Publications

2010

• Very slow creep tests on salt samples
  
  • Bérest Pierre
  • Béraud Jean-François
  • Brouard Benoit
  • Blum Pierre-Antoine
  • Charpentier Jean-Pierre
  • Greef Vincent De
  • Gharbi Hakim
  • Valès Frédéric
  EPJ Web of Conferences, EDP Sciences, 2010, 6. Long-term creep tests have been performed on rock-salt and argillite samples under very small uniaxial loadings (σ = 0.02 to 0.1 MPa) . To minimize the effects of temperature variations, testing devices were set in a mine where temperature fluctuations are of the order of one-hundredth of a degree Celsius. The mechanical loading was provided by dead weights. The deformations were measured through special displacement sensors with a resolution of ∆ε = 10-8. Strain rates as small as έ = 7 × 10-13s-1 were measured. These tests allow rock-sample creep to be investigated at very small strain rates. The tests also prove that extrapolation of constitutive laws at very small rates is often incorrect. (10.1051/epjconf/20100622002)
  DOI : 10.1051/epjconf/20100622002
• On the stick-slip waves under unilateral contact and Coulomb friction
  
  • Bui Hui Duong
  • Oueslati Abdelbacet
  Annals of Solid and Structural Mechanics, Springer Berlin Heidelberg, 2010, 1 (3-4), pp.159-172. In this paper, the construction of analytic solution of stick-slip waves propagating along the interface between an elastic half-space and a moving rigid one is investigated. The contact between the solids is governed by unilateral constraints and Coulomb friction law and the deformable body is loaded by remote uniform stresses t*yy<0, t*xy>0. The method of solution is based on the continuation of Radok's complex potentials within the framework of steady state elastodynamical problems. The governing equation combined with the boundary conditions are reduced to a Riemann-Hilbert problem with discontinuous coefficient. This approach for the stick-slip study is novel and differs from those in the literature, namely the series method and the Weertmann's dislocation formulation. We present the closed form solution of the Riemann-Hilbert problem and show that the principal unknowns are of number two: the wave celerity and the ratio of the slip length by the stick one. The considered loading introduces an additional velocity V* related to the elongation e*xx due to the normal stress t*yy. We show that if V* vanishes there is no solution. When V* is taken into account, it is possible to construct weakly singular solutions satisfying all stick-slip conditions except over a narrow zone at transition points: The shear stress is singular over a small zone and the normal stress exhibits a positive singularity over a very small zone in the slip region which implies a separation near the singular transition. (10.1007/s12356-010-0012-2)
  DOI : 10.1007/s12356-010-0012-2
• Weak variations of Lipschitz graphs and stability of phase boundaries
  
  • Grabovsky Yury
  • Kucher Vladislav
  • Truskinovsky Lev
  Cont. Mech. Therm., 2010, 23, pp.87-123. In the case of Lipschitz extremals of vectorial variational problems, an important class of strong variations originates from smooth deformations of the corresponding non-smooth graphs. These seemingly singular variations, which can be viewed as combinations of weak inner and outer variations, produce directions of differentiability of the functional and lead to singularity-centered necessary conditions on strong local minima: an equality, arising from stationarity, and an inequality, implying configurational stability of the singularity set. To illustrate the underlying coupling between inner and outer variations, we study in detail the case of smooth surfaces of gradient discontinuity representing, for instance, martensitic phase boundaries in non-linear elasticity. (10.1007/s00161-010-0171-8)
  DOI : 10.1007/s00161-010-0171-8
• Special Issue of European Journal of Computational Mechanics, vol 19, N° 1-2-3
  
  • Rey Christian
  • Raous Michel
  • Pasquet Philippe
  • Bonnet Marc
  • Feyel Frédéric
  , 2010, pp.328.
• Evaluation of Associated and Non-associated Quadratic Plasticity Models For Advanced High Strength Steel Sheets under Multi-axial Loading
  
  • Mohr Dirk
  • Dunand M.
  • Kim K.-H.
  International Journal of Plasticity, Elsevier, 2010, 26 (7), pp.939-956.
• A 3D finite element model for the vibration analysis of asymmetric rotating machines
  
  • Lazarus Arnaud
  • Prabel Benoit
  • Combescure Didier
  Journal of Sound and Vibration, Elsevier, 2010, 329. This paper suggests a 3D finite element method based on the modal theory in order to analyse linear periodically time-varying systems. Presentation of the method is given through the particular case of asymmetric rotating machines. First, Hill governing equations of asymmetric rotating oscillators with two degrees of freedom are investigated. These differential equations with periodic coefficients are solved with classic Floquet theory leading to parametric quasimodes. These mathematical entities are found to have the same fundamental properties as classic eigenmodes, but contain several harmonics possibly responsible for parametric instabilities. Extension to the vibration analysis (stability, frequency spectrum) of asymmetric rotating machines with multiple degrees of freedom is achieved with a fully 3D finite element model including stator and rotor coupling. Due to Hill expansion, the usual degrees of freedom are duplicated and associated with the relevant harmonic of the Floquet solutions in the frequency domain. Parametric quasimodes as well as steady-state response of the whole system are ingeniously computed with a component-mode synthesis method. Finally, experimental investigations are performed on a test rig composed of an asymmetric rotor running on nonisotropic supports. Numerical and experimental results are compared to highlight the potential of the numerical method. (10.1016/j.jsv.2010.03.029)
  DOI : 10.1016/j.jsv.2010.03.029
• Milieux Continus en transformations finies : Hyperélasticité, Rupture, Elastoplasticité
  
  • Stolz Claude
  , 2010, pp.1-270. L'ouvrage propose une introduction à la mécanique des milieux continus en transformations finies. Les premiers chapitres étudient les aspects cinématiques et statiques de la mécanique des milieux continus et donnent un éclairage sur les notions de transport des quantités mécaniques en suivant le mouvement de la matière. On analyse le cas des matériaux hyperélastiques incompressibles, dont les applications industrielles sont nombreuses. Cette modélisation des polymères est développée selon plusieurs aspects : une introduction statistique du comportement à partir de chaînes de monomères, puis une étude de l'équilibre du corps hyperélastique. L'introduction de la classe des déformations universelles éclaire les couplages non linéaires dus au comportement d'une part et à la géométrie d'autre part. L'étude et les conditions d'unicité de la réponse à un trajet d'équilibre sont présentées dans une approche de stabilité bifurcation. Les coques et membranes élastiques sont abordées succinctement et montre la multiplicité des modèles de description de la cinématique et de la statique de ces objets. La mécanique de la rupture en transformations finies est abordée selon deux points de vue : d'une part l'analyse des singularités potentielles en front de fissure, avec comme illustration la rupture en mode antiplan, et d'autre part au travers une modélisation d'un endommagement local de la matière défini par une élongation limite critique. Les problèmes d'évolution d'un ensemble de fissures ou de zones endommagées sont analysés. Enfin, les lois de comportement élastoplastiques sont décrites après avoir introduit la cinématique du monocristal. La loi de comportement du polycristal est alors étudiée dans une approche macroscopique utilisant la notion de configuration relâchée. Cette approche est justifiée par l'établissement de relations entre les grandeurs microscopiques, celles du monocristal, et macroscopiques. Enfin, la formulation du problème d'évolution obtenue permet d'étendre au cas élastoplastique les arguments utilisés en hyperélasticité pour l'étude de l'évolution d'un système de fissures. Quelques annexes apportent des compléments de modélisation pour les chargements thermomécaniques et cycliques, par l'introduction d'orientations privilégiées et l'existence d'élongations limites.
• Diffusion in Pyroxenes, Mica and Amphibole
  
  • Cherniak Daniele J
  • Dimanov Alexandre
  , 2010, 72 (1), pp.641-690. This chapter presents an overview of diffusion data for pyroxenes, amphiboles and micas. These minerals are grouped together since amphiboles and micas are closely related in structure to pyroxenes, with amphiboles essentially constructed of alternating layers with structures of mica and pyroxene. We begin with discussion of diffusion in pyroxenes, for which an extensive literature exists, with diffusion studies of major, minor and trace elements. We consider diffusion mechanisms in light of present understanding of defect chemistry, and discuss various crystal-chemical factors that may affect cation diffusion. The last section of the chapter presents a review of diffusion data for amphiboles and micas. Selected Arrhenius relations for these all these mineral phases are summarized in the Appendix Tables A1, A2, A3 and A4. This chapter focuses primarily on cation diffusion, since oxygen, hydrogen and noble gas diffusion are discussed in other chapters; readers interested in more detailed discussion of diffusion of these species in pyroxene, amphibole and mica are directed to Chapters 10 (Farver 2010, this volume) and 11 (Baxter 2010, this volume). (10.2138/rmg.2010.72.14)
  DOI : 10.2138/rmg.2010.72.14
• Inverse Problems
  
  • Bonnet Marc
  , 2010.
• Identification of a planar crack in Zener type viscoelasticity
  
  • Bui Hui Duong
  • Chaillat Stéphanie
  • Constantinescu Andrei
  • Grasso Eva
  Annals of Solid and Structural Mechanics, Springer Berlin Heidelberg, 2010, 1 (1), pp.3-8. The paper addresses the identification of a planar crack for Zener type linear viscoelastic solids. Under the condition of low frequency, the Zener model of viscoelasticity establishes the equivalence between viscoelasticity and elasticity and the equations are reduced to a Helmholtz type problem for time harmonic loadings. The solutions to the crack identification problems are then obtained from the corresponding solutions in elasticity, using only one frequency. (10.1007/s12356-009-0003-3)
  DOI : 10.1007/s12356-009-0003-3
• On the application of the Fast Multipole Method to Helmholtz-like problems with complex wavenumber
  
  • Frangi Attilio
  • Bonnet Marc
  Computer Modeling in Engineering and Sciences, Tech Science Press, 2010, 58, pp.271-296. This paper presents an empirical study of the accuracy of multipole expansions of Helmholtz-like kernels with complex wavenumbers of the form $k=(\alpha+\beta)\vartheta$, with $\alpha=0,\pm1$ and $\beta>0$, which, the paucity of available studies notwithstanding, arise for a wealth of different physical problems. It is suggested that a simple point-wise error indicator can provide an a priori indication on the number $N$ of terms to be employed in the Gegenbauer addition formula in order to achieve a prescribed accuracy when integrating single layer potentials over surfaces. For $\beta\geq 1$ it is observed that the value of $N$ is independent of $\beta$ and of the size of the octree cells employed while, for $\beta<1$, simple empirical formulas are proposed yielding the required $N$ in terms of $\beta$. (10.3970/cmes.2010.058.271)
  DOI : 10.3970/cmes.2010.058.271
• Beyond kinetic relations
  
  • Vainchtein Anna
  • Truskinovsky Lev
  Cont. Mech. Therm., 2010, 22, pp.485-504. We introduce the concept of kinetic or rate equations for moving defects representing a natural extension of the more conventional notion of a kinetic relation. Algebraic kinetic relations, widely used to model dynamics of dislocations, cracks and phase boundaries, link the instantaneous value of the velocity of a defect with an instantaneous value of the driving force. The new approach generalizes kinetic relations by implying a relation between the velocity and the driving force which is nonlocal in time. To make this relation explicit one may need to integrate a system of kinetic equations. We illustrate the difference between kinetic relation and kinetic equations by working out in full detail a prototypical model of an overdamped defect in a one-dimensional discrete lattice. We show that the minimal nonlocal kinetic description, containing now an internal time scale, is furnished by a system of two ordinary differential equations coupling the spatial location of defect with another internal parameter that describes configuration of the core region. (10.1007/s00161-010-0167-4)
  DOI : 10.1007/s00161-010-0167-4
• Identifying constitutive parameters from full-field measurements: a challenging issue in computational mechanics
  
  • Grediac Michel
  • Bonnet Marc
  , 2010.
• L'effondrement de 1873 à la mine de Varangéville
  
  • Berest Pierre
  • Bérest P.
  • Karimi-Jafari Mehdi
  • Brouard Benoît
  • Feuga Bernard
  Revue française de Géotechnique, edp sciences, 2010 (131-132), pp.105-118. On relate l’effondrement d’un quartier de la mine de sel de Varangéville survenu en 1873. Les descriptions de l’époque montrent que la partie centrale du recouvrement de la mine est descendue en bloc, entraînant une couronne intensément déformée. Les piliers ont poinçonné précocement le mur imbibé de saumure, mais le toit les a retenus tant que l’extension de la mine, et donc sa raideur à la flexion restaient modérées. Le calcul numérique montre que le caractère brutal de l’effondrement peut être relié au développement d’une zone dilatante, traversant toute la couche de sel, et engendrée par le report sur le contour de la mine d’une part du poids des terrains surincombants. (10.1051/geotech/2010131105)
  DOI : 10.1051/geotech/2010131105
• Fracture Mechanics
  
  • Bui Huy Duong
  , 2010, pp.400.
• Multi-scale viscoplastic behavior of Halite : In-situ SEM full field measurements, a micromechanical approach
  
  • Bourcier M.
  • Dimanov A.
  • Héripré E.
  • Bornert Michel
  • Raphanel J.
  , 2010.
• High temperature rheology of synthetic two−phase gabbroic aggregates: microstructural heterogeneities and local deformation mechanism
  
  • Raphanel Jean
  • Dimanov Alexandre
  • Nazarova L.A.
  • Nazarov L.A.
  • Artemova A.I.
  Fiziko-Tekhnicheskie Problemy Razrabotki Poleznykh Iskopaemykh / Journal of Mining Science, Springer Verlag, 2010, 46 (5), pp.495-502. The high-temperature rheology of heterogeneous anorthite — diopside aggregates has been investigated numerically, in support to experimental data obtained by triaxial torsion tests, performed at high pressure (400 MPa) and temperature (1150° C). The mechanical data exhibited linear viscous flow. Accordingly, scanning electron microscopy revealed grain sliding mechanisms, but also crystal slip plasticity, recrystallization and micro-fracturing. Finite element computations at the aggregate scale aimed at the understanding of the sequence of active mechanisms and their link to the macroscopic behavior. For instance, we show that the presence of coarser and stronger diopside inclusions in weaker and fine grained anorthite matrix results in very heterogeneous local stress fields, allowing for the activation of multiple deformation mechanisms. Our study indicates that shear zones in the lower crust should be dominated by Newtonian rheology in relation with grain sliding mechanisms, even though complementary accommodation mechanisms such as crystal plasticity and damage may be necessary at the local scale, due to the heterogeneous microstructures. (10.1007/s10913-010-0062-1)
  DOI : 10.1007/s10913-010-0062-1
• Vortex-induced vibration of a square cylinder in wind tunnel
  
  • Amandolèse Xavier
  • Hémon Pascal
  Comptes Rendus. Mécanique, Académie des sciences (Paris), 2010, 338 (1), pp.12-17. An experimental study of the vortex-induced-vibration of a flexibly mounted rigid square cylinder in a uniform airflow is presented. For this high mass ratio configuration, transverse oscillations are measured in detail for reduced velocities ranging from 5 to 20. In the lock-in region and starting from rest, the cylinder motion exhibits a transient regime followed by a limit cycle oscillation regime. New experimental data are provided in term of amplitudes and frequencies of the limit cycle oscillations. The transient behaviour is also characterized by measuring the growth rate of the oscillations amplitude. © 2009 Académie des sciences. (10.1016/j.crme.2009.12.001)
  DOI : 10.1016/j.crme.2009.12.001
• Symmetric FEM-driven BEM-FEM coupling for 3D linear fracture mechanics
  
  • Hu Heng
  • Chambon Laurent
  • Crozes Damien
  • Frangi A.
  • Bonnet Marc
  , 2010. see pdf file
• Topological sensitivity of energy cost functional for wave-based defect identication
  
  • Bonnet Marc
  Comptes Rendus. Mécanique, Académie des sciences (Paris), 2010, 338, pp.377-389. This article is concerned with establishing the topological sensitivity (TS) against the nucleation of small trial inclusions of an energy-like cost function. The latter measures the discrepancy between two time-harmonic elastodynamic states (respectively defined, for cases where overdetermined boundary data is available for identification purposes, in terms of Dirichlet or Neumann boundary data for the same reference solid) as the strain energy of their difference. Such cost function constitutes a particular form of error in constitutive relation and may be used for e.g. defect identification. The TS is expressed in terms of four elastodynamic fields, namely the free and adjoint solutions for Dirichlet or Neumann data. A similar result is also given for the linear acoustic scalar case. A synthetic numerical example where the TS result is used for the qualitative identification of an inclusion is presented for a simple 2D acoustic configuration. (10.1016/j.crme.2010.07.016)
  DOI : 10.1016/j.crme.2010.07.016
• New flow rules in elasto-viscoplastic constitutive models for spheroidal graphite cast-iron
  
  • Szmytka Fabien
  • Rémy Luc
  • Maitournam Habibou
  • Köster Alain
  • Bourgeois Myriam
  International Journal of Plasticity, Elsevier, 2010, 26, pp.905-924. A specific flow rules and the corresponding constitutive elasto-viscoplastic model combined with new experimental strategy are introduced in order to represent a spheroidal graphite cast-iron behaviour on a wide range of strain, strain rate and temperature. A “full model” is first proposed to correctly reproduce the alloy behaviour even for very small strain levels. A “light model” with a bit poorer experimental agreement but a simpler formulation is also proposed. These macroscopic models, whose equations are based on physical phenomena observed at the dislocation scale, are able to cope with the various load conditions tested – progressive straining and cyclic hardening tests – and to correctly describe anisothermal evolution. The accuracy of these two models and the experimental databases to which they are linked is estimated on different types of experimental tests and compared with the accuracy of more standard Chaboche-type constitutive models. Each test leads to the superiority of the “full model”, particularly for slow strain rates regimes. After developing a material user subroutine, FEM simulations are performed on Abaqus for a car engine exhaust manifold and confirm the good results obtained from the experimental basis. We obtain more accurate results than those given by more traditional laws. A very good correlation is observed between the simulations and the engine bench tests. (10.1016/j.ijplas.2009.11.007)
  DOI : 10.1016/j.ijplas.2009.11.007
• On the existence and uniqueness of a solution to the interior transmission problem for piecewise-homogeneous solids
  
  • Bellis Cédric
  • Guzina B. B.
  Journal of Elasticity, Springer Verlag, 2010, pp.in press. The interior transmission problem (ITP), which plays a fundamental role in inverse scattering theories involving penetrable defects, is investigated within the framework of mechanical waves scattered by piecewise-homogeneous, elastic or viscoelastic obstacles in a likewise heterogeneous background solid. For generality, the obstacle is allowed to be multiply connected, having both penetrable components (inclusions) and impenetrable parts (cavities). A variational formulation is employed to establish \emph{sufficient} conditions for the existence and uniqueness of a solution to the ITP, provided that the excitation frequency does not belong to (at most) countable spectrum of transmission eigenvalues. The featured sufficient conditions, expressed in terms of the mass density and elasticity parameters of the problem, represent an advancement over earlier works on the subject in that i) they pose a precise, previously unavailable provision for the well-posedness of the ITP in situations when both the obstacle and the background solid are heterogeneous, and ii) they are dimensionally consistent i.e. invariant under the choice of physical units. For the case of a viscoelastic scatterer in an elastic solid it is further shown, consistent with earlier studies in acoustics, electromagnetism, and elasticity that the uniqueness of a solution to the ITP is maintained irrespective of the vibration frequency. When applied to the situation where \emph{both} the scatterer and the background medium are viscoelastic i.e. dissipative, on the other hand, the same type of analysis shows that the analogous claim of uniqueness does not hold. Physically, such anomalous behavior of the ``viscoelastic-viscoelastic'' case (that has eluded previous studies) has its origins in a lesser known fact that the homogeneous ITP is not mechanically insulated from its surroundings -- a feature that is particularly cloaked in situations when either the background medium or the scatterer are dissipative. A set of numerical results, computed for ITP configurations that meet the sufficient conditions for the existence of a solution, is included to illustrate the problem. Consistent with the preceding analysis, the results indicate that the set of transmission values is indeed empty in the ``elastic-viscoelastic'' case, and countable for ``elastic-elastic'' and ``viscoelastic-viscoelastic'' configurations.
• A FEM-based topological sensitivity approach for fast qualitative identification of buried cavities from elastodynamic overdetermined boundary data
  
  • Bellis Cédric
  • Bonnet Marc
  International Journal of Solids and Structures, Elsevier, 2010, 47, pp.1221-1242. A time-domain topological sensitivity (TS) approach is developed for elastic-wave imaging of media of arbitrary geometry. The TS, which quantifies the sensitivity of the misfit cost functional to the creation at a specified location of an infinitesimal hole, is expressed in terms of the time convolution of the free field and a supplementary adjoint field as a function of that specified location. Following previous studies performed under (mostly) static or time-harmonic conditions, the TS field is here considered as a natural and computationally efficient approach for defining a defect indicator function. This study emphasizes the implementation and exploitation of TS fields using standard displacement-based FEM approaches, a straightforward task once the correct sensitivity formulation is available. A comprehensive set of numerical experiments on 3-D and 2-D elastodynamic and acoustic configurations is reported, allowing to assess and highlight many features of the proposed TS-based fast qualitative identification such as its ability to identify multiple defects and its robustness against data noise. (10.1016/j.ijsolstr.2010.01.011)
  DOI : 10.1016/j.ijsolstr.2010.01.011
• 1-D non-periodic homogenization for the seismic wave equation
  
  • Capdeville Yann
  • Guillot Laurent
  • Marigo Jean-Jacques
  Geophysical Journal International, Oxford University Press (OUP), 2010, 181 (2), pp.897-910. When considering numerical acoustic or elastic wave propagation in media containing small heterogeneities with respect to the minimum wavelength of the wavefield, being able to upscale physical properties (or homogenize them) is valuable mainly for two reasons. First, replacing the original discontinuous and very heterogeneous medium by a smooth and more simple one, is a judicious alternative to the necessary fine and difficult meshing of the original medium required by many wave equation solvers. Second, it helps to understand what properties of a medium are really ‘seen' by the wavefield propagating through, which is an important aspect in an inverse problem approach. This paper is an attempt of a pedagogical introduction to non-periodic homogenization in 1-D, allowing to find the effective wave equation and effective physical properties, of the elastodynamics equation in a highly heterogeneous medium. It can be extrapolated from 1-D to a higher space dimensions. This development can be seen as an extension of the classical two-scale homogenization theory applied to the elastic wave equation in periodic media, with this limitation that it does not hold beyond order 1 in the asymptotic expansion involved in the classical theory. (10.1111/j.1365-246X.2010.04529.x)
  DOI : 10.1111/j.1365-246X.2010.04529.x
• Éditorial
  
  • Rey Christian
  • Raous Michel
  • Pasquet Philippe
  • Bonnet Marc
  • Feyel Frédéric
  Mécanique et Industries, Elsevier, 2010, 11 (3-4), pp.165-295. Voir la collection <a href="https://hal.science/CSMA2009">Giens 2009</a>. (10.1051/meca/2010059)
  DOI : 10.1051/meca/2010059