Publications

2003

• Linear stability analysis in fluid-structure interaction with transpiration. Part II: Numerical analysis and applications
  
  • Fernández Miguel Angel
  • Le Tallec Patrick
  Computer Methods in Applied Mechanics and Engineering, Elsevier, 2003, 192 (43), pp.4837-4873. This paper constitutes the numerical counterpart of the mathematical framework introduced in Part I. We address the problem of flutter analysis of a coupled fluid-structure system involving an incompressible Newtonian fluid and a reduced structure. We use the Linearization Principle approach developed in Part I, particularly suited for fluid-structure problems involving moving boundaries. Thus, the stability analysis is reduced to the computation of the leftmost eigenvalues of a coupled eigenproblem of minimal complexity. This eigenproblem involves the linearized incompressible Navier-Stokes equations and those of a reduced linear structure. The coupling is realized through specific transpiration interface conditions. The eigenproblem is discretized using a finite element approximation and its smallest real part eigenvalues are computed by combining a generalized Cayley transform and an implicit restarted Arnoldi method. Finally, we report three numerical experiments : a structure immersed in a fluid at rest, a cantilever pipe conveying a fluid flow and a rectangular bridge deck profile under wind effects. The numerical results are compared to former approaches and experimental data. The quality of these numerical results is very satisfactory and promising. (10.1016/j.cma.2003.08.001)
  DOI : 10.1016/j.cma.2003.08.001
• Peierls-Nabarro landscape for martensitic phase transitions
  
  • Truskinowsky Lev
  • Vainchtein Anna
  Physical Review B: Condensed Matter and Materials Physics (1998-2015), American Physical Society, 2003, 67 (17). We consider a prototypical model of a martensitic phase transition, which takes discreteness and nonlocality into account and allows one to reconstruct explicitly the Peierls-Nabarro energy landscape for the phase boundaries. We solve the discrete problem exactly and obtain a simple expression for the critical Peierls force that is necessary to release a lattice-trapped phase boundary. The model suggests specific relations between the microscopic parameters of the lattice and the size of the hysteresis in martensitic materials, which we verify for the cubic-$β'_1$-monoclinic phase transition in Cu-Al-Ni alloy. (10.1103/physrevb.67.172103)
  DOI : 10.1103/physrevb.67.172103
• A “Numerical Mesoscope” for the Investigation of Local Fields in Rate-Dependent Elastoplastic Materials at Finite Strain
  
  • Haddadi Halim
  • Teodosiu Cristian
  • Héraud S.
  • Allais L.
  • Zaoui André
  , 2001, 108, pp.311-320. We propose a “numerical mesoscope” which could be used for the analysis of the local mechanical fields over small critical areas of microheterogeneous materials, in order to predict the local initiation of specific deformation or damage mechanisms. The subdomain under investigation is embedded in a very large homogeneous matrix obeying the overall behavior of the studied material, as determined experimentally. This matrix is subjected to homogeneous stress or strain boundary conditions and the homogeneous elements of the subdomain and their interfaces are given their known or assumed constitutive behavior. A finite element analysis is then performed on the whole body by making use of different constitutive equations within the subdomain and in the surrounding matrix. The general methodology of this approach is reported and applied to a metallic rate-dependent elastoplastic polycrystal and to microheterogeneous subdomains consisting of given multicrystalline patterns whose grains obey crystalline elastoplastic constitutive equations of Schmid type at finite strain. Application to the intergranular creep damage of a stainless steel shows a good agreement between the largest computed normal stresses on the grain boundaries and the observed debonded boundaries of the actual material. (10.1007/978-94-017-0297-3_28)
  DOI : 10.1007/978-94-017-0297-3_28
• Remarques sur les contraintes résiduelles
  
  • Bérest Pierre
  • Vouille Gérard
  Comptes Rendus. Mécanique, Académie des sciences (Paris), 2003, 331 (6), pp.455-460. Les contraintes résiduelles observées dans les solides peuvent résulter de déformations initiales non compatibles. Elles sont alors déterminées, en général, par le tenseur d'incompatibilité du tenseur des déformations initiales. Toutefois, réciproquement, la nullité du tenseur d'incompatibilité ne suffit pas pour conclure à l'absence de contraintes résiduelles, dans le cas où le solide est non simplement connexe, ou présente des surfaces de discontinuité. Plusieurs exemples sont présentés. (10.1016/S1631-0721(03)00090-1)
  DOI : 10.1016/S1631-0721(03)00090-1
• Prise en compte de la rugosité dans le prévision de la tenue en fatigue des roulements
  
  • Thoquenne Guillaume
  • Lubrecht Ton
  • Dang Van Ky
  • Maitournam Habibou
  • Peyrac Catherine
  • Lieurade Henri-Paul
  , 2003.
• Testing with SHPB from quasi-static to dynamic strain rates
  
  • Othman Ramzi
  • Bussac Marie-Noëlle
  • Collet Pierre
  • Gary Gérard
  , 2003, 110, pp.397-404. We have developed a new method for separating dispersive waves in elastic and viscoelastic rods from three-point strain and one-point velocity measurements. Stress, strain, displacement and velocity, which were supposed to be homogenous in a rod section, were therefore determined at any point ofthe bar. This method is based on the assumption of a one dimensional and single mode dispersive wave propagation. This method was used in the frequency domain and took into account wave dispersion. It was shown to be stable with respect to noise. The measuring time is increased considerably. Subsequently, the maximum strain which can be measured in a material tested with a classical SHPB (Split Hopkinson Pressure Bar) set-up is also increased and is no more limited by the length of the bars. The method was used to evaluate the rate sensitivity ofaluminum honeycomb over a wide range ofstrain-rates (from 10 -2 to 1000 s -1). (10.1051/jp4:20020726)
  DOI : 10.1051/jp4:20020726
• Etude micromécanique de la disparition du seuil de fissuration par fatigue dans un alliage de titane biphasé à fort K_max
  
  • Mignot Frédéric
  • Doquet Véronique
  • Sarrazin-Baudoux Christine
  • Petit Jean
  Journal de Physique IV Proceedings, EDP Sciences, 2003, 106, pp.33-42. L'alliage Ti6246 présente, lors d'essais de fissuration par fatigue à K_max constant et ΔK décroissant un comportement atypique : lorsque K_max> 0.7K_IC, on observe, sous air comme sous vide, au lieu du seuil attendu, un régime de propagation à vitesse constante, dix fois plus élevée à l'ambiante qu'à 500°C. Le fluage, qui se manifeste dès l'ambiante dans cet alliage semble jouer un rôle dans ce phénomène. Toutefois, des analyses par spectrométrie de masse d'ions secondaires font apparaître une sur-concentration en hydrogène au voisinage d'une fissure développée dans le régime anormal. Des essais de fissuration, traction et fluage sont donc entrepris sur le matériau brut, appauvri ou enrichi en hydrogène, pour partie dans la chambre d'un microscope électronique à balayage, dans le but d'explorer ce phénomène. On constate qu'un enrichissement en hydrogène augmente la ductilité du matériau et sa tendance au fluage à l'ambiante et un enrichissement plus prononcé la diminue. (10.1051/jp4:20030213)
  DOI : 10.1051/jp4:20030213
• The treatment of 'pinching locking' in 3D-shell elements
  
  • Chapelle Dominique
  • Ferent Anca
  • Le Tallec Patrick
  ESAIM: Mathematical Modelling and Numerical Analysis, Société de Mathématiques Appliquées et Industrielles (SMAI) / EDP, 2003, 37 (1), pp.143-158. We consider a family of shell finite elements with quadratic displacements across the thickness. These elements are very attractive, but compared to standard general shell elements they face another source of numerical locking in addition to shear and membrane locking. This additional locking phenomenon - that we call ''pinching locking'' - is the subject of this paper and we analyse a numerical strategy designed to overcome this difficulty. Using a model problem in which only this specific source of locking is present, we are able to obtain error estimates independent of the thickness parameter, which shows that pinching locking is effectively treated. This is also confirmed by some numerical experiments of which we give an account. (10.1051/m2an:2003015)
  DOI : 10.1051/m2an:2003015
• Crystallographic fatigue crack growth in a polycrystal: simulations based on FEM and discrete dislocation dynamics
  
  • Bertolino Graciela
  • Doquet Véronique
  • Sauzay Maxime
  , 2003. An attempt to model the variability of short cracks development in high-cycle fatigue is made by coupling finite element calculations of the stresses ahead of a microcrack in a polycrystal with simulations of crack growth along slip planes based on discrete dislocations dynamics. The model predicts a large scatter in growth rates related to the roughness of the crack path. It also describes the influence of the mean grain size and the fact that overloads may suppress the endurance limit by allowing arrested cracks to cross the grain boundaries.
• Linear stability analysis in fluid-structure interaction with transpiration. Part I: Formulation and mathematical analysis
  
  • Fernández Miguel Angel
  • Le Tallec Patrick
  Computer Methods in Applied Mechanics and Engineering, Elsevier, 2003, 192 (43), pp.4805-4835,. The aim of this work is to provide a new Linearization Principle approach particularly suited for problems in fluid-structure stability. The complexity here, and the main difference with respect to the classical approach, comes from the fact that the full non-linear fluid equations are written in a moving (i.e. time dependent) domain. The underlying idea of our approach uses transpiration techniques [J. Fluid Mech. 4 (1958) 383 ; G. Mortchéléwicz, Application of linearized Euler equations to flutter, in : 85th AGARD SMP Meeting, Aalborg, Denmark, 1997 ; P. Raj, B. Harris, Using surface transpiration with an Euler method for cost-effective aerodynamic analysis, in : AIAA 24th Applied Aerodynamics Conference, number 93-3506, Monterey, Canada, 1993 ; AIAA 27(6) (1989) 777], with the formalization and linearization recently developed in [Rév. Européenne Élém. Finis, 9(6-7) (2000) 681, A. Dervieux (Ed.), Fluid-Structure Interaction, Kogan Page Science, London, 2003 (Chapter 3)]. This allows us to obtain a new grid independent coupled spectral problem involving the linearized Navier-Stokes equations and those of a reduced linear structure. The coupling is realized through specific transpiration conditions acting on a fixed interface, while keeping a fixed fluid domain. We provide a rigorous mathematical treatment of this eigenproblem. We prove that the corresponding eigenmodes, characterizing the free evolution of the system, can be obtained from the characteristic values of a compact operator acting on a Hilbert space. Moreover, we localize the eigenfrequencies of the system in a parabolic region of the complex plan centered along the positive real axis. (10.1016/j.cma.2003.07.001)
  DOI : 10.1016/j.cma.2003.07.001
• Planar crack identification for the transient heat equation
  
  • Ben Abda A.
  • Bui Huy Duong
  Journal of Inverse and Ill-posed Problems, De Gruyter, 2003, 11, pp.27-31. We consider the inverse problem of crack determination related to the non-destructive thermal testing of materials process. Using arbitrary transient heat flux applied to the external boundary and measuring the induced planar cracks. (10.1515/156939403322004919)
  DOI : 10.1515/156939403322004919
• On the stress-wave imaging of cavities in a semi-infinite solid
  
  • Guzina B. B.
  • Nintcheu Fata S.
  • Bonnet Marc
  International Journal of Solids and Structures, Elsevier, 2003, 40, pp.1505-1523. The problem of mapping underground cavities from surface seismic measurements is investigated within the framework of a regularized boundary integral equation (BIE) method. With the ground modeled as a uniform elastic half-space, the inverse analysis of elastic waves scattered by a three-dimensional void is formulated as a task of minimizing the misfit between experimental observations and theoretical predictions for an assumed void geometry. For an accurate treatment of the gradient search technique employed to solve the inverse problem, sensitivities of the predictive BIE model with respect to cavity parameters are evaluated semi-analytically using an adjoint problem approach and a continuum kinematics description. Several key features of the formulation, including the rigorous treatment of the radiation condition for semi-infinite solids, modeling of an illuminating seismic wave field, and treatment of the prior information, are highlighted. A set of numerical examples with spherical and ellipsoidal cavity geometries is included to illustrate the performance of the method. It is shown that the featured adjoint problem approach reduces the computational requirements by an order of magnitude relative to conventional finite-difference estimates, thus rendering the three-dimensional elastic-wave imaging of solids tractable for engineering applications. (10.1016/S0020-7683(02)00650-9)
  DOI : 10.1016/S0020-7683(02)00650-9
• Fissuration par fatigue d'un acier pour application ferroviaire: effet synérgétique des modes d'ouverture et de cisaillement sous chargement séquentiel
  
  • Doquet V.
  • Pommier S.
  , 2003. No abstract provided
• Identification numérique des fissures planes en élastodynamique
  
  • Bui Huy Duong
  • Constantinescu Andrei
  • Maigre Hubert
  , 2003, 1, pp.201-208.
• Modélisation de la fatigue des matériaux à mémoire de forme
  
  • Moumni Ziad
  • Maitournam Habibou
  • Dang Van Ky
  , 2003, 1, pp.413-419.
• Analytical methods for dynamic response of underground structures
  
  • Kurose A.
  • Bérest P.
  • Brouard B.
  , 2003, pp.263-276 (tome 1). No abstract provided
• An example of stick-slip and stick-slip-separation waves
  
  • Moirot Franck
  • Son Nguyen Quoc
  • Oueslati Abdelbacet
  European Journal of Mechanics - A/Solids, Elsevier, 2003, 22, pp.107-118. The dynamical problem of a brake-like mechanical system composed of an elastic cylindrical tube with Coulomb's friction in contact with a rigid and rotating cylinder is considered. This model problem enables us to give an example of non-trivial periodic solutions in the form of stick-slip or stick-slip-separation waves propagating on the contact surface. A semi-analytical analysis of stick-slip waves is obtained when the system of governing equations is reduced by condensation to a simpler system involving only the contact displacements. This reduced system, of only one space variable in addition to time, can be solved almost analytically and gives some interesting informations on the existence and the characteristics of stick-slip waves such as the wave numbers on the circumference, stick and slip proportions, wave celerities, tangential and normal forces. It is shown in particular that the stick-slip-separation solutions would occur for small normal pressures or high rotational speeds. Since the analytical discussion becomes cumbersome in this case, a second approach based on numerical analysis by the finite element method is performed. The existence and the characteristics of stick-slip and stick-slip-separation waves are discussed numerically.
• Optimal dip based on dissipation of backthrusts and hinges in fold-and-thrust belts
  
  • Maillot Bertrand
  • Leroy Yves
  Journal of Geophysical Research : Solid Earth, American Geophysical Union, 2003, 108 (B6), pp.2320. Back thrusts and hinges are two types of transition between rigid sections of hanging walls observed in fold‐and‐thrust belts. Back thrusts are typical of frictional and homogeneous solids and hinges of creeping and layered materials. Our objective is to study the orientation of these transitions for the special case of a lower flat‐ramp transition in a fault‐bend fold with the following general two‐step methodology. In the first step, the forces acting on the transition are determined using equilibrium of each rigid section. In the second step, the optimal dip of the transition is obtained by minimizing the total dissipation of the structure. The three sources of dissipation, of comparable magnitude, are at the transition, on the flat, and on the ramp. For frictional material flows, the back thrusts are velocity discontinuities with optimal dips always less than half the complementary ramp angle, leading to hanging wall thickening. The optimal dip agrees well with the results of physical analogue and numerical experiments. For creeping and layered materials, it is shown that a destabilizing deformation mechanism, selected to be flexural slip, is necessary for the strain to localize and the existence of hinges to be justified. Activation of flexural slip reduces dissipation at the transition and affects the optimal transition dip. The two‐step methodology proposed here could be seen as a first attempt in producing mechanically balanced cross sections accounting for material rheology. This approach should complement the now classical kinematic models of folding. (10.1029/2002JB002199)
  DOI : 10.1029/2002JB002199
• Modeling the dynamics of piano keys
  
  • Brenon Céline
  • Boutillon Xavier
  , 2003. The models of piano keys available in the literature are crude: two degrees of freedom and a very few dynamical or geometrical parameters. Experiments on different piano mechanisms (upright, grand, one type of numerical keyboard) exhibit strong differences in the two successive phases of the key motion which are controlled by the finger. Understanding the controllability of the escapement velocity (typically a few percents for professional pianists), the differences between upright and grand pianos, the rationale for the numerous independent adjustments by technicians, and the feel by the pianist require sophisticated modeling. In addition to the inertia of the six independently moving parts of a grand piano mechanism, a careful modeling of friction at pivots and between the jack and the roll, of damping and nonlinearities in felts, and of internal springs will be presented. Simulations will be confronted to the measurements of the motions of the different parts. Currently, the first phase of the motion and the transition to the second phase are well understood while some progress must still be made in order to describe correctly this short but important phase before the escapement of the hammer. [Work done in part at the Laboratory for Musical Acoustics, Paris.] (10.1121/1.4777652)
  DOI : 10.1121/1.4777652
• Numerical and experimental modal analysis of the reed and pipe of a clarinet
  
  • Facchinetti Matteo
  • Boutillon Xavier
  • Constantinescu Andrei
  Journal of the Acoustical Society of America, Acoustical Society of America, 2003, 113 (5), pp.2874-2883. A modal computation of a complete clarinet is presented by the association of finite-elementmodels of the reed and of part of the pipe with a lumped-element model of the rest of the pipe. In the first part, we compare modal computations of the reed and the air inside the mouthpiece and barrel with measurements performed by holographic interferometry. In the second part, the complete clarinet is modeled by adjoining a series of lumped elements for the remaining part of the pipe. The parameters of the lumped-resonator model are determined from acoustic impedance measurements. Computed eigenmodes of the whole system show that modal patterns of the reed differ significantly whether it is alone or coupled to air. Some modes exhibit mostly reed motion and a small contribution of the acoustic pressure inside the pipe. Resonance frequencies measured on a clarinet with the mouthpiece replaced by the cylinder of equal volume differ significantly from the computed eigenfrequencies of the clarinet taking the actual shape of the mouthpiece into account and from those including the (linear) dynamics of the reed. This suggests revisiting the customary quality index based on the alignment of the peaks of the input acoustical impedance curve. (10.1121/1.1560212)
  DOI : 10.1121/1.1560212
• Identification of rock mass properties in elasto-plasticity
  
  • Deng D.
  • Nguyen Minh D.
  Computers and Geotechnics, Elsevier, 2003, 30, pp.27-40. A simple and effective back analysis method has been proposed on the basis of a new criterion of identification, the minimization of error on the virtual work principle. This method works for both linear elastic and nonlinear elasto-plastic problems. The elasto-plastic rock mass properties for different criteria of plasticity can be well identified based on field measurements. (10.1016/S0266-352X(02)00033-2)
  DOI : 10.1016/S0266-352X(02)00033-2
• Micro-mechanical modelling of small and large strain behaviour of particulate nanocomposites
  
  • Chabert Emmanuelle
  • Bornert Michel
  • Cavaillé Jean-Yves
  • Dendievel Rémy
  • Gauthier Catherine
  • Zaoui André
  , 2003, pp.75-78. This work presents experimental results and micro-mechanical modelling of the small and large strain behaviour of particulate nanocomposites consisting of a soft polymeric matrix filled with rigid submicronic (either PS or silica) inclusions. The small strain properties appeared to be governed by filler-filler interactions as soon as a percolating filler network is developed (> 20%). To account for these observations, a discrete simulation which takes into account the nature of contact between reinforcing particles has been developed. However, the large strain properties can be correctly modelled by means of homogenisation techniques, suggesting that the filler network is broken very soon. INTRODUCTION Nanocomposite materials consist of a nanometer-scale phase in combination with another phase acting as a matrix. Work about polymer nanocomposites has exploded over the last few years. Their properties are reported to be different from that of their micro-scale counterparts 1,2. These unusual properties may be a consequence of (i) the extremely high interfacial specific area which can reach 100-1000 m 2 /g and (ii) the very short average distance between reinforcing fillers (about 10-8 m), down to a value comparable with the macromolecule coils. This can favor the short-distance filler-filler interactions leading, above a critical volume, to the formation of a network (percolation). Though significant progress has been made in developing nanocomposites with different polymer matrices, a general understanding has yet to emerge. A major challenge to further development of nanocomposites is the development of specific micro-mechanical models.
• Etude expérimentale des micro-mécanismes d'endommagement et de rupture des zircaloys hydrurés
  
  • Racine A.
  • Bornert Michel
  • Sainte-Catherine C.
  • Caldemaison D.
  Journal de Physique IV Proceedings, EDP Sciences, 2003, 106, pp.109-118. Afin de mieux comprendre les mécanismes d'endommagement et de rupture des Zircaloy, des essais de traction sur anneaux ont été réalisés in-situ sous MEB sur des éprouvettes de tube de gainage de combustible, contenant environ 150 ppm d'hydrogène et avec différentes orientations d'hydrures : de circonférentielle à radiale. Ces essais ont mis en évidence deux modes de rupture selon l'orientation des hydrures. Les éprouvettes avec hydrures radiaux (perpendiculaires à la sollicitation) rompent brutalement par propagation d'une fissure suivant un chemin d'hydrures radiaux alignés. Les niveaux de déformation au voisinage de la fissure, estimés par des techniques de micro-électrolithographie associées à celle d'analyse par corrélation d'images, sont très faibles, de l'ordre du %. En revanche, dans celles avec hydrures circonférentiels (suivant l'axe de sollicitation), les effets de structure prédominent : des bandes de cisaillement macroscopique apparaissent, dans lesquelles la déformation se localise. En dehors de ces zones de localisation intense, la déformation reste inférieure à 10% et très peu d'endommagement par germination de cavités ou fissuration d'hydrures a été observé. Les hétérogénéités du champ local de déformation, corrélées à la présence des hydrures, semblent établir l'influence de ceux-ci sur le mode de déformation local, mais ces observations nécessitent d'être confirmées. (10.1051/jp4:20030221)
  DOI : 10.1051/jp4:20030221
• Materially Nonlinear Analysis
  
  • Bonnet Marc
  , 2003, pp.55-114. This chapter presents a review of domain-boundary element techniques for solving materially nonlinear solid mechanics problems. Quasi-static and dynamic formulations are addressed, with emphasis on the use of implicit constitutive integration techniques and the local and global consistent tangent operators. Symmetric Galerkin BEM formulations are also presented. A section is devoted to steady-state elastoplastic calculations for moving loads, and another to the simulation of abrasive wear, both types of nonlinear analyses being well-suited to D/BEM treatments. Another section deals with energy methods in fracture mechanics. Finally, a symmetric formulation for BEM-FEM coupling is presented as another way to use BEM, this time combined with FEM, for materially nonlinear analyses. (10.1007/978-3-7091-2790-2_2)
  DOI : 10.1007/978-3-7091-2790-2_2
• A procedure for identifying the plastic behaviour of single crystals from the local response of polycrystals
  
  • Hoc Thierry
  • Crépin Jérôme
  • Gélébart Lionel
  • Zaoui André
  Acta Materialia, Elsevier, 2003, 51, pp.5479-5490. The overall and local tensile responses of an α iron multicrystalline sample are investigated in order to derive the plastic constitutive equations for the constituent single crystals. The macroscopic stress–strain curve and some statistical characteristics of the strain field measured on the sample surface are compared with their simulated counterparts. The optimal values of the material parameters of four types of hardening laws are derived by a minimization procedure. The best results are obtained with a nonlinear anisotropic law which uses the dislocation densities on the slip systems. This procedure is then validated on a fine-grained polycrystalline sample of a similar material by using the measured displacement field on the edge of a selected area as boundary conditions for finite element method (FEM) computation. The resulting optimal material parameters for the single crystal are found to be consistent with the values available in the literature, and the whole simulated strain fields as well as the evolution of the crystallographic texture, is compared satisfactorily with the experimental data. (10.1016/S1359-6454(03)00413-0)
  DOI : 10.1016/S1359-6454(03)00413-0