Modélisation micromécanique et simulation numérique du phénomène d'auto-colmatage dans les argilites

National audienc

Micromechanical modeling of the Compression of the Damaged Zone experiment in the Callovo-Oxfordian formation

International audienceA theoretical model of the Compression of the Damaged Zone experiment is proposed. The tools of micromechanics are used to represent the fractured zone. Assuming an elastic behavior of the sound COx claystone and a simplified geometry of the drift, an analytical solution is presented and the crack closure is determined as a function of distance from the drift wall for two loading cases: a prescribed 4 MPa pressure and a stress-free strain with 1 % average value to describe the swelling due to resaturation. The results are in agreement with experimental observations and give insights into the heterogeneous character of self-sealing in the damaged zone

Closure of parallel cracks: Micromechanical estimates versus finite element computations

International audience3D finite element simulations have been performed in order to assess the ability of five classical micromechanical estimates to model the elastic behavior of solids with parallel cracks, namely the dilute, Mori-Tanaka, self-consistent and differential schemes and the Ponte-Castaneda and Willis bounds. The cracks have been represented in the simulations by right circular cylinders with aspect ratios as low as 10^-3 and with centroids randomly located in the REV. Special attention has been paid to the crack aspect ratio variation predicted by the different schemes, since the goal is ultimately to propose a non-linear micromechanical model of a cracked solid, taking complete crack closure into account.The results confirm earlier studies which showed that the differential scheme was best suited for this kind of morphology when computing elastic moduli, but additionally, we show that changes in crack aperture are also accurately predicted. It is however noted that the randomness in the positions of the cracks leads to significant scatter in the magnitude of the aperture variation inside a given simulation, which suggests that the cracks do not close simultaneously. As a consequence, non-linear numerical simulations accounting for contact between the crack lips should be performed in order to completely validate a non-linear micromechanical model in alternate tension/compression loading cases

Contribution of FE and FFT-based methods to the determination of the effective elastic and conduction properties of composite media with flat inclusions and infinite contrast

International audienc

Energetic approach for a sliding inclusion accounting for plastic dissipation at the interface, application to phase nucleation

International audienceThe energy gained at the atomic scale by modifying the crystal lattice during phase nu-cleation is an important aspect to study solid-solid phase transitions. However at the scale of continuum mechanics, the eigenstrain introduced by the geometrical transformation in the newly formed phase is also a significant issue. Indeed, it is responsible for very large elastic energy and dissipation that have to be added to the total energy in order to determine if a phase transition can occur. The eigenstrain can cause sliding of the newly formed grain. In this paper, an analytical solution coupled with numerical energetic optimization is derived to solve the problem of a two-dimensional circular elastic sliding inclusion authorizing plastic dissipation at the interface. Numerical calculations under plane stress assumption show that dissipation enables an effective decrease in the energy needed for the phase transformation to occur. The solution is validated with a comparison with a Finite Element simulation

Hydromechanical modelling and numerical simulation of self-sealingphenomena in the Callovo-Oxfordian claystone

International audienceExtensive preliminary studies have led the National RadioactiveWaste Management Agency (ANDRA) to thechoice of the Callovo-Oxfordian (COx) claystone of the Meuse/Haute-Marne as a host rock for a radioactive wasterepository because of its very low permeability and adequate mechanical properties, which allow for the geologicallayer to act as a natural barrier against the spreading of radionuclides in the biosphere. However, the concept ofunderground storage relies on the excavation of a network of wells and drifts, which damages the surrounding rock,leading to the creation of a so-called excavation damaged zone (EDZ) along the gallery walls. As a consequence,the overall water permeability is increased by several orders of magnitude. This EDZ is important in the context ofperformance assessment because it might represent a preferential pathway for dissolved radionuclides which couldreach prematurely the surrounding more permeable geological layers. Thankfully, existing fractures tend to closewhen this rock is wetted, mainly because of swelling phenomena and delayed deformations, which is referred toas self-sealing.We propose here to model the hydromechanical couplings that take place during self-sealing so that the progressiveresaturation of a drift may be studied from a theoretical standpoint. The swelling phenomena are first studied ina simplified linear elastic context to analyse the influence of geometry and boundary conditions on self-sealing,first at the scale of the sample using the finite element code Cast3M (CEA) to simulate the progressive resaturationaround a set of periodic elliptical cracks. Non trivial effects are brought to light, and lead to the conclusion that selfsealingneeds to be investigated at the level of the structure and not only at the level of the material. Thus, furtherinvestigations are performed at the scale of the underground drift. Using micromechanics, the EDZ is represented asa medium composed of a homogeneous matrix in which microcracks are distributed with preferential orientations.It should be noted that since the operation phase and the resaturation process take place over a hundred years anda few thousands of years respectively, delayed deformations are bound to develop, leading to convergence of thedrift walls. This first model provides insights that may be useful for understanding the response of the EDZ, butalso when developing a more elaborate model taking into account the viscoplastic behaviour of the rock in relationwith the water content. Both aspects indeed appear to have a significant impact on the macroscopic response ofthe COx claystone subject to swelling phenomena. We then propose to develop a model based on micromechanicsto describe the long-term response of the claystone. In this model, viscoplasticity is introduced at the interfacebetween the clay particles, and a homogenisation scheme is used to determine the behaviour of the clay matrix. Asecond homogenisation step is then required to introduce the quartz and calcite inclusions, and their damageableinterfaces with the matrix. The material response is then analysed and discussed as well as its implications withregards to self-sealing

Investigation of self-sealing phenomena in the Callovo-Oxfordian claystone through micromechanics based numerical simulations

International audienc

Adaptive mesh refinement and cycle jumps for phase-field fatigue fracture modeling

A phase-field approach was used in order to model the complex mechanisms of fatigue crack nucleation and growth. This popular method enables a flexible framework that recovers accurately expected crack patterns. However, it usually suffers from several efficiency drawbacks, such as the need for a very fine mesh, and the heavy computational cost associated with the cycle by cycle approach. For this reason, we put forward the coupling of adaptive mesh refinement and cycle jumps, to significantly accelerate computing time, at a given level of accuracy. Several numerical examples were studied to showcase the abilities of the proposed coupling and some qualitative numerical/experimental comparisons were made. In the end, the proposed coupling was able to recover non accelerated results with significant computing gains

Méthodes d'accélérations numériques dédiées à la fissuration en fatigue à grand nombre de cycle par champ de phase

International audienceLa prédiction de l’initiation et de la propagation de fissure de fatigue dans les structuresconstitue un enjeu majeur de l’industrie, qui cherche à limiter les approches habituellementconservatives pour diminuer les coûts, optimiser les formes, et garantir l’intégrité desstructures sur des durées plus longues. Un nombre important de méthodes numériquespeuvent être exploités dans ce contexte, et notamment l’approche champ de phase, quibénéficie d’une grande flexibilité pour traiter des cas de fissuration complexe, et considérerl’initiation et la propagation de fissure de façon unifiée. Cependant, le coût numériqueassocié à l’application de ce modèle sur des cas réels est aujourd’hui trop importantet limite donc son application à des cas académiques. L’objectif de ce mémoire est deproposer plusieurs approches d’accélération pour diminuer ce coût de calcul prohibitif,tout en maintenant le niveau de précision et de robustesse, dans le but de rendre possiblel’application sur des cas réels du modèle champ de phase.Pour ce faire, un modèle champ de phase étendu en fatigue est implémenté dans le codeéléments finis Cast3M. Une approche par dégradation de la ténacité est choisie et validéesur plusieurs cas usuels de la littérature champ de phase. Par ailleurs, une nouvelleméthode de décomposition de l’énergie est également mise en place, permettant d’enaméliorer l’efficacité et la robustesse. Nous proposons ensuite plusieurs modifications decette implémentation initiale qui permet d’accélérer les calculs. D’abord, le calcul de cycleest optimisé à travers l’introduction d’un schéma de résolution étagée adapté au cadreen fatigue. Ensuite, nous introduisons plusieurs schémas de saut de cycle permettant deminimiser le nombre de cycles calculés. Enfin, une approche de raffinement adaptatif demaillage est mise en place, afin de permettre d’optimiser le nombre de degrés de libertépris en compte pendant la simulation. Ces outils répondent en fait aux différentes raisonspour lesquelles le coût de calcul du modèle champ de phase en fatigue est prohibitif: larésolution d’un problème non-linéaire, sur un nombre très important de cycles, avec unmaillage extrêmement fin dans la zone endommagée.Ce cadre champ de phase accéléré est ensuite exploité sur plusieurs cas académiquesusuels pour valider son implémentation, et montrer les gains en temps de calcul possibles.Puis, deux cas de comparaisons numériques-expérimentales utilisant l’approche accéléréesont proposés. Ces essais mettent en évidence les capacités du modèle accéléré tout ensoulignant d’autres difficultés liées à l’application du modèle sur des cas réels