Homogenization of an elasticity problem in domains with a net of slender bars near surface

We consider an elasticity problem in a domain Ω⁽⁾=ΩF⁽⁾, where Ω is an open bounded domain in R³, F⁽⁾ is a connected nonperiodic set in Ω like a net of slender bars, and is a parameter characterizing the microstructure of the domain. We consider the case of a surface distribution of the set F⁽⁾, i.e., for sufficiently small , the set F⁽⁾ is concentrated in arbitrary small neighbourhood of a surface Γ. Under a hypothesis on the asymptotic behaviour of the energy functional, we obtain the macroscopic (homogenized) model. To cite this article: M. Goncharenko, L. Pankratov, C. R. Mecanique 331 (2003).     

Homogénéisation de problèmes d''évolution dans une structure renforcée de fibresHomogenization of evolution problems in a fiber reinforced structure

We study the homogenization of evolution equations such as:

where the coefficient a is -periodic and takes very high values on a subset TΩ (fibered structure) of very small measure. We find a non-local effective equation deduced from a homogenized system of several equations. To cite this article: M. Bellieud, C. R. Mecanique 330 (2002) 843–848.     

Structuration de la convection mixte en milieu poreux confiné latéralement et chauffé par le bas : effets d''inertiePattern formation of mixed convection in a porous medium confined laterally and heated from below: effect of inertia

We consider the onset of convection in a porous medium heated from below and subjected to a horizontal mean flow. The effect of porous inertia is studied, and the transverse aspect ratio a of the medium is taken into accout. We find that the dominant modes are longitudinal rolls (L.R) if a is an integer or transverse traveling rolls (T.R) if a is below a_c with a_c<1. When a is not an integer with a>a_c, the setting on patterns are oscillatory three-dimensional structures (3D) for a>1 or T.R for a_c<a<1 provided that the Reynolds number remains below a critical value Re_K^*. We show that these structures are replaced by L.R if Re_K>Re_K^*. To cite this article: A. Delache et al., C. R. Mecanique 330 (2002) 885–891.     

Impact of a bead on a rotating wall

We study experimentally the impact of a plastic bead on a rotating wall made of steel (velocity Ω; radial position x₀). The results show that the restitution coefficient is directly function of the impact velocity x₀Ω and is invariant by changing frame reference. The influence of the height of release of the particle on its angular velocity after impact is also studied. We observe an increase of the angular velocity with height followed by a saturation. We propose an interpretation for this evolution considering that the particle may roll without sliding during all the impact. This physical feature is not always taken into account in existing models of impact between rigid bodies. To cite this article: F. Rioual et al., C. R. Mecanique 336 (2008).     

Identification de la relation de dispersion dans les barresIdentification of the dispersion relation in rods

Dispersion and attenuation of longitudinal waves in elastic or weakly viscoelastic rods are measured by analysing the resonant frequencies present in the strain spectrum due to an unknown loading. The method takes the finite measuring time of the test into account. It is applied to an aluminium bar, in which the dispersion relation is identified very accurately at frequencies up to 60 kHz. To cite this article: R. Othman et al., C. R. Mecanique 330 (2002) 849–855.     

Asymptotics of Neumann harmonics when a cavity is close to the exterior boundary of the domain

We construct the asymptotics (as ε→0) of solutions to the Neumann problem for the Laplace equation and of the corresponding Dirichlet integral. The problem concerns a three-dimensional domain having two connected components of the boundary at the distance ε>0. To cite this article: G. Cardone et al., C. R. Mecanique 335 (2007).     

‘Ruban à godets’: an elastic model for ripples in plant leaves

The formation of ripples along the edge of plant leaves is studied using a model of an elastic strip with spontaneous curvature. The equations of equilibrium of the strip are established in an explicit form. A numerical method of solution is presented and carried out. Owing to the presence of geometric nonlinearities, several equilibrium configurations are found but we show that only one of them is physical. To our knowledge, this is the first investigation of ripples in plant leaves that is based on the equations of elasticity. To cite this article: B. Audoly, A. Boudaoud, C. R. Mecanique 330 (2002) 831–836.     

Elastic properties of glasses: a multiscale approach

Very different materials are named ‘Glass’, with Young's modulus E and Poisson's ratio ν extending from 5 to 180 GPa and from 0.1 to 0.4, respectively, in the case of bulk inorganic glasses. Glasses have in common the lack of long range order in the atomic organization. Beside the essential role of elastic properties for materials selection in mechanical design, we show in this analysis that macroscopical elastic characteristics (E,ν) provide an interesting way to get insight into the short- and medium-range orders existing in glasses. In particular, ν, the packing density (C_g) and the glass network dimensionality appear to be strongly correlated. Networks consisting primarily of chains and layers units (chalcogenides, low Si-content silicate glasses) correspond to ν>0.25 and C_g>0.56, with maximum values observed for metallic glasses (ν0.4 and C_g>0.7). On the contrary, ν<0.25 is associated to a highly cross-linked network with a tri-dimensional organization resulting in a low packing density. Moreover, the temperature dependence of the elastic moduli brings a new light on the ‘fragility’ of glasses (as introduced by Angell) and on the level of cooperativity of atomic movements at the source of the deformation process. To cite this article: T. Rouxel, C. R. Mecanique 334 (2006).     

Etude de la détonation de mélanges pauvres H2NO2/N2O4

Calculations of the detonation reaction zone of gaseous H₂NO₂/N₂O₄ mixtures in the range of equivalence ratio Φ between 0.25 and 0.7 show that for 0.25Φ0.4 the chemical energy is released in two distinct and successive exothermic steps characterised by different chemical characteristic times. As for rich mixtures, the first exothermic step is mainly due to the reaction NO₂ + H → NO + OH, but the second one is different since it results from the exothermic decomposition of NO into N₂ and O₂. For Φ=0.3 the measured detonation velocity in a tube of 52 mm internal diameter is very much smaller than the calculated value and the mean size of the cellular structure is very much larger than the value extrapolated from data obtained with mixtures of higher but close equivalence ratio. All these results show that the detonation, though self-sustained and steady, is ‘non-ideal’, i.e. it is supported only by a part of the available chemical energy, that provided mainly by the first exothermic step. To cite this article: D. Desbordes et al., C. R. Mecanique 332 (2004).     

A two-dimensional effective model describing fluid–structure interaction in blood flow: analysis, simulation and experimental validation

We derive a closed system of effective equations describing a time-dependent flow of a viscous incompressible Newtonian fluid through a long and narrow elastic tube. The 3D axially symmetric incompressible Navier–Stokes equations are used to model the flow. Two models are used to describe the tube wall: the linear membrane shell model and the linearly elastic membrane and the curved, linearly elastic Koiter shell model. We study the behavior of the coupled fluid–structure interaction problem in the limit when the ratio between the radius and the length of the tube, , tends to zero. We obtain the reduced equations that are of Biot type with memory. An interesting feature of the reduced equations is that the memory term explicitly captures the viscoelastic nature of the coupled problem. Our model provides significant improvement over the standard 1D approximations of the fluid–structure interaction problem, all of which assume an ad hoc closure assumption for the velocity profile. We performed experimental validation of the reduced model using a mock circulatory flow loop assembled at the Cardiovascular Research Laboratory at the Texas Heart Institute. Experimental results show excellent agreement with the numerically calculated solution. Major applications include blood flow through large human arteries. To cite this article: S. Čanić et al., C. R. Mecanique 333 (2005).     

Effective flow of a viscous liquid through a helical pipe

We study the flow of a viscous fluid through a pipe with helical shape parameterized with , where the small parameter stands for the distance between two coils of the helix. The pipe has small cross-section of size . Using the asymptotic analysis of the microscopic flow described by the Navier–Stokes system, with respect to the small parameter that tends to zero, we find the effective fluid flow described by an explicit formula of the Poisseuile type including a small distorsion due to the particular geometry of the pipe. To cite this article: E. Marušić-Paloka, I. Pažanin, C. R. Mecanique 332 (2004).

Résumé

On considère un écoulement dans un tube de section circulaire et de forme hélicoïdale paramétré par , où est la distance entre deux tours de la spirale. Le rayon de la section du tube est lui aussi supposé égal à . A partir de l'écoulement microscopique décrit par le système de Navier–Stokes et en utilisant l'analyse asymptotique par rapport à ce petit paramètre on obtient l'écoulemment effectif décrit par une formule explicite de type Poiseuille associée à une petite déviation due à la géometrie du tube. Pour citer cet article : E. Marušić-Paloka, I. Pažanin, C. R. Mecanique 332 (2004).     

Confined buckling of inextensible rods by convex difference algorithms

In this Note we present an approach to determine the local minima of a specific class of minimization problems. Attention is focused on the inextensibility condition of flexible rods expressed as a nonconvex constraint. Two algorithms are derived from a special splitting of the Lagrangian into the difference of two convex functions (DC). They are compared to the augmented Lagrangian methods used in this context. These DC formulations are easily extended to contact problems and applied to the determination of confined buckling shapes. To cite this article: P. Alart, S. Pagano, C. R. Mecanique 330 (2002) 819–824.     

Modélisation du comportement thermique d'un outil de fraisage : approche par identification de système non entierThermal modelling of a milling tool: a noninteger system identification approach

In this work we present an experimental apparatus devoted to the thermal characterisation of a milling tool. The experimental device used thermistors, one for each insert. Each thermistor is located at a point in the tool close to the tip of the insert. The heat flux in each insert is expressed according to the temperature at the sensor from a non-integer model. The parameters of the model are identified from transient evolutions measurements of the temperature on the sensor and on the cutting edge. An application shows the difference in the behaviour of each insert during machining from the estimated heat fluxes. To cite this article: J.-L. Battaglia et al., C. R. Mecanique 330 (2002) 857–864.     

Modèles discrets de structures tissées : Analyse de stabilité et de drapéDiscrete models of woven structures: stability and draping analysis

A discrete model of a woven fabric structure is established, whereby nodes endowed with a mass and a rotational rigidity are connected by rigid bars to form a two-dimensional truss. The set of four bars that delineate a quadrilateral area is further endowed with a torsion deformation mode. The kinematics of the truss reproduces the large rotations and displacements encountered for real tissues. The equilibrium shape of such a structure is obtained as the minimum of its total potential energy versus the whole set of kinematic translational and rotational variables, accounting for eventual kinematic constraints due to contact with a rigid surface by the Lagrange multipliers method. A stability analysis is conducted, and the potentiality of the model is illustrated by fabric draping simulations. To cite this article: B. Ben Boubaker et al., C. R. Mecanique 330 (2002) 871–877.     

Oscillatory fracture paths in thin elastic sheets

We report a novel mode of quasi-static oscillatory crack propagation when a cutting tip of moderately large width is driven through a thin brittle polymer film. Experiments show that the amplitude and wavelength of the oscillatory crack paths scale linearly with the width of the cutting tip over a wide range of length scales but are independent of the width of the sheet and of the cutting speed. We propose a mechanism for this instability, based on the coupling between crack propagation and out-of-plane deformations of the film. To cite this article: B. Roman et al., C. R. Mecanique 331 (2003).     

Développement d''un modèle en vue de la prédiction du rallumage d''un foyer de turboréacteur à haute altitudeDevelopment of a model to predict the ignition performance of a turbojet engine at high altitude

Within the context of turbojet engine re-ignition after in-flight extinction, a thermo-diffusive model has been developed to describe the electrical ignition, at low pressure and low temperature, of a cluster of fuel droplets. The model involves the resolution of the conservation equations of mass, species and energy. It also takes into account the various physical and chemical phenomena occurring during the ignition process. This Note presents the ignition model and preliminary results of this model applied to an experimental configuration. To cite this article: V. Quintilla et al., C. R. Mecanique 330 (2002) 811–818.     

A two grid algorithm based on perturbation and homotopy methods

In this paper, we propose a new class of bi-grid algorithm to solve large scale linear algebraic equations. This method is based on homotopy, perturbation technique and Padé approximants. To cite this article: R. El Mokhtari et al., C. R. Mecanique 330 (2002) 825–830.     

Transfert du trichloréthylène en milieu poreux à partir d'un panache de vapeursMass transfer of trichloroethylene in a porous medium from a vapor plume

A large scale experiment has been carried out on an experimental facility to study the mass transfer of trichloroethylene (TCE) in a partially saturated porous medium. 5 liters of TCE have been infiltrated in the vadose zone of the site. The mass transfer of TCE from the vapor plume in the unsaturated zone towards the top of groundwater was quantified based on an analytical and a numerical approach. The mass of the pollutant measured at the exit of the model is well represented by the two mathematical approaches. It is found that the transfer of TCE towards the groundwater from the vapor plume is weak, which corresponds to 285 g of TCE, approximately 4% of the initial mass. To cite this article: H. Benremita, G. Schäfer, C. R. Mecanique 331 (2003).     

Using data assimilation in numerical simulations of experimental geophysical flows

Data assimilation is used to couple numerical simulations and laboratory experiments of unsteady fluid flows in a stratified, rotating fluid. The experiments are performed on the large Coriolis turntable (Grenoble) and the simulations are performed with a multi-layer shallow water model. Sequential assimilation of high-resolution CIV (Correlation Image Velocimetry) measurements drives the numerical model close to the experimental flow and provides an estimation of all the flow variables at each time and each point. It is then possible (i) to analyse the flow dynamics in details, (ii) to determine the model errors starting from a realistic initial condition and (iii) to test the assimilation scheme when a reduced set of data is assimilated. To illustrate this, some results on the baroclinic instability of a two-layer vortex are presented. To cite this article: M. Galmiche et al., C. R. Mecanique 331 (2003).     

On the confinement of a viscous fluid by means of a feedback external field

In this work we consider a planar stationary flow of an incompressible viscous fluid in a semi-infinite strip governed by the standard Stokes system. We show how this fluid can be stopped at a finite distance from the entrance of the semi-infinite strip by means of a feedback source depending in a sublinear way on the velocity field. This localization effect is proved by reducing the problem to a non-linear biharmonic type one for which the localization of solutions is obtained through the application of an energy method, in the spirit of the monograph by S.N. Antontsev, J.I. Díaz and S.I. Shmarev (Energy Methods for Free Boundary Problems: Applications to Non-Linear PDEs and Fluid Mechanics, Birkäuser, Boston, 2002). Since the presence of the non-linear terms defined by the source is not standard in fluid mechanics literature, we give also some results about the existence and uniqueness of weak solutions for this problem. To cite this article: S.N. Antontsev et al., C. R. Mecanique 330 (2002) 797–802.