Publications

2012

• Une méthode de résolution efficace pour un problème multi-échelle en élasticité
  
  • Vidrascu Marina
  • Geymonat Giuseppe
  • Hendili Sofiane
  • Krasucki Françoise
  , 2012. Cette présentation décrit une méthode multi-échelle robuste et efficace qui combine développements asymptotiques raccordés et décomposition de domaines pour résoudre des problèmes d'élasticité avec un grand nombre d'hétérogénéités.
• Microscopic and macroscopic instabilities in fiber-reinforced elastomers.
  
  • Lopez-Pamies Oscar
  • Michel Jean-Claude
  • Ponte Castañeda Pedro
  • Triantafyllidis Nicolas
  , 2012.
• On the rate boundary value problem for damage modelization by thick level-set
  
  • Stolz Claude
  • Moes Nicolas
  , 2012, pp.205-220. In total damage the rupture occurs on a moving surface along which strong discontinuties of displacement gradient are localized. A damage modelisation is proposed based on a continuous transition from undamaged to damaged material. In this new framework, the evolution of damage is associated with a moving layer of finite length lc. With this description, initiation and propagation of damage can be unified in the same constitutive law. Using a normality law based on the driving force associated with the motion of the layer, the solution of the rate boundary value problem of propagation and displacement satisfies a variational inequality. Characterization of uniqueness is then given.
• Matching asymptotic method and nucleation of a defect at a notch
  
  • Dang Thi Bach Tuyet
  • Laurence Halpern
  • Marigo Jean-Jacques
  , 2012, pp.sous presse. In the present study, we use matching asymptotic expansion to treat the elastic problem associated with a small defect located at the tip of a notch. The use of such asymptotic methods is necessary because the presence both of small parameters and singularities leads to inaccurate computations by classical finite element methods. The method is applied here in an antiplane setting.
• On Duality, Symmetry and Symmetry lost in Solid Mechanics
  
  • Bui Hui Duong
  , 2012, pp.pp. 44-54. The paper recalls the concept of duality in Mathematics and extends it to Solid Mechanics. One important application of duality is to restore some symmetry between current fields and their adjoint ones. This leads to many alternative schemes for numerical analyses, different from the classical one as used in classical variational formulation of boundary value problems (Finite Element Method). Usually, Conservation laws in Fracture Mechanics make use of the current fields, displacement and stress. Many conservation laws of this type are not free of the source term. Consequently, one cannot derive path-independent integrals for use in Fracture Mechanics. The introduction of variables and dual or adjoint variables leads to true path-independent integrals. Duality also introduces some anti-symmetry in current fields and adjoint ones for some boundary value problems. The symmetry is lost between fields and adjoint fields. The last notion enables us to derive new variational formulation on dual subspaces and to exactly solve inverse problems for detecting cracks and volume defects.
• Lattice dynamics from a continuum viewpoint
  
  • Charlotte M.
  • Truskinovsky Lev
  Journal of the Mechanics and Physics of Solids, Elsevier, 2012, 60 (8), pp.1508-1544. We develop a novel continuum description of lattice dynamics for a particle chain with nearest neighbor interactions. Our continuum model interpolates discrete solutions and allows one to deal adequately with singular and impact loadings. The resulting theory is local in space and nonlocal in time. It is characterized by a nontrivial hereditary structure which blends inertial and elastic forces. The proposed methodology can be used to build continuum approximations for lattice dynamics which incorporate successively finer scales. It can also serve as a seamless interface between discrete and continuum elasticity theories. (10.1016/j.jmps.2012.03.004)
  DOI : 10.1016/j.jmps.2012.03.004
• Plasticité et Rupture
  
  • Marigo Jean-Jacques
  , 2012, pp.245.
• An Asymptotic Second Gradient Reissner-Mindlin Plate Model
  
  • Serpilli Michèle
  • Geymonat Giuseppe
  • Krasucki Francoise
  , 2012, pp.ISBN/ISSN: 9783851252231.
• NOUVELLES PROBLEMATIQUES POSEES PAR LE CYCLAGE THERMO-MECANIQUE EN CAVITES SALINES
  
  • Pellizzaro Cyrille
  • Berest Pierre
  • Brouard Benoît
  • Karimi-Jafari Mehdi
  , 2012, Tome 2, pp.691-698. Storage of natural gas in salt caverns had been developed mainly for seasonal storage, resulting in a small number of yearly pressure cycles and moderate gas-production rates. The needs of energy traders are changing towards more aggressive operational modes. The "high-frequency cycling" operation of salt caverns raises questions concerning the effects of frequently repeated and intense mechanical and thermal loading. These questions concern the constitutive creep laws for salt, laboratory test procedures, criteria to be used at the design stage to provide operability, and the long-term integrity of the underground salt caverns.
• A non-iterative sampling approach using noise subspace projection for EIT
  
  • Bellis Cédric
  • Constantinescu Andrei
  • Coquet Thomas
  • Jaravel Thomas
  • Lechleiter Armin
  Inverse Problems, IOP Publishing, 2012. This study concerns the problem of the reconstruction of inclusions embedded in a conductive medium in the context of electrical impedance tomography (EIT), which is investigated within the framework of a non-iterative sampling approach. This type of identification strategy relies on the construction of a special indicator function that takes, roughly speaking, small values outside the inclusion and large values inside. Such a function is constructed in this paper from the projection of a fundamental singular solution onto the space spanned by the singular vectors associated with some of the smallest singular values of the data-to-measurement operator. The behavior of the novel indicator function is analyzed. For a subsequent implementation in a discrete setting, the quality of classical finite-dimensional approximations of the measurement operator is discussed. The robustness of this approach is also analyzed when only noisy spectral information is available. Finally, this identification method is implemented numerically and experimentally, and its efficiency is discussed on a set of, partly experimental, examples. (10.1088/0266-5611/28/7/075015)
  DOI : 10.1088/0266-5611/28/7/075015
• Handling localization in damage models with thick level set approach (TLS)
  
  • Moes Nicolas
  • Bernard Paul Emile
  • Stolz Claude
  • Chevaugeon Nicolas
  , 2012, pp.82711. In this paper, we discuss a new way to model damage growth in solids. A level set is used to separate the undamaged zone from the damaged zone. In the damaged zone, the damage variable is an explicit function of the level set. This function is a parameter of the model. Beyond a critical length, it is assumed that the material is totally damaged, thus allowing a straightforward transition to fracture. The damage growth is expressed as a level set propagation. The configurational force driving the damage front is non local in the sense that it averages information over the thickness in the wake of the front. Three important theoretical advantages of the proposed approach are as follows : (a) The zone for which the materials is fully damaged is located inside a clearly identified domain (given by an iso- level set). (b) The non-locality steps in gradually in the model. At initiation themodel is fully local. At initiation, micro-cracks being absent no length scale should prevail. (c) It is straightforward to prove that dissipation is positive. A numerical experiment of the cracking of a multiply perforated plate is discussed. (10.1115/ESDA2012-82711)
  DOI : 10.1115/ESDA2012-82711
• Le titane et ses alliages dans les transports : atouts et problèmes
  
  • Doquet Véronique
  X, Lettre Scientifique de l'Ecole Polytechnique, 2012, ISSN 1775-0385 (Transports), pp.39-43.
• A tree-inspired damping mechanism in flexible structures: damping-by-branching
  
  • Theckes Benoît
  • de Langre Emmanuel
  • Boutillon Xavier
  , 2012. Strong dynamic loads in man-made slender structures are likely to produce large amplitude vibrations of due to their flexibility, which often cause functionality losses or inflict irreversible damages. The amplitude of motion results, on one hand, from the characteristics of the loading, and on the other hand, from the characteristics of the structure in terms of inertia, stiffness and damping. A high rate of damping, i.e. mechanical energy dissipation whatever the physical mechanism, is a standard way to limit vibrations of large amplitude and their undesirable consequences. However, adding damping in slender structures remains a challenging problem in engineering. As slender and flexible structures, trees repeatedly endure strong climatic events, yet with minor or no damages in most cases. Therefore, trees regularly submitted to natural flow excitations by wind are likely to possess efficient and specific strategies of damping. In fact, several damping mechanism have been identified in trees: viscoelastic behaviour of wood, aeroelasticity from the interactions with air, and the linear tuned-mass-damper effect between the trunk and the branches. However, the latter, as a linear mechanism, is not amplitude-dependent and therefore does not damp specifically large amplitude motions. A new amplitude-dependent damping mechanism, inspired from trees, is identified and characterised here in the simplest tree-like structure, a Y-shape branched structure. Through analytical and numerical analyses of a simple two-degree-of-freedom model, branching is shown to be the key ingredient in this protective mechanism. This damping-by-branching originates in the geometrical nonlinearities and is therefore specifically efficient to damp out large amplitudes of motion. A more realistic model of the Y-shape structure, using beam finite-element approximation, exhibits the same effect, which seems to be robust. Similarly, two arbitrary multi-branched slender architectures show significant levels of damping of the trunk motion while only the relative branch motion is damped. Finally, the same numerical analysis is performed on a digitalised walnut tree geometry showing the significant damping contribution of this mechanism during large amplitude motions.
• Asymptotic expansions and domain decomposition
  
  • Geymonat Giuseppe
  • Hendili Sofiane
  • Krasucki Françoise
  • Serpilli Michèle
  • Vidrascu Marina
  , 2013. We apply the domain decomposition method to linear elasticity problems for multi-materials where the heterogeneities are concentrated in a thin internal layer. In the first case the heterogeneities are small, identical and periodically distributed on an internal surface and in the second one all the thin, curved internal layer is made of an elastic material much more strong than the surrounding one. In the first case the domain decomposition is used to efficiently solve the non-standard transmission problems obtained by the asymptotic expansion method. In the second case a non-standard membrane transmission problem originates from a surface shell like energy.
• Approche multi-échelle du comportement mécanique des structures en béton armé - Application aux enceintes de confinement des centrales nucléaires
  
  • David Martin
  , 2012. Cette thèse développe une stratégie multi-échelle pour représenter le comportement mécanique des armatures et des câbles de précontrainte dans une structure en béton armé. Cette stratégie est déclinée en plusieurs étapes, permettant d'intégrer progressivement de nouveaux phénomènes physiques dans la modélisation. Le premier modèle asymptotique développé permet de représenter le comportement élastique effectif d'hétérogénéités périodiquement réparties sur une surface. Il combine un comportement d'interface élastique et un comportement de membrane. Un second modèle asymptotique s'intéresse ensuite au comportement de fibres rigides réparties sur une surface, et susceptibles de glisser par rapport au volume environnant. Ces modèles présentent l'avantage d'induire moins de concentrations de contraintes que les modèles de barres utilisés classiquement. Ils sont implantés dans le code éléments finis Code_Aster, et validés par rapport à des simulations tridimensionnelles de référence. Leur interaction avec une fissure présente dans le béton est étudiée. Enfin, cette stratégie permet de modéliser des essais expérimentaux réalisés sur une portion d'enceinte de confinement à l'échelle 1.
• Fast time-scale average for a mesoscopic high cycle fatigue criterion
  
  • Bosia Stefano
  • Constantinescu Andrei
  International Journal of Fatigue, Elsevier, 2012, 45, pp.39-47. The paper discusses the lifetime prediction of structures in high-cycle fatigue based on the two-scale fatigue criteria of Dang Van type and several of its extensions in finite lifetime regime. The main assumptions for this criteria are (i) the material is polycrystalline and undergoes localised plasticity in one of the misoriented grains and (ii) crack initiation arises as a consequence of cumulated plasticity in this grain. The novelty of the presented approach is twofold. On the one hand a generalisation of mesoscopic plasticity model is presented, on the other a fast time scale average is introduced for tracking the cyclic material behaviour and the subsequent evolution of damage. The tracking method is based on the split between a quick quasi-periodic response of the system to the cyclic load and a slow evolution of the internal hardening and damage parameters of the material at the mesoscopic scale. The proposed method can be extended to a large class of local material behaviours involving not only plasticity, but also crack and damage evolution. The paper proposes a simplified plasticity-based model for the mesoscopic material behaviour and presents a comparison between predicted and experimental lifetimes. The results are discussed in terms of prediction capabilities and also in terms of the identification procedure of parameters of the mesoscopic model. (10.1016/j.ijfatigue.2012.01.012)
  DOI : 10.1016/j.ijfatigue.2012.01.012
• A critical evaluation of local field statistics predicted by various linearization schemes in nonlinear mean-field homogenization
  
  • Rekik Amna
  • Bornert Michel
  • Auslender François
  Mechanics of Materials, Elsevier, 2012 (54), pp.1-17. This paper is devoted to the evaluation of various classical and more recent linearization schemes for nonlinear homogenization in terms of their efficiency to characterize local field fluctuations in nonlinear heterogeneous composites. It relies on an unbiased comparison between field statistics predicted by homogenization theories and those obtained from a reference solution solved using finite element techniques, based on the same microgeometry and boundary conditions and in which local nonlinear constitutive relations are exactly verified at each point. Two categories of linearization methods have been investigated: classical approaches based on a "stress-strain" approach (classical secant, classical and simplified affine) and methods based on "variational principles" (variational and Lahellec-Suquet procedures). For each approach, the maps and the statistical distribution functions of the local fields (strain, stress and incremental work) illustrating the intra- and inter-phase heterogeneities are provided for reinforced and porous power-law composites. This study supplements an earlier study focused on comparisons at the global level \cite{R06, R07} and provides additional information on the accuracy of some available classical and recent linearization procedures. The proposed methodology gives access to a deeper insight on nonlinear homogenization schemes and may eventually lead to improvements of these formulations. (10.1016/j.mechmat.2012.05.011)
  DOI : 10.1016/j.mechmat.2012.05.011
• A combined Kalman Filter and Error in Constitutive Relation approach for system identification in structural dynamics.
  
  • Alarcon Cot Albert
  , 2012. Error in Constitutive Relation (ECR) methods measure model error by evaluating the difference between admissible fields using an energy norm. This technique presents interesting features such as good ability to spatially localize erroneously modeled regions, strong robustness in presence of noisy data, and good regularity properties of cost functions. On the other hand, the Kalman filter (KF) is a prediction-correction algorithm for recursive system estimation. The KF is particularly suitable for studying evolutionary systems embedding noisy data from both model and observation. The main part of this work is devoted to establish and evaluate a general-purpose identification approach using ECR and KF. In order to achieve this goal, the ECR is initially used to improve the a priori knowledge of model errors. Furthermore, ECR functionals are introduced in a state-space description of the identification problem. Its resolution is performed by means of the Unscented Kalman Filter (UKF), a second-order, reduced-cost, Kalman filter. The adequacy of the ECR-UKF approach to address problems of industrial relevance is shown through different numerical examples and complex industrial cases, such as structural time-varying damage assessment, boundary conditions identification of in-operation structures and field reconstruction problems. Moreover, these examples are used to improve the performance of the ECR-UKF algorithm, particularly the introduction of algebraic constraints in the ECR-UKF algorithm and the influence of error covariance matrix design.
• Problèmes de contact frottant en grandes transformations: du continu au discret
  
  • Dhia Hachmi Ben
  • Vautier Isabelle
  • Zarroug Malek
  Revue Européenne des Éléments Finis, HERMÈS / LAVOISIER, 2012, 9 (1-3), pp.243-261. On propose une formulation continue, faible et hybride pour le problème de contact frottant entre deux solides tridimensionnels, en grandes transformations. Les champs inconnus sont un champ de déplacement, un multiplicateur scalaire de contact et un semi-multiplicateur vectoriel d'adhérence. Cette formulation permet la dérivation “naturelle“ d'éléments de contact. (10.1080/12506559.2000.10511439)
  DOI : 10.1080/12506559.2000.10511439
• Pre-yield shearing regime of a magnetorheological fluid (MRF)
  
  • Nassar Waad
  , 2012. Magneto-rheological fluids are dispersions of magnetic micro-particles in a non-magnetic carrier fluid. Their characteristics vary upon the application of a magnetic field. At large shear rates, the Bingham model predicts a linear dependency between the variations of the shear rate and the variations of the shear stress, above a so-called Bingham shear stress threshold. The MRFs behavior below this threshold has received less attention. Its understanding is needed when the fluid is used in human-machine interfaces since small stresses are observed in the transient phases in these kinds of applications. The experimental analysis of the pre-yield regime of the MRF at low shearing rates gives a shearing response ruled by two successive regimes limited by an interfacial phenomenon. In the initial regime, the MRF behaves like a pseudo-elastic material. The shearing pseudo-elasticity was found to be independent of the magnetic field and of the particle volume fraction. Polymers coating of the magnetic particles (revealed by microscopy) is likely to be responsible for this non-magnetic cohesion of the aggregates. The shear-stress limit of this regime is proportional to the square of the magnetic field and to the particle volume fraction. In the next regime, the shear strain is not uniform any more in the fluid. The increase in the measured shear stress varies linearly with the increase in average shear strain. The variation coefficient is proportional to the square of the magnetic field and decreases with the particle volume fraction. Under our experimental conditions this regime was found to be limited by a loss of adhesion between the magnetic aggregates and the shearing plate, when it is non-magnetic, or with the magnetic pole in the other case. The adhesion loss occurs at a threshold proportional to the square of the magnetic field and to the particle volume fraction. This threshold depends on the nature of the shearing plate and may be larger than the Bingham threshold
• Size effects in the conical indentation of an elasto-plastic solid
  
  • Danas Kostas
  • Deshpande Vikram S.
  • Fleck Norman
  Journal of the Mechanics and Physics of Solids, Elsevier, 2012, 60, pp.1605-1625. The size effect in conical indentation of an elasto-plastic solid is predicted via the Fleck and Willis formulation of strain gradient plasticity (Fleck, N.A. and Willis, J.R., 2009, A mathematical basis for strain gradient plasticity theory. Part II: tensorial plastic multiplier, J. Mech. Phys. Solids, 57, 1045-1057). The rate-dependent formulation is implemented numerically and the full-field indentation problem is analysed via finite element calculations, for both ideally plastic behaviour and dissipative hardening. The isotropic strain-gradient theory involves three material length scales, and the relative significance of these length scales upon the degree of size effect is assessed. Indentation maps are generated to summarise the sensitivity of indentation hardness to indent size, indenter geometry and material properties (such as yield strain and strain hardening index). The finite element model is also used to evaluate the pertinence of the Johnson cavity expansion model and of the Nix-Gao model, which have been extensively used to predict size effects in indentation hardness.
• Effect of the sol fraction and hydrostatic deformation on the viscoelastic behavior of prestrained highly filled elastomers
  
  • Azoug Aurélie
  • Constantinescu Andrei
  • Praidelles-Duval Rachel Marie
  • Vallat M. F.
  • Nevière R.
  • Haidar Bassel
  Journal of Applied Polymer Science, Wiley, 2012, 127 (3), pp.1772-1780. This study focuses on the relations between the microstructure and the viscoelastic behavior of an industrial solid propellant belonging to the class of highly filled elastomers. Precisely, the study aims at determining the impact on the viscoelastic behavior of the presence of the sol fraction inside the polymer network. The sol fraction is the part of the binder that a good solvent can extract. The solid propellant is swollen to various extents by solutions of plasticizer and polymer molecules. This swelling leads to a hydrostatic deformation of the polymer network, corresponding to an extension or contraction loading for each specimen. Prestrained dynamic mechanical analysis tests, superimposing a small oscillating strain on a prestrain, characterize the viscoelastic behavior. The degree of swelling of the network and the effective filler fraction drive the viscoelastic response. In addition, the mechanical behavior does not depend on the chemical nature of the introduced sol fraction. Moreover, a nonlinear behavior, i.e., an increase in both storage and loss moduli with increasing prestrain, is initiated at low prestrain. This nonlinearity depends on the contraction or extension of the network and could result from particles aligning with prestrain, which is expected in such highly filled materials. (10.1002/app.37800)
  DOI : 10.1002/app.37800
• Polarization-resolved second-harmonic generation in tendon upon mechanical stretching
  
  • Gusachenko Ivan
  • Tran Viet
  • Goulam Houssen Yannick
  • Allain Jean-Marc
  • Schanne-Klein Marie-Claire
  Biophysical Journal, Biophysical Society, 2012, 102 (9), pp.2220-2229. Collagen is a triple-helical protein that forms various macromolecular organizations in tissues and is responsible for the biomechanical and physical properties of most organs. Second-harmonic generation (SHG) microscopy is a valuable imaging technique to probe collagen fibrillar organization. In this article, we use a multiscale nonlinear optical formalism to bring theoretical evidence that anisotropy of polarization-resolved SHG mostly reflects the micrometer-scale disorder in the collagen fibril distribution. Our theoretical expectations are confirmed by experimental results in rat-tail tendon. To that end, we report what to our knowledge is the first experimental implementation of polarization-resolved SHG microscopy combined with mechanical assays, to simultaneously monitor the biomechanical response of rat-tail tendon at macroscopic scale and the rearrangement of collagen fibrils in this tissue at microscopic scale. These experiments bring direct evidence that tendon stretching corresponds to straightening and aligning of collagen fibrils within the fascicle. We observe a decrease in the SHG anisotropy parameter when the tendon is stretched in a physiological range, in agreement with our numerical simulations. Moreover, these experiments provide a unique measurement of the nonlinear optical response of aligned fibrils. Our data show an excellent agreement with recently published theoretical calculations of the collagen triple helix hyperpolarizability. Copyright © 2012 Biophysical Society (10.1016/j.bpj.2012.03.068)
  DOI : 10.1016/j.bpj.2012.03.068
• Entropy and temperature gradients thermomechanics: Dissipation, heat conduction inequality and heat equation
  
  • Maitournam Habibou
  Comptes Rendus. Mécanique, Académie des sciences (Paris), 2012, 340 (6), pp.434-443. An alternative and consistent approach, not appealing to the principle of virtual power and to Coleman-Noll procedure, is used to derive constitutive and governing equations involving temperature or entropy gradients, in thermomechanics of materials. Using the balance of energy, an analysis of the dissipation naturally leads to the definition of the temperature and the entropy as variational derivatives. The approach preserves the classical forms of the equations and yields to consistent form of the second law and heat conduction inequality. The framework of generalized standard materials is then suitable for deriving admissible constitutive laws. The methodology is applied, first using entropy and its gradient as state variables (with internal energy as thermodynamic potential), and second using temperature and its gradient (starting from the free energy). (10.1016/j.crme.2012.04.001)
  DOI : 10.1016/j.crme.2012.04.001
• Rapid Depresurizations: Can they lead to irreversible damage?
  
  • Berest Pierre
  • Djakeun-Djizanne Hippolyte
  • Brouard Benoît
  • Hévin Grégoire
  , 2012, pp.63-86. Rapid gas depressurization leads to gas cooling that is followed by slow gas warming when the cavern is kept idle. The decrease in the temperature of gas depends upon the relative withdrawal rate (in %/day), and cavern size and shape. Gas cooling may result in the onset of tensile stresses at cavern walls and roofs that may generate fractures or cracks. However, in most cases, the depth of penetration of these fractures is small, and they are perpendicular to the cavern wall. The distance between two parallel fractures becomes larger when fractures penetrate deeper into the rock mass, as some fractures stop growing. Fractures form a polygonal pattern. Salt slabs are created, with boundaries formed by the opened fractures. As long as the depth of penetration of the fracture remains small, these slabs remain strongly bonded to the rock mass, and it is believed that, in many cases, their weights are not large enough to allow them to break off the cavern wall.