Comptes Rendus de l'Académie des Sciences - Series IIB - Mechanics-Physics-Astronomy最新文献

The problems of feedback minimax control for parabolic variational inequalities are considered. Algorithms solving these problems which are stable with respect to informational noises and computational errors are outlined. The algorithms are based on the principle of feedback control with a model [1].

A multilevel method for Large-Eddy Simulation of turbulent unsteady compressible flows is proposed. It relies on the splitting of the turbulent flowfield into several frequency bands in space and time, each band being associated to a computational grid in physical space, allowing to take into account in a deterministic way the information contained on finer grids. A subgrid-scale model adapted to such a decomposition — based on a generalization of the Germano's identity to multilevel decomposition — is also introduced. The approach is validated by a simulation in a subsonic plane channel flow configuration.

James and Guth [3] have used the inverse Langevin function-based expression of tension in a polymer chain to build the so-called 3-chain model of uncompressible rubber elasticity. It is an analytical model, but it is not isotropic. If one considers an isotropic superposition of an infinite number of chains in all the directions, one obtains an isotropic model, but it is no more tractable analytically. Following Cohen [12], we propose to replace the inverse Langevin function by its Padé approximant, the two functions being very close. The isotropic model is then analytically integrable, and yields large strain strain-stress relationship.

We develop a technique for computing incompressible two-phase flows on a fixed grid without using any interface reconstruction procedure. We discuss the grounds, the motivations and the advantages of such an approach and we present several tests of validation, especially concerning the constitutive law for the viscosity. We finally show that the method is able to reproduce the essential features of the flow induced by the rise of a Taylor bubble in a vertical tube.

Matrix crack deflection by an interface increases the apparent toughness of a composite. Criteria developed to predict such a mechanism never gave a complete and satisfying answer. They require additional assumptions on a characteristic fracture length and are sensitive to these choices. The criterion proposed here is based on the maximum total energy decrease, it is independent of any length and is well-suited to study a stiff matrix crack impinging on a soft inclusion.

Conditions for absolute instability of the elastic walls of a plane channel with potential flow are investigated. The absolute instability threshold is given in closed form in the thin film approximation for walls made of plates or membranes. The more general case is solved numerically and is compared with more classical results for a single wall in the presence of a semi-infinite fluid domain. It is found that absolute instability is strongly influenced by the membrane or plate nature of the wall stiffness.

The analysis of the hodographs corresponding to the interferometric observations of Dayton C. Miller 1925–1926 demonstrates the existence of a very marked coherence underlying these observations, quite unexplainable by perverse effects (e.g. temperature).

The “Schistes carton” formation is highly overconsolidated and hardened in its intact form. The variations of hydraulic and/or mechanical stresses on this material lead to an alteration as well as a change in its mechanical properties. Experiments have been carried out to study the advancement of the desiccation front and the hydraulic conductivity of this unsaturated soil. The samples are from Pont-à-Mousson Lorraine. The evolution of the volumetric water content versus the depth and the variations of the hydraulic conductivity have permitted the estimation of the alteration depth in this formation.

From the K-L turbulence model proposed by Lewellen [1], an analytical expression of turbulence macroscale is established. This expression, obtained with the hypothesis of a null horizontal pressure gradient, can be used for inertial or Couette flow. This formulation is better than the classical linear expression and, moreover, this analytical computation and numerical computations are in a good agreement.

The elastic field of a planar two-period network of misfit dislocations parallel to the two free surfaces of a thin bimaterial is explicitly determined from the assumption of an isotropic elasticity for each crystal. A few calculations of normal stresses enable the elastic field relaxation to be illustrated for CoSi₂/Si(111).