Yield design formulation for porous media subjected to flow, using approximate pressure field. Calcul à la rupture en présence d'un écoulement : formulation cinématique avec un champ de pression approché

International audienceYield design formulation for porous media subjected to flow, using approximate pressure field. We attempt here to use the kinematic method of yield design in the case of a porous medium subjected to flow (with or without free surface), without looking for the exact solution of the pressure field. The method proposed here is based on the use of approximate pressure fields. In this paper, we show how, under different conditions concerning the yield criterion and the velocity field, the use of such approximate fields allows to obtain a necessary condition for stability without having to find the real pressure field. Nous cherchons ici à utiliser la méthode cinématique du calcul à la rupture dans le cas d'un milieu poreux soumis à un écoulement avec ou sans surface libre sans connaître la solution exacte du champ de pression. La méthode proposée ici repose sur l'utilisation de champs de pression approchés par défaut. Nous montrerons comment sous certaines conditions portant sur le critère de résistance et sur le champ de vitesse utilisé, l'utilisation de tels champs de pression approchés permet d'obtenir une condition nécessaire de stabilité sans avoir à déterminer exactement l'écoulement

Yield design for porous media subjected to unconfined flow: construction of approximate pressure fields.––– Calcul à la rupture en présence d'un écoulement à surface libre : construction de champs de pression approchés

International audienceWe consider the stability of a porous medium submitted to a steady-state flow with free-boundary. Assuming some hypotheses, it is possible to implement the kinematic method by using an approximate pressure field bounding the true pressure field from below. We are interested in finding such approximate pressure fields and in proving that they bound the true pressure field from below without knowing the true pressure field. We use fields which are solutions of a problem with relaxed conditions with regard to the real problem. Under a uniqueness condition of the solution of a weak formulation of the problem, such fields are lower bounds for the true pressure field. Finally, we give the example of a vertical dam

Annular shear of cohesionless granular materials: from inertial to quasistatic regime

Using discrete simulations, we investigate the behavior of a model granular material within an annular shear cell. Specifically, two-dimensional assemblies of disks are placed between two circular walls, the inner one rotating with prescribed angular velocity, while the outer one may expand or shrink and maintains a constant radial pressure. Focusing on steady state flows, we delineate in parameter space the range of applicability of the recently introduced constitutive laws for sheared granular materials (based on the inertial number). We discuss the two origins of the stronger strain rates observed near the inner boundary, the vicinity of the wall and the heteregeneous stress field in a Couette cell. Above a certain velocity, an inertial region develops near the inner wall, to which the known constitutive laws apply, with suitable corrections due to wall slip, for small enough stress gradients. Away from the inner wall, slow, apparently unbounded creep takes place in the nominally solid material, although its density and shear to normal stress ratio are on the jammed side of the critical values. In addition to rheological characterizations, our simulations provide microscopic information on the contact network and velocity fluctuations that is potentially useful to assess theoretical approaches

Importance of excitonic effects and the question of internal electric fields in stacking faults and crystal phase quantum discs: The model-case of GaN

We compute using envelope function calculations the energy and the oscillator strength of excitons in zinc blende/wurtzite quantum wells (QWs), such as those that appear in many examples of semiconductor nanowires, and in basal plane stacking faults (BSFs). We address specifically the model-case of GaN. In addition to the electron-hole Coulomb interaction, we account for the quantum-confined Stark effect. We demonstrate that despite the type-II band alignment at the zinc blende/wurtzite interfaces, a significant binding and a rather strong oscillator strength are preserved by excitonic effects. When adjacent crystal phase QWs are coupled together, we compute increased as well as decreased exciton oscillator strength with respect to the single QW case, depending on the QW-QW coupling scheme. Comparing the results of our calculations with available data, we finally conclude in favor of the absence of built-in electric fields perpendicular to the BSF planes.We acknowledge financial support from the European Union Seventh Framework Programme under Grant Agreement No. 265073

Variational Formulation and Upper Bounds for Degenerate Scales in Plane Elasticity

International audienceDegenerate scales appear when certain plane boundary value problems solved using Boundary Integral Equations do not have a unique solution. The main contribution of this paper is to prove four inequalities that constrain the degenerate scales for plane elasticity. These results are based on a new variational formulation. It is shown that the degenerate scales depend only on Poisson’s ratio. The bounds on the degenerate scales for plane elasticity in a given boundary are obtained mainly from the degenerate scales obtained from the Laplace equation for the same boundary, which are well documented

Role of the dielectric mismatch on the properties of donors in semiconductor nanostructures bounded by air

We compute by envelope function calculations the binding energy EB of donor atoms in thin slabs of semiconductor bounded by air, accounting for the dielectric mismatch between air and the semiconductor. We detail how EB depends on the donor-site and on the thickness of the slab. We show that due to the competition between surface and dielectric mismatch effects, EB does not monotonically decrease from the center to the surface of the nanostructures. Finally, we discuss our results in regard to recent photoluminescence experiments performed on ensemble and single GaN nanowires.We acknowledge financing from the European Union Seventh Framework Program under Grant Agreement No. 265073

Limit design of axisymmetric shells with application to cellular cofferdams

This paper is devoted to the limit design of cellular cofferdams that are regarded as mixed structures where the backfill is modeled as a three-dimensional continuum, while the surrounding sheet pile wall is treated as a cylindrical shell. Dealing with this structure from a static point of view, it turns out that the problem under consideration requires the calculation of the ultimate load value of a circular cylindrical shell subjected to a linearly varying pressure distribution representing the thrust of the backfill material. Extending the results of previous works, a complete solution to this problem is developed for different boundary conditions. The corresponding results are discussed, notably the influence of the shell relative thickness. They are applied to the design of a single cellular cofferdam whose stability under gravity forces is examined, with the strength of the granular backfill material being described by a Mohr-Coulomb criterion