Modified fixed point algorithm in fluid–structure interactionAccélération avec des conditions de transpiration d'un algorithme de point fixe en interaction fluide–structure

In this work, we address the numerical solution of some non-linear problems arising in the time discretization of fluid–structure interaction problems with fully implicit schemes. At each time step, we have to solve a highly non-linear coupled system, since the fluid domain depends on the unknown displacement of the structure. We propose a modified fixed-point algorithm which combines the Block-Gauss–Seidel iterations with a transpiration formulation. Numerical experiments show the great improvement in computing time with respect to the standard method. To cite this article: S. Deparis et al., C. R. Mecanique 331 (2003).     

Approximate yield criteria for anisotropic metals with prolate or oblate voidsCritères macroscopiques pour des métaux plastiques anisotropes contenant des cavités non sphériques

Following the study of Gologanu et al. (1997) which has extended the well-known approach of Gurson (1975), we propose approximate yield criteria for anisotropic plastic voided metals containing non spherical cavities. The plastic anisotropy of the matrix is described by means of Hill's quadratic criterion. The procedure to establish the closed form expression of approximate macroscopic criteria, in which void shape and plastic anisotropic effects are included, is detailed. The new criteria allow us to recover existing results in the cases of spherical and cylindrical voids in an Hill type plastic matrix. Moreover, they agree with previous criteria for non spherical voids in an isotropic plastic matrix. Finally, for validation purposes, we provide, in the general case of non spherical cavities in the anisotropic matrix, a comparison with the numerical exact two field criteria. To cite this article: V. Monchiet et al., C. R. Mecanique 334 (2006).     

Artificial boundary conditions on polyhedral truncation surfaces for three-dimensional elasticity systemsConditions aux limites artificielles sur des surfaces polyhédrales de troncature pour des systèmes d'élasticité tridimensionalle

For a three-dimensional exterior problem in the framework of anisotropic elasticity, artificial boundary conditions are constructed on a polyhedral truncation surface. These conditions do not need an explicit formula for the fundamental matrix. An approach to adapt the shape of truncation surfaces to the shape of the enclosed cavity is discussed. To cite this article: S. Langer et al., C. R. Mecanique 332 (2004).     

Nonlinear composites: a linearization procedure,exact to second-order in contrast and for which the strain-energy and affine formulations coincideComposites non linéaires : un schéma exact au second ordre pour lequel la formulation en énergie de déformation coı̈ncide avec la formulation affine

This Note presents a new approximate scheme for nonlinear composites. The approximation which is made preserves certain features of the original second-order scheme of Ponte Castañeda, exactness to second-order in the contrast and existence of an effective energy, but improves on one drawback, which is the gap between the strain-energy formulation and the affine formulation. A numerical example shows the accuracy of the present method. To cite this article: N. Lahellec, P. Suquet, C. R. Mecanique 332 (2004).     

Mathematical modeling of an array of underground waste containersModélisation mathématique d'un réseau souterrain de stockage de déchets

We consider a mathematical model describing the behavior of an underground waste repository, once the containers start to leak. Due to the high contrast of the characteristic lengths, numerical simulations on a such model are unrealistic. After renormalization, a small parameter ε appears and the global model is obtained when ε tends to zero, by means of homogenization and boundary layers methods. The asymptotic model obtained could be used as a global repository model for large field numerical simulations. To cite this article: A. Bourgeat et al., C. R. Mecanique 330 (2002) 371–376.     

Un modèle paramétrique d'évolution de surface pour matériaux contraints : modélisationA parametric model of surface evolution for materials under constraint; part I: modeling

We present a model describing the surface changes of an elastic preconstrained material which is valid for large deformations. The surface profile is described by a parametric curve that allows the emergence of infinite tangents and back return point as the surface evolves. The proposed model covers a number of classic models: Spencer (1994), Yang (1993), Kassner (1994), Chiu (1994). These latter models were limited to surface profiles with one-to-one representations and low amplitudes of deformation. To cite this article: M. Carrive, J. Grilhé, C. R. Mecanique 334 (2006).     

Modélisation des problèmes d'impact avec dissipation d'énergie par frottement

The bi-potential method has been successfully applied for the modeling of frictional contact problems in static cases. This paper presents the application of this method for dynamic analysis of impact problems with multiple deformable bodies. A first order algorithm is applied for numerical integration of the time-discretized equation of motion. The numerical results show clearly the physical energy dissipation introduced by frictional effects between the solids in contact. To cite this article: B. Magnain et al., C. R. Mecanique 333 (2005).     

Calcul de l'écoulement autour d'un cylindre semi-circulaire par une méthode de collocationNumerical study of the flow over a half-circular cylinder by a diffuse approximation-based collocation method

A diffuse approximation based collocation method is used for the study of the flow over a half-circular cylinder. We give some results on the instationary wake at a Reynolds number Re=65. To cite this article: T. Sophy et al., C. R. Mecanique 330 (2002) 193–198.     

Control of three-dimensional wakes using evolution strategies

We investigate three-dimensional cylinder wakes of incompressible fully developed flows at $\mathit{Re}=300$, resulting from control induced by tangential motions of the cylinder surface. The motion of the cylinder surface, in two dimensions, is optimized using evolution strategies, resulting in significant drag reduction and drastic modification of the wake as compared to the uncontrolled flow. The quasi-optimal velocity profile obtained in 2D is modified by spanwise harmonics and applied to 3D flows. The results indicate important differences in the flow physics induced by two and three dimensional control strategies. To cite this article: P. Poncet et al., C. R. Mecanique 333 (2005).     

Verification of higher-order discontinuous Galerkin method for hexahedral elements

A high-order implementation of the Discontinuous Galerkin (dg) method is presented for solving the three-dimensional Linearized Euler Equations on an unstructured hexahedral grid. The method is based on a quadrature free implementation and the high-order accuracy is obtained by employing higher-degree polynomials as basis functions. The present implementation is up to fourth-order accurate in space. For the time discretization a four-stage Runge–Kutta scheme is used which is fourth-order accurate. Non-reflecting boundary conditions are implemented at the boundaries of the computational domain.The method is verified for the case of the convection of a 1D compact acoustic disturbance. The numerical results show that the rate of convergence of the method is of order $p+1$ in the mesh size, with p the order of the basis functions. This observation is in agreement with analysis presented in the literature. To cite this article: H. Özdemir et al., C. R. Mecanique 333 (2005).