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     

Représentation de la ligne de contact mobile dans les équations de la mécanique des fluides

Although the contact angle at equilibrium has a well understood theory for the case of flat homogeneous solid surfaces, the displacement of the contact line is still not well understood. We propose to introduce in the dynamics of the contact line a mobility relation between the deviation of the contact angle out of its equilibrium value and the speed of the line on the solid. When the line slides on the solid thanks to an evaporation/condensation process, this introduces a dynamical Arrhenius factor that may be sufficiently small to make the mobility of the contact line the limiting factor of the dynamics in many physical situations. Then, the shape of the liquid/vapor interface will be in quasi equilibrium giving a contact angle that will define ultimately the speed of the contact line.     

Méthode de Le Verrier–Souriau et équations différentielles linéaires

A crucial step of algorithms allowing the study of discrete mechanical system vibrations is the determination of eigenmodes and eigenvalues. The accuracy of the results is of great importance because the stability study of the system depends on them. Eigenvalues can be found with a very good precision, however the eigenmodes determination is awkward: their direction could present significant instabilities. We proposed a method which avoids the necessity of doing eigenmodes research and so the attendant instabilities. It is based on Le Verrier–Souriau algorithm usually reserved for the resolution of linear algebraic systems.     

Une méthode inverse à régularisation évanescente

A new resolution method for inverse Cauchy problems is presented. The proposed method is iterative. It possesses the advantage to not perturbe the problem neither by an operator modification nor by introduction of an a priori information on the solution. The presentation is made on a model problem for the Laplace's equation. Numerical simulations prove the method efficiency.     

Une méthode mécanique pour déterminer la porosité totale d'un sol

This paper presents a mechanical method for the determination of the total porosity of soil. The presented method consists in inserting a sample of soil into a cell that can be regulated by varying the volume of the gas by increments using a piston. The porosity of the soil is deduced from the variation of the total pressure of the gaseous phase during the realization of volume increments. The method has been validated on a soil considering five samples with different porosities. The experimental results on the total porosity are in good agreement with the theoretical results over all tests.     

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.

     

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.     

Calcul numérique des ondes de surface par une méthode de projection avec un maillage eulérien adaptatif

A non hydrostatic vertical two-dimensional numerical model is proposed to calculate free-surface flows. This model is based on resolving the full Navier–Stokes equations by a finite-difference method coupled with Chorin's projection method. An adaptative-Eulerian grid in the sigma-coordinate system is used. The model permits the calculation of surface-waves in estuarine and coastal zones. A benchmark test relative to the soliton propagation is realised to validate the model.     

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.     

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.     

Analyse de la répartition du potentiel électrique dans les flammes

Distribution of electrical potential is investigated for two kinds of flames: Bunsen burner and counterflow flames. Different electrode materials have been tested to determine these potentials. Measurable potentials and organized structures are found. Premixed Bunsen burner flames show a zero potential cone at their base just under the most intense potential region. One-dimensional counterflow diffusion flames are characterized by the stretch rate. The potential reaches its minimum value in the reaction zone and its absolute value decreases when stretch increases.     

Un résultat d'absence de valeurs propres plongées pour le guide topographique élastique

In this work, we prove a nonexistence result about embedded eigenvalues for the elastic topographical waveguide. We give an answer to a question raised by Bonnet-Bendhia et al. (1999).     

Abaissement différé de la limite apparente d'élasticité des aciers après une déformation sous une tension atteignant cette limite

Résumé Le fluage des aciers doux, demi-durs et durs possédant une limite apparente d'élasticité se présente sous la forme particulière d'un écoulement rapide et différé, lorsque ces aciers ont été d'abord soumis à un étirage sous une tension atteignant la limite apparente d'élasticité et lorsqu'ils ont été soumis immédiatement après décharge à l'effet d'une charge permanente de fluage réalisant une tension inférieure à la limite apparente d'élasticité.Plusieurs essais de fluage et de relaxation ont été réalisés dans ces conditions pour déterminer l'ordre de grandeur de la tension la plus basse susceptible de provoquer cet écoulement caractéristique.

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Summary The creep of different kinds of steels with a yield point has the particular form of a delayed yield when the bars have previously been strained at a stress equal to the yield point and afterwards submitted to creep under a constant stress lower than the yield point.Several creep and relaxation tests have been performed under these conditions in order to appreciate the lower stress which is able to produce the delayed yield.

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Zusammenfassung Das Kriechen der Stähle von verschiedener Güte mit natürlicher Streckgrenze stellt sich dar in charakteristischer Form eines verspäteten Fließens, wenn diese Stähle zuerst beim Zuge bis zur Streckgrenze verformt werden und dann nach Entspannung dem Kriechversuch übergeben werden unter eine Zugspannung kleiner als die Streckgrenze.Mehrere Kriech- und Relaxationsversuche wurden in diesen Angelegenheiten durchgeführt, um die kleinste Zugspannung zu bestimmen, welche noch geeignet ist, das verspätete Fließen zu bewirken.

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Professeur à l'Université de Liège, directeur des Laboratoires d'Essais des Constructions du Génie Civil.

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Agrégé à l'Université de Liège, chef de section aux Laboratoires d'Essais des Constructions du Génie Civil.     

Équation énergétique locale pour la prevision des niveaux vibratoires et acoustiques instationnaires

Insights and additionnal clarifications concerning the energy diffusion model [4] are in concern herein. We showed in former times under steady state conditions, that the diffusion model is well suited for an uncorrelated plane wave dynamics [7], energy behaviour modelling. We will prove, in this short note, that the later is not enough when transient dynamics is in concern. We thus propose a new equation alternative to the diffusion equation.     

Homogénéisation d'équations et d'inéquations à paramètres oscillants. Application à l'étude d'écoulement de faible épaisseur en régime transitoire

Double scale homogenization is used to average stationary equation or inequalities in which both highly oscillating variables and parameters appear. We demonstrate how the limit is obtained using a two-stage procedure , firstly by carrying out a classical homogenization process by freezing the oscillating parameter, then by averaging the result with respect to this parameter. These results allow us to average the pressure for a newtonian fluid in a narrow gap between two rough unstationnary surfaces.     

Mise en évidence par granularité en lumière blanche de phénomènes de multilocalisation de la déformation pour les bétons de poudres réactives sollicités en traction

From kinematic observations by granularity in whiting light mode based on a technique of digital speckle images correlation, the behaviour in tension of a reactive powders concrete is studied. The measures show several localisation areas of the deformation fields and the role of the fibres in the transmission of the stresses in the neighbourhood of a damaged area.     

Impact non-pénétrant sur le thorax : une contribution à l'étude de la propagation des ondes

The stress wave generated by a nonpenetrating impact on the thorax is likely to cause severe injury to the lung. Theoretical studies are necessary to help the understanding of injury mechanisms. Within the framework of elastodynamics, we study the transmission of a wave at the interface between two weakly coupled semi-infinite media representing the thoracic wall and the lung. By using an appropriate method, we describe the distribution of energy carried by the shear and pressure waves in the medium representing the lung. These results should contribute to a better interpretation of the experimental results.