A direct method for the solution of evolution problemsLa méthode directe

An alternative numerical method to solve structural evolution problems is presented. It belongs to the family of Large Time Increment Methods. The problem is solved on the whole time interval separating a global stage where a SA and KA solution is searched and a local stage where the constitutive law is satisfied. To solve the global stage, consuming the most CPU time, the mechanical fields are decomposed in a wavelet basis and the equilibrium is solved only for the largest coefficients. To cite this article: F. Comte et al., C. R. Mecanique 334 (2006).     

Identification of elastic parameters by displacement field measurementIdentification de paramètres mécaniques par mesure de champ de déplacement

In this Note we study a parameter identification problem associated with a two-dimensional mechanical problem. In a first part, the experimental technique of determining the displacement field is presented. The variational method proposed herein is based on the minimization of a separate convex functional which leads to the reconstruction of the elastic tensor and the stress field. These two reconstructed fields are continuous and piecewise linear on a triangulation of the two-dimensional problem. Some numerical and experimental examples are presented to test the performance of the algorithm. To cite this article: G. Geymonat et al., C. R. Mecanique 330 (2002) 403–408.     

Détermination de la réponse asymptotique d'une structure anélastique sous chargement thermomécanique cycliqueDetermination of the asymptotic response of a structure under cyclic thermomechanical loading

A method for the solution of cyclic thermomechanical nonlinear problems is presented: it is a Direct Cyclic Method which is an alternative approach to classical methods. It consists in directly seeking the asymptotic response of an inelastic structure subjected to a periodic thermomechanical loading without following the loading path. It is based on the Large Time Increment Method, the periodicity of the limit state and the Fourier transform. To cite this article: M.H. Maitournam et al., C. R. Mecanique 330 (2002) 703–708.     

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.     

Détermination du critère de rupture macroscopique d'un milieu poreux par homogénéisation non linéaireDetermination of the macroscopic strength criterion of a porous medium by nonlinear homogenization

A porous medium, which matrix is a perfectly plastic solid, is considered. This paper proposes a method to determine the macroscopic admissible stress states. The method is based on a homogenization technique which takes advantage of the equivalence, under certain conditions, between a problem of limit analysis and a ficticious nonlinear elastic problem. The particular case of a Drucker–Prager solid matrix is considered. The method provides an analytical expression for the complete macroscopic strength criterion. To cite this article: J.-F. Barthélémy, L. Dormieux, C. R. Mecanique 331 (2003).     

Comportement mécanique et rupture de milieux granulaires cohésifsMechanical behaviour and rupture of cohesive granular media

The modelling of mechanical behaviour and rupture of cohesive granular media is carried out on a model medium made of aluminium cylinders and cohesive bonds playing the role of cohesion points. The mechanical behaviour of the cohesion point is studied under different loading situations (compression, traction, shearing, torque). The results are introduced into a code, which is based on a discrete element method extended to the cohesive case. The validation is achieved with compression tests of macroscopic samples. We notice a good correlation between simulation and experiment on the mechanical behaviour, on the appearance of fractures and their propagation. To cite this article: J.-Y. Delenne et al., C. R. Mecanique 330 (2002) 475–482.     

The elastic torus: anomalous stiffness of shells with mixed typeLe tore élastique : raideur anormale des coques de type mixte

We investigate the deformation of a thin elastic torus under axisymmetric surface loads. The strain concentrates near the top and bottom parallels and the inner and outer halves essentially undergo rigid-body translations in opposite directions. An analysis of the inner boundary layers is presented, which allows one to compute the effective stiffness of the torus for this loading. This stiffness is found anomalous compared to classical shells. These mechanical properties are interpreted using purely geometrical arguments. To cite this article: B. Audoly, Y. Pomeau, C. R. Mecanique 330 (2002) 425–432.     

Problème spectral pour la propagation conique des ondes élastiques dans un réseau de galeriesA spectral problem for conically propagating elastic waves through an array of cylindrical channels

This Note is devoted to the analysis of elastic waves conically propagating through a doubly periodic array of cylindrical channels. A new method, based on a multiple scattering approach, has been proposed to reduce the problem to an algebraic system of the Rayleigh type. We obtain an eigenvalue problem formulation that enables us to construct the high-order dispersion curves and to study phononic band gap structures in oblique propagation. We note an effect of singular perturbation associated with a small angle of conical propagation. To cite this article: S. Guenneau et al., C. R. Mecanique 330 (2002) 491–497.     

Adaptive remeshing for ductile fracture prediction in metal formingRemaillage adaptatif pour la prévision de la rupture ductile en mise en forme

The analysis of mechanical structures using the Finite Element Method in the framework of large elastoplastic strain, needs frequent remeshing of the deformed domain during computation. Indeed, the remeshing is due to the large geometrical distortion of finite elements and the adaptation to the physical behavior of the solution. This paper gives the necessary steps to remesh a mechanical structure during large elastoplastic deformations with damage. An important part of this process is constituted by geometrical and physical error estimates. The proposed method is integrated in a computational environment using the ABAQUS/Explicit solver and the BL2D-V2 adaptive mesher. To cite this article: H. Borouchaki et al., C. R. Mecanique 330 (2002) 709–716.     

Une technique de lissage de données basée sur la théorie de la régularisationA filter technique based on regularization theory

A simple filter technique based on the regularization theory is presented. We consider the problem as an optimization one. The regularization theory gives us a suitable theoretical framework to define a functional to minimize. We make a numerical comparation between this method and a classical Fourier technique. To cite this article: J.-M. Fullana, C. R. Mecanique 330 (2002) 647–652.     

On the optimization of higher eigenvaluesSur l'optimisation de valeurs propres supérieures

A new approach is proposed for the study of the classical Lagrange problem on the optimal form of a column with clamped ends and a fixed volume. It is proved that there exists a column with the maximal possible value of the kth eigenvalue and that such a column is unique. A method for the numerical solution is proposed. The method is based on the analysis of the critical points of a non-linear functional related to the Lagrange problem. To cite this article: Y.V. Egorov, C. R. Mecanique 332 (2004).     

Convection induced by composition gradients in miscible systemsConvection induite par des gradients de composition dans les systèmes miscibles

When two miscible fluids, such as glycerol (glycerin) and water, are brought in contact, a large concentration (and density) gradient exists, which relaxes through diffusion. With a mathematical model based on the Korteweg stress, we show that convection can occur which is analogous to surface-tension induced convection (STIC) or Marangoni convection. Specifically, we show that with realistic parameters significant flows can occur with plane interfaces and that drops of miscible fluids can act like their immiscible counterparts. Regarding plane interfaces, an experimental confirmation of this phenomenon is planned for the International Space Station. To cite this article: V.A. Volpert et al., C. R. Mecanique 330 (2002) 353–358.     

Drapage géométrique des compositesGeometrical draping of composite fabrics

This paper presents a study devoted to the composite fabric shaping simulation in finite strain analysis. We introduce a new geometrical approach based on the fishnet method for which the deformation of a fabric mesh element consists in a pure trellis effect. Such a fabric mesh element is then defined by a curved quadrilateral whose edges are geodesic lines with the same length plotted onto the surface to drape. Given three vertices of the fabric mesh element on the surface, we propose an optimization algorithm to define the fourth vertex of the fabric mesh element. This algorithm allows us to drape the surface using an advancing front approach from the data of an initial impact point between the fabric and the surface and the initial fibre directions at this point. A numerical draping simulation example using this approach is given. To cite this article: H. Borouchaki, A. Cherouat, C. R. Mecanique 331 (2003).     

Une approche de plasticité au gradient en construction métalliqueA gradient plasticity approach for steel structures

Local buckling of steel structural members has to be well understood in order to design accurately steel structures in seismic areas. Induced softening moment-curvature law leads to a well known ill-posedness elastoplastic evolution problem. Localization is chosen to be controlled with a gradient plasticity approach. The concept of cross-section behavioural classes, classically adopted in modern rule design, should be substituted by the concept of member behavioural classes. To cite this article: N. Challamel, C. R. Mecanique 331 (2003).     

Integral formulation and self-consistent modelling of elastoviscoplastic behavior of heterogeneous materials

Summary Based on projection operators, an integral formulation is proposed for elastoviscoplastic heterogeneous materials. The problem requires a complete mechanical formulation, including the static equilibrium property concerning the known field σ, in addition to the classical field equations concerning the unknown fields ɛ˙ and σ˙. The formulation leads to an integral equation, in which elasticity and viscoplasticity effects interact through an homogeneous elastoviscoplastic medium with elastic moduli C and viscoplastic moduli B. To approximate the integral equation, the self-consistent scheme is followed. In order to obtain consistent approximation conditions, we introduce fluctuations of elastic and viscoplastic strain rate fields with respect to known kinematically compatible fields. It results in a strain rate concentration relation connecting the strain rate at each point to the macroscopic loading conditions and the local stress field. The results are presented and compared with other models and with experimental data in the case of a two-phase material. Received 26 August 1997; accepted for publication 2 July 1998     

Second-order work and dissipation on indirect pathsTravail du deuxième ordre et dissipation sur des chemins indirects

The concept of the second-order dissipation on arbitrary complex paths in the space of internal state variables is developed. A general framework for time-independent dissipative solids is adopted which encompasses plasticity, micro-cracking or martensitic phase transformation. Circumstances are established in which the dissipation evaluated to the second order is minimized on a radial path. As an application, this minimum property is used to simplify a sufficiency condition for stability of equilibrium. To cite this article: H. Petryk, C. R. Mecanique 330 (2002) 121–126.     

Analysis of viscoelastic contact with normal compliance,friction and wear diffusionAnalyse d'un problème viscoélastique avec compliance normale,frottement et diffusion d'usure

We consider a quasistatic problem of frictional contact between a viscoelastic body and a moving foundation. The contact is with wear and is modeled by normal compliance and a law of dry friction. The novelty in the model is that it allows for the diffusion of the wear debris over the potential contact surface. Such kind of phenomena arise in orthopaedic biomechanics and influence the properties of joint prosthesis. We derive a weak formulation of the problem and state that, under a smallness assumption on the problem data, there exists a unique weak solution for the model. To cite this article: M. Shillor et al., C. R. Mecanique 331 (2003).     

Critère de fatigue polycyclique pour des matériaux anisotropes : application aux monocristauxA high cycle fatigue criterion for anisotropic materials: application to single crystals

The high-cycle fatigue criteria based on a macroscopic–mesoscopic scale interpretation, initiated by Dang Van, were used essentially for polycrystalline materials. In the existing criteria the material isotropy at both mesoscopic and macroscopic scales plays a key role. The purpose of this paper is to revisit the macroscopic to mesoscopic fatigue approach taking into account the material anisotropy and some results obtained by Bui. The possible applications are some anisotropic steels or monocrystalline structures such as stitanium turbine blades. To cite this article: F. Cano et al., C. R. Mecanique 332 (2004).     

Calcul à la rupture en présence d'un écoulement à surface libre : construction de champs de pression approchésYield design for porous media subjected to unconfined flow: construction of approximate pressure fields

We consider the stability of a porous medium submitted to a steady-state flow with free-boundary. Assuming some hypotheses, it is possible to implement the kinematic method by using an approximate pressure field bounding the true pressure field from below. We are interested in finding such approximate pressure fields and in proving that they bound the true pressure field from below without knowing the true pressure field. We use fields which are solutions of a problem with relaxed conditions with regard to the real problem. Under a uniqueness condition of the solution of a weak formulation of the problem, such fields are lower bounds for the true pressure field. Finally, we give the example of a vertical dam. To cite this article: A. Corfdir, C. R. Mecanique 334 (2006).     

Un modèle discret du couplage entre les fils dans une structure tisséeA discrete model for the coupling between the yarns in a woven fabric

The coupling between yarns in a piece of fabric has been analysed at the mesoscopic scale, in terms of its impact on the macroscopic unidirectional behaviour. Starting from a discrete model of a woven structure associated to a variational formulation of the equilibrium of the structure, the coupling between both yarns is introduced, the potential energy of which is calculated. The initial shape of the yarn, represented by a planar undulated beam supposed to be periodic, is described by a Fourier series. The coefficients of the series are expressed vs. the contact force exerted at the top of the undulations, and vs. the mechanical properties of the solicited yarn. The contact force is then expressed vs. the mechanical properties of the transverse yarn and vs. the vertical displacement of the contact point. The potential energy of the coupling is then built, assuming the continuity of the displacement at the contact points. The equilibrium shape of the yarn submitted to unidirectional traction is obtained numerically as the minimum of the total potential energy. The simulated traction curve reproduces in a satisfactorily manner the observed behaviour. The respective contributions of the flexional and extensional effects of the yarn are analysed. The consideration of the coupling enhances the rigidity of the response of the yarn; one demonstrates the effect of the geometrical and mechanical parameters of the transverse yarn. To cite this article: B. Ben Boubaker et al., C. R. Mecanique 331 (2003).