On the slow gravity-driven migration of arbitrary clusters of small solid particles

A new approach is advocated to compute at a low cpu time cost the rigid-body motions of settling solid particles when inertial effects are negligible. In addition to the relevant boundary-integral equations, the numerical implementation and a few convincing benchmark tests we address two configurations of equivalent spheres and spheroids, i.e. that exhibit when isolated the same settling velocity. To cite this article: A. Sellier, C. R. Mecanique 332 (2004).

Résumé

On propose une approche originale pour déterminer le mouvement d'une assemblée de particules solides et de formes arbitraires soumise à l'action de la pesanteur dans l'approximation de Stokes. Outre les intégrales de frontière et la méthode numérique associées on présente quelques comparaisons et examine le cas de deux configurations de sphères et ellipsoides de révolution équivalents, c'est-à-dire dotés lorsqu'ils sont seuls de la même vitesse de sédimentation. Pour citer cet article : A. Sellier, C. R. Mecanique 332 (2004).     

Experimental observation of frequency doubling in a viscoelastic mixing layer

An experimental mixing layer in water at Reynolds number 440 is investigated. A colored viscoelastic solution is introduced in the shear layer before the roll-up dynamics. On the basis of flow visualization and local velocity measurements, it is found that compared to the Newtonian case, the roll-up process is affected by the non-Newtonian behavior of the viscoelastic solution. The effect consists of the appearance of secondary eddies in the mixing layer corresponding to the production of higher harmonics in the vorticity distribution. Consequently, there is a frequency doubling of the local velocity oscillations in the mixing layer. To cite this article: F. Sausset et al., C. R. Mecanique 332 (2004).

Résumé

Une étude expérimentale de la couche de mélange à un nombre de Reynolds de 440 est réalisée. Une solution viscoélastique colorée est introduite dans la couche cisaillée stationnaire juste avant la formation des tourbillons. En utilisant un mesure locale de la vitesse et une technique de visualisation par fluorescence, il est montré que la formation tourbillonnaire est affectée par le comportement non-Newtonien de la solution viscoélastique par rapport au cas Newtonien. Cet effet correspond à la formation de tourbillons secondaires produisant un harmonique supérieur dans la répartition spatiale de vorticité. En conséquence, un doublement de la fréquence des oscillations de la vitesse locale dans la couche de mélange est observé. Pour citer cet article : F. Sausset et al., C. R. Mecanique 332 (2004).     

Variance of the virtual displacement

We show that the affine structure of the 3-dimensional space is deeply enmeshed with the static laws expression. The relevance of tensorial rules for calculus in mechanics is thus enhanced. The virtual work principle is stated precisely but a little twist is given to the usual statements: the tensorial nature of the so-called virtual displacement vector is asserted to be covariant. To cite this article: C. Vallée et al., C. R. Mecanique 332 (2004).

Résumé

Nous montrons que la structure affine de l'espace tridimensionnel est fortement imbriquée avec l'expression des lois de la statique. La pertinence de l'application des règles du calcul tensoriel à la mécanique est ainsi renforcée. Le principe des travaux virtuels est établi précisément avec une seule entorse aux exposés classiques : la nature tensorielle de l'habituel vecteur déplacement virtuel est affirmée covariante. Pour citer cet article : C. Vallée et al., C. R. Mecanique 332 (2004).     

Chaos synchronization on the N-torus and cryptography

A class of chaotic dynamical systems on the N-dimensional torus is proposed for masking some information in secure communications. The information is then recovered thanks to a chaos synchronization process. To cite this article: L. Rosier et al., C. R. Mecanique 332 (2004).

Résumé

Nous proposons une classe de systèmes chaotiques sur le tore N-dimensionnel pour masquer une information à transmettre dans une communication sécurisée. Cette information est ensuite reconstruite à l'aide d'un mécanisme de synchronisation du chaos. Pour citer cet article : L. Rosier et al., C. R. Mecanique 332 (2004).     

The influence of crack-imbalance orientation and orbital evolution for an extended cracked Jeffcott rotor

Vibration peaks occurring at rational fractions of the fundamental rotating critical speed, here named Local Resonances, facilitate cracked shaft detection during machine shut-down. A modified Jeffcott-rotor on journal bearings accounting for gravity effects and oscillating around nontrivial equilibrium points is employed. Modal parameter selection allows this linear model to represent first mode characteristics of real machines. Orbit evolution and vibration patterns are analyzed, yielding useful results. Crack detection results indicate that, instead of 1x and 2x components, analysis of the remaining local resonances should have priority; this is due to crack-residual imbalance interaction and to 2x multiple induced origins. Therefore, local resonances and orbital evolution around 1/2, 1/3 and 1/4 of the critical speed are emphasized for various crack-imbalance orientations. To cite this article: J. Gómez-Mancilla et al., C. R. Mecanique 332 (2004).

Résumé

Les pics de vibration apparaissant au passage des fractions de la vitesse de critique de rotation des systèmes tournants, appelées résonances locales, facilitent la détection de fissures sur les machines. Dans cette étude, un modèle de rotor Jeffcott modifié avec une fissure tournante, comportant des coussinets et prenant en compte les effets de pesanteur et de balourd est présenté. Le choix modal des paramètres permet de représenter les caractéristiques liées au premier mode des machines tournantes usuelles. Les évolutions des vibrations et des orbites du système comportant une fissure sont analysées et permettent d'obtenir des résultats utiles pour la détection des fissures sur les machines tournantes. Ainsi, ces résultats indiquent que, en plus des composants 1x et 2x, l'analyse des autres résonances locales restantes doivent être regardées avec attention du fait de l'interaction possible entre les différentes orientations de la fissure et du balourd, et des origines multiples pouvant engendrer la présence des résonances 2x. Par conséquent les résonances et l'évolution des orbites obtenus autour de 1/2, 1/3 et 1/4 de la vitesse critique sont étudiées pour différentes variations d'angle entre le balourd et l'orientation de la fissure. Pour citer cet article : J. Gómez-Mancilla et al., C. R. Mecanique 332 (2004).     

Random-field model for the elasticity tensor of anisotropic random media

This Note deals with the construction of a non-Gaussian positive definite matrix-valued random field whose mathematical properties allow the fourth-order elasticity tensor of random non homogeneous anisotropic three dimensional elastic media to be modelled. If the usual parametric probabilistic approach was used, then 21 mutually dependent random fields should be modelled and identified by using experimental data. Such an approach would be very difficult because the systems of the marginal probability distributions of these random fields have to be identified due to the fact that, for a boundary value problem, the displacement field of the random medium is a non-linear mapping of the random elasticity tensor. The theory presented in this paper allows such a probabilistic model of the fourth-order elasticity tensor field to be constructed and depends only of four scalar parameters: three spatial correlation lengths and one parameter allowing the level of the random fluctuations to be controlled. To cite this article: C. Soize, C. R. Mecanique 332 (2004).

Résumé

On présente la construction d'un champ aléatoire à valeurs dans les matrices définies positives dont les propriétés mathématiques permettent de modéliser le tenseur d'élasticité du quatrième ordre des mileux élastiques anisotropes tridimensionnels aléatoires. Si l'approche probabiliste paramétrique usuelle était utilisée, alors il serait nécessaire de modéliser et d'identifier à l'aide de données expérimentales 21 champs aléatoires mutuellement dépendants. Une telle approche serait très difficile de part le fait que le système de lois marginales de ces champs aléatoires doit être identifié parce que, pour un problème aux limites, le champ de déplacement est une transformation non linéaire du tenseur d'élasticité. La théorie présentée dans ce papier permet de construire une modélisation probabiliste du champ de tenseur d'élasticité qui ne dépend que de quatre paramètres scalaires : trois échelles de corrélation spatiale et un paramètre permettant de contrôler le niveau des fluctuations aléatoires. Pour citer cet article : C. Soize, C. R. Mecanique 332 (2004).     

Effective flow of a viscous liquid through a helical pipe

We study the flow of a viscous fluid through a pipe with helical shape parameterized with , where the small parameter stands for the distance between two coils of the helix. The pipe has small cross-section of size . Using the asymptotic analysis of the microscopic flow described by the Navier–Stokes system, with respect to the small parameter that tends to zero, we find the effective fluid flow described by an explicit formula of the Poisseuile type including a small distorsion due to the particular geometry of the pipe. To cite this article: E. Marušić-Paloka, I. Pažanin, C. R. Mecanique 332 (2004).

Résumé

On considère un écoulement dans un tube de section circulaire et de forme hélicoïdale paramétré par , où est la distance entre deux tours de la spirale. Le rayon de la section du tube est lui aussi supposé égal à . A partir de l'écoulement microscopique décrit par le système de Navier–Stokes et en utilisant l'analyse asymptotique par rapport à ce petit paramètre on obtient l'écoulemment effectif décrit par une formule explicite de type Poiseuille associée à une petite déviation due à la géometrie du tube. Pour citer cet article : E. Marušić-Paloka, I. Pažanin, C. R. Mecanique 332 (2004).     

Extended three-dimensional digital image correlation (X3D-DIC)

A correlation algorithm is proposed to measure full three-dimensional displacement fields in a three-dimensional domain. The chosen kinematic basis for this measurement is based on continuous finite-element shape functions. It is furthermore proposed to account for the presence of strong discontinuities, similarly to extended finite element schemes, with a suited enrichment of the kinematics with discontinuities supported by a (crack) surface. An optimization of the surface geometry is proposed based on correlation residuals. The procedure is applied to analyze one loading cycle of a fatigue-cracked nodular graphite cast iron sample by using computed tomography pictures. Subvoxel crack openings are revealed and measured. To cite this article: J. Réthoré et al., C. R. Mecanique 336 (2008).     

Comportement des matériaux plastiques parfaits,non visqueux

Résumé Dans une première partie, partant d'une relation générale entre contraintes, vitesses de déformations et masse spécifique, nous démontrons l'existence d'une surface d'écoulement (critère d'écoulement en contraintes). Dans une deuxième partie, nous proposons une loi d'écoulement. Celle-çi admet comme cas particuliers: la théorie du potentiel plastique pour les matériaux incompressibles à critère d'écoulement indépendant de la contrainte moyenne, la théorie deBrown etGudehus pour les matériaux compressibles à critère d'écoulement indépendant de la contrainte moyenne, et la théorie de la courbe intrinséque (cisaillement selon un plan) pour les matériaux à critère d'écoulement indépendant de la contrainte intermédiaire.Avec 3 figures     

A two grid algorithm based on perturbation and homotopy methods

In this paper, we propose a new class of bi-grid algorithm to solve large scale linear algebraic equations. This method is based on homotopy, perturbation technique and Padé approximants. To cite this article: R. El Mokhtari et al., C. R. Mecanique 330 (2002) 825–830.     

Vérification expérimentale de la relation de réciprocité d'Onsager pour l'électro-osmose et l'électro-filtration dans une argile naturelleExperimental verification of the Onsager's reciprocal relations for electro-osmosis and electro-filtration phenomena on a saturated clay

This Note is devoted to the experimental verification of the Onsager's reciprocal relations in the particular case of electro-osmosis and electro-filtration. A special set up has been designed to carry out the measurements of both the electro-osmotic permeability and the streaming potential. This has been performed by using a natural material i.e., saturated kaolinite. To cite this article: K. Beddiar et al., C. R. Mecanique 330 (2002) 893–898.     

Thermodynamical functions for a gas of point vortices

We formulate nonlinear integro-differential equation for the averaged collective Hamiltonian of a gas of interacting two-dimensional vortices, derive its analytical solution, and discuss the equilibrium, axially-symmetrical, probability distributions that are possible for such a model. We also theoretically prove that the probability distribution for a system of 2D point vortices takes a form similar to the Gibbs distribution, but point out that the physical fundamentals of such a system differ from the standard theory of interacting particles. Furthermore, we find thermodynamical functions for positive and negative “temperature” of the system, and point out that the states with positive “temperature” correspond to stationary bell-shape vortex distributions, while the states with negative “temperature” correspond to distributions localized near container walls. To cite this article: E. Bécu et al., C. R. Mecanique 336 (2008).     

Direct simulation of the motion of neutrally buoyant balls in a three-dimensional Poiseuille flow

In a previous article the authors introduced a Lagrange multiplier based fictitious domain method. Their goal in the present article is to apply a generalization of the above method to: (i) the numerical simulation of the motion of neutrally buoyant particles in a three-dimensional Poiseuille flow; (ii) study – via direct numerical simulations – the migration of neutrally buoyant balls in the tube Poiseuille flow of an incompressible Newtonian viscous fluid. Simulations made with one and several particles show that, as expected, the Segré–Silberberg effect takes place. To cite this article: T.-W. Pan, R. Glowinski, C. R. Mecanique 333 (2005).     

Impact of a bead on a rotating wall

We study experimentally the impact of a plastic bead on a rotating wall made of steel (velocity Ω; radial position x₀). The results show that the restitution coefficient is directly function of the impact velocity x₀Ω and is invariant by changing frame reference. The influence of the height of release of the particle on its angular velocity after impact is also studied. We observe an increase of the angular velocity with height followed by a saturation. We propose an interpretation for this evolution considering that the particle may roll without sliding during all the impact. This physical feature is not always taken into account in existing models of impact between rigid bodies. To cite this article: F. Rioual et al., C. R. Mecanique 336 (2008).     

Transfert du trichloréthylène en milieu poreux à partir d'un panache de vapeursMass transfer of trichloroethylene in a porous medium from a vapor plume

A large scale experiment has been carried out on an experimental facility to study the mass transfer of trichloroethylene (TCE) in a partially saturated porous medium. 5 liters of TCE have been infiltrated in the vadose zone of the site. The mass transfer of TCE from the vapor plume in the unsaturated zone towards the top of groundwater was quantified based on an analytical and a numerical approach. The mass of the pollutant measured at the exit of the model is well represented by the two mathematical approaches. It is found that the transfer of TCE towards the groundwater from the vapor plume is weak, which corresponds to 285 g of TCE, approximately 4% of the initial mass. To cite this article: H. Benremita, G. Schäfer, C. R. Mecanique 331 (2003).     

Homogenization of an elasticity problem in domains with a net of slender bars near surface

We consider an elasticity problem in a domain Ω⁽⁾=ΩF⁽⁾, where Ω is an open bounded domain in R³, F⁽⁾ is a connected nonperiodic set in Ω like a net of slender bars, and is a parameter characterizing the microstructure of the domain. We consider the case of a surface distribution of the set F⁽⁾, i.e., for sufficiently small , the set F⁽⁾ is concentrated in arbitrary small neighbourhood of a surface Γ. Under a hypothesis on the asymptotic behaviour of the energy functional, we obtain the macroscopic (homogenized) model. To cite this article: M. Goncharenko, L. Pankratov, C. R. Mecanique 331 (2003).     

Asymptotics of Neumann harmonics when a cavity is close to the exterior boundary of the domain

We construct the asymptotics (as ε→0) of solutions to the Neumann problem for the Laplace equation and of the corresponding Dirichlet integral. The problem concerns a three-dimensional domain having two connected components of the boundary at the distance ε>0. To cite this article: G. Cardone et al., C. R. Mecanique 335 (2007).     

Weighted Korn inequalities for thin-walled elastic structures

Appropriate weighted norms in H¹ are presented such that the Korn type inequality is asymptotically sharp with respect to relative thickness and stiffness of the elastic plates. The weights depend crucially on the geometric structure of the plates' junction. To cite this article: O.V. Izotova et al., C. R. Mecanique 334 (2006).     

Sur les approximations « isotrope » et « anisotrope » de l''opérateur tangent pour les méthodes tangentes incrémentale et affineOn the ‘isotropic’ and ‘anisotropic’ approximations of the tangent operator in the incremental tangent and affine methods

Three localisation rules, TFA, the incremental tangent, and the affine method, are recalled and evaluated in the context of the elastoplastic micromechanical analysis of heterogeneous materials, composites or polycrystals. With the help of a severe example, it is shown how methods based on the complete anisotropic elastoplastic tangent operator yield very stiff predictions which are far from the reference solution; the same conclusion holds for the method using the elastic accommodation rule. On the other hand, using an isotropic form of the tangent operator delivers much better responses. The reasons for such differences are discussed, together with possible justifications for the choice of the isotropic form. To cite this article: J.-L. Chaboche, P. Kanouté, C. R. Mecanique 331 (2003).     

Numerical analysis of a quasistatic piezoelectric problem with damage

The quasistatic evolution of the mechanical state of a piezoelectric body with damage is numerically studied in this paper. Both damage and piezoelectric effects are included into the model. The variational formulation leads to a coupled system composed of two linear variational equations for the displacement field and the electric potential, and a nonlinear parabolic variational equation for the damage field. The existence of a unique weak solution is stated. Then, a fully discrete scheme is introduced by using a finite element method to approximate the spatial variable and an Euler scheme to discretize the time derivatives. Error estimates are derived on the approximate solutions, from which the linear convergence of the algorithm is deduced under suitable regularity conditions. Finally, a two-dimensional example is presented to demonstrate the behaviour of the solution. To cite this article: J.R. Fernández et al., C. R. Mecanique 336 (2008).