Characterization of a class of polycrystals whose effective elastic bulk moduli can be exactly determinedCaractérisation d'une classe de polycristaux dont les modules de compression isotrope effectifs peuvent exactement être déterminés

Necessary and sufficient conditions are established for the stress response of a linearly elastic material to an isotropic stain to be hydrostatic. In the 3D case, these conditions are satisfied not only by the isotropic and cubic materials but also by all other anisotropic materials provided appropriate restrictions are imposed. In the 2D case, only the isotropic and square materials have an isotropic stress response to an isotropic strain. Using a uniform field argument, the elastic bulk modulus of a polycrystal consisting of monocrystals compatible with the established conditions is shown to equal that of any constituent monocrystal. Thus, Hill's relevant result about a polycrystal composed of cubic monocrystals is generalized. To cite this article: Q.-C. He, C. R. Mecanique 331 (2003).     

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).     

Selection of two-dimensional nonlinear strain waves in micro-structured mediaSelection d'ondes de déformation non linéaires à deux dimensions dans des milieux à microstructure

It is shown that the micro-displacement gradient allows the propagation of two-dimensional localized long nonlinear strain waves in a medium with microstructure. These waves may exist even in the presence of dissipation and energy input in the microstructured medium but with selected values of the wave amplitude and velocity. An increase or a decrease in the wave amplitude and velocity happens faster at the initial stage than that of the plane localized wave. However, their steady values selected by the energy input/output, are higher for the plane waves. To cite this article: A.V. Porubov et al., C. R. Mecanique 332 (2004).     

On particle–particle interactions in solid,non-conducting impurity removalSur l'interaction particule–particule lors de l'extraction d'impuretés solides isolantes

A whole boundary-integral formulation is proposed to determine the rigid-body motions of two solid and insulating particles, freely-suspended in a metal liquid and subject to uniform ambient electric and magnetic fields. As revealed by our numerical results, particle–particle interactions may become significant for close enough bodies. To cite this article: A. Sellier, 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.     

Numerical implementation of composite Koiter shells including membrane/bending coupling coefficientsImplémentation numérique des coques composites de Koiter prenant en considération les coefficients de couplage membrane/flexions

We propose a way for determining the generalized coefficients of rigidity – some of which are membrane/bending coupling coefficients – which appear in the deformation energy of the Koiter model of thin shells. This is concerned with a heterogeneous material in the thickness direction. A new program to compute these coefficients is implemented in the finite element code Modulef, in order to simulate problems of thin multilayered shells with linearly elastic anisotropic layers. We propose an example of an inhibited multilayered thin shell, with hyperbolic middle surface, involving a composite material with unidirectional fibres. To cite this article: H. Ranarivelo, C. R. Mecanique 330 (2002) 273–278.     

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).     

Cylindre transverse isotrope poroélastique chargé cycliquement : application à un ostéonCyclic loading of a transverse isotropic poroelastic cylinder: a model for the osteon

The poroelastic problem associated with a hollow cylinder under cyclic loading is solved. Both fluid and solid phases are supposed compressible. Solid matrix is modeled as an elastic transverse isotropic material. An explicit close-form solution for the steady state is obtained. This cylinder is considered as a model for an osteon, the basic unit of cortical bone. The fluid flow distribution as a function of poroelastic properties and cyclic loading is discussed, as this could influence bone remodeling. To cite this article: A. Rémond, S. Naili, C. R. Mecanique 332 (2004).     

The elastic torus: anomalous stiffness of shells with mixed typeLe tore élastique : raideur anormale des coques de type mixte

We investigate the deformation of a thin elastic torus under axisymmetric surface loads. The strain concentrates near the top and bottom parallels and the inner and outer halves essentially undergo rigid-body translations in opposite directions. An analysis of the inner boundary layers is presented, which allows one to compute the effective stiffness of the torus for this loading. This stiffness is found anomalous compared to classical shells. These mechanical properties are interpreted using purely geometrical arguments. To cite this article: B. Audoly, Y. Pomeau, C. R. Mecanique 330 (2002) 425–432.     

On the thermal anisotropy affecting transfers in a multilayer porous mediumSur l'effet de l'anisotropie thermique sur les transferts dans un milieu poreux multicouches

An analytical model for studying double-diffusive natural convection within a multilayer anisotropic porous medium is developed and validated with respect to a direct numerical silmulation. The studied domain is composed of two horizontal porous layers where the lower one is thermally anisotropic and is submitted to a uniform horizontal heat flux and a vertical mass flux. The assumption of parallel flow is validated and the effect of anisotropy on dynamic transitions is investigated. To cite this article: R. Bennacer et al., C. R. Mecanique 332 (2004).     

Second-order estimates for the large-deformation response of particle-reinforced rubbersEstimations homogénéisées pour le comportement mécanique des caoutchoucs renforcés en grandes déformations

This paper presents the application of a recently proposed ‘second-order’ homogenization method (J. Mech. Phys. Solids 50 (2002) 737–757) to the estimation of the effective behavior of hyperelastic composites subjected to finite deformations. The main feature of the method is the use of ‘generalized’ secant moduli that depend not only on the phases averages of the fields, but also on the phase covariance tensors. The use of the method is illustrated in the context of particle-, or fiber-reinforced elastomers and estimates analogous to the well-known Hashin–Shtrikman estimates for linear-elastic composites are generated. The new estimates improve on earlier estimates (J. Mech. Phys. Solids 48 (2000) 1389–1411) neglecting the use of fluctuations. In particular, the new estimates, unlike the earlier ones, are capable of recovering the exact incompressibility constraint when the matrix is also taken to be incompressible. To cite this article: O. Lopez-Pamies, P. Ponte Castañeda, C. R. Mecanique 331 (2003).     

Stress equivalence principle for saturated porous mediaPrincipe d'équivalence en contrainte pour milieux poreux saturés

The stress equivalence principle for saturated porous media is studied in the plastic domain using a homogenization approach. The skeleton is composed of a micro-isotropic and micro-homogeneous material. The stress localization law in saturated porous media is first obtained. This makes it possible to define an appropriate effective stress tensor in the sense of the stress equivalence principle. The form of the effective stress tensor is examined for two particular yield functions of skeleton material. To cite this article: D. Lydzba, J.-F. Shao, C. R. Mecanique 330 (2002) 297–303.     

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).     

Chargements axisymétriques d'un bicouche transversalement isotropeAxisymmetric loading on a transversely isotropic two-layered medium

An exact three-dimensional analysis is developped for an axisymmetric loading acting on the surface of a semi-infinite medium composed by two transversely isotropic materials. The loading is assumed to be parallel to the elastic symmetry axis of the upper layer. The solutions of a concentrated force and a uniform loading distributed on a circle are obtained by exact integral expressions. The numerical results are performed to show the anisotropic effect with isovalue curves of stress. To cite this article: C. Ruimy, M. Dahan, C. R. Mecanique 330 (2002) 469–473.     

Partial homogenizationHomogénéisation partielle

The method of partial homogenization is proposed and justfied for equations with rapidly oscillating coefficients. Such equations simulate fields in composite materials. The proposed method keeps the initial equation in some thin boundary strip, homogenizes the equation in the resting part of the domain and prescribes the appropriate interface conditions for homogenized and non-homogenized parts. To cite this article: G.P. Panasenko, C. R. Mecanique 330 (2002) 667–672.     

Instabilité d'une nappe de vorticité étirée instationnaireInstability of an unsteady stretched vortex layer

We consider how the Kelvin–Helmholtz instability is affected by an external hyperbolic strain flow. The basic flow being unsteady, the inviscid evolution of perturbations is studied within the framework of a non-normal analysis in which the maximum amplification is computed for any given time. A positive or negative stretching is shown to enhance or reduce, respectively, the instability even for weak stretching rates. To cite this article: T. Gomez, M. Rossi, C. R. Mecanique 331 (2003).     

Eléments finis stochastiques en élasticité linéaireA stochastic finite element method in linear mechanics

The stochastic finite element method presented in this Note consists in representing in a probabilistic form the response of a linear mechanical system whose material properties and loading are random. Each input random variable is expanded into a Hermite polynomial series in standard normal random variables. The response (e.g., the nodal displacement vector) is expanded onto the so-called polynomial chaos. The coefficients of the expansion are obtained by a Galerkin-type method in the space of probability. To cite this article: B. Sudret et al., C. R. Mecanique 332 (2004).     

Approche globale,minima relatifs et Critère d'Amorçage en Mécanique de la RuptureGlobal approach,relative minima and yield criterion in Fracture Mechanics

We show that it is possible to predict the onset of cracking by searching relative minima of the total energy of a body, the yield criterion depending on the choice of the energies. In particular in the case where the bulk energy is elastic and the surface energy depends on the jump of the displacement, we prove that the yield criterion is formulated in terms of the stress tensor and of intrinsic curve type. To cite this article: J. Laverne, J.-J. Marigo, C. R. Mecanique 332 (2004).     

Homogénéisation d'un milieu élastique fortement hétérogèneHomogenization of a strongly heteregeneous elastic medium

We consider the homogenization of an elastostatic problem in a strongly heterogeneous periodic medium made of two connected components having comparable tensors of elastic moduli, separated by a third medium (soft layer), the thickness of which is of the same order ε than the basic periodicity cell, and such that its elastic moduli tensor becomes infinitely small following a rate ε^r, r>0. If r?2, we identify the homogenized problem. Otherwise, we have to assume moreover that there are no volume forces in the third medium. To cite this article: M. Mabrouk, A. Boughammoura, C. R. Mecanique 330 (2002) 543–548.