Publications

2007

• éléments finis étendus pour la modélisation des structures soudées par points
  
  • Burry Pierre
  • Maitournam Habibou
  • Billotey Geoffroy
  , 2007. Cet article présente un élément de coque bilinéaire enrichi, adapté à la modélisation des tôles soudées par points de soudure électrique, et implémenté sous Abaqus. L’élément de base est un élément de Simo-Rifaï en petits déplacements et en élasticité linéaire. La modélisation proposée des points de soudure s’inspire des méthodes de modélisation d’inclusion dans un milieu infini par éléments finis étendus. Le point de soudure est considéré comme quasi ponctuel dans le milieu continu 2D de la tôle ; les fonctions d’enrichissement de l’espace d’approximation des déplacements représentent les modes de déformation locaux des tôles autour des points de soudure, et permettent de représenter correctement les déformées de tôles assemblées sans avoir à mailler les points de soudure. Des exemples démontrent la possibilité de calculer des assemblages de tôles maillées indépendamment.
• 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.
• Stress dependent permeabilities of sandstones : anisotropic response and end effects
  
  • Gland N.
  • Dautriat J.
  • Dimanov A.
  , 2007.
• 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.
• 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
• 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.
• 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.
• Transient Behaviour of salt caverns. Interpretation of Mechanical Integrityb Tests
  
  • Berest Pierre
  • Bérest P.
  • Karimi-Jafari Mehdi
  • Brouard Benoît
  • van Sambeek Leo
  International Journal Rock Mechanics & Mining Sciences, 2007 (44), pp.767-786.
• Field statistics in nonlinear composites. I. Theory
  
  • Idiart Martin
  • Ponte Castañeda Pedro
  Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Royal Society, 2007, 463 (2077), pp.183-202. This work presents a means for extracting the statistics of the local fields in nonlinear composites from the effective potential of suitably perturbed composites. The idea is to introduce a parameter in the local potentials, generally a tensor, such that differentiation of the corresponding effective potential with respect to the parameter yields the volume average of the desired quantity. In particular, this provides a generalization to the nonlinear case of well-known formulas in the context of linear composites, which express phase averages and second moments of the local fields in terms of derivatives of the effective potential. Such expressions are useful since they allow the generation of estimates for the field statistics in nonlinear composites, directly from homogenization estimates for appropriately defined effective potentials. Here, use is made of these expressions in the context of the ‘variational’, ‘tangent second-order’ and ‘second-order’ homogenization methods, to obtain rigorous estimates for the first and second moments of the fields in nonlinear composites. While the variational estimates for these quantities are found to be identical to those proposed in previous works, the tangent second-order and second-order estimates are found be different. In particular, the new estimates for the first moments given in this work are found to be entirely consistent with the corresponding estimates for the macroscopic behaviour. Sample results for two-phase, power-law composites are provided in part II of this work. (10.1098/rspa.2006.1756)
  DOI : 10.1098/rspa.2006.1756
• FM-BEM and topological derivative applied to inverse acoustic scattering
  
  • Bonnet Marc
  • Nemitz Nicolas
  , 2007, pp.187-212. This study is set in the framework of inverse scattering of scalar (e.g. acoustic) waves. A qualitative probing technique based on the distribution of topological sensitivity of the cost functional associated with the inverse problem with respect to the nucleation of an infinitesimally-small hard obstacle is formulated. The sensitivity distribution is expressed as a bilinear formula involving the free field and an adjoint field associated with the cost function. These fields are computed by means of a boundary element formulation accelerated by the Fast Multipole method. A computationally fast approach for performing a global preliminary search based on the available overspecified boundary data is thus defined. Its usefulness is demonstrated through results of numerical experiments on the qualitative identification of a hard obstacle in a bounded acoustic domain, for configurations featuring O(10⁵) nodal unknowns and O(10⁶) sampling points. (10.1007/978-3-540-47533-0_8)
  DOI : 10.1007/978-3-540-47533-0_8
• Bifurcation of equilibrium solutions and defects nucleation
  
  • Stolz Claude
  International Journal of Fracture, Springer Verlag, 2007, 147, pp.103-107. The purpose of this article is to revise some concepts on defects nucleation based on bifurcation of equilibrium solutions. Equilibrium solutions are obtained on a homogeneous body and on a body with an infinitesimal defect such as cavity under the same prescirbed dead load. First void formation and growth in non linear mechanics are examined. A branch of radial transformation bifurcates from the undeformed configuration in presence of a small cavity. Two cases of behaviour is examined. One case is the growth of cavity by only the deformation of the matrix. In another modelling the cavity evolves like a damaged zone. The transition between the sound part and the damaged one is governed by a local criterium. Each configuration leads to the definition of a nucleation criterium based on a presence of a bifurcation state, comman state of the homogeneous boby and a body with an infinitesimal defect. (10.1007/s10704-007-9147-5)
  DOI : 10.1007/s10704-007-9147-5
• Micromechanical modeling of packing and size effects in particulate composites
  
  • Marcadon V.
  • Herve E.
  • Zaoui A.
  International Journal of Solids and Structures, Elsevier, 2007, vol. 44, pp.pp. 8213−8228.
• Study of non-proportionnal loading paths : comparison between experimental results and simulations performed by finite element and homogenized models
  
  • Gérard Céline
  • Bacroix Brigitte
  • Bornert Michel
  • Brenner Renald
  • Cailletaud Georges
  • Caldemaison Daniel
  • Chauveau Thierry
  • Crépin Jérôme
  • Leclercq Sylvain
  • Mounoury Valérie
  , 2007. The plastic behavior of fcc materials is studied under complex loading path at room temperature. Multi-scale experimental results are compared to finite element computations of polycrystalline aggregates, and to simulation by homogenization techniques. Combinations of sequences of simple loading paths such as tension, simple shear, rolling, cyclic tension-compression, with different orientations with regard to rolling direction, are considered. The material used in the study has been cold rolled and annealed. Specimen are marked with several gold microgrids to measure local strain field by digital correlation of scanning electron microscope images, whereas global strains are measured by classical extensometry. A polycrystalline aggregate taking into account the material microstructure is used to perform finite element simulations corresponding to the experiments. The texture measured by X-ray diffraction is represented. Several single crystal models, using the 12 slip systems of the octahedral families, are introduced. Various assumptions are considered for the description of the self and latent hardening. The comparisons between the simulation and the experiments are made on three types of variables~: on a global level, with the description of the macroscopic stress-strain curve, on a local level, by considering the local fields, and in terms of phase averages. Informations about the consistency of the transition rules are deduced.
• Localization of elastic deformation in strongly anisotropic, porous, linear materials with periodic microstructures: exact solutions and dilute expansions
  
  • Willot François
  • Pellegrini Yves-Patrick
  • Ponte Castañeda Pedro
  Journal of the Mechanics and Physics of Solids, Elsevier, 2007, 56, pp.1245-1268. Exact solutions are derived for the problem of a two-dimensional, infinitely anisotropic, linear-elastic medium containing a periodic lattice of voids. The matrix material possesses either one infinitely soft, or one infinitely hard loading direction, which induces localized (singular) field configurations. The effective elastic moduli are computed as functions of the porosity in each case. Their dilute expansions feature half-integer powers of the porosity, which can be correlated to the localized field patterns. Statistical characterizations of the fields, such as their first moments and their histograms are provided, with particular emphasis on the singularities of the latter. The behavior of the system near the void close packing fraction is also investigated. The results of this work shed light on corresponding results for strongly nonlinear porous media, which have been obtained recently by means of the ``second-order'' homogenization method, and where the dilute estimates also exhibit fractional powers of the porosity. (10.1016/j.jmps.2007.10.002)
  DOI : 10.1016/j.jmps.2007.10.002
• Mise en point d'un nouveau modèle de comportement élasto-viscoplastique. Application au dimensionnement à la fatigue d'un collecteur d'échappement de moteur diesel en fonte
  
  • Szmytka Fabien
  • Rémy Luc
  • Maitournam Habibou
  • Köster Alain
  • Bourgeois Myriam
  • Mac Lan Nguyen-Tajan T.
  , 2007, pp.8 p..
• Elasticity with Mathematica
  
  • Constantinescu Andrei
  • Korsunsky Alexander
  , 2007, pp.255. This book gives a an introduction to the key ideas and principles in the theory of elasticity with the help of symbolic computation. Differential and integral operators on vector and tensor fields of displacements, strains and stresses are considered on a consistent and rigorous basis with respect to curvilinear orthogonal coordinate systems. As a consequence, vector and tensor objects can be manipulated readily, and fundamental concepts can be illustrated and problems solved with ease. The method is illustrated using a variety of plane and three-dimensional elastic problems. General theorems, fundamental solutions, displacements and stress potentials are presented and discussed. The Rayleigh-Ritz method for obtaining approximate solutions is introduced for elastostatic and spectral analysis problems. The book contains more than 60 exercises and solutions in the form of Mathematica notebooks that accompany every chapter. Once the reader learns and masters the techniques, they can be applied to a large range of practical and fundamental problems. (10.1017/CBO9780511546167)
  DOI : 10.1017/CBO9780511546167
• Deep salt-cavern abandonment
  
  • Berest Pierre
  • Karimi-Jafari Mehdi
  • Brouard Benoît
  , 2007, pp.445-452.
• Equations intégrales en mécanique de la rupture: aspects théoriques et numériques
  
  • Bonnet Marc
  , 2007.