Using the gradients of temperature and internal parameters in Continuum ThermodynamicsIntroduction des gradients de température et de paramètres internes en Thermodynamique des Milieux Continus

In this paper, the possibility of using the gradients of the temperature and of the internal parameters as additional state variables in Continuum Thermodynamics is considered. The expressions of the two principles are discussed and Clausius–Duhem inequality is derived under an appropriate statement of the internal entropy production. Several formulations are proposed and compared to existing results in the literature. To cite this article: P. Ireman, Q.S. Nguyen, C. R. Mecanique 332 (2004).     

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).     

Particle-size segregation in dense granular avalanches

Particles of differing sizes are notoriously prone to segregate, which is a chronic problem in the manufacture of a wide variety of products that are used by billions of people worldwide every day. Segregation is the single most important factor in product non-uniformity, which can lead to significant handling problems as well as complete batches being discarded at huge financial loss. It is generally regarded that the most important mechanism for segregation is the combination of kinetic sieving and squeeze expulsion in shallow granular avalanches. These free-surface flows are more common than one might expect, often forming part of more complicated flows in drums, heaps and silos, where there is mass exchange with underlying regions of static or slowly moving grains. The combination of segregation and solid–fluid granular phase transitions creates incredibly complicated and beautiful patterns in the resulting deposits, but a full understanding of such effects lies beyond our capabilities at present. This paper reviews recent advances in our ability to model the basic segregation processes in a single avalanche (without mass exchange) and the subtle feedback effects that they can have on the bulk flow. This is particularly important for geophysical applications, where segregation can spontaneously self-channelize and lubricate the flow, significantly enhancing the run-out of debris-flows, pyroclastic flows, rock-falls and snow-slab avalanches.     

Simulation numérique des détonations à double structure cellulaireNumerical simulation of detonations with double cellular structure

We present the results of numerical two-dimensional simulations of detonation cellular structures under non-monotonous heat release provided by a chemical reaction comprising two successive exothermic steps. The influence of the rate of the second step of chemical reaction on the detonation cellular structure has been investigated. Our simulations are the first that reproduce a cellular structure composed of two clearly distinct sets of cells with different characteristic sizes where fine cells completely fill up larger ones, as has been observed experimentally. To cite this article: V. Guilly et al., C. R. Mecanique 334 (2006).     

Stress-based upper-bound method and convex optimization: case of the Gurson materialMéthode cinématique par les contraintes et optimisation convexe : cas du matériau de Gurson

A nonlinear interior point method associated with the kinematic theorem of limit analysis is proposed. Associating these two tools enables one to determine an upper bound of the limit loading of a Gurson material structure from the knowledge of the sole yield criterion. We present the main features of the interior point algorithm and an original method providing a rigorous kinematic bound from a stress formulation of the problem. This method is tested by solving in plane strain the problem of a Gurson infinite bar compressed between rough rigid plates. To cite this article: F. Pastor et al., C. R. Mecanique 334 (2006).     

Évaluation de l'influence des changements de géométrie sur les déformations de séchage d'un milieu poreux fissuréInfluence of geometry changes on drying-induced strains in a cracked solid

The macroscopic response of a cracked solid subjected to drying is investigated within the framework of micromechanics. The originality of this contribution lies in the fact that the variations of the aspect ratios of cracks induced by the capillary pressure increase are accounted for. When the initial aspect ratio is small enough, it is shown that neglecting the geometrical changes yields an erroneous prediction of the sign of the macroscopic volume strain rate. To cite this article: X. Chateau et al., C. R. Mecanique 331 (2003).     

Small vibrations of a linearly elastic body surrounded by heavy,incompressible, non-Newtonian fluids with free surfaces

We consider the small transient motions of a coupled system constituted by a linearly elastic body and two heavy, incompressible, non-Newtonian fluids.Through a formulation in terms of non-linear evolution equations in Hilbert spaces of possible states with finite mechanical energy, we obtain existence and uniqueness results and study the influence of gravity. To cite this article: C. Licht, Tran Thu Ha, C. R. Mecanique 333 (2005).     

Singular nature of nonlinear macroscale effects in high-rate flow through porous mediaNature singulière des effets macroscopiques non linéaires dans un écoulement à hautes vitesses en milieux poreux

The quadratic law of laminar flow through porous media at high Reynolds numbers, which is well confirmed by the multiple experimental data, is shown to give rise to three fundamental paradoxes. All them can be resolved by assuming the singular structure of flow. The singularity is produced by the formation of jet brunches which invade the stagnant zones and sharply loss their kinetic energy. The numerical simulation confirms this effect. To cite this article: M. Panfilov et al., C. R. Mecanique 331 (2003).     

Variance of the virtual displacement

We show that the affine structure of the 3-dimensional space is deeply enmeshed with the static laws expression. The relevance of tensorial rules for calculus in mechanics is thus enhanced. The virtual work principle is stated precisely but a little twist is given to the usual statements: the tensorial nature of the so-called virtual displacement vector is asserted to be covariant. To cite this article: C. Vallée et al., C. R. Mecanique 332 (2004).

Résumé

Nous montrons que la structure affine de l'espace tridimensionnel est fortement imbriquée avec l'expression des lois de la statique. La pertinence de l'application des règles du calcul tensoriel à la mécanique est ainsi renforcée. Le principe des travaux virtuels est établi précisément avec une seule entorse aux exposés classiques : la nature tensorielle de l'habituel vecteur déplacement virtuel est affirmée covariante. Pour citer cet article : C. Vallée et al., C. R. Mecanique 332 (2004).