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.
• 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.
• Inverse acoustic scattering by generalized topological expansion
  
  • Bonnet Marc
  , 2007.
• 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.
• 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, 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
• Experimental study of the quasi-static and dynamic behaviour of cork under compressive loading
  
  • Gameiro Celina Pires
  • Cirne José
  • Gary Gérard
  J. Matter Sci, 2007, 42 (12), pp.4316-4324. Cork is a natural cellular material with increasing industrial applications due to its remarkable combination of properties. Its mechanical behaviour explains why it is often used for applications like sealing, packaging, insulation, vibration control, weight reduction, flotation, sound damping, etc. However, the mechanical behaviour of cork when subjected to impact has not been well investigated yet since the studies described in the literature generally focus strain rates below 10−1 s−1. Understanding the behaviour of cork at high rates of deformation becomes imperative when considering applications such as crash protection. Hence, in the present work, the authors compare the quasi-static and dynamic response of four types of cork when compressed axially at strain rates from 10−3 s−1 to 600 s−1. Data from the Split-Hopkinson Pressure Bars are used to generate stress–strain curves for natural and agglomerate cork samples, and the results are discussed in terms of the cellular structure of cork. (10.1007/s10853-006-0675-6)
  DOI : 10.1007/s10853-006-0675-6
• A fast multipole accelerated BEM for 3-D seismic wave computation
  
  • Chaillat Stéphanie
  • Bonnet Marc
  • Semblat Jean-François
  , 2007.
• MR-fluid-based haptic interface
  
  • Lozada José
  • Boutillon Xavier
  • Hafez Moustapha
  , 2006, pp.4 p.. A haptic interface based on magneto-rheological (MR) fluids is presented. The device is aiming for low inertia and the possibility of emulating quasi free-space motion as well as moderate resistive forces. It is based on the direct shear operating mode of the MR fluid with a slider. Friction caused by the translation motion of the slider is highly reduced by the use of a membrane that ensures sealing for the fluid container. The first experimental results are reported.
• On the cumulative microslip phenomenon
  
  • Antoni Nicolas
  • Son Nguyen Quoc
  • Ligier Jean-Louis
  • Saffré Philippe
  • Pastor Joseph
  European Journal of Mechanics - A/Solids, Elsevier, 2007, 26 (4), pp.626-646. The cumulative microslip phenomenon is the accumulation of relative slips in a tangential direction on the contact interface of two solids under cyclic loadings. This lead to significant global relative displacement between components and can account for the failure of some assembly parts in mechanical structures. Practical examples from the automotive industry are presented in this paper to describe the cumulative microslip in real situations. The phenomenon is then discussed from a theoretical point of view as an asymptotic behaviour by analogy with the ratchetting effects in elastoplasticity. Accommodation and slip shakedown are introduced in the same spirit. A slip shakedown theorem is proposed and leads to the definition of a safety coefficient with respect to slips when a standard law of friction is assumed. The safety coefficient can be computed from two static and kinematic approches in min-max duality. A simple example is given.
• Nonlinear sequential laminates reproducing hollow sphere assemblages
  
  • Idiart Martín I.
  Comptes Rendus. Mécanique, Académie des sciences (Paris), 2007, 335 (7), pp.363-368. A special class of nonlinear porous materials with isotropic ‘sequentially laminated’ microstructures is found to reproduce exactly the hydrostatic behavior of ‘hollow sphere assemblages’. It is then argued that this result supports the conjecture that Gurson's approximate criterion for plastic porous materials, and its viscoplastic extension of Leblond et al. (1994), may actually yield rigorous upper bounds for the hydrostatic flow stress of porous materials containing an isotropic, but otherwise arbitrary, distribution of porosity. (10.1016/j.crme.2007.04.003)
  DOI : 10.1016/j.crme.2007.04.003