Modèles discrets de structures tissées : Analyse de stabilité et de drapéDiscrete models of woven structures: stability and draping analysis

A discrete model of a woven fabric structure is established, whereby nodes endowed with a mass and a rotational rigidity are connected by rigid bars to form a two-dimensional truss. The set of four bars that delineate a quadrilateral area is further endowed with a torsion deformation mode. The kinematics of the truss reproduces the large rotations and displacements encountered for real tissues. The equilibrium shape of such a structure is obtained as the minimum of its total potential energy versus the whole set of kinematic translational and rotational variables, accounting for eventual kinematic constraints due to contact with a rigid surface by the Lagrange multipliers method. A stability analysis is conducted, and the potentiality of the model is illustrated by fabric draping simulations. To cite this article: B. Ben Boubaker et al., C. R. Mecanique 330 (2002) 871–877.     

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).     

Développement d''un modèle en vue de la prédiction du rallumage d''un foyer de turboréacteur à haute altitudeDevelopment of a model to predict the ignition performance of a turbojet engine at high altitude

Within the context of turbojet engine re-ignition after in-flight extinction, a thermo-diffusive model has been developed to describe the electrical ignition, at low pressure and low temperature, of a cluster of fuel droplets. The model involves the resolution of the conservation equations of mass, species and energy. It also takes into account the various physical and chemical phenomena occurring during the ignition process. This Note presents the ignition model and preliminary results of this model applied to an experimental configuration. To cite this article: V. Quintilla et al., C. R. Mecanique 330 (2002) 811–818.     

Using data assimilation in numerical simulations of experimental geophysical flows

Data assimilation is used to couple numerical simulations and laboratory experiments of unsteady fluid flows in a stratified, rotating fluid. The experiments are performed on the large Coriolis turntable (Grenoble) and the simulations are performed with a multi-layer shallow water model. Sequential assimilation of high-resolution CIV (Correlation Image Velocimetry) measurements drives the numerical model close to the experimental flow and provides an estimation of all the flow variables at each time and each point. It is then possible (i) to analyse the flow dynamics in details, (ii) to determine the model errors starting from a realistic initial condition and (iii) to test the assimilation scheme when a reduced set of data is assimilated. To illustrate this, some results on the baroclinic instability of a two-layer vortex are presented. To cite this article: M. Galmiche et al., 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).     

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.     

Homogénéisation de problèmes d''évolution dans une structure renforcée de fibresHomogenization of evolution problems in a fiber reinforced structure

We study the homogenization of evolution equations such as:

where the coefficient a is -periodic and takes very high values on a subset TΩ (fibered structure) of very small measure. We find a non-local effective equation deduced from a homogenized system of several equations. To cite this article: M. Bellieud, C. R. Mecanique 330 (2002) 843–848.     

Identification de la relation de dispersion dans les barresIdentification of the dispersion relation in rods

Dispersion and attenuation of longitudinal waves in elastic or weakly viscoelastic rods are measured by analysing the resonant frequencies present in the strain spectrum due to an unknown loading. The method takes the finite measuring time of the test into account. It is applied to an aluminium bar, in which the dispersion relation is identified very accurately at frequencies up to 60 kHz. To cite this article: R. Othman et al., C. R. Mecanique 330 (2002) 849–855.     

Modélisation du comportement thermique d'un outil de fraisage : approche par identification de système non entier

In this work we present an experimental apparatus devoted to the thermal characterisation of a milling tool. The experimental device used thermistors, one for each insert. Each thermistor is located at a point in the tool close to the tip of the insert. The heat flux in each insert is expressed according to the temperature at the sensor from a non-integer model. The parameters of the model are identified from transient evolutions measurements of the temperature on the sensor and on the cutting edge. An application shows the difference in the behaviour of each insert during machining from the estimated heat fluxes. To cite this article: J.-L. Battaglia et al., C. R. Mecanique 330 (2002) 857–864.     

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).     

On the confinement of a viscous fluid by means of a feedback external field

In this work we consider a planar stationary flow of an incompressible viscous fluid in a semi-infinite strip governed by the standard Stokes system. We show how this fluid can be stopped at a finite distance from the entrance of the semi-infinite strip by means of a feedback source depending in a sublinear way on the velocity field. This localization effect is proved by reducing the problem to a non-linear biharmonic type one for which the localization of solutions is obtained through the application of an energy method, in the spirit of the monograph by S.N. Antontsev, J.I. Díaz and S.I. Shmarev (Energy Methods for Free Boundary Problems: Applications to Non-Linear PDEs and Fluid Mechanics, Birkäuser, Boston, 2002). Since the presence of the non-linear terms defined by the source is not standard in fluid mechanics literature, we give also some results about the existence and uniqueness of weak solutions for this problem. To cite this article: S.N. Antontsev et al., C. R. Mecanique 330 (2002) 797–802.     

Confined buckling of inextensible rods by convex difference algorithms

In this Note we present an approach to determine the local minima of a specific class of minimization problems. Attention is focused on the inextensibility condition of flexible rods expressed as a nonconvex constraint. Two algorithms are derived from a special splitting of the Lagrangian into the difference of two convex functions (DC). They are compared to the augmented Lagrangian methods used in this context. These DC formulations are easily extended to contact problems and applied to the determination of confined buckling shapes. To cite this article: P. Alart, S. Pagano, C. R. Mecanique 330 (2002) 819–824.     

Chemical kinetics modeling and LES combustion model effects on a perfectly premixed burner

Chemical kinetics modeling and coupling with turbulent combustion models for compressible Large Eddy Simulations (LES) is a critical issue. Accurate flow predictions can only be guaranteed if the coupling is well mastered. In a first attempt to qualify the effect of each model, the case of a lean premixed swirled combustor with comprehensive measures is targeted (species mass fractions and temperature fields). For the investigation, two turbulent combustion models are considered. The first model relies on a presumed PDF approach coupled to a look-up chemistry table obtained with a reduced chemical scheme. The second model makes use of the thickened flame approach using the same reduced chemical scheme but with reaction rates computed explicitly as the computation advances. Then, to estimate kinetic schemes reduction effects, the first model is compared to a third one, with the same PDF approach, but coupled to a look-up chemistry table obtained with a complete chemical scheme. All LES are very close to each other. The main difference between the different predictions relies on CO mass fractions. Although they are all able to return good outlet mass fractions, CO values inside the flame are different depending on the model used. To cite this article: G. Albouze et al., C. R. Mecanique 337 (2009).     

‘Ruban à godets’: an elastic model for ripples in plant leaves

The formation of ripples along the edge of plant leaves is studied using a model of an elastic strip with spontaneous curvature. The equations of equilibrium of the strip are established in an explicit form. A numerical method of solution is presented and carried out. Owing to the presence of geometric nonlinearities, several equilibrium configurations are found but we show that only one of them is physical. To our knowledge, this is the first investigation of ripples in plant leaves that is based on the equations of elasticity. To cite this article: B. Audoly, A. Boudaoud, C. R. Mecanique 330 (2002) 831–836.     

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).     

Elastic properties of glasses: a multiscale approach

Very different materials are named ‘Glass’, with Young's modulus E and Poisson's ratio ν extending from 5 to 180 GPa and from 0.1 to 0.4, respectively, in the case of bulk inorganic glasses. Glasses have in common the lack of long range order in the atomic organization. Beside the essential role of elastic properties for materials selection in mechanical design, we show in this analysis that macroscopical elastic characteristics (E,ν) provide an interesting way to get insight into the short- and medium-range orders existing in glasses. In particular, ν, the packing density (C_g) and the glass network dimensionality appear to be strongly correlated. Networks consisting primarily of chains and layers units (chalcogenides, low Si-content silicate glasses) correspond to ν>0.25 and C_g>0.56, with maximum values observed for metallic glasses (ν0.4 and C_g>0.7). On the contrary, ν<0.25 is associated to a highly cross-linked network with a tri-dimensional organization resulting in a low packing density. Moreover, the temperature dependence of the elastic moduli brings a new light on the ‘fragility’ of glasses (as introduced by Angell) and on the level of cooperativity of atomic movements at the source of the deformation process. To cite this article: T. Rouxel, C. R. Mecanique 334 (2006).     

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).     

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).     

Numerical calculation of wall effect and ‘backflow’ on the Stokes force

We give numerical results on the modification of the drag force F_x exerted on a sphere positioned eccentrically and moving at very low Reynolds number, at constant velocity within and along a cylindrical tube. The numerical results computed by Lattice-Boltzmann method or by finite volume formulation are in good agreement with the experimental results obtained by Ambari et al. (J. Fluid Mech. 149 (1984) 235–253). In particular, they confirm the existence of a minimum of the force F_x away from the axis of the cylinder and a sharp increase when the sphere approaches the sidewall. To cite this article: T. Godin et al., C. R. Mecanique 330 (2002) 837–842.     

Nonlinear models of vehicular traffic flow – new frameworks of the mathematical kinetic theory

This paper deals with the design of mathematical frameworks for the modeling of traffic flow phenomena by suitable developments of classical models of the kinetic theory. Various types of evolution equations are deduced, and different mathematical structures are proposed toward conceivable applications. To cite this article: M. Delitala, C. R. Mecanique 331 (2003).