Publications

2010

• Multi-scale viscoplastic behaviour of Halite: In-situ SEM full field measurements, a micro-mechanical approach
  
  • Bourcier Mathieu
  • Dimanov Alexandre
  • Héripré Eva
  • Bornert Michel
  • Raphanel Jean
  , 2010. Halite geological formations are already extensively used for underground storage of hydrocarbons. For example, the entire USA federal reserve of petrol resides in deep (500 - 1000 m) artificial salt caverns, which are realized by controlled dissolution. In France, many such salt caverns are used for storage of natural gas by GDF. Salt caverns and carries are also intended to become nuclear waste repositories. At this point, salt caverns are also seriously envisaged for the daily storage of energy from renewable, but intermittent sources (photovoltaic, Aeolian), under the form of compressed air. Halite mechanical behaviour was extensively studied for the purpose of safe geothechnical applications. Halite is a ductile type rock. Its differed (time-dependent) mechanical response dominates by far, and therefore deep salt caverns experience convergence (closure), which may result in catastrophic subsidence of the overlaying geological layers. Hence, a particular attention was drawn to characterize salt single crystal creep properties (active slip systems and critical resolved shear stresses), and the rheology of poly-crystalline salt, at various temperatures, pressures, differential stresses and water contents (Ter Heege et al., 2007). But, most studies were concerned with macroscopically derived flow laws, corresponding to rather high differential stresses (as compared with those experienced on site), where crystal slip plasticity (CSP) dominates. But, many studies have also shown that halite is very sensitive to solution-precipitation creep (SPC) mechanisms, which may result in solution transfer accommodated grain boundary sliding (GBS). Conversely, some recent studies report that halite is able to flow at ambient conditions, and under very small loads, with strain rates much faster (four orders of magnitude) than those extrapolated from high stress experiments (Bérest et al., 2005). Though, the specific creep micro-mechanisms were not identified, Bérest et al. (2005) invoked possible SPC. Additionally, the effects on long term behaviour of cyclic loading (fatigue) are still poorly known. It is therefore still questionable weather it is really possible to safely extrapolate the laboratory data to the long term envisaged geotechnical applications. To answer we need i) additional experimental work in order to up date the deformation mechanism maps on the basis of better identified micro-physical mechanisms and quantification of their respective activity; and ii) numerical modelling at the scales of the material, and of the underground storage structures, in respect with the appropriated thermo-hygro-mechaniclal loadings. In the present work, we present our preliminary investigation of viscoplastic global and local responses of synthetic fine grained (50 - 500 m) halite by the means of full field measurements (FFM) of local strain by digital image correlation (DIC) during simple compression in-situ SEM (Doumalain et al., 2003). Figure 1 shows a typical loading curve obtained incrementally at the constant strain rate of c.a. 5x10-5 s-1. CSP evidenced by the development of slip lines on the free grain surfaces, and characterized by quasi-linear strain hardening, dominates the overall response up to several % of strain (microfracturing did not appear before 8 % strain). Yet, at the scale of the microstructure, the development of viscoplastic strain is heterogeneous, as shown by the strain maps obtained by DIC and corresponding to four incremental stages of the loading sequence. The heterogeneity of the strain field relates to the loading boundary conditions and to the local microstructure, such crystal size and orientation (which is characterized by electron back scattering diffraction, EBSD). Such micromechanical approach aims to provide the basis for the development of FE (finite element) computational CSP of polycrystalline halite.
• On standard dissipative gradient models
  
  • Nguyen Quoc Son
  Ann. Solid Struct. Mech., 2010, 1 (2), pp.59-75. A general presentation on gradient models for solids in thermo- mechanics is given in this paper. Firstly, it is shown that the introduction of the gradients of the internal variables can be conveniently done under the formalism of the generalized standard materials. The derivation of the governing equations and the associated boundary conditions of a solid can be derived in a straightforward manner from the basic assumption of existence of an energy potential and a dissipation potential. Secondly, the attention is focussed on the introduction of the temperature gradient. Two descriptions, respectively by Forest & al. and by Nguyen & Andrieux are discussed. The last one is based upon an interesting definition of the entropy and of the internal energy by Legendre transform of the free energy with respect to the temperature and the temperature gradient. The obtained results are justified in a simple example of micro-macro modeling of thermal conduction in a rigid composite. In particular, it is shown that the associated thermal equation removes the paradox of instantaneous propagation. (10.1007/s12356-010-0006-0)
  DOI : 10.1007/s12356-010-0006-0
• Approche variationnelle de l'endommagement : II. Les modèles à gradient
  
  • Pham Kim
  • Marigo Jean-Jacques
  Comptes Rendus. Mécanique, Académie des sciences (Paris), 2010, 338 (4), pp.199-206. This second part of the variational approach to damage is devoted to the construction of non-local gradient-enhanced models. That consists in extending to these regularized models the concepts introduced in the first part for local damage models. Specifically, once the gradient of damage has been inserted into the energy expression, the damage evolution problem is still based on the three physical principles of irreversibility, stability and energy balance. This new formulation is compared with that usually postulated and its merits are emphasized. (10.1016/j.crme.2010.03.012)
  DOI : 10.1016/j.crme.2010.03.012
• Approche variationnelle de l'endommagement : I. Les concepts fondamentaux
  
  • Marigo Jean-Jacques
  • Pham Kim
  Comptes Rendus. Mécanique, Académie des sciences (Paris), 2010, 338 (4), pp.191-198. This Note is devoted to the construction of local brittle damage laws. We first justify by the Drucker–Ilyushin postulate to set their formulation within the framework of Generalized Standard Materials. Accordingly, the strain work becomes a state function whose convexity properties are directly related to the hardening or softening properties of the material. Moreover, the evolution problem can be read as a variational problem which is reinforced so that it finally contains the concepts of stability and of energy conservation. (10.1016/j.crme.2010.03.009)
  DOI : 10.1016/j.crme.2010.03.009
• Elastic and nonlinear behaviour of argillaceous rocks under combined moisture and mechanical loads investigated by means of multiscale full full-field strain measurement techniques
  
  • Yang D.S.
  • Bornert Michel
  • Nguyen Minh D.
  • Chanchole S.
  • Gharbi H.
  • Valli P.
  , 2010.
• Identification of Young's Modulus from Indentation Testing and Inverse Analysis
  
  • Prou Joris
  • Kishimoto Kikuo
  • Constantinescu Andrei
  Journal of Solid Mechanics and Materials Engineering, 2010, 4 (6), pp.781--795. In this study, a numerical method for the identification of the Young's modulus of linear elastic coated materials from continuous indentation test is first presented. The identification is based on an inverse analysis where the minimization of a cost functional is performed by a gradient descent algorithm. The main result is the computation of cost function gradient by using a direct differentiation technique, resulting in a time saving method compared to the widely used finite difference method. The validity and illustration of this approach is shown through several numerical examples. The second part of this article is dedicated to the identification of elasto-plastic thin films Young's modulus. A new method is proposed, where the inverse analysis relies only on finite element computations for elastic materials.
• Déchets nucléaires : le stockage doit-il être réversible ?
  
  • Berest Pierre
  • Bérest P.
  , 2010, pp.82-83.
• Revisiting energy release rates in brittle fracture
  
  • Chambolle Antonin
  • Francfort Gilles A.
  • Marigo Jean-Jacques
  Journal of Nonlinear Science, Springer Verlag, 2010, 20 (4), pp.395-424. We revisit in a 2d setting the notion of energy release rate, which plays a pivotal role in brittle fracture. Through a blow-up method, we extend that notion to crack patterns which are merely closed sets connected to the crack tip. As an application, we demonstrate that, modulo a simple meta-stability principle, a moving crack cannot generically kink while growing continuously in time. This last result potentially renders obsolete in our opinion a longstanding debate in fracture mechanics on the correct criterion for kinking. (10.1007/s00332-010-9061-2)
  DOI : 10.1007/s00332-010-9061-2
• Displacement correction for punching at a dynamically loaded bar end
  
  • Safa Kamal
  • Gary Gérard
  International Journal of Impact Engineering, Elsevier, 2010, 37, pp.371-384. The object of this work is to provide a 3-D displacement correction for local punching due to axial load at the end of a bar. For this purpose, an analytical calculation of the indentation at the end of an elastic isotropic bar subjected to a dynamic loading is carried out. It provides a first-order correction of the displacement obtained through the 1-D wave analysis commonly used in SHPB processing. This correction improves the results obtained for the dynamic behavior of the specimen, in particular at early instants of loading where its response is often purely elastic. Tabulated values are provided for easy use in SHPB testing. (10.1016/j.ijimpeng.2009.09.006)
  DOI : 10.1016/j.ijimpeng.2009.09.006
• Evaluation of Stress-strain Curve Estimates in Dynamic Experiments
  
  • Mohr Dirk
  • Gary Gérard
  • Lundberg Bengt
  International Journal of Impact Engineering, Elsevier, 2010, 37, pp.161-169. Accurate measurements of the forces and velocities at the boundaries of a dynamically loaded specimen may be obtained using split Hopkinson pressure bars (SHPB) or other experimental devices. However, the determination of a representative stress-strain curve based on these measurements can be challenging. Due to transient effects, the stress and strain fields are not uniform within the specimen. Several formulas have been proposed in the past to estimate the stress-strain curve from dynamic experiments. Here, we make use of the theoretical solution for the waves in an elastic specimen to evaluate the accuracy of these estimates. It is found that it is important to avoid an artificial time shift in the processing of the experimental data. Moreover, it is concluded that the combination of the output force based stress estimate and the average strain provides the best of the commonly used stress-strain curve estimates in standard SHPB experiments. (10.1016/j.ijimpeng.2009.09.007)
  DOI : 10.1016/j.ijimpeng.2009.09.007
• Localisation de la déformation dans un milieu granulaire vue jusqu'à l'échelle du grain à l'aide de la tomographie à rayons X
  
  • Bésuelle Pierre
  • Hall S.
  • Viggiani Gioacchino Cinno
  • Lenoir Nicolas
  • Desrues J.
  • Pannier Y.
  • Bornert Michel
  , 2010.
• On micro-macro transition in non linear mechanics
  
  • Stolz Claude
  Materials, MDPI, 2010, 3 (1), pp.296-317. This paper is devoted to the description of the general relationships between microscopic and macroscopic mechanical quantities in non-linear mechanics. From a thermodynamical viewpoint, it is only necessary to know the two macroscopic potentials (macroscopic free energy and macroscopic potential of dissipation) to describe the state of the body and its quasistatic evolution. These global potentials are the averages of the local ones. We point out some particular cases of non-linearities, especially the case of damaged materials. (10.3390/ma3010296)
  DOI : 10.3390/ma3010296
• Coupling of finite element and boundary integral methods for a capsule in a Stokes flow
  
  • Walter J.
  • Salsac A.-V.
  • Barthès-Biesel D.
  • Le Tallec Patrick
  International Journal for Numerical Methods in Engineering, Wiley, 2010, 83 (7), pp.829-850. We introduce a new numerical method to model the fluid-structure interaction between a microcapsule and an external flow. An explicit finite element method is used to model the large deformation of the capsule wall, which is treated as a bidimensional hyperelastic membrane. It is coupled with a boundary integral method to solve for the internal and external Stokes flows. Our results are compared with previous studies in two classical test cases: a capsule in a simple shear flow and in a planar hyperbolic flow. The method is found to be numerically stable, even when the membrane undergoes in-plane compression,which had been shown to be a destabilizing factor for other methods. The results are in very good agreement with the literature. When the viscous forces are increased with respect to the membrane elastic forces, three regimes are found for both flow cases. Our method allows a precise characterization of the critical parameters governing the transitions. (10.1002/nme.2859)
  DOI : 10.1002/nme.2859
• Simulations des verres nucléaires simplifiés par dynamique moléculaire : de l'ajustement des potentiels à la fracturation
  
  • Kieu Le-Hai
  • Delaye Jean-Marc
  • Stolz Claude
  , 2010.
• Thermalization of a driven bi-stable FPU chain
  
  • Efendiev Yalchin
  • Truskinovsky Lev
  Continuum Mechanics and Thermodynamics, Springer Verlag, 2010, 22, pp.679-698. We study Hamiltonian dynamics of a Fermi–Pasta–Ulam (FPU) chain with bi-stable elements. We show, that a quasi-static driving of a ‘cold’ chain beyond the spinodal threshold leads to complex dynamical behavior involving equipartition which suggests thermalization. The subsequent quasi-static cycling between the two energy wells produces reversible temperature oscillations which we link to the release (or absorbtion) of the latent heat. By adopting canonical distribution we obtain a thermodynamical description of the chain which agrees well with numerically computed time-averaged behavior of the corresponding dynamical system. (10.1007/s00161-010-0166-5)
  DOI : 10.1007/s00161-010-0166-5
• On the application of Fast Multipole Methods to Helmholtz problems with complex wavenumber
  
  • Frangi A.
  • Bonnet Marc
  , 2010. see full text
• Compliant interfaces: A mechanism for relaxation of dislocation pile-ups in a sheared single crystal
  
  • Danas Kostas
  • Deshpande Vikram S.
  • Fleck Norman A.
  International Journal of Plasticity, Elsevier, 2010, 26, pp.1792-1805. Discrete dislocation plasticity models and strain-gradient plasticity theories are used to investigate the role of interfaces in the elastic–plastic response of a sheared single crystal. The upper and lower faces of a single crystal are bonded to rigid adherends via interfaces of finite thickness. The sandwich system is subjected to simple shear, and the effect of thickness of crystal layer and of interfaces upon the overall response are explored. When the interface has a modulus less than that of the bulk material, both the predicted plastic size effect and the Bauschinger effect are considerably reduced. This is due to the relaxation of the dislocation stress field by the relatively compliant surface layer. On the other hand, when the interface has a modulus equal to that of the bulk material a strong size effect in hardening as well as a significant reverse plasticity are observed in small specimens. These effects are attributed to the energy stored in the elastic fields of the geometrically necessary dislocations (GNDs). (10.1016/j.ijplas.2010.03.008)
  DOI : 10.1016/j.ijplas.2010.03.008
• Microscopic and macroscopic instabilities in finitely strained fiber-reinforced elastomers
  
  • Michel Jean-Claude
  • Lopez-Pamies Oscar
  • Ponte Castañeda Pedro
  • Triantafyllidis Nicolas
  Journal of the Mechanics and Physics of Solids, Elsevier, 2010, 58 (11), pp.1776-1803. The present work is a detailed study of the connections between microstructural instabilities and their macroscopic manifestations -- as captured through the effective properties -- in finitely strained fiber- reinforced elastomers, subjected to finite, plane-strain deformations normal to the fiber direction. The work, which is a complement to a previous and analogous investigation by the same authors on porous elastomers, (Michel et. al. , 2007), uses the linear comparison, second-order homogenization (S.O.H.) technique, initially developed for random media, to study the onset of failure in periodic fiber-reinforced elastomers and to compare the results to more accurate finite element method (F.E.M.) calculations. The influence of different fiber distributions (random and periodic), initial fiber volume fraction, matrix constitutive law and fiber cross- section on the microscopic buckling (for periodic microgeometries) and macroscopic loss of ellipticity (for all microgeometries) is investigated in detail. In addition, constraints to the principal solution due to fiber/matrix interface decohesion, matrix cavitation and fiber contact are also addressed. It is found that both microscopic and macroscopic instabilities can occur for periodic microstructures, due to a symmetry breaking in the periodic arrangement of the fibers. On the other hand, no instabilities are found for the case of random microstructures with circular section fibers, while only macroscopic instabilities are found for the case of elliptical section fibers, due to a symmetry breaking in their orientation. (10.1016/j.jmps.2010.08.006)
  DOI : 10.1016/j.jmps.2010.08.006
• 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
• 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
• 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.
• 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.
• 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
• 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