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

This note deals with the problem of a penny-shaped hydraulic fracture propagating in an impermeable elastic solid. Growth of the fracture is driven by injection of an incompressible Newtonian fluid at the center of the fracture. The solution is restricted to the so-called viscosity-dominated regime where it can be assumed that the solid has zero toughness. The paper describes the construction of a semi-analytical similarity solution, which incorporates the known singularity of the fluid pressure at the center of the fracture and at the tip and which is based on series expansions of the fracture opening and fluid pressure in terms of Jacobi polynomials.

The present note describes the process settled for analysis of coated contacts submitted either to a normal load or a tangential one. This hybrid method uses a Finite Element Method in addition to the experimental results. Effects of a soft coating and a hard layer are studied on elastic contact parameters (F.E.M.), and on the resistance to fretting fatigue (experimentation + F.E.M.). The use of Dang Van criterion allows us to determine the crack initiation threshold.

Analytical techniques are used to study the onset of convection in three-dimensional boxes of fluid saturated porous material heated from below and subjected to vertical high-frequency vibration. Increasing the vibration amplitude delays the onset of convection and may even create subcritical solutions so as generate different structures of flows.

We propose an improvement of the bolus passive viscoelastic wall model [1], by adding an active muscular layer situated on the internal side of the wall. This new model permits, for a suitable choice of the active force, to obtain analytically a closed bolus on its two ends and to get a close approach of the medical observations.

A micromechanical analysis of brittle damage is proposed. This analysis consists of a 3-D generalization of the study performed by Andrieux et al. In this approach, the macroscopic free energy for open microcracks and frictionless closed microcracks is built. The conditions for unilateral contact (opening/closure criterion, elastic moduli recovery) are also presented. The proposed construction ensures at the macroscopic level the symmetry of the elastic stiffness tensor and the continuity of stress at the damage deactivation.

The three-dimensional perturbation of a Blasius boundary layer induced by a small hump (or a trough) placed at the wall is studied for a Reynolds number going to infinity. For certain dimensions of the hump, a four deck structure is obtained. The main features of this structure are described.

A new nonparametric probabilistic approach is presented for modeling random uncertainties in transient linear elastodynamics. The information used does not require a description of the local parameters of the mechanical model. The probability model is constructed in the generalized coordinates associated with the elastic eigenmodes. The available information is constituted of the algebraic properties of the generalized mass, damping and stiffness matrices which have to be positive-definite symmetric matrices, and the knowledge of these matrices for the mean reduced matrix model. The convergence of the stochastic solution with respect to the dimension of the random reduced matrix model is analysed.

In this note we discuss the application of a methodology combining distributed Lagrange multiplier based fictitious domain techniques, finite element approximations and operator splitting, to the numerical simulation of the motion of an elliptic body falling in a Newtonian incompressible viscous fluid. The motion of the body is driven by the hydrodynamical forces and gravity. As qualitatively expected, the elliptic body rotates so that its broad side tends to be perpendicular to the flow direction.

We suggest a new expression of the scattering kernel for a polyatomic gas lying in the Knudsen layer when impinging on the wall. We consider a vibrational strong non-equilibrium case for the gas. The global scatterring kernel is a linear combination of partial operators describing the reflection of the various mode of energy. The scattering kernel allows to write a consistent boundary condition for the kinetic equation of polyatomic molecules.

We study the initial-boundary value problem for a system of quasilinear equations of one-dimensional nonlinear thermoviscoelasticity with rapidly oscillating nonsmooth coefficients and initial data. We rigorously justify the passage to the corresponding limit initial-boundary value problem for a system of two-scale homogenized integro-differential equations, including the existence theorem for the limit problem. The results are global with respect to the time interval and the data.