Modélisation des milieux à microstructure : approches par la méthode des puissances virtuelles

The first part (chapt. 1) of this Ph.D. thesis is dedicated to a bibliographic analysis. A rapid survey of the main works on the topic of continua with microstructure is used as an introduction to the simple materials theory of W. Noll and to a short exposition of the works of G. Capriz. The next step (chapt. 2) consists in the explanation of the "deep" space notion and of the relevant microplacement and macroplacement of a set of particles in that deep space. The properties of these placements determine the definitions of each continuum : monoparticular, multiparticular, multiconstituents or multiphasic. We give the cinematic and dynamic properties of those continua, and propose the possibility for the use of a phase functions field to deal with the evolution of the phases. Two different ways (chapt.3) are proposed to write the field and boundary equations of a multiparticular continuum with microstructure. The aim is to describe the equilibrium state of a Cosserat multiparticular continuum - i. e. a continuum in each point of which a continuum of triads is to be considered. Chapter four is the exposition of a new micro-macro transformation method which we named "globalization." This one is derived from the classical homogenization methods. It consists in defocusing a classical continua with microstructure (monoparticular), in order to obtain either the equilibrium equations or the constitutive variables of the macro continua from those of the initial medium. The method is developed for the case of microstructures represented in a manifold on which the action of the group of the rotations of the three dimensional Euclidean space is transitive. The end of the report (chapt. 5) deals with a few proposals to try to determine the behavior - in relation with the behavior of the micro-continuum. - of such multiparticular continua with microstructure.La première partie du mémoire est consacrée à une étude bibliographique. Après un rapide aperçu historique des travaux portant sur les milieux à microstructure, une étude de la théorie des matériaux simples de W. Noll est présentée, ainsi qu'un exposé des travaux de G. Capriz sur les matériaux à microstructure. On introduit ensuite les notions d'univers d'observation "profond", de microplacement et de macroplacement dans cet univers d'un ensemble de particules. Les propriétés de ces placements conditionnent les définitions des milieux monoparticulaires, multiparticulaires, multiconstituants ou multiphasiques que l'on donne. On décrit les propriétés cinématiques et dynamiques de ces milieux. On propose l'introduction d'un champ de fonctions de phase pour traiter les problèmes de changements de phases. Deux approches complémentaires pour obtenir les équations d'équilibre d'un milieu multiparticulaire à microstructure sont ensuite mises en oeuvre, en s'intéressant plus particulièrement aux milieux de Cosserat multiparticulaires (distribution continue d'orientation de trièdres au même point de l'espace physique). Le chapitre IV consiste en un exposé complet d'une méthode de changement d'échelle apparentée aux outils classiques de l'homogénéisation que nous nommons globalisation. Cette méthode permet, par défocalisation d'un milieu à microstructure "classique", de déduire les équations d'équilibre macro des équations d'équilibre du milieu initial. L'intérêt réside dans l'identification physique des grandeurs constitutives du milieu macro à partir des grandeurs constitutives du milieu micro. La démarche est menée à terme dans le cadre général des microstructures sur lesquelles l'action du groupe des rotations de IR3 est transitive. La fin du mémoire apporte quelques indications sur l'ébauche d'une méthode de détermination du comportement d'un milieu multiparticulaire à partir de la globalisation des principales équations de bilan du milieu micro

ECORCE 1.0 : Eco-comparateur routes, construction et entretien

Logiciel d'évaluation environnementale des projets routiers qui a été développé par LCPC dans le cadre de la méthodologie d'analyse globale des procédés du Génie civil

Visco-elastic modelling for asphalt pavements : Software ViscoRoute

International audienceHuet-Sayegh model (1963) gives a set of constitutive equations of a viso-elastic material which accounts well for the behaviour of asphalt pavement layers, especially regarding thermal effects. This model allows rather good predictions of experimental data. The French pavement design method consists in a pavement mechanistic analysis based on the Burmister multilayer elastic model (1943) -LCPC Software ALIZE (1982)-. In that model the Huet-Sayegh behaviour is taken into account with its equivalent elastic modulus at the 15°C French average temperature and a 10 Hz frequency. That frequency value is assumed to be equivalent to the standard 72 km/h French vehicle speed. Such semi-analytical calculations provide relatively good stress and strain fields for heavy traffic pavements but it is less satisfactory for flexible pavements with low traffic, for high temperature gradients and for the analysis of damages under slow heavy loads. Therefore the complete visco-elastic behaviour of each asphalt pavement layers has to be taken into account. The aim of this paper is to present a thermo-visco-elastic multi-layer model using the Huet-Sayegh behaviour. By means of the Fast Fourier transform method, the equations of the model are solved in the coordinate system of the moving load. Results are successfully compared with an analytical solution, finite element results and accelerated pavement testing data. A software called ViscoRoute (i.e. ViscoRoad) based on this modelling has been developed. The second part of this work deals with the relevance of the assumption on the time-frequency equivalence of the French design method

Viscoroute : Logiciel de modélisation viscoélastique des chaussées bitumineuses

The design of French road pavements makes use of Burmister's elastic model, which yields satisfactory results for both stress and strain fields in the case of pavements submitted to heavy truck loads. In order to study flexible pavements submitted to low traffic volumes or to strong temperature gradients however, it becomes necessary to incorporate the viscoelastic behavior of asphalt overlays. The "ViscoRoute" software application, which relies upon a semi-infinite multilayer structural model that takes into account Huet and Sayegh's law of thermo-viscoelastic behavior, is presented herein. The method employed consists of calculating within the frame of reference of the moving load and then, by means of a double Fourier transform, laying out the problem within the horizontal wave number space. Displacement and stress results at various points on the pavement vs. loading, temperature or vehicle speed will also be provided.Le dimensionnement des chaussées françaises utilise le modèle élastique de Burmister qui donne des résultats satisfaisants pour les champs de contraintes et de déformations dans le cas de chaussées soumises à de forts trafics de poids lourds. Par contre, pour l'étude des chaussées souples à faible trafic ou soumises à de forts gradients de température, il est nécessaire de prendre en compte le comportement viscoélastique des enrobés bitumineux. Le logiciel ViscoRoute, qui repose sur un modèle de structure multicouche semi-infinie prenant en compte la loi de comportement thermoviscoélastique de Huet et Sayegh, est présenté. La méthode utilisée consiste à se positionner dans le repère de la charge roulante puis, par double transformation de Fourier, à poser le problème dans l'espace des nombres d'onde horizontaux. Des résultats de déplacements et de contraintes en différents points de la chaussée en fonction du chargement, de la température ou de la vitesse des Îhicules sont présentés

Visco-elastic modelling for asphalt pavements : Software ViscoRoute

International audienceHuet-Sayegh model (1963) gives a set of constitutive equations of a viso-elastic material which accounts well for the behaviour of asphalt pavement layers, especially regarding thermal effects. This model allows rather good predictions of experimental data. The French pavement design method consists in a pavement mechanistic analysis based on the Burmister multilayer elastic model (1943) -LCPC Software ALIZE (1982)-. In that model the Huet-Sayegh behaviour is taken into account with its equivalent elastic modulus at the 15°C French average temperature and a 10 Hz frequency. That frequency value is assumed to be equivalent to the standard 72 km/h French vehicle speed. Such semi-analytical calculations provide relatively good stress and strain fields for heavy traffic pavements but it is less satisfactory for flexible pavements with low traffic, for high temperature gradients and for the analysis of damages under slow heavy loads. Therefore the complete visco-elastic behaviour of each asphalt pavement layers has to be taken into account. The aim of this paper is to present a thermo-visco-elastic multi-layer model using the Huet-Sayegh behaviour. By means of the Fast Fourier transform method, the equations of the model are solved in the coordinate system of the moving load. Results are successfully compared with an analytical solution, finite element results and accelerated pavement testing data. A software called ViscoRoute (i.e. ViscoRoad) based on this modelling has been developed. The second part of this work deals with the relevance of the assumption on the time-frequency equivalence of the French design method

Modélisation de chaussées viscoélastiques

16ème Congrès Français de Mécanique, NICE, FRANCE, 01-/09/2003 - 05/09/2003The calculation of French roads uses the Burmister elastic model and gives good stress and strain fields for roads with high lorry traffics. On the contrary, to study soft roads with small traffic or with high temperature gradients, it is necessary to take into account the viscoelastic behaviour of asphalt materials. In this paper, a model for a semi-infinite multilayer taking into account the thermo-viscoelastic Huet-Sayegh constitutive relation is presented. The proposed method consists in positionning in the moving load reference system then using a double Fourrier transform. We set the problem in the horizontal wavenumber domain and we solve it analytically along the depth. Then one calculate the displacements and the stresses in different positions in the road according to the intensity of the load, the temperature or the speed of the vehicles.Le dimensionnement des chaussées françaises utilise le modèle classique de Burmister qui donne de bons champs de contraintes et de déformations dans le cas de chaussées soumises à de forts trafics de poids lourds. Par contre, pour l'étude des chaussées souples à faible trafic ou soumises à de forts gradients de température, il est nécessaire de prendre en compte le comportement viscoélastique des enrobés bitumineux. Dans ce papier, un modèle de structure multicouche semi-infinie prenant en compte la loi de comportement thermo-viscoélastique de Huet-Sayegh est présenté. La méthode utilisé consiste à se positionner dans le repère de la charge roulante puis par la double transformation de Fourrier, à poser le problème dans l'espace des nombres d'onde horizontaux et à le résoudre analytiquement suivant l'épaisseur. On étudie ensuite les déplacements et les contraintes en différents points de la chaussée en fonction du chargement, de la température ou de la vitesse des Îhicules

Modeling of stresses for cracking in pavements

5th international CROW-workshop on fundamental modelling of the design and performance of concrete pavements , ISTANBUL, TURQUIE, 31-/03/2004 - 02/04/2004Pavement degradations are not directly taken into account in current pavement design methods (de Lurdes Antunes, 2002). They can be modeled using 3D finite element methods, but such calculations can be very time-consuming. To make a proper analysis of crack initiation and propagation in asphalt or concrete pavement structures, we propose to use a simplified plate model linked to the Boussinesq model for the soil (Johnson, 1992). This simplified model is built with a polynomial approximation of stress fields for each layer (Chabot, 1997) (Chabot et Ehrlacher, 1998). It introduces, as variables, stresses defined at each interface and leads to a 2D model. It can be viewed as superposition of Reissner's plates linked together by interface forces. The stress fields obtained are very close to those given by 3D finite elements (Carreira et al., 1998). This approach is very fast and produces regular stress fields near cracks at the interface of two different layers. Equations are solved numerically under Matlab. Results are compared successfully with finite element calculations on 3D pavements and 2D cracked pavements