A collision strategy for particles in particulate flow simulationsSur le traitement des collisions lors de la simulation numérique des écoulements particulaires

A novel collision strategy has been implemented for simulation of particulate flows using a Lagrange multiplier/fictitious domain method. In this Note, we present this new collision strategy that is based on Newton's principle of transfer of momentum. With this method, we have simulated motion of two discs under the influence of gravity in a viscous fluid, and the motion of 1008 discs under the effect of gravity. To cite this article: P. Parthasarathy, C. R. Mecanique 330 (2002) 77–81.     

Effet de l'orientation d'un champ magnétique horizontal sur la stabilité de l'écoulement de HadleyEffet of the orientation of a horizontal magnetic field on the stability of Hadley flow

A numerical study based on the linear stability analysis is undertaken, in order to determine the influence of a horizontal magnetic field on the marginal modes occuring in a fluid layer subjected to a horizontal temperature gradient. A particular interest is devoted to the influence of the magnetic field orientation on both nature and critical values of the unstable modes. Calculations show, that when it is subjected to such a magnetic field, this type of flow, known as Hadley flow, can present oblique waves, hitherto non-existent when no magnetic field is applied and even when a vertical, a transverse or a longitudinal magnetic field is imposed. A new asymptotic behavior is also observed for the stabilizing effects. To cite this article: S. Kaddeche et al., C. R. Mecanique 331 (2003).     

Pont entre les « micro » et « méso » mécaniques des composites stratifiésRelationships between ‘micro’ and ‘meso’ mechanics of laminated composites

A relatively complete bridge is built between the micromechanics of laminates for which there are numerous theoritical and experimental works and the mesomechanics of laminates introduced and developped in particular at Cachan for more than 15 years. At the ‘meso’ scale, the ply and the interface are homogeneized. To cite this article: P. Ladevèze, G. Lubineau, C. R. Mecanique 331 (2003).     

A mixed formulation for elastic multilayer platesUne formulation variationnelle mixte pour les plaques élastiques multicouches

A new approach based on a mixed formulation is proposed. The main advantage of such a formulation is that the transverse shear stress continuity is automatically satisfied in a natural way. In order to validate the model, comparisons of the proposed theory to Pagano's exact elasticity solutions are made for a bi-layer and a sandwich plate. To cite this article: A. Fernandes, C. R. Mecanique 331 (2003).     

Un modèle viscoélastique de remodelage osseux : approche unidimensionnelleA viscoelastic model of bone remodeling: unidimensional approach

A bone remodeling model taking into account the viscoelastic properties of the material is proposed. The nonlinear equations governing the evolution of the bone apparent density are solved by a finite difference method in the unidimensional case of a n-unit elements model. The results show the effects of the viscous damping on the structure for a controlled mechanical loading. To cite this article: S. Baïotto, M. Zidi, C. R. Mecanique 332 (2004).     

Contribution de la logique floue à la représentation des dimensions des pièces d'un ensemble mécaniqueFuzzy logic contribution to the representation of mechanical assembly pieces

The cotation process of a mechanical assembly is a long and complex step of the design. The piece dimensions are often modeled with 2D vectors or torsors. A new representation based on fuzzy logic is presented in this article. The calculus methods of fuzzy dimensions are examined and an application to the extreme positions of a rod-crank system with uncertain dimensions is also presented. To cite this article: C. Lelu, M. Dahan, C. R. Mecanique 330 (2002) 133–140.     

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).     

Homogénéisation de coques minces piézoélectriques perforées

In this Note we establish the limit constitutive law of a piezoelectric material with periodically perforated microstructures and whose reference configuration is a thin shell with fixed thickness. The justification of the new associated model (we show that the limit global and local problems are more complicated than the intial one) is obtained using the periodic unfolding method introduced by Cioranescu, Damlamian and Griso. To cite this article: M. Ghergu et al., C. R. Mecanique 333 (2005).     

Estimation of the mesoscopic thermoplastic dissipation in High-Cycle FatigueEstimation de la dissipation thermoplastique en fatigue à grand nombre de cycles

A series of High-Cycle Fatigue (HCF) criteria for polycrystalline materials is based on a multiscale interpretation, proposed initially by Dang Van, in which the principal concepts are a two scales model and a shakedown condition. The purpose of this Note is to extend the study of the different dissipative regimes during cyclic loading within this framework by using a self consistent homogenization scheme in coupled thermoplasticity. It is shown that the Sachs and Lin-Taylor schemes are not able to represent the thermal evolutions observed during fatigue tests. To cite this article: E. Charkaluk, A. Constantinescu, C. R. Mecanique 334 (2006).     

A numerical experiment on the interaction between a film and a turbulent jet

This work is focused on the study of the impingement of a turbulent plane jet on a moving film. A computational fluid dynamics code has been used to simulate the interaction between the turbulent plane jet and the moving film. Since the problem of coupling between turbulence and free surface flow is poorly understood and experiments in this problem are difficult to carry out, this new numerical tool has been designed to give insight into global and local parameters of the free surface flow. To cite this article: D. Lacanette et al., C. R. Mecanique 333 (2005).     

An advanced design method for propellers behind bodies of revolutionCalcul de l'hélice fonctionnant en arrière d'un corps à symétrie axiale

The flow around the unshrouded marine propellers operating in the wake of an axisymmetric body is rotational and tridimensional. An inverse method based on the model of inviscid and rotational fluid and coupling two complementary steps (axisymmetric computation + 3D panel method) is proposed for the design of the marine propellers. The meridional flow computation leads to the determination of axisymmetrical stream sheets as well as the approximate camber surface of the blades and gives a good estimation of the surface of the free vortex wake. The new aspects developed in this method are the involvement of the contraction and the stretching of the free vortex wake, the rotational character of the incoming flow in the axisymmetric computation with tridimensional effects due to 3D panel method. To cite this article: N. Settou, B. Viney, C. R. Mecanique 331 (2003).     

The mixing layer instability of wind over a flexible crop canopyInstabilité de couche de mélange dans le vent sur un couvert végétal souple

A coupled fluid-stucture model is proposed to study the dynamics of a flexible crop canopy exposed to wind. The canopy is represented by an elastic continuous medium and coupled to the wind mixing layer through a drag load. The mixing layer instability is shown to remain the principle instability mechanism but its characteristics are modified when taking into account the flexible canopy. The size of the coherent structures is decreased as well as the instability growth rate. To cite this article: C. Py et al., C. R. Mecanique 332 (2004).     

Approche micromécanique du couplage perméabilité–endommagementMicromechanical approach to the coupling between permeability and damage

A self-consistent scheme is used in order to determine the permeability of a cracked porous medium. For weak values of the permeability of the uncracked porous matrix, it is found that the order of magnitude of the permeability increases beyond a critical threshold of the crack density parameter. In the framework of a micromechanical model, it is shown that both the evolution of crack opening and the crack propagation are controlled by Terzaghi's effective stress which therefore captures the coupling between permeability and mechanical loading. To cite this article: L. Dormieux, D. Kondo, C. R. Mecanique 332 (2004).     

Symmetrization of Lagrangian gas dynamic in dimension two and multidimensional solversSymétrisation de la dynamique des gaz en dimension deux et solveurs multidimensionnels

We propose a new formulation of multidimensional Euler equations in Lagrange coordinates as a system of conservation laws associated with free-divergent constraints. This formulation leads to a natural class of entropic Lagrangian schemes, based on a multidimensional node solver. For the sake of simplicity the study is done in 2D, but most of the ideas can be generalized in 3D. To cite this article: B. Després, C. Mazeran, C. R. Mecanique 331 (2003).     

Nonlinear composites: a linearization procedure,exact to second-order in contrast and for which the strain-energy and affine formulations coincideComposites non linéaires : un schéma exact au second ordre pour lequel la formulation en énergie de déformation coı̈ncide avec la formulation affine

This Note presents a new approximate scheme for nonlinear composites. The approximation which is made preserves certain features of the original second-order scheme of Ponte Castañeda, exactness to second-order in the contrast and existence of an effective energy, but improves on one drawback, which is the gap between the strain-energy formulation and the affine formulation. A numerical example shows the accuracy of the present method. To cite this article: N. Lahellec, P. Suquet, C. R. Mecanique 332 (2004).     

Homogenization of an elastic medium reinforced by anisotropic fibersHomogénéisation d'un milieu élastique renforcé par des fibres anisotropes

We present results in this Note concerning a vector version in the framework of linearized elasticity (see A. Sili, Homogenization of an elastic medium reinforced by anisotropic fibers, in press), of our previous work in which we have studied the homogenization of a scalar nonlinear monotone problem posed on a fibered medium (see A. Sili, Homogenization of a nonlinear monotone problem in an anisotropic medium, in press). Here, we assume that parallel elastic anisotropic fibers, periodically distributed with a period of size ε in a cube $\text{Ω}$, are surrounded by a soft elastic material, the elasticity coefficients of this material being in the ratio ε² with those of the fibers. We prove that the homogenized problem is nonlocal and involves variables linked together with the anisotropy of the fibers. To cite this article: A. Sili, C. R. Mecanique 331 (2003).     

Effective equations describing the flow of a viscous incompressible fluid through a long elastic tubeEquations efficaces décrivant l'écoulement d'un fluide visqueux incompressible dans un tuyau long et élastique

We study the flow of a viscous incompressible fluid through a long and narrow elastic tube whose walls are modeled by the Navier equations for a curved, linearly elastic membrane. The flow is governed by a given small time dependent pressure drop between the inlet and the outlet boundary, giving rise to creeping flow modeled by the Stokes equations. By employing asymptotic analysis in thin, elastic, domains we obtain the reduced equations which correspond to a Biot type viscoelastic equation for the effective pressure and the effective displacement. The approximation is rigorously justified by obtaining the error estimates for the velocity, pressure and displacement. Applications of the model problem include blood flow in small arteries. We recover the well-known Law of Laplace and provide a new, improved model when shear modulus of the vessel wall is not negligible. To cite this article: S. ?ani?, A. Mikeli?, C. R. Mecanique 330 (2002) 661–666.     

Flow in wavy tube structure: asymptotic analysis and numerical simulationÉcoulement dans une structure tubulaire ondulée : analyse asymptotique et résolution numérique

This paper deals with the study of the stationary, incompressible, 2D flow of a fluid in a thin wavy tube. In this work, we consider a domain which is the union of two wavy tubes depending on a small parameter. The asymptotic expansion is constructed. The method of partial asymptotic decomposition is applied. The numerical implementation of this method for the extrusion process is developed. The new physical effects are discussed. To cite this article: A. Ainser et al., C. R. Mecanique 331 (2003).     

Un nouveau préconditionneur pour les problèmes elliptiques à coefficients variablesA new preconditonner for general elleptic problems

In this Note we describe a preconditionner for iteratively solving the linear system arising from the discretization of a general nonseparable elliptic problem by spectral element method. This preconditionner is constructed from approximating the original problem with the closest (in some sense) separable elliptic problem. A direct method is then used to invert the preconditionner. To cite this article: M. Azaïez et al., C. R. Mecanique 331 (2003).