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
• 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.
• Fast multipole method formulation for 3D elastodynamics in the frequency domain
  
  • Chaillat Stéphanie
  • Bonnet Marc
  • Semblat Jean-François
  , 2007.
• 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.
• Inverse acoustic scattering by generalized topological expansion
  
  • Bonnet Marc
  , 2007.
• A multiple fine-scale satellite-derived landscape approach: example of bluetongue modelling in Corsica.
  
  • Guis Hélène
  • Tran Annelise
  • Mauny Frédéric
  • Baldet Thierry
  • Barragué Bruno
  • Gerbier Guillaume
  • Viel Jean-François
  • Roger François
  • de La Rocque Stéphane
  Veterinaria Italiana, 2007, 43 (3), pp.669-683.
• Homogenization-based constitutive models for porous elastomers and implications for macroscopic instabilities: II-Results
  
  • Lopez-Pamies Oscar
  • Ponte Castañeda Pedro
  Journal of the Mechanics and Physics of Solids, Elsevier, 2007, 55 (8), pp.1702-1728. In Part I of this paper, we developed a homogenization-based constitutive model for the effective behavior of isotropic porous elastomers subjected to finite deformations. In this part, we make use of the proposed model to predict the overall response of porous elastomers with (compressible and incompressible) Gent matrix phases under a wide variety of loading conditions and initial values of porosity. The results indicate that the evolution of the underlying microstructure—which results from the finite changes in geometry that are induced by the applied loading—has a significant effect on the overall behavior of porous elastomers. Further, the model is in very good agreement with the exact and numerical results available from the literature for special loading conditions and generally improves on existing models for more general conditions. More specifically, we find that, in spite of the fact that Gent elastomers are strongly elliptic materials, the constitutive models for the porous elastomers are found to lose strong ellipticity at sufficiently large compressive deformations, corresponding to the possible onset of “macroscopic” (shear band-type) instabilities. This capability of the proposed model appears to be unique among theoretical models to date and is in agreement with numerical simulations and physical experience. The resulting elliptic and non-elliptic domains, which serve to define the macroscopic “failure surfaces” of these materials, are presented and discussed in both strain and stress space. (10.1016/j.jmps.2007.01.008)
  DOI : 10.1016/j.jmps.2007.01.008
• Variational linear comparison bounds for nonlinear composites with anisotropic phases. II. Crystalline materials
  
  • Idiart Martin
  • Ponte Castañeda Pedro
  Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Royal Society, The, 2007, 463, pp.925-943. In part I of this work, bounds were derived for the effective potentials of nonlinear composites with anisotropic constituents, making use of an appropriate generalization of the linear comparison variational method. In this second part, the special case of nonlinear composites with crystalline constituents is considered. First, it is shown that, for this special but very important class of materials, the ‘variational’ bounds of part I are at least as good as an earlier version of the bounds due to deBotton & Ponte Castañeda. Then, the relative merits of these two types of bounds are studied in the context of a model, two-dimensional, porous composite with a power-law crystalline matrix phase, under anti-plane loading conditions. The results show that, indeed, the variational bounds of part I improve, in general, on the earlier bounds, with the former becoming progressively sharper than the latter as the number of slip systems of the crystalline matrix phase increases. In particular, it is shown that, unlike the bounds of deBotton & Ponte Castañeda, the variational bounds of part I are able to recover the variational bound for composites with an isotropic matrix phase, as the number of slip systems, all having the same flow stress, tends to infinity. (10.1098/rspa.2006.1804)
  DOI : 10.1098/rspa.2006.1804
• Two-scale Dirichlet-Neumann Preconditioners for Boundary Refinements
  
  • Hauret Patrice
  • Le Tallec Patrick
  , 2007, 55, pp.447-454. The present work introduces simple Dirichlet-Neumann preconditioners for the solution of elasticity problems in presence of numerous small disjoint geometric refinements on the boundary of the domain, situation which typically occurs in the tire industry. Moreover, the condition number of the preconditioned system is proved to be independent of the number and the size of the small details on the boundary. Finally, as an enhancement, a second proposed preconditioner makes use of a coarse space counterbalancing the effect of essential boundary conditions on the small details, and a simple numerical academic test illustrates the increased ef- ficiency. Further details on the motivation as well as complete proofs can be found in [4, 5]. (10.1007/978-3-540-34469-8_56)
  DOI : 10.1007/978-3-540-34469-8_56
• Questions of Prediction of the Long-Term Behaviour of Underground Openings, KeyNote Lecture
  
  • Berest Pierre
  • Bérest P.
  , 2007, Vol. 3, pp.1413-1425.
• 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