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.     

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.     

Sur les approximations « isotrope » et « anisotrope » de l''opérateur tangent pour les méthodes tangentes incrémentale et affineOn the ‘isotropic’ and ‘anisotropic’ approximations of the tangent operator in the incremental tangent and affine methods

Three localisation rules, TFA, the incremental tangent, and the affine method, are recalled and evaluated in the context of the elastoplastic micromechanical analysis of heterogeneous materials, composites or polycrystals. With the help of a severe example, it is shown how methods based on the complete anisotropic elastoplastic tangent operator yield very stiff predictions which are far from the reference solution; the same conclusion holds for the method using the elastic accommodation rule. On the other hand, using an isotropic form of the tangent operator delivers much better responses. The reasons for such differences are discussed, together with possible justifications for the choice of the isotropic form. To cite this article: J.-L. Chaboche, P. Kanouté, C. R. Mecanique 331 (2003).     

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.     

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.     

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).     

An approximate solution to the integral radiative transfer equation in an optically thick slab

We consider the problem of solving the integral form of the radiative transfer equation in an atmosphere with optical thickness τ₀1. We propose a method transforming this problem in the same problem posed in an atmosphere with optical thickness τ₁τ₀. An error over- estimation is derived. To cite this article: A. Amosov et al., C. R. Mecanique 331 (2003).     

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).     

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).     

‘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.     

Vérification expérimentale de la relation de réciprocité d'Onsager pour l'électro-osmose et l'électro-filtration dans une argile naturelleExperimental verification of the Onsager's reciprocal relations for electro-osmosis and electro-filtration phenomena on a saturated clay

This Note is devoted to the experimental verification of the Onsager's reciprocal relations in the particular case of electro-osmosis and electro-filtration. A special set up has been designed to carry out the measurements of both the electro-osmotic permeability and the streaming potential. This has been performed by using a natural material i.e., saturated kaolinite. To cite this article: K. Beddiar et al., C. R. Mecanique 330 (2002) 893–898.     

Micromechanical computational modeling of expansive porous media

A modified Terzaghi principle is proposed to describe the influence of locally coupled electro-chemo-mechanical processes in highly compacted swelling clays upon the form of the macroscopic modified effective stress principle. The two-scale model is derived using the homogenization procedure to upscale the microscopic behavior of a two-phase system composed of clay particles saturated by a completely dissociated electrolyte aqueous solution. Numerical experiments are performed to illustrate the results in a particular cell geometry. To cite this article: M.A. Murad, C. Moyne, C. R. Mecanique 330 (2002) 865–870.     

Identification de la relation de dispersion dans les barres

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.     

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.     

A model for frictional slip in woven fabrics

A continuum model for frictional slip of the yarns of a plain-weave fabric is presented. The model is based on the assumption that the weave is composed of two families of continuously distributed yarns constrained at all times to occupy a common evolving surface in three-dimensional space. The two families may slide relative to one another on the surface, subject to their respective equations of motion, fiber constitutive equations, and frictional slip rules. The theory is intended for the quantitative analysis of deformation, slip and energy dissipation during a ballistic impact event. To cite this article: B. Nadler, D.J. Steigmann, C. R. Mecanique 331 (2003).     

Domain decomposition for an asymptotic geological fault modeling

We present in this paper a domain decomposition method to treat faults in geological basin modeling. The particularity of this model is that the faults whose widths are very small in comparison with the basin size, are not characterized as subdomains any more but as interfaces between sedimentary blocks. The originality of this work lies in the formulation of this new fault model and in the definition and the computation of the interface conditions between the subdomains. To cite this article: E. Flauraud et al., C. R. Mecanique 331 (2003).     

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).     

Solute diffusion in fractured porous media with memory effects due to adsorption

Modelling of solute transport in fractured porous media is a subject of intensive research in many engineering disciplines, such as petroleum engineering, water resources management, civil engineering. Recent field and laboratory experiments show that, in presence of strong adsorption, the behaviour of solute penetrating into the fractured porous medium diverges from classical hypotheses, rendering impossible the adjustment of classical transport models. The aim of this paper is to develop a mathematical continuous model of solute transport, when strong adsorption of solute occurs on the grains of the porous matrix. The macroscopic model is obtained by upscaling the pore and the fracture behaviours, by using the multiple scale expansion method. We obtain a non-standard diffusion behaviour of solute which shows local non-equilibrium between transport in the fractures and in the porous matrix, as well as memory effects. To cite this article: J. Lewandowska et al., C. R. Mecanique 330 (2002) 879–884.     

Nonlinear models of vehicular traffic flow – new frameworks of the mathematical kinetic theory

This paper deals with the design of mathematical frameworks for the modeling of traffic flow phenomena by suitable developments of classical models of the kinetic theory. Various types of evolution equations are deduced, and different mathematical structures are proposed toward conceivable applications. To cite this article: M. Delitala, C. R. Mecanique 331 (2003).