Nouveau fondement fonctionnel de la Mécanique

Sans résumé Mémoire transmis par C. Truesdell     

Une technique de suivi d'interfaces pour la modélisation de la cavitation par poche

A tracking method is presented for the modeling of partial and supercavitation. The velocity and pressure fields in the cavitating flow are computed by a Navier–Stokes solver using a pseudo-compressibility method. The cavity flow is computed from the velocity field by a tracking method based on a volume of fluid technique (VOF). The method is illustrated by several computations, two cases of partial cavitation on a hydrofoil and a case of a cavitating body emerging at a free surface.     

Extension de la DRBEM à la propagation guidée en écoulement cisaillé

The present study aims to extend the Dual Reciprocity Boundary Element Method in order to solve acoustic wave propagation equations in the frequency domain for a parallel shear flow. The Linearized Euler Equations are written as a coupled pair of equations, which are second-order in terms of acoustic pressure and first-order in terms of normal acoustic velocity. Good agreement between numerical results and analytical solutions for a low Mach number shear flow (M<0.1) shows the interest of the method.     

Mécanique de la rupture fragile en présence de plasticité : définition d'un taux de restitution d'énergie

This study aims at defining an energetic parameter which characterises progressive crack growth in a brittle elastoplastic medium. First, Francfort and Marigo's elastic fracture theory, based on a minimum energy principle, is recalled. Then, a link with the framework of generalised standard materials is exhibited and allows to introduce the new energetic contributions due to plasticity.     

Interprétation de la double structure observée dans l'onde de détonation du nitrométhane gazeux

Calculations of the reaction zone of the detonation of gaseous nitromethane, either pure or diluted with oxygen, in the range of equivalence ratio Φ between 0.1 and 1.75, show that for 1.75⩾Φ⩾1.3 the chemical energy is released in two main successive reaction steps characterized by very different induction times. These results corroborate the experimental observations of two levels of cellular structures in the same range of equivalence ratios. To our knowledge this work is the first which deals with the problem of nonmonotonous chemical energy release behind the leading shock of a detonation wave.     

Calcul numérique de la déformation mécanique d'un modèle de cellule endothéliale

Mechanical forces influence endothelial cell's (EC) morphology and functions. In this work it was proposed a numerical analysis of steady laminar flows near a modeled monolayer of elastic ECs in order to determine the local distributions of mechanical forces on the surface and inside of the cell. The numerical results showed that the flow induced mechanical stresses led to a cell deformation and that the distributions of these stresses were not uniform on cell surface. It will be interesting to study eventual correlations between the distributions of biological receptors (cytoskeleton, adhesion molecules, etc.) and that of the non-uniform mechanical forces.     

Application de la méthode des approximations successives à la résolution d'un problème aux limites de l'hydrodynamique

Sans résumé Mémoire transmis par R. Finn     

Étude numérique des instabilités de la phase fluide et de l'interface de solidification en croissance dirigée horizontale

Convective instabilities of low Prandtl number fluids are subject to various studies. The purpose here is an extension to hydrodynamic transitions in the fluid phase with a free or rigid surface under phase change and to construct the corresponding bifurcation diagram. Investigations interesting the process control by using the latent heat and the solid/liquid thermal conductivity difference are considered. The solution methodology is based on a front localisation approach showing a very good ability to describe convection regimes coupled to the phase change transition in the case of vertical solidification with confinement. To cite this article: E.A. Semma et al., C. R. Mecanique 331 (2003).     

Interprétation géométrique de la décomposition des équations de compatibilité en grandes déformations

In this paper, we establish compatibility equations satisfied by the right Cauchy–Green stress tensor by annihiling the associated curvature and torsion. The cancelation of torsion, using variables introduced by the polar decomposition, is not trivial as is usually the case. This point is the key to the decomposition of compatibility conditions in two first-order EDPs.     

Fonction de distribution pour les gaz polyatomiques dans la couche de Knudsen. Solution approchée de l'équation de Boltzmann

Polyatomic gases in strong non equilibrium vibrational state are studied in the Knudsen layer. A kinetic equation is derived from the Boltzmann equation for a stationary gas without macroscopic velocity. The simplification are basically deduced from the order of magnitude of adimmensional gradient terms. The approximate solution of this equation is deduced from a recurrent algorithm on the adimensional space variable power. Furthermore, the boundary condition allows us to obtain density and temperature jumps at the wall.     

Phénomènes transitoires au cours de la déformation plastique à chaud de l'acier

Sans résumé     

Sur la nature de la transition à l'instationnaire d'un écoulement de convection naturelle en cavité différentiellement chauffée à grands écarts de température

Natural convection of air inside a rectangular cavity, differentially heated under large temperature gradients, is considered. The low Mach approximation equations are those obtained by Paolucci allowing for filtering of sound waves. Transition to unsteadiness is studied with numerical simulation, with a finite volume code based on a fractional time step method derived from projection methods used for incompressible flows. When the fluid physical properties are prescribed constants, transition to unsteadiness follows the classical scheme of a Hopf bifurcation. The transition is quite different when viscosity obeys Sutherland's law while the Prandtl number is kept constant. There is evidence of hysteresis, therefore the transition seems to be subcritical. In the vicinity of the transition, on the large amplitude branch, an intermittent solution is observed, with periodic bursts separating quasi-steady states.     

Caractérisation de la gélification d'une résine thermodurcissable par méthode rhéologique

Résumé Une nouvelle façon de repérer la gélification d'une résine thermodurcissable est proposée, à partir de mesures rhéologiques. Le point de gel est relié à une diminution de la vitesse de croissance du module visqueux observée sur les courbes expérimentales en cours de cinétique à température constante. Les temps de gel obtenus sont du même ordre que ceux donnés par les autres méthodes rhéologiques, mais font cependant apparaître des différences sensibles. Le temps de gel obéit à une loi d'Arrhénius en fonction de la température de cuisson.Le module visqueux au point de gel et, par conséquent la viscosité en ce point, varient avec la température. Il en est de même pour le facteur de perte tan . Par contre, le module élastique au point de gel se conserve quelle que soit la température. Ces résultats ont été obtenus sur deux formulations de résine: DGEBA (n = 0) – mPDA et DGEBA (n = 0) – DDM à la stoechiométrie.

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A new method of characterizing gelation of a thermosetting resin from rheological measurements is proposed. Gelation is associated with a reduction in the speed of growth of the viscous modulus which is observed on the experimental curves during isothermal kinetics. Times of gelation obtained in this way are of the same order of magnitude as those found with other rheological methods, however distinct differences are observed. These times follow the Arrhenius' law as a function of the processing temperature.The viscous modulus at the gelation point and, as a consequence, the viscosity at this point, vary with temperature. This comes also true for the loss factor tan . In contrast, the elastic modulus at the gelation point does not change with the temperature. These results were obtained with two resin formulas: DGEBA (n = 0) – mPDA and DGEBA (n = 0) – DDM in stoechiometric concentration.

     

Variation de la vitesse de propagation d'ondes ultrasoniques au cours du passage de l'état liquide à l'état solide

Résumé Une étude théorique de la vitesse de propagation des ondes ultrasoniques dans les liquides et solides rend plausible l'hypothèse que l'évolution de l'état liquide à l'état solide doit être accompagnée d'une variation de la vitesse de propagation des ondes ultrasoniques.Il résulte des essais d'orientation relatés dans ce mémoire que la variation de la vitesse de propagation des ondes ultrasoniques est susceptible de caractériser la vitesse de passage de l'état liquide à l'état solide d'une matière ou d'un matériau.La méthode est applicable dans un domaine étendu et est sensible même assez loin du point de solidification. Elle se prête à l'étude du processus de l'évolution de la solidification des suspensions, des solutions, des matériaux organiques à longue chaîne, etc.

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Zusammenfassung Die theoretische Überlegung über die Geschwindigkeit der Ausbreitung von Ultraschallwellen in Flüssigkeiten und festen Körpern kann die Hypothese angenommen werden, daß die Umwandlung vom flüssigen in den festen Zustand von einer Geschwindigkeitsänderung der Ultraschallwellen begleitet wird.Aus den in diesem Bericht gebrachten Einführungsversuchen ergibt sich, daß die Variation der Ausbreitung von Ultraschallwellen dazu geeignet ist, die Umwandlungsgeschwindigkeit der Materialien von flüssigem in festen Zustand zu bewerten.Die Methode ist in einem weitem Bereiche brauchbar und ist auch weit vom Erstarrungspunkt empfindlich. Sie kann angewendet werden, um den Erstarrungsprozeß von Suspensionen, Lösungen und organischen Stoffen zu untersuchen.

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Ingénieur des constructions civiles. Docteur spécial en connaissance des matériaux. Agrégé près la Faculté des Sciences Appliquées de l'Université de Liège (Belgique).     

Sur une méthode de pénalisation tensorielle pour la résolution des équations de Navier–Stokes

An original reformulation of the viscous stress tensor is proposed for the motion equations dedicated to an incompressible fluid. Four different tensors appear in this decomposition, associated with viscosities of compression, elongation, shearing and rotation. This new model allows us to build a numerical solver of the Navier–Stokes equations based on a technique of tensorial penalization which is generalized with all the stresses acting on a flow. The processing of incompressibility and the rotation of a rigid body in a flow are described thanks to the model. Several numerical applications are proposed to illustrate the abilities of the new penalization method.     

Vérification expérimentale de la relation de réciprocité d'Onsager pour l'électro-osmose et l'électro-filtration dans une argile naturelle

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.     

Effet du couplage thermomécanique sur la propagation d'un front de changement de phase

Calorimetric effects related to the propagation of a phase change front in a monocrystalline shape memory alloy CuZnAl were derived from thermographic data analysis. At constant load, the displacement of the front induces a creep of the sample strongly depending on thermal exchanges with the surroundings. The main role played by the thermomechanical couplings can be pointed out by reversing the heat flux at the boundary of the sample: this leads to an inversion of the front propagation way associated with a recovery of the creep strain.     

Étude expérimentale du dépôt de particules colloïdales en milieu poreux : Influence de l'hydrodynamique et de la salinité

This study deals with colloid transport in porous media which applications are found in subsurface water, petroleum engineering or civil engineering. An experimental study of colloidal polystyrene Latex particles deposition in a consolidated porous medium is presented. The influence of ionic strength of the colloid suspension and the flow rate on particle deposition is investigated. We see first that beyond a critical salt concentration, the total collector efficiency increases with the ionic strength. Moreover, such collector efficiency decreases as the flow rate increases according to theory. In other respects, using a γ ray attenuation technique allows us to measure local porosity fluctuation due to particles deposition. By this way deposition kinetics may be followed locally and precisely. Nevertheless when considering the thickness of the adsorbed layer over large scales, obtained results using the γ rays attenuation technique are found in good agreement with those obtained by means of an usual technique especially at latest stages of adsorption process. To cite this article: A. Djehiche et al., C. R. Mecanique 337 (2009).