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

In this paper, we present a justification of the linear Novozhilov-Donnell model using an asymptotic approach. This model has already been obtained from linearized three-dimensional elasticity. We propose here to justify this model directly from the nonlinear three-dimensional elasticity equations. In the case of shallow shells and for small enough applied loads, we prove that the first term of the strain measures is linear with respect to the displacements. The equilibrium equations of the asymptotic model are those of the Novozhilov-Donnell model. So, the domain of validity of the linear Novozhilov-Donnell model is clearly determined.

During three-point-bending fatigue tests with predominant shearing on a unidirectional glass/epoxy composite, caulking is observed under the rollers on all loaded specimens. If fatigue tests are controlled in displacement, caulking induces a change in loading conditions during cycling, and the damage in the material is reduced.

In this paper, we present the construction of a membrane model for shallow shells using asymptotic approach. This model is valid for important applied loads where the tangential part is supposed to be more important than the normal part. To our knowledge, this membrane model obtained from three-dimensional elasticity, does not exist in the literature. Although it is nonlinear, it resolution can be split into two linear problems.

We consider a parabolic equation with highly contrasted diffusion coefficients in the blocks set ℳ^(ɛ) and in the surrounding fissures system ℱ^(ɛ). Without a assumption, for a large range of contrast and by mean of variational homogenization, we find the global behavior when the numbers of blocks tends to infinity, for both the non stationary and the stationary model.

The transfer of the electromagnetic field from a toric emitter to a receiver of same kind is expressed by a two-dimensional integral which can be split into two one-dimensional integrals. Each one-dimensional integral can be seen as a fractionnal Fourier transform whose order is related to the distance between the emitter and the receiver and to their principal curvatures. The knowledge of these orders is alone sufficient to solve practical problems (such as image formation) without explicit use of the integral formulae.

The urine transport through the ureter is made with isolated pockets denoted “bolus”. We adopt some hypothesis, as axial symmetry, constancy of the bolus velocity and steadiness of the whole motion.

Taking into account the important terms, the analytical resolution of the equations leads to the determination of the field of velocities in the urine, in the wall and the bolus shape, depending on 5 parameters whose some suitable choice of the values permits to obtain solutions compatible with medical observations.

A new micro-macro computational strategy is proposed for the analysis of structures which are described up to the “micro” level, such as composite structures. It is intended to replace standard homogenization techniques coupled with a local reanalysis, at least for several domains of interest. This paper describes the basis of the new approach.

A formulation for anisotropic damage is established in the framework of the principle of strain equivalence. The damage variable is still related to the surface density of microcracks and microvoids, and, as its evolution is governed by the plastic strain, it is represented by a second-order tensor and is orthotropic. The coupling of damage with elasticity is expressed in tensor form on the deviatoric part of the stress tensor and in scalar form by its trace on the hydrostatic part. The kinetic law of damage evolution is an extension of the isotropic case. Here the principal components of the damage rate tensor are proportional to the absolute value of the principal components of the plastic strain rate tensor. The proposed damage evolution law does not introduce any other material parameter. Several series of experiments give a good validation of this theory.

This note presents, in the framework of three-dimensional linear elastodynamics in the time domain, a method for evaluating sensitivities of integral functionals to crack shapes, based on the adjoint state approach and resulting in a sensitivity formula expressed in terms of surface integrals (on the external boundary and the crack surface) and contour integrals (involving the direct and adjoint stress intensity factor distributions on the crack front). This method is well-suited to boundary element treatments of e.g. crack reconstruction inverse problems.

We study crack kinking in the situation where the crack is initially closed by compression forces but opens up as a result of kinking. This problem was considered very recently by the authors in the case where contact between the crack lips occurred without friction. The study is extended here to the (obviously more physically realistic) case where friction is present and obeys Coulomb 's law. We consider in particular the problem of configurational stability of the propagation path, as governed by the applied load. It is found that introduction of friction does not qualitatively modify the conclusions drawn in the frictionless case.