BEMs) gives rise to fully-populated matrix equations. Earlier investigations on the Helmholtz and Maxwell equations have established that the Fast Multipole (FM) method reduces the complexity of a BEM solution to $N \mbox{log}_{2}N$ per GMRES teration. The present Note address the extension of the FM-BEM strategy to 3D elastodynamics in the frequency domain. Its efficiency and accuracy are demonstrated on numerical examples involving up to $N=O(10^{6})$ nodal unknowns. (10.1016/j.crme.2007.07.001)
  DOI : 10.1016/j.crme.2007.07.001
• A thermodynamical approach to contact wear as application of moving discontinuities
  
  • Stolz Claude
  Archive of Applied Mechanics, Springer Verlag, 2007, 77 (2-3), pp.165-175. The propagation of a moving surface inside a body is analysed within the framework of thermomechanical couplings when the moving surface is associated with an irreversible change in mechanical properties. The moving surface is a surface of heat sources and of entropy production whose intensities are related to particular energy release rates defined in terms of Hamiltonian gradients. For example, we analyse the wear process. Wear phenomena due to contact and relative motion between two solids depend on the loading conditions and material mechanical properties. Friction between contacting bodies induces damage of materials, producing surface and subsurface cracks. Particles are detached from sound solids when some local criteria are satisfied at the boundary. As wear occurs, geometrical changes take place and contact conditions are modified, and the particle induces a specific layer with particular properties. Then the interface between the bodies is a complex medium made of detached particles, eventually a lubricant fluid, and damaged zones. We propose to describe the evolution of the interface using a framework developed earlier for inducing the general form of a wear law. (10.1007/s00419-006-0057-1)
  DOI : 10.1007/s00419-006-0057-1
• Second order homogenization of the elastic wave equation for non-periodic layered media
  
  • Capdeville Yann
  • Marigo J.-J
  Geophysical Journal International, Oxford University Press (OUP), 2007, 170 (2), pp.823 - 838. In many cases, in the seismic wave propagation modelling context, scales much smaller than the minimum wavelength are present in the earth model in which we wish to compute seismograms. For many numerical methods these small scales are a challenge leading to high numerical cost. The purpose of this paper is to understand and to build the effective medium and equations allowing to average the small scales of the original medium without losing the accuracy of the wavefield computation. In this paper, only the simple layered medium case is studied, leaving the general 3-D medium case for future work. To obtain such an effective medium and equations, we use high order two scale homogenization applied to the wave equation for layered media with rapid variation of elastic properties and density compared to the smallest wavelength of the wavefield. We show that the order 0 homogenization gives the result that was obtained by Backus in 1962. Order 0 homogenized models are transversely isotropic even though the original model is isotropic. It appears that order 0 is not enough to obtain surface waves with correct group and phase velocities and higher order homogenization terms up to two are often required. In many cases, the order one and two simply require to correct the boundary conditions of the wave equation to obtain an accurate solution, even for surface waves. We show how to extend the theory from the periodic case to the non-periodic case. Examples in periodic and non-periodic media are shown. The accuracy of the results obtained by homogenization is checked against the normal mode solution computed in the original medium and shows good agreement. (10.1111/j.1365-246X.2007.03462.x)
  DOI : 10.1111/j.1365-246X.2007.03462.x
• Estimating the parameters of a generalized lambda distribution
  
  • Fournier Benjamin
  • Rupin Nicolas
  • Bigerelle Maxence
  • Najjar Denis
  • Iost Alain
  • Wilcox R
  Computational Statistics and Data Analysis, Elsevier, 2007, 51 (6), pp.2813-2835. The method of moments is a popular technique for estimating the parameters of a generalized lambda distribution (GLD), but published results suggest that the percentile method gives superior results. However, the percentile method cannot be implemented in an automatic fashion, and automatic methods, like the starship method, can lead to prohibitive execution time with large sample sizes. A new estimation method is proposed that is automatic (it does not require the use of special tables or graphs), and it reduces the computational time. Based partly on the usual percentile method, this new method also requires choosing which quantile u to use when fitting a GLD to data. The choice for u is studied and it is found that the best choice depends on the final goal of the modeling process. The sampling distribution of the new estimator is studied and compared to the sampling distribution of estimators that have been proposed. Naturally, all estimators are biased and here it is found that the bias becomes negligible with sample sizes n⩾2×103. The .025 and .975 quantiles of the sampling distribution are investigated, and the difference between these quantiles is found to decrease proportionally to View the MathML source. The same results hold for the moment and percentile estimates. Finally, the influence of the sample size is studied when a normal distribution is modeled by a GLD. Both bounded and unbounded GLDs are used and the bounded GLD turns out to be the most accurate. Indeed it is shown that, up to n=106, bounded GLD modeling cannot be rejected by usual goodness-of-fit tests. (10.1016/j.csda.2006.09.043)
  DOI : 10.1016/j.csda.2006.09.043
• Modélisations mécaniques de la touche de piano et de son imitation haptique
  
  • Lozada José
  • Boutillon Xavier
  • Hafez Moustapha
  , 2007, pp.6 p.. Le toucher d'un piano est une information sensorielle essentielle pour le contrôle de la nuance de jeu. Elle provient de la dynamique complexe du mécanisme d'actionnement qui transmet l'énergie mécanique du doigt au marteau. Les pianos numériques mettent en oeuvre des claviers qui ne reproduisent pas les finesses du toucher d'un piano traditionnel. Afin de palier cette défaillance, nous avons réalisé une interface haptique semi-active capable de reproduire le toucher du piano traditionnel. Ceci nécessite une modélisation fine du comportement dynamique du système traditionnel. Nous présentons le modèle dynamique de la touche de piano ; ses simulations sont comparées aux mesures de la réponse du système sous l'action du doigt. L'interface haptique est composée d'un levier auquel est appliqué un système d'amortissement actif à base de fluide magnéto-rhéologique (MRF). Nous présentons le modèle de l'interface ; ses simulations sont comparées à la réponse du système sous l'action du doigt.
• A quasi-static stability analysis for Biot’s equation and standard dissipative systems
  
  • Abed-Meraim Farid
  • Nguyen Quoc Son
  European Journal of Mechanics - A/Solids, Elsevier, 2007, 26 (3), pp.383-393. In this paper, an extended version of Biot's differential equation is considered in order to discuss the quasi-static stability of a response for a solid in the framework of generalized standard materials. The same equation also holds for gradient theories since the gradients of arbitrary order of the state variables and of their rates can be introduced in the expression of the energy and of the dissipation potentials. The stability of a quasi-static response of a system governed by Biot's equations is discussed. Two approaches are considered, by direct estimates and by linearizations. The approach by direct estimates can be applied in visco-plasticity as well as in plasticity. A sufficient condition of stability is proposed and based upon the positivity of the second variation of energy along the considered response. This is an extension of the criterion of second variation, well known in elastic buckling, into the study of the stability of a response. The linearization approach is available only for smooth dissipation potentials, i.e. for the study of visco-elastic solids and leads to a result on asymptotic stability. The paper is illustrated by a simple example. (10.1016/j.euromechsol.2006.06.005)
  DOI : 10.1016/j.euromechsol.2006.06.005
• Objective evaluation of linearization procedures in nonlinear homogenization: a methodology and some implications on the accuracy of micromechanical schemes
  
  • Rekik Amna
  • Auslender François
  • Bornert Michel
  • Zaoui André
  International Journal of Solids and Structures, Elsevier, 2007, 44 (10), pp.3468-3496. A systematic methodology for an accurate evaluation of various existing linearization procedures sustaining mean fields theories for nonlinear composites is proposed and applied to recent homogenization methods. It relies on the analysis of a periodic composite for which an exact resolution of both the original nonlinear homogenization problem and the linear homogenization problems associated with the chosen linear comparison composite (LCC) with an identical microstructure is possible. The effects of the sole linearization scheme can then be evaluated without ambiguity. This methodology is applied to three different two-phase materials in which the constitutive behavior of at least one constituent is nonlinear elastic (or viscoplastic): a reinforced composite, a material in which both phases are nonlinear and a porous material. Comparisons performed on these three materials between the considered homogenization schemes and the reference solution bear out the relevance and the performances of the modified second-order procedure introduced by Ponte Castañeda in terms of prediction of the effective responses. However, under the assumption that the field statistics (first and second moments) are given by the local fields in the LCC, all the recent nonlinear homogenization procedures still fail to provide an accurate enough estimate of the strain statistics, especially for composites with high contrast. (10.1016/j.ijsolstr.2006.10.001)
  DOI : 10.1016/j.ijsolstr.2006.10.001
• Homogenization-based constitutive models for porous elastomers and implications for macroscopic instabilities: I-Analysis
  
  • Lopez-Pamies Oscar
  • Ponte Castañeda Pedro
  Journal of the Mechanics and Physics of Solids, Elsevier, 2007, 55 (8), pp.1677-1701. The purpose of this paper is to provide homogenization-based constitutive models for the overall, finite-deformation response of isotropic porous rubbers with random microstructures. The proposed model is generated by means of the “second-order” homogenization method, which makes use of suitably designed variational principles utilizing the idea of a “linear comparison composite.” The constitutive model takes into account the evolution of the size, shape, orientation, and distribution of the underlying pores in the material, resulting from the finite changes in geometry that are induced by the applied loading. This point is key, as the evolution of the microstructure provides geometric softening/stiffening mechanisms that can have a very significant effect on the overall behavior and stability of porous rubbers. In this work, explicit results are generated for porous elastomers with isotropic, (in)compressible, strongly elliptic matrix phases. In spite of the strong ellipticity of the matrix phases, the derived constitutive model may lose strong ellipticity, indicating the possible development of shear/compaction band-type instabilities. The general model developed in this paper will be applied in Part II of this work to a special, but representative, class of isotropic porous elastomers with the objective of exploring the complex interplay between geometric and constitutive softening/stiffening in these materials. (10.1016/j.jmps.2007.01.007)
  DOI : 10.1016/j.jmps.2007.01.007
• Volumetric digital image correlation applied to X-Ray microtomography images form triaxial compression tests on argillaceaous rocks
  
  • Lenoir Nicolas
  • Bornert Michel
  • Desrues Jacques
  • Bésuelle Pierre
  • Viggiani Gioacchino Cinno
  Strain, Wiley-Blackwell, 2007, 43 (3), pp.193–205. A set of triaxial compression tests on specimens of argillaceous rock were performed under tomographic monitoring at the European Synchrotron Radiation Facility in Grenoble, France, using an original experimental set-up developed at Laboratoire 3S, Grenoble. Complete 3D images of the specimens were recorded throughout each test using X-ray microtomography. Such images were subsequently analysed using a Volumetric Digital Image Correlation software developed at the Laboratoire de Me?canique des Solides in Palaiseau, France. Full-field incremental strain measurements were obtained, which allow to detect the onset of shear strain localisation and to characterise its development in a 3D complex pattern. Volumetric Digital Image Correlation revealed patterns which could not be directly observed from the original tomographic images, because the deformation process in the zones of localised deformation was essentially isochoric (i.e. without volumetric strain), hence not associated to density changes. (10.1111/j.1475-1305.2007.00348.x)
  DOI : 10.1111/j.1475-1305.2007.00348.x