Reconstruction of the three mechanical material constants of a lossy fluid-like cylinder from low-frequency scattered acoustic fieldsReconstruction des trois constants mécaniques matériels d'un cylindre fluide dissipatif à partir de champs acoustiques basses fréquences

The inverse medium problem for a circular cylindrical domain is studied using low-frequency acoustic waves as the probe radiation. To second order in k₀a (k₀ the wavenumber in the host medium, a the radius of the cylinder), only the first three terms (i.e., of orders 0, ?1 and +1) in the partial wave representation of the scattered field are non-vanishing. This enables the scattered field to be expressed algebraically in terms of the unknown material constants, i.e., the density ρ₁, and the real and imaginary parts of complex compressibility κ₁ of the cylinder. It is shown that these relations can be inverted to yield explicit, decoupled expressions for ρ₁ and κ₁ in terms of the totality of the far-zone scattered field. These expressions furnish accurate estimations of the material parameters provided the probe frequency is low and the radius of the cylinder is known very precisely. To cite this article: T. Scotti, A. Wirgin, C. R. Mecanique 332 (2004).     

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).     

On the optimization of higher eigenvaluesSur l'optimisation de valeurs propres supérieures

A new approach is proposed for the study of the classical Lagrange problem on the optimal form of a column with clamped ends and a fixed volume. It is proved that there exists a column with the maximal possible value of the kth eigenvalue and that such a column is unique. A method for the numerical solution is proposed. The method is based on the analysis of the critical points of a non-linear functional related to the Lagrange problem. To cite this article: Y.V. Egorov, C. R. Mecanique 332 (2004).     

Une méthode inverse d'ordre un pour les problèmes de complétion de données

An iterative resolution method for inverse Cauchy problems is presented. The successive iterations satisfy the equilibrium equations exactly. Numerical simulations prove the accuracy of the method and its ability to solve Cauchy problems when the domain boundary is not regular. To cite this article: A. Cimetière et al., C. R. Mecanique 333 (2005).     

Utilisation de la phase stationnaire pour localiser la provenance du bruit sur l'axe d'une structure élastique à symétrie de révolutionUse of the stationary phase method to localize the source of noise on the axis of an axisymmetric elastic structure

Consider the problem numbered (1) in the text. Along the axis, the pressure may be expressed as a combination of axisymmetric modes only. For high wave numbers, the method of stationary phase may be used to show that the pressure on the axis comes only from the vicinities of a few parallels. Generally, only the parallel constituting the points nearest to this axis point is to be considered. For low circumferential mode numbers (especially $n=0$), the curvature greatly influences the wavelength of the modes of the structure in vacuo: thus, the method of stationary phase can be applied, for most aeronautical airborne structures, even from the first axisymmetric mode and not only above the coincidence frequency. Using an expression established earlier, we can give an expression for the pressure on the axis of an axisymmetric enclosure. To cite this article: D. Brenot, C. R. Mecanique 334 (2006).     

Développement en polynômes de chaos d'un modèle lagrangien d'écoulement autour d'un profilPolynomial chaos expansion of a Lagrangian model for the flow around an airfoil

A polynomial chaos (PC) expansion a the Lagrangian model for the stochastic incompressible inviscid flow around an airfoil is presented. The flow field is modeled using a distribution of lumped vortices on the airfoil surface while the wake is modeled with Lagrangian point vortices. An original technique is proposed for the computation of the PC coefficients of the velocities induced by the vortices. Two computational examples for random airfoil motions are provided to illustrate the capability of the method to deal with complex situations. To cite this article: O. Le Maître, C. R. Mecanique 334 (2006).     

‘Les fleurs du mal’ – an adaptive wavelet method of arbitrary lines I: convection–diffusion problems« Les fleurs du MAL » – une méthode d'ondelettes adaptive de lignes arbitraires I : problèmes de convection–diffusion

Baudelaire's ‘les fleurs du mal’ refers to various new developments (‘les fleurs’) of the method ofarbitrarylines (mal), since it was first published (in C. R. Acad. Sci. Paris, Sér. I, in 1991). Here we revisit the basic mal (semi-discretization) methodology for stationary convection–diffusion problems and develop an adaptive, wavelet-based solver that is capable of capturing the thin layers that arise in such problems. We show the efficacy and high accuracy of the wavelet-mal solver by applying it to a challenging 2D problem involving both boundary and interior layers. To cite this article: X. Ren, L.S. Xanthis, C. R. Mecanique 332 (2004).     

High-order evolution equation for nonlinear wave-packet propagation with surface tension accountingÉquation d'évolution d'ordre élevé de groupes d'ondes non linéaires en présence de tension superficielle

The nonlinear problem for propagation of wave-packets along the interface of two semi-infinite fluids is solved on the basis of multiple scale asymptotic expansions. Unlike all previous investigations dealing only with third-order approximations, here fourth-order approximation is developed. The corresponding solvability condition is obtained and the evolution equation in the case away from the cut-off wave number is derived. As a result, the nonlinear higher-order Schrödinger equation is obtained which contains the nonlinear part in a compact form. This equation is valid for a wide range of wave numbers. The stability diagram shows regions of stability and instability of capillary-gravity wave-packets. To cite this article: I. Selezov et al., C. R. Mecanique 331 (2003).     

Asymptotically sharp uniform estimates in a scalar spectral stiff problemEstimations asymptotiques uniformes pour le spectre d'un problème scalaire raide

Estimates of convergence rates for rescaled eigenvalues of the stiff Neumann problem for the Laplacian are obtained. The bounds are expressed in terms of the stiffness ratio and properties of the limit spectrum both for low and middle frequency ranges. To cite this article: M. Lobo et al., C. R. Mecanique 331 (2003).     

Recovery of small electromagnetic inhomogeneities from partial boundary measurementsIdentification de petites inhomogénéités diélectriques à partir de mesures partielles

We consider for the inverse problem of identifying locations and certain properties of the shapes of small dielectric inhomogeneities in a homogeneous background medium from boundary measurements on part of the boundary or dynamic boundary measurements for a finite time interval. Using as weights particular background solutions we develop asymptotic methods based on appropriate averaging of the data. To cite this article: H. Ammari, A.G. Ramm, C. R. Mecanique 330 (2002) 199–205.     

Identification of damage fields using kinematic measurementsIdentification de champs d'endommagement à l'aide de mesures cinématiques

It is proposed to determine damage fields on the surface of a material by using only full-field displacement measurements. A finite element approach is developed for which the unknown damage field is assumed to be piece-wise constant. Two examples are discussed in which the displacement field is either obtained by finite element analyses or measured by digital image correlation. To cite this article: D. Claire et al., C. R. Mecanique 330 (2002) 729–734.     

Fermetures entropiques pour les systèmes bifluides à sept équations

In this Note, we propose a way to obtain two-fluid two-pressures multiphase models that satisfy an entropy inequality. We first notice that the continuous model associated to the discrete model of Abgrall and Saurel (2003) satisfies the entropy principles. Thanks to this, we show how to modify existing models in order to achieve the second law of thermodynamics. To cite this article: M. Papin, R. Abgrall, C. R. Mecanique 333 (2005).     

Identification of elastic parameters by displacement field measurementIdentification de paramètres mécaniques par mesure de champ de déplacement

In this Note we study a parameter identification problem associated with a two-dimensional mechanical problem. In a first part, the experimental technique of determining the displacement field is presented. The variational method proposed herein is based on the minimization of a separate convex functional which leads to the reconstruction of the elastic tensor and the stress field. These two reconstructed fields are continuous and piecewise linear on a triangulation of the two-dimensional problem. Some numerical and experimental examples are presented to test the performance of the algorithm. To cite this article: G. Geymonat et al., C. R. Mecanique 330 (2002) 403–408.     

Uniqueness in the water-wave problem for bodies intersecting the free surface at arbitrary anglesL'unicité du problème des ondes de surface pour les corps qui intersectent la surface libre sous des angles arbitraires

This Note deals with the linearized water-wave problem involving a surface-piercing cylinder in water of infinite depth. A solution to this problem is proved to be unique for all values of the radian frequency when the cylinder intersecting the free surface at arbitrary angles is subjected to certain geometric arrangements. To cite this article: N. Kuznetsov, C. R. Mecanique 332 (2004).     

Réduction a priori de modèles thermomécaniquesAn a priori model reduction method for thermomechanical problems

A model reduction method is proposed for finite element models. A previous computation of the state of the structure is not necessary. Residuals defined over the entire time interval and the Karhunen–Loève method provide basis functions. A non-incremental algorithm, from the LATIN method, is used to compute this basis functions. Because of the non-incremental feature, the reduced order model is representative for a large evolution of the state of the structure. To cite this article: D. Ryckelynck, C. R. Mecanique 330 (2002) 499–505.     

Identification of the scatter in high cycle fatigue from temperature measurementsIdentification de la dispersion des limites d'endurance à l'aide d'un essai d'échauffement.

It is proposed to determine the scatter in a Wöhler diagram by analyzing temperature changes induced by microplasticity. A unified framework is introduced to study both phenomena. The identification procedure is applied to a dual-phase steel. To cite this article: C. Doudard et al., C. R. Mecanique 332 (2004).     

Characterization of the flow for a single fluid in an excavation damaged zoneCaractérisation de l'écoulement d'un fluide monophasique en zone endommagée

The aim of this Note is to quantify the change of characteristics of the media of an Excavated Damaged Zone (EDZ) affected by several fractures. For this, we consider Darcy flow through matrix blocks and fractures with permeability of order ε²δ^θ and 1 respectively. ε is the size of a typical porous block, δ representing the relative size of the fracture and θ is a parameter characterising the permeability ratio. We derive the global behavior from the limit as ε and δ tend to zero. The resulting homogenized equation is of dual-porosity type for θ=2, but it is a simple-porosity model with effective coefficients for θ>2, and there is no flow at the macroscopic level when 0<θ<2. To cite this article: B. Amaziane et al., C. R. Mecanique 332 (2004).     

Coupling of a simplified flow with a phenomenological fire spread modelCouplage d'un écoulement simplifié à un modèle phénoménologique de propagation des feux

Our long-range aim is to propose a forest fire simulator. To this end, we have developed a phenomenological model of fire spread. Then, we have improved it in order to take into account advective transfers thanks to a simplified flow. In this paper, we present in a synthetic way our modelling approach that can also be applied to other phenomenological models. Finally, we compare the model predictions to laboratory experiments. To cite this article: A. Simeoni et al., C. R. Mecanique 330 (2002) 783–790.     

On loading criteria in plasticitySur des critères de chargement en plasticité

The loading criteria of the Lagrangian strain-space formulation of rate-independent plasticity are compared with those of Nguyen and Bui and those of Kuhn–Tucker type. When the latter two sets of conditions are expressed in a fully strain-space form, their relationship to the loading criteria of the strain-space formulation becomes transparent. To cite this article: J. Casey, C. R. Mecanique 330 (2002) 285–290.