Décomposition des déplacements d'une poutre : simplification d'un problème d'élasticité

We present a decomposition of rod displacements. Then we use this decomposition to simplify an 3D linearized elasticity problem. The formal problem obtained is a differential system which depends on the thickness of the rod. We give error estimates. To cite this article: G. Griso, C. R. Mecanique 333 (2005).     

L'approche variationnelle de la fatigue : des premiers résultats

By using a principle of least energy and a Dugdale surface energy with an irreversibility condition, we build a debonding model of thin films valid both for monotone and cyclic loading. We show that, if the internal length introduced in Dugdale model is small in comparison to the film length, then the growth of the debonding follows Griffith's law under monotone loading and a Paris-type law under cycling loading. To cite this article: A. Jaubert, J.-J. Marigo, C. R. Mecanique 333 (2005).     

Modélisation des problèmes d'impact avec dissipation d'énergie par frottement

The bi-potential method has been successfully applied for the modeling of frictional contact problems in static cases. This paper presents the application of this method for dynamic analysis of impact problems with multiple deformable bodies. A first order algorithm is applied for numerical integration of the time-discretized equation of motion. The numerical results show clearly the physical energy dissipation introduced by frictional effects between the solids in contact. To cite this article: B. Magnain et al., C. R. Mecanique 333 (2005).     

Quelques aspects de l'écoulement potentiel autour d'un corps en rotation

On the basis of simple conformal mappings, we present a method to describe a two-dimensional potential flow around a rotating obstacle of arbitrary section. As a result, a simplified expression of the matrix of added mass and added moment of inertia is obtained. We also underline the need to determine this perturbation potential all over the fluid domain. Indeed, this is of practical interest in order to express the hydrodynamic moment in incompressible viscous flow. To cite this article: Y.-M. Scolan, C. R. Mecanique 333 (2005).     

Data assimilation and pollution forecasting in Burgers' equation with model error function

This article presents a correction method for a better resolution of the problem of estimating and predicting pollution, governed by Burgers' equations. The originality of the method consists in the introduction of an error function into the system's equations of state to model uncertainty in the model. The initial conditions and diffusion coefficients, present in the equations for pollution and concentration, and also those in the model error equations, are estimated by solving a data assimilation problem. The efficiency of the correction method is compared with that produced by the traditional method without introduction of an error function.Three test cases are presented in this study in order to compare the performances of the proposed methods. In the first two tests, the reference is the analytical solution and the last test is formulated as part of the “twin experiment”.The numerical results obtained confirm the important role of the model error equation for improving the prediction capability of the system, in terms of both accuracy and speed of convergence.     

Influence d'une polarisation électrique sur l'instabilité d'une interface liquide/liquide

One studies the influence of the surface tension on the stability of a liquid electrolyte/liquid metal interface. The control of this parameter is obtained by an electric polarization imposed on the liquid metal. The flow is carried out in a cylindrical cavity with turning lid and fixed bottom on the level of which a annular drain filled with liquid gallium is set. One analyzes the phenomenon of appearance of the waves of instability according to the surface tension. The experimental results are compared with a Kelvin–Helmholtz model, purely non-viscous or corrected by taking into account the normal component of the viscous constraints. To cite this article: M. Al Radi et al., C. R. Mecanique 333 (2005).     

Simulation du front d'écoulement dans les procédés de moulage des composites liquides

This work proposes a procedure of finite difference discretized in a system of curvilinear coordinates adapted to the shape of the saturated zone, to simulate a flow in the LCM (Liquid Composites Molding) process. Formulation and the numerical application of the procedure are described. We describe two configurations of injections. A good agreement is found between numerical, analytical and literature experimental results. To cite this article: M. Hattabi et al., C. R. Mecanique 333 (2005).     

Effet d'un champ magnétique transversal sur la stabilité de l'écoulement de Hartmann : les modes tridimensionnels

A numerical study is conducted in order to determine the influence of a transverse magnetic field on the three-dimensional instabilities of the Hartmann flow. We prove that the Squire transformation currently used to characterize such instabilities give satisfactory results only in the case where Ha is weak and 3D modes are slightly deviated from the 2D modes. Such a study is justified by the fact that the two-dimensional instabilities could not always explain successfully the experimental observations relating to the transition phenomenon. To cite this article: M. Jédidi et al., C. R. Mecanique 333 (2005).     

Représentation à l'échelle microscopique d'un mécanisme de rupture dans un milieu a joints

. A representation of a class of failure mechanisms defined on a homogenized jointed medium by a velocity jump along a planar surface, is analyzed at the scale of the joints. The approach consists in representing a velocity jump at the macroscopic level by the kinematics of a finite band in the heterogeneous medium characterized by a piecewise rigid body motion of elementary blocs. The equivalence (in the sense of the yield design theory) between the macroscopic and macroscopic representations of such failure mechanisms is ensured by the equality of the corresponding maximum resisting rates of work. To cite this article: S. Maghous et al., C. R. Mecanique 333 (2005).     

Conséquences de l'agrégation et de la percolation de charges sur le comportement viscoélastique de nanocomposites

The aim of the present Note is to differentiate the relative contributions of the aggregation and the percolation phenomena to the viscoelastic behaviour of composites. This separation is performed through the development of a micromechanical model, by taking into account the percolation concept. To cite this article: P. Mélé et al., C. R. Mecanique 333 (2005).     

Hybrid schemes to compute contact discontinuities in Euler equations with any EOSSchémas hybrides pour la simulation des discontinuités de contact des équations d'Euler avec une loi d'état quelconque

We propose here some explicit hybrid schemes which enable accurate computation of Euler equations with arbitrary (analytic or tabulated) equation of state (EOS). The method is valid for the exact Godunov scheme and some approximate Godunov schemes. To cite this article: T. Gallouët et al., C. R. Mecanique 330 (2002) 445–450.     

Étude numérique de l'écoulement d'un fluide non newtonien thermodépendant entre deux plaques parallèles

In this study, the heat transfer of a non Newtonian thermodependent fluid flowing between two parallel plates is considered. The effects of different parameters on the evolutions of thermal boundary layer and of Nusselt number are numerically investigated in two heating cases and correlations are proposed to compute the heat transfer. To cite this article: N. Van Tuan, M. Lebouche, C. R. Mecanique 333 (2005).     

Une méthode inverse d'ordre un pour les problèmes de complétion de données

An iterative resolution method for inverse Cauchy problems is presented. The successive iterations satisfy the equilibrium equations exactly. Numerical simulations prove the accuracy of the method and its ability to solve Cauchy problems when the domain boundary is not regular. To cite this article: A. Cimetière et al., C. R. Mecanique 333 (2005).     

Frottements et pertes de pression des fluides non newtoniens dans des conduites non circulaires

The study of fluid flow in a duct requires characteristic parameters of the flow and dimensionless numbers to correlate and compare experimental results. For Newtonian fluids in simple configurations, the definition of the Reynolds number is quite standard, but for non-Newtonian fluid flows in ducts with arbitrary shape of cross section, the dependence of the apparent viscosity with the shear rate requires a generalization of this dimensionless number. This note proposes a general method valid for a large class of non-Newtonian fluids and for all duct shapes. An application is developed for a viscoelastic flow through a rectangular duct. Results obtained in the present investigation are in a good agreement with available correlations. To cite this article: M. Mahfoud et al., C. R. Mecanique 333 (2005).     

Identification of the scatter in high cycle fatigue from temperature measurementsIdentification de la dispersion des limites d'endurance à l'aide d'un essai d'échauffement.

It is proposed to determine the scatter in a Wöhler diagram by analyzing temperature changes induced by microplasticity. A unified framework is introduced to study both phenomena. The identification procedure is applied to a dual-phase steel. To cite this article: C. Doudard et al., C. R. Mecanique 332 (2004).     

Artificial boundary conditions on polyhedral truncation surfaces for three-dimensional elasticity systemsConditions aux limites artificielles sur des surfaces polyhédrales de troncature pour des systèmes d'élasticité tridimensionalle

For a three-dimensional exterior problem in the framework of anisotropic elasticity, artificial boundary conditions are constructed on a polyhedral truncation surface. These conditions do not need an explicit formula for the fundamental matrix. An approach to adapt the shape of truncation surfaces to the shape of the enclosed cavity is discussed. To cite this article: S. Langer et al., C. R. Mecanique 332 (2004).     

Piston Stokes flow in a semi-infinite channelL'écoulement de Stokes autour d'un piston dans un conduit semi-infini

The piston flow is bounded by rigid walls at y=±1, x>0 and generated by the uniform translation of the end wall x=0. After Katopodes, Davis and Stone [3] constructed a solution in terms of biorthogonal eigenfunctions, Meleshko and Krasnopolskaya [1] used a variation of an asymptotic technique developed by Meleshko and Gomilko [2] to examine the pointwise convergence of the non-orthogonal series. However, they overlooked the nonuniqueness of their solution and the consequent solvability condition which is shown here to necessitate a minor modification without significant harm to their contribution. To cite this article: A.M.J. Davis, C. R. Mecanique 330 (2002) 457–459.     

Self-demodulation acoustic signatures for nonlinear propagation in glass beadsSignatures acoustiques de l'auto-démodulation basse fréquence lors de la propagation non linéaire dans des billes de verres

The present Note describes some experimental work related to the nonlinear propagation of acoustic waves in granular media such as unconsolidated glass beads. The studied nonlinear effect is a self-demodulation process performed with the operation of the so-called parametric transmitting antenna. The pump (or carrier) wave is generated by a high power ultrasonic broad-band transducer (100 kHz central frequency) which is LF (low frequency, i.e., a few kHz) amplitude modulated. As the attenuation of acoustic waves increases with frequency, only the LF demodulated wave can be transmitted. A parametric study is performed where the HF central frequency is monitored between 60 and 300 kHz. The LF demodulation profile versus the HF frequency is modified, its shape being temporally derived almost twice. A numerical analysis of the order of temporal derivation is done in the Fourier domain, its value varying from 1.25 to 2.7. Qualitative agreement with current theoretical models is described, and an advanced theoretical analysis by the same authors [Phys. Rev. E 66 (2002) 041303], taking into account absorption, nonlinearity, dispersion and scattering, is briefly discussed. To cite this article: V. Tournat et al., C. R. Mecanique 331 (2003).     

Résistance d'un milieu poreux à phase solide hétérogène

The strength of a porous medium, the solid phase of which is made up of composite spheres is determined in the framework of a micromechanical self-consistent reasoning. The strength of the spherical cores is infinite while the surrounding layers are made up of a von Mises material. Application of the modified secant method yields an analytical expression of the macroscopic strength. Such results can be used in order to predict the setting and strength criterion of a cement paste during hydration. To cite this article: J. Sanahuja, L. Dormieux, C. R. Mecanique 333 (2005).