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

A stochastic model for fatigue short crack growth is presented. It takes into account the interaction between the crack-tip plastic zone and grain boundaries. The process is Markovian. It is completely described by the crack length and the size of the plastic zone. The integro-differential equation giving the evolution of the transition probability distribution is derived.

The ductile failure of porous metallic materials is studied here using both Limit Analysis (LA) methods, a problem treated by Gurson with his famous kinematic approach in 1977. The present work is devoted to determining the strength of porous materials with long circular cylindrical cavities in the case of plane stress. The numerical methods developed here use the Hill–Mandel method based on the homogenization theory of heterogeneous media within the LA framework. The use of kinematic and static approaches gave an excellent estimation of the yield criterion for all the cases studied. The numerical results based on LA methods have been compared with analytical and semi-analytical yield domain expressions proposed by different authors. The results show that the Richmond model was the most accurate in terms of our predictions.

The eigenvalue problem of the Dirichlet Laplacian in a singularly perturbed region, which is described as a bounded domain with a thin appendix is considered. The expansion of eigenvalues in the power series with respect to a small parameter (radius of the cross-section of the appendix) is constructed. This result is extended to the Helmholtz resonator with the finite thickness of a shell.

At small magnetic Reynolds number, a two-dimensional model is proposed for MHD flows in a nonuniform magnetic field and in a cavity of nonuniform depth in the direction of the magnetic field. The characteristic surfaces appear when deriving the model and play a crucial role in the resulting solutions. A new type of free shear layers are found for the first time, developing along such surfaces, of thickness of order Ha^−1/4.

Starting from some experimental observations on shear strength of stiff clays [3,2], a isotropic, geometrically non-linear second gradient elastoplastic model is proposed for pressure dependent, brittle geomaterials. The development of the model follows the general theory presented in [1]. Due to the internal length scale provided by the microstructure, the model is ideally suited for the analysis of failure problems in which strain localization into shear band occurs, see, e.g., [4,5].

The singular perturbed eigenvalue problem for the Laplace operator in a cylindrical body with frequently alternating boundary conditions is considered. The asymptotics for the eigenelements are constructed.

In this paper the Hook law for cylindrical springs is derived from the linearized elasticity. The cylindrical spring is an elastic curved rod with helicoidal middle curve. The curved rod model is used to obtain the behaviour of the spring subjected to the longitudinal force. The obtained coefficient in Hook's law, expressed in terms of the elastic and geometrical properties of the spring, matches the known coefficient.

We present the interest and some characteristics of the inverse transformation of a 2D Stokes flow. This method is applied to the cellular flow between two parallel plates induced by a rotating cylinder to obtain the flow around two circular cylinders in contact placed in the centre of a rotating circular cylinder.

The transition in confined rotating flows is a topical problem with many industrial and fundamental applications. The purpose of this study is to investigate the Taylor–Couette flow in a finite-length cavity with counter-rotating walls, for two aspect ratios L=5 or L=6. Two complex regimes of wavy vortex and spirals are emphasized for the first time via direct numerical simulation, by using a three-dimensional spectral method. The spatio-temporal behavior of the solutions is analyzed and compared to the few data actually available.

In this paper we first establish two necessary and sufficient conditions in order that incremental constitutive equations expressing the strain rate tensor as a function of the Jaumann's derivative of the Cauchy's stress tensor can be inverted under the general form of hypoplastic models when the stress state is located inside the domain bounded by the limit state surface. We are then interested in the physical meaning of these conditions with regard to the incremental response of the material.