Fissuration multiple par corrosion sous contrainte : Modélisation du comportement mécanique par une méthode d'homogénéisation

Stress Corrosion Cracking (SCC) phenomenon is characterised by initiation and propagation of surface cracks frequently multiple. In order to model the mechanical behaviour of such materials we propose, as for composites, the use of homogenization techniques. Two materials are considered, first one corresponding to the cracked external volume and the second to the internal safe material. The cracked volume is considered as a two phase material, i.e., elastic matrix containing elliptical voids. The overall behaviour of the equivalent material is obtained applying the usual homogenization rules. Comparison between simulations and experimental results is done.     

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.     

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.

     

Une analyse micromécanique 3-D de l'endommagement par mésofissuration

A micromechanical analysis of brittle damage is proposed. This analysis consists of a 3-D generalization of the study performed by Andrieux et al. In this approach, the macroscopic free energy for open microcracks and frictionless closed microcracks is built. The conditions for unilateral contact (opening/closure criterion, elastic moduli recovery) are also presented. The proposed construction ensures at the macroscopic level the symmetry of the elastic stiffness tensor and the continuity of stress at the damage deactivation.     

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.     

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.     

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.     

Joseph Kampé de Fériet et la mécanique des fluides en France durant l'entre-deux-guerres

Up until the twentieth century, fluid mechanics was characterised by a strong division between theory and practice. The formulas of mathematicians and physicists were difficult to apply experimentally and their relevance was neither well accepted nor well understood by engineers. In France, where priority was given to the theoretical aspects of this subject, the creation of several centres of fluid mechanics in the 1930s (Lille, Marseille, Paris and Toulouse) represented an attempt at a rapprochement between fluid mechanics, experimental aerodynamics, and hydrodynamics. The aim was to re-establish France's international profile, which had been lost after 1918. In Lille, the leadership of the “Institut de mécanique des fluides” (IMFL) was entrusted to Jospeh Kampé de Fériet, who was able to address questions of both theoretical and experimental nature in the context of his work at the IMFL and at the “Commission de la turbulence atmosphérique”. On the one hand, Kampé de Fériet used a probabilistic approach to give greater mathematical rigour to the statistical theory of turbulence due to Taylor–von Kármán. On the other hand, he played an active part in his group's experimental research on atmospheric turbulence. This paper aims to show in what way Kampé de Fériet's approach to fluid mechanics enabled him to contribute to the international development of the statistical theory of turbulence during the interwar period.     

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.     

Un modèle mésoscopique en grandes perturbations de matériaux textiles – Application à l'armure toile

A constitutive law in large transformations of soft structures has been elaborated, starting from a micropolar constituve law, whereby a microrotation takes into account the microstructure effect. In fabric, one undulation defines the mesoscopic scale. The hyperelastic law describes in a satisfactory manner the uniaxial traction curve of the fabric.     

Détonabilité de mélanges stoechiométriques méthane–hydrogène–oxygène–azoteDetonation characteristics of stoichiometric mixtures of methane–hydrogen–oxygen–nitrogen

The goal of this Note is to determine the influence of H₂ addition on the detonation and detonability of stoichiometric CH₄/O₂/N₂ mixtures for three values of the nitrogen dilution $\beta ={\mathrm{N}}_2/{\mathrm{O}}_2$ ($\beta =0$ (oxygen); 2; 3.76 (air)) and also of the influence of the initial temperature. It is based on the measurement of the mean cell size of the steady self-sustained detonation in these mixtures, this characteristic length being representative of the mixture detonability. Results indicate that the detonability of the (CH₄H₂) mixture is mainly controlled by the heavier fuel, i.e., CH₄ and for instance the detonability of the mixture where 20% of CH₄ volume has been replaced by H₂ is nearly the same as that of the mixture where CH₄ is the only fuel. The influence of the initial temperature on the detonability depends on N₂ concentration. To cite this article: C. Matignon et al., C. R. Mecanique 334 (2006).     

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     

Classification théorique des propriétés rhéologiques des corps réels

Résumé Une classification des propriétés rhéologiques fondée sur l'analyse théorique du comportement est proposée. L'attention y est attirée sur la non réparabilité des comportements elementaires ainsi que sur les propriétés de compressibilité.Une tentative est haute en vue d'effectuer un classement des propriétés dans á une modification de structuredes matériaux en cours de déformation.     

The stochastic energy-Casimir methodLa méthode d'énergie-Casimir stochastique

In this paper, we extend the energy-Casimir stability method for deterministic Lie–Poisson Hamiltonian systems to provide sufficient conditions for stability in probability of stochastic dynamical systems with symmetries. We illustrate this theory with classical examples of coadjoint motion, including the rigid body, the heavy top, and the compressible Euler equation in two dimensions. The main result is that stable deterministic equilibria remain stable in probability up to a certain stopping time that depends on the amplitude of the noise for finite-dimensional systems and on the amplitude of the spatial derivative of the noise for infinite-dimensional systems.     

Modélisation du bolus urétéral humain

We propose an improvement of the bolus passive viscoelastic wall model [1], by adding an active muscular layer situated on the internal side of the wall. This new model permits, for a suitable choice of the active force, to obtain analytically a closed bolus on its two ends and to get a close approach of the medical observations.     

Comportement thermomécanique d'un béton ordinaire en compression cyclée : expérience et modélisation

Infrared thermography observations permit to show thermal phenomena occurring on a plain concrete during a compressive test. A modelling of the thermomechanical behaviour of this materials is proposed as an extension of M. Frémond and B. Nedjar's model. It permits an interesting dialog between the experimental results and those obtained by a numerical simulation of a simple compressive test.     

Homogénéisation d'une poutre périodique : limite des développements asymptotiques

Starting from the equations of two-dimensional elasticity, a double-scale asymptotic expansion method is applied to a thin structure which is periodic in the direction perpendicular to the thickness. Under the given loading, all the terms of the displacement and stress expansions are determined. These expansions have finite limits under some conditions depending on the number of cells and the solutions of the cellular problems. Application examples show the contribution of higher-order terms in case the number of cells is small.