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).     

A harmonic balance method for the non-linear vibration of viscoelastic shellsVibrations non linéaires des structures viscoélastiques par une méthode de la balance harmonique

In this Note, we deal with the non-linear vibration of viscoelastic shell structures. Coupling a harmonic balance method with a one mode Galerkin's procedure, one obtains an amplitude equation depending on two complex coefficients. These are determined by solving a classical eigenvalue problem and two linear problems. This permits us to characterize the evolution of the loss factor with the vibration amplitude. To validate our approach, the amplitude-frequency and the amplitude-loss factor relationships are illustrated in the case of a circular ring. To cite this article: E.H. Boutyour et al., C. R. Mecanique 334 (2006).     

A two scale method for modulated vibration modes of large,nearly repetitive,structuresUne méthode asymptotique à deux échelles pour les modes de vibrations modulés des longues structures presque répétitives

Nearly repetitive structures can present at least two kinds of vibration modes: localized modes and modulated ones. In this Note, the multiple scale method is applied to characterize a packet of modulated modes. In this respect, only small size problems are to be solved: periodic problems posed on a few basic cells and amplitude equations, which define a sort of homogenized model for this type of modes. It is established that the influence of the non-repetitive part of the structure is accounted by a boundary condition. To cite this article: E.M. Daya et al., C. R. Mecanique 331 (2003).     

Shape optimization of an accommodative intra-ocular lens

Cataract surgery consists in replacing the clouded or opacified crystalline lens by an Intra-Ocular Lens (IOL) having the same mean dioptrical power. Clear vision is then achieved at a given distance and glasses are needed in many situations. A new kind of IOL, potentially accommodative, is proposed. Its design is based on the deep understanding of the accommodation mechanism and on the mathematical modeling and the numerical simulation of the IOL's comportment in vivo. A preliminary version of this IOL is now commercialized by the company HumanOptics under the name ‘1CU’. In a second phase, shape optimization techniques equipped with strong mechanical and physiological constraints, are used to enhance the IOL performance and build a new design. To cite this article: F. Jouve, K. Hanna, C. R. Mecanique 333 (2005).     

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).     

Mixing and coherent vortices in turbulent coaxial jets

Direct numerical simulations associated with mixing in constant-density round coaxial jets are performed. They are validated by comparison against laboratory experiments. The mixing process is studied by seeding a passive tracer first in the outer annular jet, then in the inner jet. We demonstrate the important role played by coherent vortices in the mixing mechanisms. The turbulent mixing exhibits an intermittent character as a consequence of fluid ejections caused by the counter-rotating streamwise vortices. We quantify also the domination of the outer jet and show that the fluid issuing from the central jet remains confined. To cite this article: G. Balarac, M. Si-Ameur, C. R. Mecanique 333 (2005).     

Écart à la réciprocité et identification de fissures en thermoélasticité isotrope transitoireReciprocity gap and identification of cracks in transitory isotropic thermoelasticity

We consider a three-dimensional homogeneous isotropic elastic solid containing a family of planar cracks submitted to a time-dependent thermal loading. The displacement and surface traction fields are measured over the whole external boundary of the solid. We propose in this Note to define and exploit a reciprocity gap, based only on the mechanical quantities available on the boundary, and which enables us to derive explicit formula for the location of the plane where the cracks are lying. Boundary conditions on the cracks can be of any nature provided they ensure that the normal heat flux and surface traction vector are continuous across the crack surfaces. To cite this article: S. Andrieux, H.D. Bui, C. R. Mecanique 334 (2006).     

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).     

Complexification phenomenon in an example of sensitive singular perturbationPhénomène de complexification dans un exemple de perturbation singulière sensitive

We consider singular perturbation problems depending on a parameter ε?0 such that for ε>0 the solution u^ε belongs to a Sobolev space on a domain $\text{Ω}$, but the limit u⁰ is not a distribution on $\text{Ω}$. A very simple model problem, solvable by Fourier transform allows us to study the complexification process of u^ε as $\text{ε↘0}$. The limit holds in the topology of a space of analytical functionals. To cite this article: C.A. De Souza, É. Sanchez-Palencia, C. R. Mecanique 332 (2004).     

Asymptotic analysis of layered elastic beams

We consider an elastic beam formed by three layers, fixed at one end and loaded at the free end. We call adherents the upper and lower layers ${\Omega }_{+}^{?}$ and ${\Omega }_{?}^{?}$ and an adhesive layer ${\Omega }_m^{?}$. We denote by $?h_{\pm ,m}$ the thickness of each layer and we suppose that the stiffness of the adhesive layer is ${?}^2$, with respect to that of the adherents. By an asymptotic analysis we obtain the zeroth order limit problem and the form of the second order displacements. To cite this article: M. Serpilli, C. R. Mecanique 333 (2005).     

On the Lagrange problem about the optimal form for circular hollow columnsSur le problème de Lagrange de la forme optimale d'une colonne circulaire aux parois minces

A new approach to the problem of finding the form of the strongest clamped circular column with thin walls of fixed volume and height is proposed. The same model describes also the form of the horizontal beam with rectangular vertical sections of a fixed height and variable widths. The existence and the uniqueness of the optimal column are proved here for the first time and the optimal form is found. To cite this article: Yu.V. Egorov, 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).     

Une comparaison des schémas d'intégration temporelle explicites de Chung–Lee et Tchamwa–WielgoszA comparison between the Tchamwa–Wielgosz and the Chung–Lee explicit time integration algorithms.

Numerous effort during the past ten years have focused on developing explicit time integration algorithms for structural dynamics that include controllable numerical dissipation of the spurious oscillations. Stability and consistency of the Tchamwa–Wielgosz algorithm are analysed for the linear damped/undamped cases. Furthermore, numerical results are compared for this algorithm and the Chung–Lee explicit method. To cite this article: V. Grolleau et al., C. R. Mecanique 332 (2004).     

On the effect of small fluctuations in the volume fraction of constituents on the effective properties of composites

This study deals with three-scale composite materials comprised of nonlinear constituents. At the meso scale the composite can be considered as locally homogeneous with a macroscopic spatial variation of the constituents volume fraction. When these variations about a mean value are small, a Taylor expansion to second-order of the effective properties of the composite with respect to the fluctuations is given. This expansion can be used to discuss the beneficial or deleterious effects of clusters of inhomogeneities. It can also be used to derive new upper and lower bounds for the effective properties of nonlinear composites from dilute results. To cite this article: P. Suquet, C. R. Mecanique 333 (2005).     

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).     

Kinematic shakedown by the Norton–Hoff–Friaa regularising method and augmented LagrangianAdaptation cinématique par la methode de régularisation de Norton–Hoff–Friaa et du Lagrangien augmenté

The shakedown analysis of elastic perfectly plastic structures is formulated as a discrete nonlinear mathematical programming problem by means of the finite element technique. The kinematical problem is regularized through the introduction of the Norton–Hoff viscoplastic material to overcome the non-differentiability of the objective function, and can be solved numerically by the augmented Lagrangian technique. To cite this article: M.A. Hamadouche, C. R. Mecanique 330 (2002) 305–311.     

A direct method for the solution of evolution problemsLa méthode directe

An alternative numerical method to solve structural evolution problems is presented. It belongs to the family of Large Time Increment Methods. The problem is solved on the whole time interval separating a global stage where a SA and KA solution is searched and a local stage where the constitutive law is satisfied. To solve the global stage, consuming the most CPU time, the mechanical fields are decomposed in a wavelet basis and the equilibrium is solved only for the largest coefficients. To cite this article: F. Comte et al., C. R. Mecanique 334 (2006).     

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).     

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).     

Justification of the kinematic assumptions for thin-walled rods with shallow profile

In this Note we present a justification of the kinematic assumptions for thin-walled rods with shallow profile. These assumptions are fundamental to writing the one-dimensional equilibrium equations for such structures. The obtained kinematics are different from the Vlassov case, which is only valid for strongly curved profiles. They are also different from the that classically used in shell theory. The justification given in this Note is based on an asymptotic approach. To cite this article: L. Grillet et al., C. R. Mecanique 333 (2005).