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International audience; Understanding strain localization in titanium and titanium alloys is central to depicting better how individual grains plastically deform and how grain orientation distribution, i.e., the local texture, affects the strain distribution within large regions of interest. High-resolution imaging over large fields of view is vital in detecting the nanometer-scale elementary and irreversible deformation mechanisms as a function of the variability of mesoscopic deformation inherited from the former millimeter-scale β-grains. High Resolution-Digital Image Correlation (HR-DIC) is used to assess quantitative deformation fields from the macroscopic to the microscopic scales. Moreover, HR-DIC is used to identify slip activity in the various polycrystalline Ti and Ti-alloys. Identification of slip systems was obtained using imaging from both scanning electron microscope (SEM) and laser scanning confocal microscope (LSCM). SEM provides a high spatial resolution in the surface plane, while LSCM micrographs provide out-of-plane measurements. Both imaging techniques are complementarily used to identify deformation slip and sliding at the sub-grain scale. In-situ HR-DIC under SEM paired with ex-situ LSCM and conventional SEM observations were used to identify three-dimensional surface strain localization and subsequently slip activity in the various Ti and Ti-alloys under tensile loading at room temperature. Interrupted tensile tests were performed to inform sliding evolution as a function of the applied plastic strain. Both in-plane and out-of-plane sliding displacement were evidenced at the sub-grain level leading to an increase in roughness with increasing applied plastic strain. Interestingly, former β-grains strongly affect both strain distribution and slip activity.

International audience; This chapter presents a review of investigations into the complexity of the plastic flow associated with the Portevin-Le Chateliereffect, or jerky flow, in traditional alloys that have basic elements determining the crystal lattice of the material. The main accent is put onthe illustration of the state-of-the art of this research under the angle of distinct regimes of collective dislocation dynamics, e.g., self-organizedcriticality, deterministic chaos, or synchronization. Finally, an extension of the research toward finer scales, which are resolved using acoustic emission and image correlation techniques, is discussed.

Funding Information: Ivan Lomakin and Xavier Sauvage are grateful to the Embassy of France in Russia for supporting their collaboration through Mechnikov’s Scholarship. This work was partially supported by Saint Petersburg State University, Russia via Lot 2017 applied (id: 26130576 ). This work was partially supported by Academy of Finland through grant 317464 . XRD results were obtained by the “Center for X-ray Diffraction Methods” of the Research park of Saint Petersburg University. Anvils for HPT tool were produced in collaboration with center “Applied aerodynamics” of the Research park of Saint Petersburg University. Authors acknowledge the provision of facilities and technical support by Aalto University at OtaNano - Nanomicroscopy Center (Aalto-NMC). Funding Information: Ivan Lomakin and Xavier Sauvage are grateful to the Embassy of France in Russia for supporting their collaboration through Mechnikov's Scholarship. This work was partially supported by Saint Petersburg State University, Russia via Lot 2017 applied (id: 26130576). This work was partially supported by Academy of Finland through grant 317464. XRD results were obtained by the ?Center for X-ray Diffraction Methods? of the Research park of Saint Petersburg University. Anvils for HPT tool were produced in collaboration with center ?Applied aerodynamics? of the Research park of Saint Petersburg University. Authors acknowledge the provision of facilities and technical support by Aalto University at OtaNano - Nanomicroscopy Center (Aalto-NMC). Publisher Copyright: © 2021 The Author(s) The influence of the structural state on deformation mechanisms under large strains was investigated in a Cu – 2 wt.% Be alloy. Torque evolutions during straining exhibit serrations typical of structural relaxations in the precipitation-hardened alloy, but not in the solid solution state. Microstructure characterization revealed that homogeneous deformation of the solid solution led to strong grain size reduction (20 nm), while localization occurred in the precipitated state with numerous shear bands. The role of CuBe precipitates on hindering dislocation glide and the resulting shear localization under large strain is discussed.

Active deformation in the Earth's crust manifests as various geological extreme phenomena that include slow and fast earthquakes, volcanic eruptions and landslides. During these events, strain may be accumulated along localized faults that extend over hundreds of kilometers. In faults, slip may occur as slow aseismic creep or unstable sliding causing rapid earthquakes. In some cases, seismic activity called foreshocks, precedes the largest event or mainshock. Detection of foreshock activity may vary from minutes to days and months before the mainshock. However, the relationships between foreshocks and nucleation of mainshock remain unresolved. Majority of large earthquakes nucleate in the upper crust, which is essentially brittle. Strain localization also results in features that extend at depth below crustal faults and known as shear zones. Shear zones control deformation along plate boundaries and strength of the lithosphere and lack a constitutive description of mechanisms of their formation. Active fault systems in the upper crust show statistical self-similarity (fractal structure) for a range of scales from kilometer down to centimeter, which further extends down to micro fracturing in laboratory specimen. Thus, the macroscopic brittle deformations in crust are intimately related to the micro scale mechanisms of deformation in rocks. Unraveling the mechanisms of brittle compressive failure at micro scale can further assist in understanding the geological phenomena. In crustal rocks, nucleation and localization of damage is guided by the microscale heterogeneities, which correspond to grains and grain boundaries in non-porous rocks, and complex pore space in porous rocks. Using the novel experimental technique of in-situ triaxial deformation coupled with dynamic X-ray micro tomography, the evolution of microstructures of rock types with porosities varying from less than 1% to 23% are explored. The experimental technique allows for real time imaging and quantification of damage that accumulates through both dynamic crack propagation (seismic) and slow crack propagation (aseismic). Results allow identifying properties of brittle failure in rocks of varying porosities subjected to deformation under crustal conditions. In the first study, precursors to brittle compressive failure are explored in non-porous rocks. At microscale, precursory events correspond to microfractures originating from microscale heterogeneities. Dynamics of these precursors show an evolution towards macroscopic failure following power-laws. Using a progressive damage model developed to explain fracture in heterogeneous solids, brittle compressive failure in non-porous rock is argued to be a critical phenomenon. However, breaking of scaling observed very close to failure is linked to localization of a shear fault and can be proposed as a new precursory signal for macroscopic failure. Therefore, failure can be predicted to some extent. In the second study, micro-scale mechanisms of strain localization in reservoir rocks were explored. Digital volume correlation calculations were used to compute components of accumulated strain. Dominant strain localization mechanisms contain contributions from the three components of strain: dilation, compaction and shear. Porosity evolutions are strongly linked to the dominant mechanisms of strain localization. Confining pressure is a guiding parameter for defining dominant strain localization mechanisms. Presence of pore fluid facilitates strain localization much earlier to macroscopic failure. Pore emanating cracks, pore space dilation, pore collapse and grain crushing constitute the microstructural mechanisms of strain localization in porous reservoir rocks., Les déformations de la croûte terrestre se manifestent par divers phénomènes géologiques extrêmes, notamment les tremblements de terre, les éruptions volcaniques et les glissements de terrain. Lors de ces événements, des déformations s'accumulent le long des failles actives qui s'étendent sur des centaines de kilomètres. Dans les failles, le glissement peut se produire soit sous forme de fluage asismique soit par des glissements instables lors de tremblements de terre. Une activité sismique précédant les séismes est souvent, mais pas toujours, observée et appelée signal précurseur. Ces précurseurs sont détectés de quelques minutes à quelques mois avant le séisme principal. Cependant, les relations entre les précurseurs et la nucléation du séisme principal restent globalement inconnues. La majorité des grands tremblements de terre nucléent dans la croûte supérieure qui est essentiellement fragile. La localisation de la déformation s'étend aussi en profondeur dans les zones de cisaillement. Ces zones de cisaillement contrôlent la déformation le long des limites des plaques et la résistance de la lithosphère. Les systèmes de failles actives dans la croûte supérieure montrent des lois d'échelle (structure fractale) pour une gamme d'échelles allant de kilomètres à quelques centimètres, et qui s'étend jusqu'à la micro-fracturation dans les échantillons de laboratoire. Ainsi, la déformation fragile macroscopique dans la croûte est intimement liée aux mécanismes micro-échelle de déformation des roches. Identifier les mécanismes de rupture lors de la compression fragile à micro-échelle peut aider à mieux comprendre les phénomènes géologiques à plus grande échelle. Dans les roches crustales, la nucléation et la localisation de l'endommagement sont guidées par les hétérogénéités microscopiques telles que les grains, joints de grains et pores. En utilisant une nouvelle technique expérimentale de déformation triaxiale in situ couplée à la microtomographie dynamique par rayons X, l'évolution des microstructures de diverses roches avec des porosités variant entre 1% et 23% est explorée. Cette technique expérimentale permet d'imager et quantifier en temps réel l'endommagement accumulé à la fois par la propagation dynamique (sismique) et la propagation lente (asismique) des fissures. Les résultats permettent d'identifier les propriétés de rupture fragile dans des roches de porosités variables soumises à une déformation dans des conditions crustales. Dans une première étude, les précurseurs de la rupture cassante dans des roches à faible porosité sous compression sont explorés et des lois d'échelle sont mesurées. Les précurseurs correspondent à des microfractures et leur dynamique montre une évolution vers une rupture macroscopique. Cette évolution suit des lois de puissance, cohérentes avec les concepts décrivant la rupture fragile dans des solides hétérogènes comme un phénomène critique. Cependant, une déviation des lois d'échelle observée très proche de la rupture est liée à la localisation d'une faille et peut être proposée comme nouveau signal précurseur de rupture macroscopique. Par conséquent, la rupture finale peut être prédite dans une certaine mesure. Dans une seconde étude, les mécanismes de localisation des déformations à micro-échelle dans des roches réservoirs poreuses sont explorés. La corrélation numérique de volume est utilisée pour calculer les composants de la déformation. Les mécanismes de localisation contiennent des contributions des trois composantes de la déformation: dilatation, compaction et cisaillement. Les évolutions de porosité sont fortement liées aux mécanismes de localisation. La pression de confinement et la présence de fluide interstitiel sont des paramètres essentiels de contrôle de la localisation. Les fissures émanant des pores, la dilatation des espaces poreux, l'effondrement des pores et l'écrasement des grains constituent les mécanismes microstructuraux de localisation dans les roches réservoirs poreuses

International audience; Granular materials can develop two different failure modes following their initial density and the loading path: a localized mode, generally characterized by shear bands, and a diffuse mode without any macroscopic localized bands. In fact detailed analyses of experiments by tomography, of finite element computations and more recently of discrete element models (DEM) simulations show that two different localized objects co-exist at two different scales: a network of meso-slip lines appearing from the very beginning of deviatoric loading and a few macro-shear bands when approaching limit stress states. This paper aims to compare and analyze these two localized patterns, based on DEM results obtained for a given class of loading paths applied to several 2D numerical granular samples with different initial densities. It is first shown that void ratios and granular meso-structures are the same inside shear bands and for the whole samples in case of diffuse failure. Then slip lines and shear bands are shown to be distinct localized objects. Eventually, the questions of why and how the network of meso-slip lines is sometimes bifurcating into a set of few macro-shear bands are discussed.

The mechanical response of nuclear structural materials and their lifetime are strongly affected by radiation effects. This influence is of concern, especially in body centered cubic materials, which exhibiting a well-defined ductile to brittle transition. The ductile to brittle transition temperature itself is dose-dependent and may rise to or above the room temperature. In the current work, irradiation effect is modeled to predict the dose-dependent changes of the effective dislocation mobility, represented by the Defect Induced Apparent Temperature shift ( Δ DIAT). Mainly dislocation based crystal plasticity material model is used rather than a phenomenological approach. This material model accounts for both thermally activated dislocation mobility and dislocation mobility in an athermal regime of body centered cubic materials. The defect-induced evolution of Δ DIAT in turn analyzed and their relations with the fracture response are highlighted and discussed.

International audience; To address the question of the initiation and mechanisms involved in the process of subduction zone formation, we explored most of the available evidence for the subduction initiation (SI) during the Cenozoic. For this, we targeted a total of 70 candidate sites for subduction initiation cumulating ~70,000 km of trench, two thirds of which are still active and a majority still immature. Our strategy is to define four stages reached for each subduction initiation site (SIS) from the incipient-diffuse stage through incipient-localized stage and early arc magma production to self-sustained subduction. We have paid special attention to prematurely extinguished, i.e., aborted, subduction attempts in order to better understand the reasons for the termination of the process, and thus to clarify the conditions of success. The failure of SI results from a combination of hindering parameters (e.g., lithosphere cooling, frictional resistance, unfavorable age contrasts for intra-oceanic SISs) and insufficient external forcings (e.g., too low convergence velocity). From this comprehensive study, we find that new subduction zones regularly nucleate, at a mean rate of about once every Myr, and with a success rate of more than 70% to reach subduction maturity, generally in less than ~15 Myr, ~3-8 Myr for the shortest time between the very early stage and the self-sustained stage. A majority forms at the transition between an ocean and a continent, plateau or volcanic arc, demonstrating that large differences in composition, topography and/or lithospheric weaknesses favor the localization of the strain. Lithospheric forces are required to ensure the success of the process in the early (immature) stages, with the help of mantle forces in a third of the cases. Multiple triggers are common. Stress during the SI process is compressive in most, if not all, cases and oriented obliquely to the nascent plate boundary in more than half of the cases. The incipient plate boundary generally reactivates an old lithospheric fault, most often with a change in its kinematics, i.e., conversion of a transform plate boundary, a former normal or a detachment fault, or even a former spreading center. Sometimes, the new lithospheric fault reactivates a former subduction fault. There is no rule concerning the age of the subducting plate which varies from 0 to 140 Ma in the examples studied. In the same vein, the subducting plate is not necessarily older than the overriding plate when it is oceanic. Both situations are equally observed.

International audience; The recent development of the high resolution and discontinuity-tolerant digital image correlation technique enables the extraction of discontinuities within a displacement field. The technique provides quantitative analysis of discontinuities arising from slip, shear bands, cracks, and grain boundary sliding in a variety of material systems, including polycrystalline metallic materials. The discontinuity-tolerant digital image correlation method can be implemented to retrieve not only quantitative discontinuity analysis but also the local strain and rotation fields that operate near these discontinuities. The present implementation includes high-resolution digital image correlation (HR-DIC) measurements collected in a scanning electron microscope for analysis of both the plastic and elastic fields that develop during deformation of polycrystalline metallic materials. The combination of the discontinuity-tolerant DIC technique with the computation of internal gradients enables extraction of non-localized strain and rotation fields during plastic deformation of a nickel-based superalloy. Therefore the lattice rotation/expansion and plastic localization that occur during deformation can be determined in a single experiment. This method is validated using synthetic images with preset deformation, and experimental measurements using the electron back scatter diffraction (EBSD) technique.

International audience; To investigate the mechanism of exhumation of deep crustal rocks in hot orogens, we focus on the southwestern part of the Variscan Canigou gneiss dome (Pyrenees) where the transition between the middle and upper crust can be observed. On the basis of new structural data, geological mapping, cross sections, microstructural analyses, and petrologic observations, we propose that flat-lying foliation within the gneiss dome and steep cleavage developed above it formed coevally. We note the presence of regional-scale shear zones at the boundary between the middle crust (Núria-Canigou Unit) and upper crust (Puigmal unit). At this boundary, the E-W South Canigou Shear Zone is an extensional shear zone showing top-to-the- southwest kinematics. Deformation, which is localized within the andalusite-biotite transition zone, occurred under retrogressive conditions, from high-grade ductile to brittle conditions during the main deformation stage (D2). The tectonic contact was folded during a later stage (D3). We propose that the shape of the Canigou dome resulted from the activation of extensional shear zones at the top of the orthogneiss, leading to partial exhumation of high-grade rocks. The Canigou gneiss dome can be considered an extensional dome that formed during late Variscan (ca. 310-290Ma) transpression.

Geomaterials may exhibit timedependent behaviors as their microstructures evolve. This process may vary from a few minutes (sand) to several days or even years (soft soils). To describe this time-dependent behavior, viscoplastic models are commonly used. Other than providing an intrinsic description of the viscous behavior, rate-dependent constitutive laws are sometimes presented in the literature as a regularization technique. In this thesis, we study the possibility to use viscoplastic constitutive laws in transient problems to describe the time-dependent response of soft soils and strain localization. Analytical and numerical studies are presented and several conclusions are found based on the Hill’s criterion, the Rice’s criterion, a numerical perturbation algorithm and classical linear perturbation theory. It turns out that the use of viscoplastic models in transient problems is not able to regularize the problem. Viscoplastic models are then integrated in a higher order continuum, the second gradient model. Problems concerning the uniqueness, bifurcation and mesh dependency are examined and a classical linear perturbation analysis is presented. The combination of a second gradient model with viscoplastic laws makes possible both to regularize the problem and to take into account rate effects. Finally, the bearing capacity and progressive failure of a shallow foundation are analyzed in order to demonstrate the performance of the approach on a real case study.; Les géomatériaux présentent des comportements plus ou moins dépendants du temps, car leur microstructure évolue. Ce processus peut varier entre quelques minutes (sable) et plusieurs jours voire plusieurs années (sols mous). Pour décrire un comportement dépendant du temps, des modèles viscoplastiques, dépendant de la vitesse, sont couramment utilisés. Autre qu'une description intrinsèque du comportement visqueux, la dépendance à la vitesse de la loi constitutive est également présentée quelques fois dans la littérature comme une technique de régularisation. On étudie dans cette thèse la possibilité d'utiliser une loi de comportement viscoplastique pour décrire le comportement transitoire des sols mous dépendant du temps et la localisation des déformations. Des études analytiques et numériques sont présentées et plusieurs conclusions sont trouvées sur la base du critère de Hill, du critère de Rice, d'un algorithme de perturbation numérique et de la théorie classique de perturbation linéaire. Il s'avère que l'utilisation d'un modèle viscoplastique pour des chargements transitoires ne permet pas de régulariser le problème. Afin de proposer une stratégie de modélisation performante, les modèles viscoplastiques sont ensuite intégrées dans un milieu à microstructure et plus spécifiquement dans un modèle second gradient. Des problèmes concernant l'unicité, la bifurcation et la dépendance au maillage sont examinés et une analyse classique de perturbation linéaire est présentée. La combinaison d'un modèle second gradient avec des lois viscoplastiques permet de régulariser le problème et de prendre en compte l'influence de la vitesse de la sollicitation. Afin de démontrer la performance de l'approche dans un cas réel, une fondation superficielle est analysée en mettant l’accent sur sa capacité portante et sa défaillance progressive.

Geomaterials may exhibit timedependent behaviors as their microstructures evolve. This process may vary from a few minutes (sand) to several days or even years (soft soils). To describe this time-dependent behavior, viscoplastic models are commonly used. Other than providing an intrinsic description of the viscous behavior, rate-dependent constitutive laws are sometimes presented in the literature as a regularization technique. In this thesis, we study the possibility to use viscoplastic constitutive laws in transient problems to describe the time-dependent response of soft soils and strain localization. Analytical and numerical studies are presented and several conclusions are found based on the Hill’s criterion, the Rice’s criterion, a numerical perturbation algorithm and classical linear perturbation theory. It turns out that the use of viscoplastic models in transient problems is not able to regularize the problem. Viscoplastic models are then integrated in a higher order continuum, the second gradient model. Problems concerning the uniqueness, bifurcation and mesh dependency are examined and a classical linear perturbation analysis is presented. The combination of a second gradient model with viscoplastic laws makes possible both to regularize the problem and to take into account rate effects. Finally, the bearing capacity and progressive failure of a shallow foundation are analyzed in order to demonstrate the performance of the approach on a real case study.; Les géomatériaux présentent des comportements plus ou moins dépendants du temps, car leur microstructure évolue. Ce processus peut varier entre quelques minutes (sable) et plusieurs jours voire plusieurs années (sols mous). Pour décrire un comportement dépendant du temps, des modèles viscoplastiques, dépendant de la vitesse, sont couramment utilisés. Autre qu'une description intrinsèque du comportement visqueux, la dépendance à la vitesse de la loi constitutive est également présentée quelques fois dans la littérature comme une technique de régularisation. On étudie dans cette thèse la possibilité d'utiliser une loi de comportement viscoplastique pour décrire le comportement transitoire des sols mous dépendant du temps et la localisation des déformations. Des études analytiques et numériques sont présentées et plusieurs conclusions sont trouvées sur la base du critère de Hill, du critère de Rice, d'un algorithme de perturbation numérique et de la théorie classique de perturbation linéaire. Il s'avère que l'utilisation d'un modèle viscoplastique pour des chargements transitoires ne permet pas de régulariser le problème. Afin de proposer une stratégie de modélisation performante, les modèles viscoplastiques sont ensuite intégrées dans un milieu à microstructure et plus spécifiquement dans un modèle second gradient. Des problèmes concernant l'unicité, la bifurcation et la dépendance au maillage sont examinés et une analyse classique de perturbation linéaire est présentée. La combinaison d'un modèle second gradient avec des lois viscoplastiques permet de régulariser le problème et de prendre en compte l'influence de la vitesse de la sollicitation. Afin de démontrer la performance de l'approche dans un cas réel, une fondation superficielle est analysée en mettant l’accent sur sa capacité portante et sa défaillance progressive.

International audience; We develop a crystal plasticity model to investigate the coupled actions of crystal orientation, grain neighborhood and grain-to-grain elasto-plastic interactions on dynamic strain aging (DSA) and the onset and development of associated plastic strain localization in Al-Li alloys. Considering simple model multilayered microstructures with preferred orientations representative of rolled alloys, the aim is to identify grain orientation couples that can limit dynamic strain aging induced strain localization without compromising the flow stress and strain hardening properties. To this end, a slip system-based formulation of dynamic strain aging is implemented in a crystal plasticity finite element framework. The model validity is first checked with the simulation of a tensile specimen loaded at quasi-static applied strain rate. The introduction of dynamic strain aging allows predicting complex propagation of intense plastic localization bands. We further investigate the influence of crystal orientations on early strain localization in Al-Cu-Li-Mg alloys, by performing simulations representative of the early stage of a Kahn Tear test for single crystals and layered polycrystals. Using experimentally reported crystal orientations for rolled microstructures, the simulation results show that in both single and multilayered crystals, there is a strong influence of dynamic strain aging on localization patterns, as well as a significant orientation dependence. In multilayered crystals, the nature of strain localization can be remarkably modified when stand-alone crystals of a certain orientation are coupled with other orientations: strain localization may intensify or fade away depending on the coupling with neighboring orientations.

International audience; The present paper proposes a new efficient and robust algorithm for evaluating the loss of ellipticity criterion. While commonly used in two-dimensional models for thin metal sheet forming processes, it is rarely evaluated in three-dimensional structures due to the computational cost. The proposed algorithm is based on a Newton-Raphson scheme and a multisampling optimization method based on a discretization method of the half unit sphere. First the new process is compared to the existing methods in the literature and then it is applied to a structural problem, namely tubes in torsion. The evolution of the loss of ellipticity in these structures is analyzed leading to conclusions about the failure of the structure. Meanwhile, the stability of the discretized problem is analyzed in order to better understand the loss of regularity of the finite element method problem. These results are then used to predict the failure of an experimentally tested torsion sample. K E Y W O R D S elastoplasticity, finite deformation, loss of ellipticty, numerical method, strain localization 1 INTRODUCTION Even though strain localization is one of the most critical phenomena leading to the failure of elasto-plastic structures, its emergence is still not fully understood. Indeed, the term "localization" itself is interpreted differently depending on the context. In a loose sense, localization means the development of high strains in a narrow region of the body, like in a shear band with through thickness necking in a thin plate in tension. A more precise definition is the emergence of strain rate discontinuities through surfaces usually associated with loss of ellipticity, and we use this latter definition in the present work. In some situations, both definitions may even coincide, for instance, a one-dimensional bar displaying a softening behavior experiences simultaneously necking and loss of ellipticity, 1,2 or in thin plates modeled under plane stress conditions. 3 However, these definitions do not coincide for three-dimensional (3D) models in general. When localization starts in complex structures and whether it leads to catastrophic failure is still an open problem in many situations , especially when certifying industrial components. The example of tubes loaded in torsion, 1 shows that even an apparently simple structure can lead to difficulties in defining localization and the localization's influence on the safety of the global structure. When dealing with localization, a first distinction needs to be made between types of loss of ellipticity. Strong ellipticity corresponds to definite positiveness of the eigenvalues of the symmetrized acoustic tensor whereas ellipticity refers to the absence of vanishing eigenvalue of the general acoustic tensor. 4,5 Int J Numer Methods Eng. 2019;1-25. wileyonlinelibrary.com/journal/nme

International audience; The most commonly observed ductile fracture mechanism is void nucleation, growth and coalescence. Fully coupled "porous plasticity" models (GTN, Rousselier) are presented and their limits are discussed in relation with quantitative observations and micromechanical simulations. Strain localization in a macroscopic planar band represents the void coalescence phase. (Micromechanical modeling of nucleation is not presented.) These models are well suited for laboratory specimen calculations, including the multi-scale version with a reasonable computation time due to reduced texture identification (8 to 15 crystal orientations). A trans-granular crystallographic ductile fracture mechanism is also modeled in the multi-scale framework. Examples of numerical simulations are given for aluminum and steel specimens. The experimental and numerical results are in good agreement with regard to fracture strains and locations as well as macroscopic/microscopic features. The effect of the carbides-nucleated secondary population of voids in low alloyed steels is modeled in the multi-scale framework and used in calculations.

International audience; The Eikonal Non-Local damage model (ENL) is an integral-based regularization method with damage-dependent non-local interactions. This contribution introduces the transition from an ENL formulation to a strong discontinuity model in a one-dimensional case. By introducing the formation of a cohesive crack in highly damaged areas, this new formulation seeks to solve problems of objectivity of results with respect to the mesh size for regularization methods with evolution of non-local interactions leading to strain localization.

The understanding of polymineralic rock rheology and their relationship with strain localization is a crucial point to decipher lithospheric deformation properties. For this purpose, numerical models appear to be a powerful tool as they allow for scaled experiments. In this thesis we quantitatively analyze the textural evolution of granulitic gabbros from Hokkaido (Japan) during mylonitization and compare the data to a physical model built upon the two-phase and damage theory. The study of this natural example shows an evolution of both the grain-sizes distributions and the spacial organization of the mineral phases during mylonitization. The rock displays a stage of clustering followed by a stage of intense mixing. This evolution appears to be directly related to the active creep mecanisms. In order to represent this evolution, we present a physical model where the interface depend on the mean grain-size of both phases, a variable measuring the mixture quantity is also proposed. The numerical results using two different mineral phases demonstrate the central role of the deformational work rate partition functions. Comparing numerical results with the naturalcase studies data allows to constrain their values., Pour comprendre la rhéologie de la lithosphère il est crucial de bien comprendre le comportement des agrégats poly-minéraux sous contrainte dans le domaine ductile et en particulier les phénomènes de localisation de la déformation. La modélisation numérique constitue un outil indispensable pour remplir cet objectif car elle permet des expériences mises à l’échelle dans le temps et dans l’espace de la déformation naturelle. Dans cette thèse nous analysons quantitativement l’évolution texturale des gabbros d’une zone cisaillement granulitique d’Hokkaido (Japon) au cours de la mylonitisation et nous comparons ces données à un modèle physique développé directement à partir de la théorie biphasique de l’endommagement. L’étude de cet exemple naturel montre une évolution non seulement des distributions de tailles de grains mais aussi de l’organisation spatiale des phase minérales au cours de la mylonitisation avec une phase de ségrégation ou « clustering » des phases suivie d’une phase de mélange. Cette évolution découle directement des mécanismes de fluage actifs. Pour représenter cette évolution nous présentons un modèle physique où l’interface dépend des tailles moyennes de grains, une variable mesurant la quantité de mélange est aussi proposée. Les résultats numériques avec deux phases minérales différentes montrent que ce sont les fonctions de partition du taux de travail de déformations qui contrôlent l’évolution de la texture modélisée. La comparaison avec les données naturelles permet d’en contraindre les valeurs.

International audience; It is well known that it is necessary to introduce a length scale parameter in a continuum damage mechanics model to correctly simulate strain localization. The second gradient model, a special case of kinematically enriched continua, considers an internal length parameter by taking into account the second-order derivatives of the displacements in the virtual power principle. In this paper, we show that the original second gradient finite element of Chambon and co-workers can present spurious oscillations, especially for mode I crack propagation problems. After providing the plane stress second gradient constitutive law, we propose to add a penalty term in the original formulation in order to improve numerical convergence and to avoid spurious oscillations in the local variables distributions. Two numerical examples using classical damage mechanics laws, a three-point reinforced concrete beam and a trapezoidal notched specimen are used to test the performance of the formulation. Parametrical studies are also shown on the influence of the penalty parameter. The problem of unrealistic damage spreading for damage values close to 1, occurring often in mode I crack propagation problems, is finally discussed.

Shear zones arise from strain localization into rocks of the crust and uppermost mantle during deformation of the lithosphere. By accommodating a large amount of strain, these shear zones have a direct control on rheology and dynamics of the lithosphere. Based on field observations and deformation experiments, this study aims at extending the current knowledge about the rheological behavior and the development of shear zones. In this study, we highlight that the rheological behavior of polyphase materials is extremely sensitive to their mineralogical composition and that small chemical variations can initiate strain localization – even at small shear strain - and induce large differences in resistance. Our results also show the ability of deformation to enhance mineral reactions, nucleation, the development of fine-grained mixed zones and, conversely, how such an evolution in microstructures eventually results in strain localization and weakening of polyphase aggregates. Phase compositions, in as much they control the reactivity, play a first-order role on both the initiation of weakening but also on the long-term evolution and strength of shear zones. Overall, our study illustrates that the rheology of rocks cannot be summarized as being controlled by monophase materials. In order to further use the rheological models as a predictive tool for lithospheric rheology, it seems essential to take into account both the complexity of regional structures (such as shear zone areas) and the complete nature of rocks that compose them, including the rheology of polyphase material in presence—or in absence—of feedback between deformation and reactions., Les zones de cisaillement résultent de la localisation de la déformation dans les roches de la croûte et du manteau supérieur au cours de la déformation de la lithosphère. En accommodant une importante quantité de déformation, ces zones de cisaillement exercent un contrôle direct sur la rhéologie et la dynamique de la lithosphère. En s’appuyant sur des observations de terrain et des expériences de déformation, cette étude aspire à élargir les connaissances actuelles sur la rhéologie et le développement des zones de cisaillement. Dans cette étude, nous mettons en évidence que le comportement rhéologique des matériaux polyphasés est extrêmement sensible à la composition minéralogique, dans la mesure où de faibles variations chimiques peuvent initier la localisation de la déformation – même à faible contrainte de cisaillement – et induire de larges différences de résistance. Nos résultats exposent également la capacité dont fait preuve la déformation pour faciliter les réactions minérales, la nucléation, la formation de mélange de phases à grains fins et, inversement, comment une telle évolution des microstructures aboutit à la localisation de la déformation et à l’affaiblissement des matériaux. La composition des phases minérales, dans la mesure où elles régissent la réactivité, participe grandement à l’initiation de l’affaiblissement et à l’évolution à long terme de la résistance des zones de cisaillement. Globalement, notre étude atteste que la rhéologie des roches ne peut se résumer au comportement rhéologique des matériaux monophasés. Afin de recourir à l’utilisation de modèles rhéologiques pour prédire la résistance de la lithosphère, il semble nécessaire de prendre en compte à la fois la complexité des structures régionales (comme les zones de cisaillement) et la nature complète des roches qui les composent, notamment la rhéologie des matériaux polyphasés en présence — ou non — de la rétroaction entre la déformation et les réactions.

International audience; High-resolution digital image correlation (HR-DIC) techniques have become essential in material mechanics to assess strain measurements at the scale of the elementary mechanisms responsible of the deformation in polycrystalline materials. The purpose of this study is to demonstrate the use of laser scanning confocal microscopy (LSCM) coupled with DIC techniques to deepen knowledge on the deformation process of polycrystalline nickel-based superalloy at room temperature. The LSCM technique is capable of detecting both in-plane and out-of-plane strain localization within slip bands at the sub-grain level. The LSCM observations are consistent with previous in-situ scanning electron microscopy (SEM) studies: The onset of crystal plasticity occurs primarily near Σ3 twin boundaries with bulk locations in the elastic domain (macroscopic stress as low as 80% of the 0.2 % offset yield strength (Y.S.0.2%)). This intense irreversible strain localization occurs with either a high Schmid factor (μ > 0.43) or a significant elastic modulus difference between the pair of twins (ΔΕ > 100 GPa). In the plastic deformation domain, transgranular slip activity following slip systems with the highest Schmid factor is mostly responsible for the deformation at the grain level, thus leading to strain percolation. The simultaneous in-plane and out-of-plane deformation assessment via the HR-LSCM-DIC technique was found to be essential for the identification of active slip systems. Finally, the HR-LSCM-DIC technique enabled the quantification of the real glide amplitude involved in the three-dimensional shearing process at the grain level that solely in-plane measurements cannot provide.

International audience; Lüders bands and the Portevin-Le Chatelier effect are both due to plastic flow instabilities that affect a wide variety of metallic materials. The present study focuses on understanding these behaviors. Field kinematic measurements combined with the comparison of two specimen sizes are used here to characterize the Al-Mg alloy AA5086, by investigating the kinetics of individual localization bands. A unifying point of view is proposed for the classification of these bands together with the identification of a constitutive relation linking strain increments and nucleation stress, as well as evidence of the factors determining the development of serration behaviors. This leads to a novel interpretation of the spatiotemporal behavior of the bands as being the result of a competition between the influence of plastic strain and its gradient.

International audience; A numerical model for thermo-hydro-mechanical strong couplings in an elasto-plastic Cosserat continuum is developed to explore the influence of frictional heating and thermal pore fluid pressurization on the strain localization phenomenon. This model allows specifically to study the complete stress–strain response of a rock specimen, as well as the size of the strain localization zone for a rock taking into account its microstructure. The numerical implementation in a finite element code is presented, matching adequately analytical solutions or results from other simulations found in the literature. Two different applications of the numerical model are also presented to highlight its capabilities. The first one is a biaxial test on a saturated weak sandstone, for which the influence on the stress–strain response of the characteristic size of the microstructure and of thermal pressurization is investigated. The second one is the rapid shearing of a mature fault zone in the brittle part of the lithosphere. In this example, the evolution of the thickness of the localized zone and the influence of the permeability change on the stress–strain response are studied.

International audience; The present work aims at numerically predicting the current residual strength of large engineering structures made of ductile metals against accidental failure. With this aim in view, the challenge consists in reproducing within a unified finite element-based methodology the successive steps of micro-voiding-induced damage, strain localization and crack propagation, if any. A key ingredient for a predictive ductile fracture model is the proper numerical treatment of the critical transition phase of damage-induced strain localization inside a narrow band. For this purpose, the strong discontinuity cohesive model and the eXtended Finite Element Method are combined. A propagation algorithm is proposed and studied in the context of ductile materials. Physics-motivated criteria to pass from the phase of more or less diffuse damage to strain localization and from strain localization to crack propoagation are proposed. Finally, a 2D numerical example is shown to study the performance of the failure analysis model when implemented into an engineering finite element computation code, namely Abaqus.

International audience; High resolution scanning electron microscopy (HR-SEM) and laser scanning confocal microscopy (HR-LSCM) digital image correlation (DIC) techniques were investigated for assessing strain distribution within individual grains during deformation in the macroscopic elastic and plastic regime. The anisotropic response of a Ni-based polycrystalline superalloy was experimentally demonstrated at the grain scale. Local plastic strain localization within preferentially oriented grains was documented under loading as low as 80% of the macroscopic yield strength of the material. Intense strains along bands were observed in the macroscopic plastic regime, correlating with {111}[1-10] slip systems.

During the last decade, Isogeometric Analysis (IGA) has drawn the attention of the Finite Element community to its superior capabilities over the standard Finite Element Method (FEM). The IGA concept uses the same basis functions used in Computed Aided Design (CAD) for the approximation of the unknown fields such as displacements, pore pressure or temperature in the Finite Element solution of a (possibly coupled) thermo– hydro–mechanical problem. Among the most relevant features of IGA, its smoothness, its convergence rate and particularly its intrinsic higher–order continuity between elements represent a definite improvement over the standard FEM, which allow to obtain significant computational advantages in terms of accuracy of the solution and computa- tional efficiency.This work attempts to exploit the characteristics of IGA for the numerical solution of coupled hydro–mechanical (HM) problems in saturated and partially saturated second gradient poro–elastoplastic geomaterials. On one hand, the second gradient model belonging to the theory of continua with microstructure ensures the objectivity of the results in presence of strain localization phenomena in terms of mesh independence of the numerical solution, which cannot be achieved with classical constitutive models without an internal length scale. On the other hand, the C1–continuity achievable by means of IGA basis functions allows a straightforward implementation of such higher order constitutive models, within a HM formulation derived from the classical mixture approach. In addition, the smoothness of the IGA basis functions proved to be very efficient in the modeling of coupled processes characterized by strong hydraulic gradients – such as the simulation of the downward propagation of a saturation front in a partially saturated slope subject to rainfall infiltration. Last but not least, it is worth noting that, as compared to the existing approaches based on Lagrange multipliers, the IGA approach to the solution of coupled hydro-mechanical (HM) problems in saturated and partially saturated second gradient materials allows a dramatic reduction in the number of degrees of freedoms required to achieve the same level of accuracy. This not only results in a significant increase of the computational efficiency, but also allows to extend the complete second gradient formulation to the analysis of realistic 3D problems, the solution of which has been presented in this work for the first time.The local second gradient poro–elastoplastic formulation developed in this work is implemented in the research-oriented code GeoPDEs, a Matlab open source IGA–FEM code developed at the University of Pavia. Based on the results obtained in a large series of representative 2D and 3D initial–boundary value problems analyzed in this work, it can be concluded that the combination of IGA and the second gradient elastoplasticity represents a powerful tool for the numerical simulation of geotechnical problems characterized by strong multiphysics couplings, highly nonlinear behavior of the soil, and strongly localized displacement and pore pressure gradients., Au cours de la dernière décennie, la méthode d’analyse isogéométrique (AIG) a attiré l’attention des chercheurs grâce à ses capacités supérieures à la méthode standard des éléments finis (MEF). Le concept AIG utilise les mêmes fonctions de base que celles utilisées dans la conception assistée par ordinateur (CAO) pour l’approximation des champs inconnus tels que les déplacements, pression interstitielle ou la température dans la solution des éléments finis d’un problème thermo–hydro–mécanique (éventuellement couplé). Parmi les caractéristiques les plus importantes d’AIG, la régularité, le taux de convergence et surtout sa continuité intrinsèque d’ordre supérieur représentent une nette amélioration par rapport à la méthode standard des éléments finis, permettant d’obtenir des avantages computationnels significatifs en termes de précision de la solution et de efficacité.Ce travail tente d’exploiter les caractéristiques d’AIG pour la résolution numérique des problèmes hydromécaniques (HM) couplés dans les géomatériaux de second gradient de type poro–élastoplastiques partiellement saturés. D’une part, le modèle second gradient appartenant à la théorie des milieux continus avec microstructure assure l’objectivité des résultats en présence de phénomènes de localisation de la déformation en termes d’indépendance de maillage de la solution numérique, ce qui ne peut être réalisé avec des modèles constitutifs classiques qui n’implique pas l’intervention d’une longueur interne. D’autre part, la continuité C1 réalisable au moyen de fonctions de base AIG permet une implémentation directe de tels modèles constitutifs d’ordre supérieur, dans une formulation HM dérivée de l’approche de mélange classique. De plus, la régularité des fonctions de base AIG s’est révélée très efficace dans la modélisation de processus couplés caractérisés par de forts gradients hydrauliques – comme la simulation de la propagation d’un front de saturation dans une pente partiellement saturée. Dernier point, mais non des moindres, il convient de noter que, par rapport aux approches existantes basées sur les multiplicateurs de Lagrange, la méthode AIG pour résoudre les problèmes hydromécaniques (HM) couplés dans les matériaux du second gradient saturé et partiellement saturé permet une réduction considérable du nombre de degrés de libertés requis pour atteindre le même niveau de précision. Cela entraîne non seulement une augmentation significative de l’efficacité de calcul, mais permet également d’étendre la formulation du second gradient à l’analyse de problèmes réalistes en 3D, dont la solution a été présentée pour la première fois dans ce travail.La formulation poro–élastoplastique du second gradient développée dans ce travail est mise en œuvre dans le code orienté vers la recherche GeoPDEs, un code IAG–MEF open source écrit en Matlab et développé à l’Université de Pavia. Sur la base des résultats obtenus dans une large série de problèmes aux limites en 2D et 3D analysées dans ce travail, on peut conclure que la combinaison de AIG et d’élastoplasticité du second gradient représente un outil puissant pour la simulation numérique de problèmes géotechniques caractérisés par de forts couplages multiphysiques, un comportement fortement non linéaire du sol, et des gradients de déplacement et de pression interstitielle fortement localisés.

In this paper we study the phenomenon of localization of deformation in fault gouges during seismic slip. This process is of key importance to understand frictional heating and energy budget during an earthquake. A infinite layer of fault gouge is modeled as a Cosserat continuum taking into account Thermo-Hydro-Mechanical (THM) couplings. The theoretical aspects of the problem are presented in the companion paper (Rattez et al., 2017a), together with a linear stability analysis to determine the conditions of localization and estimate the shear band thickness. In this Part II of the study, we investigate the post-bifurcation evolution of the system by integrating numerically the full system of non-linear equations using the method of Finite Elements. The problem is formulated in the framework of Cosserat theory. It enables to introduce information about the microstructure of the material in the constitutive equations and to regularize the mathematical problem in the post-localization regime. We emphasize the influence of the size of the microstructure and of the softening law on the material response and the strain localization process. The weakening effect of pore fluid thermal pressurization induced by shear heating is examined and quantified. It enhances the weakening process and contributes to the narrowing of shear band thickness. Moreover, due to THM couplings an apparent rate-dependency is observed, even for rate-independent material behavior. Finally, comparisons show that when the perturbed field of shear deformation dominates, the estimation of the shear band thickness obtained from linear stability analysis differs from the one obtained from the finite element computations, demonstrating the importance of post-localization numerical simulations.

International audience; A micromorphic single crystal plasticity model is formulated at finite deformations as an extension of Mandel’s classical theory based on a multiplicative decomposition of the deformation gradient. It involves a single microslip degree of freedom in addition to the usual displacement components. Two main variants of the constitutive equations are proposed. The first one relies on a Lagrangian microslip gradient and leads to a Laplace term in the isotropic hardening law. In contrast, the second formulation, based on a generalized strain measure defined with respect to the intermediate configuration, is shown to induce both isotropic and kinematic enhanced hardening. The first formulation is implemented in a 3D finite element code. The model is applied first to strain localization phenomena in a single crystal in tension undergoing single slip. The regularization power of the model is illustrated by mesh-independent simulations of the competition between kink and slip bands. The model is then used to investigate void growth and coalescence in FCC single crystals. Cylindrical and spherical voids are considered successively. The simulations show, for the first time in the case of spherical voids embedded in a single crystal matrix, that smaller voids grow slower than bigger ones, and that the onset of void coalescence is delayed for smaller voids. These results are related to the fact that the field of plastic slip is found to be more diffuse around smaller voids.

International audience; The reduction of grain size is believed to play a critical role in strain localization to form shear zones. Although many mechanisms have been proposed, the source of grain size reduction remains debated. The South Armorican Shear Zone (SASZ) is a crustal-scale strike-slip fault that deforms granitoids at mid-crustal conditions. The SASZ records the transition from protolith to ultramylonite, representative of increasing ductile shear strain. To investigate the evolution of strain localization, the different states of deformation were studied using a combination of detailed microstructural, chemical and electron backscatter diffraction analyzes. Increasing strain from protolith to ultramylonite resulted in (1) grain size reduction, (2) the development of interconnected monophase layers of mica and incipient mixed-phase zones composed of phengite-quartz ± K-feldspar in protomylonite and low-strain mylonite, and (3) the formation of fine-grained mixed-phase zones composed of K-feldspar-quartz ± phengite in high-strain mylonite and ultramylonite. We propose that the causes for interconnection of mica are the formation of cracks in the protolith combined with fluid-assisted nucleation. The latter process also plays a major role in phase mixing, as attested by the precipitation of K-feldspar at triple junctions in quartz-rich layers and in fine-grained tails of inherited K-feldspar porphyroclasts in ultramylonite. The transition from quartz-rich layers and mixed-phase zones is accompanied by a strong dispersion of the quartz lattice preferred orientation. These microstructural and textural evidences suggest that phase nucleation is the major process behind phase mixing, possibly accompanied by the action of grain-boundary sliding to open cavities during deformation. Instead of a single process, we therefore highlight a succession of weakening processes in the evolution of the SASZ, starting with the crystallization of mica as a first weakening material, and then evolving with the formation of very fine-grained mixed-phase zones made principally of feldspar, quartz and phengite.

International audience; The increasing importance of performance-based earthquake engineering analysis points out the necessity to assess quantitatively the risk of liquefaction of embankment-type structures. In this extreme scenario of soil liquefaction, devastating consequences are observed, e.g., excessive settlements, lateral spreading and slope instability. The present work discusses the global dynamic response and interaction of an earth structure-foundation system, so as to determine quantitatively the collapse mechanism due to foundation’s soil liquefaction. A levee-foundation system is simulated, and the influence of characteristics of input ground motion, as well as of the position of liquefied layer on the liquefaction-induced failure, is evaluated. For the current levee model, its induced damage level (i.e., induced crest settlements) is strongly related to both liquefaction apparition and dissipation of excess pore water pressure on the foundation. The respective role of input ground motion characteristics is a key component for soil liquefaction apparition, as long duration of mainshock can lead to important nonlinearity and extended soil liquefaction. A circular collapse surface is generated inside the liquefied region and extends toward the crest in both sides of the levee. Even so, when the liquefied layer is situated in depth, no significant effect on the levee response is found. This research work provides a reference case study for seismic assessment of embankment-type structures subjected to earthquake and proposes a high-performance computational framework accessible to engineers.

The statistics of grain displacements probability distribution function (pdf) during the shear of a granular medium displays an unusual dependence with the shear increment upscaling as recently evinced (see &ldquo, experimental validation of a nonextensive scaling law in confined granular media&rdquo, ). Basically, the pdf of grain displacements has clear nonextensive (q-Gaussian) features at small scales, but approaches to Gaussian characteristics at large shear window scales&mdash, the granulence effect. Here, we extend this analysis studying a larger system (more grains considered in the experimental setup), which exhibits a severe shear band fault during the macroscopic straining. We calculate the pdf of grain displacements and the dependency of the q-statistics with the shear increment. This analysis has shown a singular behavior of q at large scales, displaying a non-monotonic dependence with the shear increment. By means of an independent image analysis, we demonstrate that this singular non-monotonicity could be associated with the emergence of a shear band within the confined system. We show that the exact point where the q-value inverts its tendency coincides with the emergence of a giant percolation cluster along the system, caused by the shear band. We believe that this original approach using Statistical Mechanics tools to identify shear bands can be a very useful piece to solve the complex puzzle of the rheology of dense granular systems.

Shear bands with characteristic spatial patterns observed in an experiment for a cubic or parallelepiped specimen of dry dense sand were simulated by numerical bifurcation analysis using the Cam-clay plasticity model. By incorporating the subloading surface concept into the plasticity model, the model became capable of reproducing hardening/softening and contractive/dilative behavior observed in the experiment. The model was re-formulated to be compatible with the multiplicative hyperelasto-plasticity for nite strains. This enhanced constitutive model was implemented into a nite-element code reinforced by a stress updating algorithm based on the return-mapping scheme, and by an efficient numerical procedure to compute critical eigenvectors of elastoplastic tangent stiffness matrix at bifurcation points. The emergence of diamond-like and column-like diffuse bifurcation modes breaking uniformity of the materials, followed by the evolution of shear bands through strain localization, was observed in the analysis. In the bifurcation analysis of plane strain compression test, unexpected bifurcation modes, which break out-of-plane uniformity and lead to three-dimensional diamond-like patterns, were detected. Diffuse bifurcations, which are difficult to observe by experiments, have thus been found as a catalyst creating diverse shear band patterns.

This work presents the results of plane strain tests carried out at the Laboratoire 3SR Grenoble (France) on undisturbed samples of very sensitive Norwegian soft clay. Discussion of the results focuses on the observed failure mechanisms and zones of localized deformation. The tested clay is defined as quick clay because it liquefies completely upon remolding. Thus, careful handling was necessary, and original procedures were developed to place samples in the plane strain testing device with minimum disturbance. Results show that excess pore-water pressure had developed during shear loading and shear strength was lost after the peak, which is a typical phenomenon in sensitive soils. The sample was held between two glass plates to enable visual tracking of the deformations. A digital image correlation analysis revealed a complex pattern of emerging shear bands, with one or two bands dominating and providing a final failure mechanism. Two local pore-water pressure transducers were attached to the sample boundary and showed differences in local excess pore-water pressure. It is suggested that excess pore-water pressure depends on the distance from the transducers to the zones of concentrated shear strains. © 2018. This is the authors' accepted and refereed manuscript to the article. The final authenticated version is available online at: https://doi.org/10.1139/cgj-2016-0443

International audience; In polycrystalline metallic materials, quantitative and statistical assessment of the plasticity in relation to the microstructure is necessary to understand the deformation processes during mechanical loading. Plastic deformation often localizes into physical slip bands at the sub-grain scale. Detrimental microstructural configurations that result in the formation and evolution of slip bands during loading require advanced strain mapping techniques for the identification of these atomically sharp discontinuities. A new discontinuity-tolerant DIC method, Heaviside-DIC, has been developed to account for discontinuities in the displacement field. Displacement fields have been measured at the scale of the physical slip bands over large areas in nickel-based superalloys by high resolution scanning electron microscopy digital image correlation (SEM DIC). However, conventional DIC methods cannot quantitatively measure plastic localization in the presence of discontinuous kinematic fields such as those produced by slip bands. The Heaviside-DIC technique can autonomously detect discontinuities, providing information about their location, inclination, and identify slip systems (in combination with orientation mapping). Using Heaviside-DIC, discontinuities are physically evaluated as sharp shear-localization events, allowing for the quantitative measure of strain amplitude nearby the discontinuities. Measurements using the new Heaviside-DIC technique are compared to conventional DIC methods for identical materials and imaging conditions.

Magma intrusions within the lithosphere are often considered as thermomechanical instabilities capable to locally and transiently stimulate strain localization. With the aim of testing this model and determining possible mechanisms that govern the initiation of localized deformation at the contact and within magmatic bodies, this thesis combine a fieldwork with an experimental approach. The Cyclades (Aegean Sea, Greece) form a highly extended continental domain in which five metamorphic core complexes (MCCs) were intruded by magmatic complexes, themselves capped by detachment systems. All collected structural and kinematic data, combined with previous investigations, converge toward a regional scheme in which magmatic bodies dynamically impacted the late evolution of the Cycladic MCCs. Granitoids were emplaced in relatively short time period (15-9 Ma) while metamorphic domes were largely exhumed after more than 10 Myrs of extension. None of those intrusions thereby proves to be a real candidate for the genesis of MCCs. However, continuums of deformation recorded within granitoids (magmatic to ductile/brittle states) as well as geometrical relationships with detachments suggest a pivotal role of magmatic complexes in redistribution and localization processes of the deformation, with in particular the sequential development of detachments. Precursors of strain localization within partially cristallized magmas have been concurrently deciphered by an experimental study. The investigation of the structural behavior of magmas, chemically and texturally similar to natural systems, corroborates that strain localization is efficiently activated along interfaces with contrasting rheology such as in the vicinity of synplutonic dikes. It has been also shown that the initial presence of textural inhomogeneities (e.g. like clusters) in medium-crystallized magmas can drastically influence the degree of strain localization during subsequent cooling stages.; Les intrusions magmatiques au sein d’une lithosphère soumise aux contraintes tectoniques sont souvent considérées comme des instabilités thermomécaniques à même de stimuler transitoirement et localement la localisation de la déformation. Dans le but de tester ce modèle et de déterminer les possibles mécanismes gouvernant l’initiation d’une déformation localisée au contact et au sein de corps magmatiques en cours de consolidation, ce travail de thèse se propose de coupler une étude de terrain à une approche expérimentale. Les Cyclades (Mer Égée, Grèce) constituent un domaine de croûte continentale en extension dans lequel se sont mises en place au cœur de cinq dômes métamorphiques extensifs (MCCs) des intrusions magmatiques, elles-mêmes coiffées par des systèmes de détachements. Les diverses campagnes de terrain, combinées aux données de la bibliographie, ont permis de proposer un modèle d’interaction régional dans lequel ces corps magmatiques impactent l’évolution tardive de MCCs cycladiques. Au vu des âges de mise en place des intrusions (15-9 Ma), soit plusieurs millions d’années après le début de l’extension et les premiers stades d’exhumation de roches métamorphiques, le magmatisme dans les Cyclades ne peut être considéré comme un candidat réel pour la genèse de MCCs. Néanmoins, les continuums de la déformation enregistrés en bordure des intrusions (depuis l’état magmatique jusqu’aux conditions ductile/cassant) et les relations géométriques avec les détachements laissent supposer un rôle majeur des complexes magmatiques dans les processus de redistribution et de localisation de la déformation, notamment sur le développement séquentiel de détachements. Les vecteurs de localisation de la déformation au sein de magmas partiellement cristallisés ont été en parallèle recherchés par la voie expérimentale. L’étude du comportement structural de magmas, chimiquement et texturalement proches de systèmes naturels, a permis d’une part de confirmer que la déformation se localise préférentiellement le long d’interfaces à rhéologie contrastée tels aux abords de filons syn-plutoniques. Il est d’autre part montré que la présence initiale d’inhomogénéités texturales (e.g. concentration de cristaux en amas) au sein de magmas moyennement cristallisés peut de manière drastique influencer le degré de localisation de la déformation au cours des stades de refroidissement ultérieurs.

Granular materials have been studied for decades, but the description of the behaviors observed of these materials is still an open question. They display localization of deformation when submitted to a large enough stress. The objective of this work is to study experimentally and numerically the deformation of a granular material and to characterize observed behaviors in a biaxial text. The first part is devoted to the realization of plane strain biaxial tests. In order to visualize very small deformations, we use an interferometric method based on the multiple light scattering. The second part is devoted to the numerical modeling of a 2D biaxial test under conditions similar to those of the experiment by the discrete element method. Finally, in the last part, tools developed for the analysis of images used to study as well the experiences as the numerical simulations are approached. The study of the average plastic field in the experiments shows that the localization of the deformation is a progressive process initiated by a bifurcation which corresponds to the appearance of a well defined direction. This direction is in agreement with the angle of Mohr-Coulomb and its appearance takes place before the failure of the material. The study of the fluctuations of the plasticity in the experiments and the numerical simulations seems to show an increase of a characteristic length., Les milieux granulaires sont très étudiés depuis des décennies mais la description de l'ensemble des comportements observés de ces matériaux reste une grande question ouverte. Lorsqu'ils sont soumis à une contrainte suffisamment importante, une caractéristique est de présenter de la localisation de la déformation. L'objectif du travail présenté dans ce mémoire est d'étudier expérimentalement et numériquement la déformation d'un milieu granulaire et de caractériser des comportements observés lors d'un text biaxial. La première partie est consacrée à la réalisation des tests biaxiaux en déformation plane. Pour pouvoir visualiser de très petites déformations, nous utilisons une méthode interférométrique basée sur la diffusion multiple de la lumière. La deuxième partie est dédiée à la modélisation numérique d'un test biaxial en 2D dans des conditions similaires à celles de l'expérience par la méthode des éléments discrets. Enfin, dans la dernière partie, des outils développés pour l'analyse d'images utilisés pour étudier aussi bien les expériences que les simulations numériques sont abordés. L'étude du champ plastique moyen dans les expériences montre que la localisation de la déformation est un processus progressif initié par une bifurcation qui correspond à l'apparition d'une direction bien définie. Cette direction est en accord avec l'angle de Mohr-Coulomb et son apparition a lieu avant la rupture du matériau. L'étude des fluctuations de la plasticité dans les expériences et les simulations numériques semble mettre en évidence une croissance d'une longueur caractéristique.

This study reports petrostructural observations in the pargasite and phlogopite-bearing Finero peridotite massif (Italian Western Alps), which suggest that the pervasive foliation in this massif was formed by deformation concomitant with percolation of hydrous Si-rich melts: (1) diffuse contacts, but systematic parallelism between the pyroxenitic layers and the foliation of the peridotite (2) strong shape and crystal preferred orientations (SPO and CPO), but subhedral or interstitial shapes and weak intracrystalline deformation of the hydrous phases, (3) CPO, but interstitial shapes of the pyroxenes, (4) very coarse olivine grain sizes, which are correlated to the olivine abundance, and (5) elongated shapes, but weak intracrystalline deformation, and extremely weak and highly variable CPO of olivine. The pervasive deformation of the Finero peridotite occurred therefore under conditions that allowed coexistence of H2O-CO2-bearing melts, pargasite, and spinel, that is, temperatures of 980-1080 degrees C and pressures

Numerous studies have shown the impact of deformation on the K-Ar system, and therefore ⁴⁰Ar/³⁹ Ar ages. These studies often do not provide data characterizing deformation and are limited to a comparison of the ages obtained indeformed rocks and an undeformed protolith. The first part of this study thus consisted in studying the strain distribution at different scales and finely describing strain intensity gradients. The study focused on two granitic protoliths, associated respectively with a difference in age between the formation of the protolith and the age of the tectonometamorphic events that is low ( 240 Ma ; Tenda massif). In the firstcase study, deformation results in a 40Ar loss in K-bearing phases, interpreted as resulting from the reduction of diffusion domains sizes which is not accentuated by an increasing strain intensity. In the second case study, the 40Arinheritance of the protolith results in fluids and extraneous 40Ar circulation through the actively deforming structures,ages in phengite being increasingly older approaching the most localizing structures in some sections, while others behave in an opposite way, more in line with the progressive strain localization in time. For both cases, interpretation of ages obtained in the newly formed phases during deformation is ambiguous between cooling, crystallization and mixing, and requires a detailed examination of the data confronted with the possible closing temperatures.Interpretations indicate for the Ikaria case study a strain localization in less than 1-3 Ma along a second order gradient of about ten meters in thickness. Strain localization at the scale of a shear zone occurs more rapidly in the case of a post-orogenic exhumation of a MCC (~ 7 Ma) than in the case of the exhumation of continental material involved in a subduction prism (~ 14-10 Ma).; De nombreuses études ont montré l’impact de la déformation sur le système K-Ar, et donc les âges ⁴⁰Ar/³⁹ Ar. Ces études se limitent souvent à une comparaison des âges obtenus dans des roches déformées et un protolithe indemne de déformation. La première partie de cette étude a inversement consisté à étudier la distribution de la déformation à différentes échelles et à décrire finement les gradients d’intensité de la déformation. L’étude a porté sur deux protolithes de nature granitique, associés à une différence d’âge entre leur formation et les évènements tectonométamorphiques faible (< 1 Ma ; massif d’Ikaria) ou élevée (>240 Ma ; massif du Tende). Pour le premier cas, la déformation entraine une perte de 40Ar dans les clastes des phases potassiques, interprétée comme résultant de la réduction des tailles des domaines de diffusion qui n’est pas accentuée par une intensité de déformation croissante. Pour le second cas, l’héritageen 40Ar du protolithe se traduit par la circulation de fluides et de 40Ar externe au système via les structures se déformant activement, produisant parfois un vieillissement des âges grandissant dans la phengite des structures les plus localisantes, alors que sur d’autres coupes il est observé un rajeunissement plus logique. Pour les deux cas,l’interprétation des âges obtenus dans les phases néoformées pendant la déformation est ambiguë entre refroidissement,cristallisation et mélange, et nécessite un examen détaillé des données confrontées aux températures de fermeture possibles. Les interprétations indiquent pour le cas d’Ikaria une localisation de la déformation ductile en moins de 1-3Ma le long d’un gradient de second ordre d’une dizaine de mètre d’épaisseur. La localisation de la déformation à l’échelle d’une zone de cisaillement se réalise plus rapidement dans le cas de l’exhumation post-orogénique d’un MCC(~7 Ma) que dans le cas de l’exhumation de matériel continental impliqué dans un prisme de subduction (~14-10 Ma).

Exhumation mechanisms of high-pressure low-temperature (HP-LT) metamorphic rocks in subduction zones are complex and actively discussed. The study of fossilized subduction zones allows a better comprehension of these mechanisms, showing that exhumation of HP-LT rocks is mainly accommodated along crustal-scale ductile shear zones. This study aims at constraining the geometry, the kinematic and the timing of the tectonometamorphic history of the HP-LT Cycladic Blueschist Unit (CBU) cropping out in Greece. A main objective is to constrain the timing of strain localization at different scales during exhumation to better understand the mechanical behaviour of subduction zones. Three principal methods of investigation have been used, including i) a structural fieldwork that allows to characterize the geometry, the kinematic and the distribution of deformations, highlighting progressive strain localization during exhumation toward the base of the CBU and along shear zones, ii) a metamorphic petrology study aiming at determining the P-T evolution of the CBU, and iii) ⁴⁰AR/³⁹AR dating used to constrain the timing of the tectonometamorphic evolution of the CBU and the timing of strain localization within kilometre- to millimetre-scale shear zones showing different degrees of retrogression. We observe an obvious correlation between the intensity of finite deformation, the degree of retrogression and youngest mica ages. A major result of this thesis work is that the preservation of eclogite and blueschist-facies rocks does not necessarily imply fast exhumation rates. Our results instead suggest that the exhumation history of the CBU is relatively long, spanning over ca. 30 Ma. Consequently, it appears that the exhumation rate is not the main parameter controlling the degree of retrogression of HP-LT metamorphic rocks in the CBU compared to progressive strain localization during exhumation along a cold retrograde P-T evolution within the subduction channel.; Les mécanismes d’exhumation des roches de haute-pression basse-température (HP-BT) au sein des zones de subduction sont nombreux, complexes et toujours activement débattus. L’étude des zones de subduction fossiles permet alors de mieux comprendre ces mécanismes, montrant notamment que l’exhumation des roches métamorphiques HP-BT est en grande partie accommodée le long de zones de cisaillement ductiles d’échelle crustale. Ce travail de thèse vise à contraindre la géométrie, la cinématique et la durée de l’histoire tectono-métamorphique des roches de HP-BT du complexe de subduction des Schistes Bleus Cycladiques située en Grèce. Un des objectifs est de contraindre, à différentes échelles, le calendrier de la localisation de la déformation au cours de l’exhumation dans le but de mieux comprendre le comportement mécanique des zones de subduction. Trois méthodes principales d’investigation ont été utilisées : i) une étude de terrain permettant de caractériser la géométrie, la cinématique et la distribution de la déformation, montrant notamment une localisation progressive de la déformation vers la base de l’unité des Schistes Bleus Cycladiques au cours de l’exhumation et le long de zones de cisaillement, ii) des outils de pétrologie métamorphique permettant de contraindre l’évolution P-T des roches métamorphiques au sein de la zone de subduction, et iii) des datations ⁴⁰AR/³⁹AR afin de déterminer le calendrier de l’histoire tectono-métamorphique des Schistes Bleus Cycladiques et de la localisation de la déformation au sein de zones de cisaillement d’échelle kilométrique à millimétrique associées à des degrés de rétromorphose variés. Une corrélation nette est clairement observée entre l’intensité de la déformation, le degré de rétromorphose et les âges les plus jeunes. Un des résultats de ce travail est que la préservation à l’affleurement d’éclogites et schistes bleus n’implique pas forcément une exhumation rapide. En effet, nos résultats suggèrent que l’unité des Schistes Bleus Cycladiques a enregistré une histoire d’exhumation longue d’environ 30 Ma. Le taux d’exhumation n’est donc pas le seul paramètre contrôlant le degré de rétromorphose des unités HP-BT, la remontée le long d’un gradient métamorphique froid dans le canal de subduction et la localisation progressive de la déformation ductile au cours de l’exhumation étant également des facteurs majeurs.

International audience; Back-arc extension in the Aegean Sea has been accommodated by several large-scale detachments such as the West Cycladic Detachment System (WCDS) in the Oligocene and Miocene. The WCDS especially crops out on Serifos Island (Cyclades) with a synkinematic granodioritic intrusion. As skarns represent metasomatic reactions near the contact between intrusions and the host rocks, they sign the position of the main drains used by fluids. While the mineralogy of the Serifos skarns is well known, geometrical and kinematic relations between the detachments and ore bodies remains poorly studied. This study allows us to distinguish different types of skarn. High Temperature skarns correspond to (1) massive garnet endoskarns, (2) ribbon and “bubble” garnet-pyroxene endoskarns, (3) garnet-pyroxene cracks exoskarns, whereas medium-temperature pyroxene ± ilvaite bearing skarn breccias within the Meghàlo Livadhi and Kàvos Kiklopas detachments belonging to the WCDS. Our observations show that skarn formation is associated with the activity of detachments and the syntectonic pluton emplacement. Endo and exoskarn deposits formed coeval with the ductile and brittle structures resulting from the activity of the WCDS, such as echelon veins, veins with antithetic shear and boudinaged veins wrapped within sheath folds, with a top-to-the SSW or SW shear senses compatible with the regional kinematics. Some skarn breccias formed within detachment planes far from the contact of the main granodioritic body, attesting for the intense flow of magmatic fluids along these discontinuities. These over-pressurized fluids play a major role in the mechanical behaviour of the detachments and strain localization. The two detachments acting as preferential crustal-scale drains, the pattern of magmatic fluid flows is not centred on the intrusion. In this context, iron-rich skarns and associated primary magnetite deposits have been remobilized during late brittle increments of motion along the detachments, together with surface-derived fluids responsible for deposition of the economic Fe/Ba mineralization.

International audience; In order to address the question of strain localization within continental units during subduction and exhumation, a large-scale portion of an exhumed continental crust was structurally revisited. The Tenda massif (Alpine Corsica) has recorded burial (D1; top-to-the-SW kinematics) down to blueschist-facies conditions followed by exhumation (D2; top-to-the-NE kinematics). It was so far regarded as a quite rigid unit with strain localization at the upper contact with the overlying oceanic material, the East Tenda Shear Zone (ETSZ), where previous studies were focused. A structural analysis carried out from the core to the boundaries of this continental unit shows instead that deformation is pervasive in the whole section. A reappraisal of the finite structure shows that this unit corresponds to a N140°E elongated dome of D2 fabrics severely overprinting earlier D1 structures, locally preserved in the core of the dome. Field observations show that deformation was distributed at maximum burial, pervasively affecting both the Tenda massif and the overlying tectonically coupled oceanic material. Strain remained distributed during the first steps of exhumation that probably started during the last stages of subduction. After a regional switch from compression to extension, deformation localized toward the ETSZ and other internal shear zones such as the newly described Saleccia Shear Zone, as shown by strain intensity mapping in the eastern granitic protoliths. Doming occurred during this localization when crossing the brittle-ductile transition. This large-scale structural study shows that lithological boundaries controlled the place where strain localized, while the general style of deformation (distributed vs localized) was controlled by depth (i.e. pressure-temperature conditions), interacting with other parameters such as fluid circulation and protolith composition.

International audience; The numerical simulation of two-dimensional fracture processes of quasi-brittle materials by means of the Embedded Finite Element Method is dealt with. The attention is paid to the coupling with the global crack-tracking strategy often used to ensure the crack path continuity. It has been proposed in the literature in the form of a heat conduction-like problem. It turns out that the stiffness-like matrix associated with this formulation is singular and a numerical perturbation has to be introduced in order to overcome the ill-posedness of the problem. The sensitivity of the solution on this parameter may represent a limitation for the global tracking approach. In addition, it is found that if the root of each discontinuity is not updated during an incremental analysis, a loss of continuity of the crack path may appear when principal stress directions rotate. This contribution aims to provide a solution to the aforementioned issues. A new interpretation of the mathematical problem based upon Navier-Stokes equations is proposed in order to link the diffusive contribution to a characteristic mesh length. Furthermore, a modified crack-tracking algorithm, considering the evolution of the root for the identification of the crack path, is proposed. The numerical assessment of the proposed tracking strategy is reported by means of benchmark tests at the structural level.

Magma intrusions within the lithosphere are often considered as thermomechanical instabilities capable to locally and transiently stimulate strain localization. With the aim of testing this model and determining possible mechanisms that govern the initiation of localized deformation at the contact and within magmatic bodies, this thesis combine a fieldwork with an experimental approach. The Cyclades (Aegean Sea, Greece) form a highly extended continental domain in which five metamorphic core complexes (MCCs) were intruded by magmatic complexes, themselves capped by detachment systems. All collected structural and kinematic data, combined with previous investigations, converge toward a regional scheme in which magmatic bodies dynamically impacted the late evolution of the Cycladic MCCs. Granitoids were emplaced in relatively short time period (15-9 Ma) while metamorphic domes were largely exhumed after more than 10 Myrs of extension. None of those intrusions thereby proves to be a real candidate for the genesis of MCCs. However, continuums of deformation recorded within granitoids (magmatic to ductile/brittle states) as well as geometrical relationships with detachments suggest a pivotal role of magmatic complexes in redistribution and localization processes of the deformation, with in particular the sequential development of detachments. Precursors of strain localization within partially cristallized magmas have been concurrently deciphered by an experimental study. The investigation of the structural behavior of magmas, chemically and texturally similar to natural systems, corroborates that strain localization is efficiently activated along interfaces with contrasting rheology such as in the vicinity of synplutonic dikes. It has been also shown that the initial presence of textural inhomogeneities (e.g. like clusters) in medium-crystallized magmas can drastically influence the degree of strain localization during subsequent cooling stages., Les intrusions magmatiques au sein d’une lithosphère soumise aux contraintes tectoniques sont souvent considérées comme des instabilités thermomécaniques à même de stimuler transitoirement et localement la localisation de la déformation. Dans le but de tester ce modèle et de déterminer les possibles mécanismes gouvernant l’initiation d’une déformation localisée au contact et au sein de corps magmatiques en cours de consolidation, ce travail de thèse se propose de coupler une étude de terrain à une approche expérimentale. Les Cyclades (Mer Égée, Grèce) constituent un domaine de croûte continentale en extension dans lequel se sont mises en place au cœur de cinq dômes métamorphiques extensifs (MCCs) des intrusions magmatiques, elles-mêmes coiffées par des systèmes de détachements. Les diverses campagnes de terrain, combinées aux données de la bibliographie, ont permis de proposer un modèle d’interaction régional dans lequel ces corps magmatiques impactent l’évolution tardive de MCCs cycladiques. Au vu des âges de mise en place des intrusions (15-9 Ma), soit plusieurs millions d’années après le début de l’extension et les premiers stades d’exhumation de roches métamorphiques, le magmatisme dans les Cyclades ne peut être considéré comme un candidat réel pour la genèse de MCCs. Néanmoins, les continuums de la déformation enregistrés en bordure des intrusions (depuis l’état magmatique jusqu’aux conditions ductile/cassant) et les relations géométriques avec les détachements laissent supposer un rôle majeur des complexes magmatiques dans les processus de redistribution et de localisation de la déformation, notamment sur le développement séquentiel de détachements. Les vecteurs de localisation de la déformation au sein de magmas partiellement cristallisés ont été en parallèle recherchés par la voie expérimentale. L’étude du comportement structural de magmas, chimiquement et texturalement proches de systèmes naturels, a permis d’une part de confirmer que la déformation se localise préférentiellement le long d’interfaces à rhéologie contrastée tels aux abords de filons syn-plutoniques. Il est d’autre part montré que la présence initiale d’inhomogénéités texturales (e.g. concentration de cristaux en amas) au sein de magmas moyennement cristallisés peut de manière drastique influencer le degré de localisation de la déformation au cours des stades de refroidissement ultérieurs.

Analyzing dynamic fragmentation of metallic shells is imperative for aerospace, nuclear and defense applications. The defense administration has to guarantee safety zones around warheads from ballistic studies and experiments. The fragment size distribution, one major input to the ballistic models, is modelled in present PhD. The main physical phenomena controlling bomb fragmentations are and analyzed.The study focuses on modeling a high explosive warhead fragmentation. The fragments mass and spatial distributions are required. Our approach is based on the dynamic and probabilistic studies of Mott. High dynamic unidimensional bar and torus fragmentations are analyzed. Three interdependent physical phenomena control fragmentation: nucleation of macroscopic defects, damage growth leading to local failures while a unloading Mott wave propagates and finally the interaction of Mott’s wave. Mott considered a statistical law describing macroscopic defect nucleation as a function of the strain. Modelling strain localization at the scale of the real material heterogeneities, justifies theoretically Mott’s assumption and enhances its predictions. Once a defect nucleates, Mott simplified this situation to be instantaneous through thickness failure, stress dropping locally to zero followed by an unloading wave starting at the crack. Grady introduced a non-zero stress at the damaged section, highlighting the relation between local damage development and the Mott wave speed. The wave front delay, due to damage development, predicted by Grady, has been revised and ameliorated. Finally, Mott’s stress release waves’ interactions are analyzed to obtain the fragments mass distribution., Les études de la fragmentation dynamique d’enveloppes métalliques sont importantes dans ledomaine militaire, aérospatial, automobile ou encore nucléaire. Pour la Défense, ces études permettentd’estimer des zones de sécurité autour des corps de bombes. On ne s’intéresse pas dans ces travaux aux étudesbalistiques ou à la définition statistique des zones de sécurité. On cherche à analyser les phénomènesphysiques influençant la fragmentation.L’objectif est de prévoir les dispersions massiques et spatiales des éclats générés par la fragmentationd’une enveloppe métallique en expansion inertielle très rapide. Les travaux sont basés sur l’approchedynamique et probabiliste de Mott. Dans cette thèse, on étudie les cas d’une barre et d’un tore. On distinguetrois phénomènes physiques primordiaux :- Le premier phénomène consiste à étudier une loi statistique de localisations de déformation. Mott aproposé plusieurs modèles, mais aucun ne tient compte des hétérogénéités initiales du matériau. Nous avonsidentifié cette loi pour une nuance d’acier 35NCD16 et réalisés une étude paramétrique dont les résultatspermettent de mieux comprendre la formation de ces localisations.- On modélise ensuite l’endommagement des sites de localisations de déformation. Nous avonsintroduit dans nos modèles une loi d’endommagement innovante qui ne tient pas compte du chemin depropagation des fissures. Cette dernière nous permet de modéliser une zone de relâchement de contraintes.- Le dernier phénomène étudié est l’interaction entre les ondes successivement générées. Nous avonsainsi pu obtenir la dispersion massique des éclats à partir d’un modèle physique pour un tore unidimensionnelen expansion.

This work presents an experimental characterization of the strain localization and the rupture on a granular rock analogue material under different conditions of axisymmetric loading. The evolution of the strain localization was characterized by the two-dimensional image correlation technique. Two series of triaxial compression and extension tests were carried out at different confining pressure Pc. Taking advantage of the DIC technique and detailed characterization of GRAM1’s constitutive properties by Mas and Chemenda (2014, 2015), we show that the initiation of deformation localization bands is preceded by the uniform elastic and then elasto-plastic deformation. The strain localization is initiated in the dilatant regime (positive dilatancy factor β) and strain-softening (negative hardening modulus h). During the band evolution, the deformation within it becomes compactive (β0), which causes the band to widen and new bands to form successively. The formation of new bands causes a slowing down the deformation within the prior bands, which makes the progressively densified band network to continuously evolve. In axisymmetric extension tests, the fractures are formed perpendicular to the minor principal stress σ3 in an extensive stress state at low Pc then compressive when Pc increases. Our results show a continuous transition from the extensive fracture to shear fracture with an increase of compressive stress. This is suitable of the results obtained for extension tests performed on natural rocks (Ramsey and Chester, 2004; Bobich, 2005), Ce travail présente une caractérisation expérimentale de la localisation de la déformation et la rupture sur un matériau synthétique analogue de la roche dans différentes conditions de chargement axisymétrique. L’évolution de la localisation de la déformation a été caractérisée par la technique de corrélation d’images bidimensionnelle. Deux gammes d’essais en compression et en extension ont été réalisées à différentes pressions de confinement Pc. Profitant de la technique DIC et de la caractérisation détaillée des propriétés constitutives de GRAM1 par Mas et Chemenda (2014; 2015), nous montrons que l'initiation de la localisation des bandes de déformation est précédée par la déformation élastique uniforme puis la déformation élasto-plastique. La localisation de la déformation est initiée dans le régime de dilatance (la dilatance β est positive) et d’adoucissement (le module d’écrouissage h est négatif). Au cours de l'évolution du chargement, la déformation à l'intérieur de la bande de localisation de la déformation devient compactive (β 0). Ceci provoque dans un premier temps l’élargissement de la bande puis l’apparition de nouvelles bandes qui se forment successivement. La formation de ces nouvelles bandes provoque un ralentissement de la déformation dans les bandes préexistantes, ce qui densifie progressivement le réseau. Dans les essais en extension axisymétrique, les fractures se forment perpendiculaires à la contrainte principale mineure σ3 sous un état de contrainte extensif à faible Pc puis compressif quand Pc augmente. Nos résultats présentent une transition continue de la fracture extensive à la fracture cisaillante avec une augmentation de la contrainte compressive. Ceci est en accord avec les résultats obtenus pour les essais en extension réalisées sur des roches naturelles (Ramsey et Chester, 2004 ; Bobich 2005)

International audience; The present paper examines failure in discrete granular media with respect to its mode and nature based on energetic considerations through a comprehensive discrete element modelling computational analysis. The mode of failure refers to whether deformations will localize into an intense shear band or be diffuse. More subtly, a given failure mode can be effective with a burst of kinetic energy, or non-effective with a more controlled release of kinetic energy, depending on the control parameter. Physical quantities based on energy considerations with elementary decompositions of externally applied energy into elastic, plastic and kinetic contributions at the particle level are computed for a number of granular assemblies under a variety of failure scenarios. With the picture of a particle system experiencing macroscopic deformations according to underlying micro- and meso-mechanisms, it is concluded that computed grain-energy components depend on the microstructural detail that emerges as a function of loading program and control parameter. The relationship between elastic unloading outside a shear band and plastic dissipation inside it under both strain and stress control modes determines the genesis of shear banding in terms of plastic work dissipation minimization. Most interestingly, it is found that the energy signature inside the shear band in a dense granular packing is germane to energy characteristics of diffuse failure in a loose assembly, suggesting some similarities in microscopic failure processes between shear banding and diffuse failure.

International audience; The Mertz shear zone (MSZ) is a lithospheric scale structure that recorded mid-crustal deformation during the 1.7 Ga orogeny. We performed a microstructural and crystallographic preferred orientation (CPO) study of samples from both mylonites and tectonic boudins that constitute relics of the Terre Adelie Craton (TAC). The deformation is highly accommodated in the MSZ by anastomosed shear bands, which become more scattered elsewhere in the TAC. Most of the MSZ amphibolite-facies mylonites display similar CPO, thermal conditions, intensity of deformation and dominant shear strain. Preserved granulite-facies boudins show both coaxial and non coaxial strains related to the previous 2.45 Ga event. This former deformation is more penetrative and less localized and shows a deformation gradient, later affected by a major phase of recrystallization during retrogression at 2.42 Ga. Both MSZ samples and granulite-facies tectonic boudins present microstructures that reflect a variety of deformation mechanisms associated with the rock creep that induce contrasted CPO of minerals (quartz, feldspar, biotite, amphibole and orthopyroxene). In particular, we highlight the development of an "uncommon" CPO in orthopyroxene from weakly deformed samples characterized by (010)-planes oriented parallel to the foliation plane, [001]-axes parallel to the stretching lineation and clustering of [100]-axes near the Y structural direction. Lastly, we computed the seismic properties of the amphibolite and granulite facies rocks in the MSZ area in order to evaluate the contribution of the deformed intermediate and lower continental crust to the seismic anisotropy recorded above the MSZ. Our results reveal that (i) the low content of amphibole and biotite in the rock formations of the TAC, and (ii) the interactions between the CPO of the different mineralogical phases, generate a seismically isotropic crust. Thus, the seismic anisotropy recorded by the seismic stations of the TAC, including the MSZ, must be due to mantle rather than crustal structures. (C) 2016 Elsevier B.V. All rights reserved.

In press, accepted manuscript; International audience; Since 35 Ma, the kinematics of the Aegean domain has been mainly controlled by the southward retreat of the African slab, inducing back-arc extension. The main structures and associated kinematics are well constrained, but the kinematics of deformation before 35 Ma, coeval with the exhumation of blueschists and eclogites of the Cycladic Blueschist Unit, is still poorly understood. The earlier Eocene syn-orogenic evolution is strongly debated and very different geometrical interpretations and kinematic histories have been proposed in the literature. This study focuses on the high-pressure and low-temperature (HP-LT) parageneses spectacularly exposed and well preserved on Sifnos Island. The new field work provides new structural constraints on the tectonic history of HP-LT units generated in the subduction zone during the Eocene. It further shows how lithological heterogeneities localize strain within an accretionary wedge and how the localisation of strain evolves through time during exhumation. We show, through new geological and metamorphic maps, cross-sections and analyses of kinematic indicators, that Sifnos is characterized by shallow-dipping shear zones reactivating weak zones due to competence contrasts or earlier tectonic contacts. Structures and kinematics associated with these shear zones, show a top-to-the-N to −NE ductile deformation. The lower part of the tectonic pile shows a downward gradient of shearing deformation and is actually a thick top-to-the-NE shear zone, which we name the Apollonia Shear Zone. Through time shearing deformation tends to localize downward, leaving the upper part of the subduction complex preserved from late deformation. The present-day shape and topography of the island is largely controlled by late brittle faults reworking the earlier ductile shear zones. Comparing with the nearby island of Syros, we propose a new tectono-metamorphic evolution of the Cycladic Blueschists Unit, which partly explains the different degrees of retrogression observed on the Cycladic Islands.

International audience; Grain crushing plays an important role in the mechanical behavior of granular media, in chemo-hydro-thermo-mechanical couplings, in instabilities related to strain localization such as shear bands and compaction bands, in geophysical and geotechnical processes, in reservoir and petroleum engineering and in many other domains. The strength of brittle particles seems to be quite well described by a two-parameter Weibull distribution. Nevertheless, such a distribution predicts that failure is possible under any level of applied stress. On the contrary a three-parameter Weibull distribution contains a stress threshold under which grain failure is unlikely. Based on existing experiments on crushing of individual grains from various geomaterials and surrogate materials, and on new experiments performed on rock sugar particles, the present paper explores and compares the applicability of a two-versus a three parameter Weibull distribution. It is shown that in most of the cases the three-parameter Weibull distribution better describes the experimental results.

International audience; The lithospheric mantle is intrinsically heterogeneous and anisotropic. These two properties govern the repartition of deformation, controlling intraplate strain localization and development of new plate boundaries. Geophysical and geological observations provide clues on the types, ranges, and characteristic length scales of heterogeneity and anisotropy in the lithospheric mantle. Seismic tomography points to variations in geothermal gradient and hence in rheological behavior at scales of hundreds of km. Seismic anisotropy data substantiate anisotropic physical properties consistent at scales of tens to hundreds of km. Receiver functions imply lateral and vertical heterogeneity at scales < 10 km, which might record gradients in composition or anisotropy. Observations on naturally deformed peridotites establish that compositional heterogeneity and Crystal Preferred Orientations (CPOs) are ubiquitous from the mm to the km scales. These data allow discussing the processes that produce/destroy heterogeneity and anisotropy and constraining the time scales over which they are active. This analysis highlights: (i) the role of deformation and reactive percolation of melts and fluids in producing compositional and structural heterogeneity and the feedbacks between these processes, (ii) the weak mechanical effect of mineralogical variations, and (iii) the low volumes of fine-grained microstructures and difficulty to preserve them. In contrast, olivine CPO and the resulting anisotropy of mechanical and thermal properties are only modified by deformation. Based on this analysis, we propose that strain localization at the plate scale is, at first order, controlled by large-scale variations in thermal structure and in CPO-induced anisotropy. In cold parts of the lithospheric mantle , grain size reduction may contribute to strain localization, but the low volume of fine-grained domains limits this effect.

Feasibility studies for deep geological radioactive waste disposal facilities have led to an increased interest in the geomechanical modelling of its host rock. In France, a potential host rock is the Callovo-Oxfordian claystone. The low permeability of this material is of key importance, as the principal of deep geological disposal strongly relies on the sealing capacity of the host formation. The permeability being coupled to the mechanical material state, hydromechanical coupled behaviour of the claystone becomes important when mechanical alterations are induced by gallery excavation in the so-called excavation damaged zone (EDZ). In materials with microstructure such as the Callovo-Oxfordian claystone [Robinet et al., 2012], the macroscopic behaviour has its origin in the interaction of its mi- cromechanical constituents. In addition to the coupling between hydraulic and mech- anical behaviour, a coupling between the micro (material microstructure) and macro will be made. By means of the development of a framework of computational homo- genization for hydromechanical coupling, a doublescale modelling approach is formu- lated, for which the macroscale constitutive relations are derived from the microscale by homogenization. An existing model for the modelling of hydromechanical coupling based on the distinct definition of grains and intergranular pore space [Frey, 2010] is adopted and modified to enable the application of first order computational homogenization for obtaining macroscale stress and fluid transport responses. This model is used to constitute a periodic representative elementary volume (REV) that allows the rep- resentation of the local macroscopic behaviour of the claystone. As a response to deformation loading, the behaviour of the REV represents the numerical equivalent of a constitutive relation at the macroscale. For the required consistent tangent operators, the framework of computational homogenization by static condensation [Kouznetsova et al., 2001] is extended to hy- dromechanical coupling. The theoretical developments of this extension are imple- mented in the finite element code Lagamine (Li` ege) as an independent constitutive relation. For the modelling of localization of deformation, which in classical FE meth- ods suffers from the well-known mesh dependency, the doublescale approach of hy- dromechanical coupling is combined with a local second gradient model [Collin et al., 2006] to control the internal length scale of localized deformation. By accepting the periodic boundary conditions as a regularization of the microscale deformation, the use of the multiscale model in combination with the local second gradient model can be used for modelling localization phenomena in HM-coupled settings with material softening. The modelling capacities of the approach are demonstrated by means of simula- tions of oedometer tests and biaxial compression tests. The approach is demonstrated to be a powerful way to model anisotropy in the mechanical as well as the hydraulic behaviour of the material both in the initial material state and as an effect of hy- dromechanical alterations. For the application to the modelling of Callovo-Oxfordian claystone, microstructural REVs are calibrated to geometrical characteristics of the inclusion that form the microstructure under consideration and to macroscale ex- perimental results of the mechanical behaviour. The calibrated constitutive relation is used in the simulation of gallery excavation processes. These computations give a proof of concept of the doublescale assessment of the hydromechanical behaviour of the excavation damaged zones around galleries in the context of nuclear waste disposal.; Les études de faisabilité concernant le stockage géologique profond des déchets radioactifs ont conduit un intérêt accru concernant la modélisation géomécanique de la roche hte. En France, une roche hte potentielle est l'argilite du Callovo-Oxfordien du site de Meuse/Haute Marne. Etant donné que le principe de stockage géologique profond repose fortement sur la capacité de confinement de la formation hte, sa faible perméabilité est d'une importance clé. La perméabilité étant dépendante de la microstructure du matériau et de son évolution sous chargement, le comportement couplé hydro-mécanique de l'argilite est important. En effet, des modifications mécaniques sont induites par le creusement de la galerie d'entreposage, générant une zone endommagée (EDZ), pouvant conduire une modification de la perméabilité dans le voisinage de la galerie. Dans les matériaux microstructure complexe comme l'argilite du Callovo-Oxfordien, le comportement macroscopique trouve son origine dans l'interaction des constituants micro-mécaniques. En plus du couplage entre le comportement hydraulique et mécanique, un couplage entre les échelles micro et macro existe. Par le biais de l'élaboration d'un cadre d'homogénéisation du couplage hydro-mécanique, une approche de modélisation deuxéchelles est développée dans ce travail, dans laquelle la relation constitutive macroscopique découle directement du comportement à l'échelle microscopique. Un modèle existant du couplage hydro-mécanique, reposant sur l'identification de grains et d'espaces poreux intergranulaires à l'échelle micro est adopté comme point de départ. Ce modèle repose sur une homogénéisation numérique du comportement à la petite échelle afin d'obtenir à l'échelle macroscopique la réponse en contrainte et de transport du fluide interstitiel. Ce modèle est basé sur un VER périodique qui permet de déduire le comportement macroscopique local de l'argilite. En réponse, en un point d'intégration macro donné, à un incrément de la déformation et du gradient de pression, la réponse du VER permet d'exprimer l'incrément de contrainte et de flux associé, constituant de fait un équivalent numérique de la relation constitutive. Les problèmes aux conditions limites macro et micro sont traités simultanément par la méthode élément fini. Pour obtenir les opérateurs tangents consistants à l'échelle macro, la méthode d'homogénéisation par condensation statique des opérateurs tangeants micro est étendu au cas avec couplage hydro-mécanique. L'implémentation du modèle double échelle et la mise en uvre des développements théoriques d'homogénéisation ont été effectués dans le code élément fini Lagamine (Université de Liège). Pour la modélisation de la localisation de la déformation à l'échelle macro, qui, dans un formalisme de milieu continu classique, souffre de la dépendance au maillage, l'approche double-échelle a été utilisée dans un formalisme de milieu enrichi de type milieu de second gradient pour matériau poreux saturé. Les capacités du modèle homogénéisé numériquement, utilisé dans un cadre de milieu de second gradient, sont ensuite démontrées par des simulations d'essais dométriques et d'essais de compression biaxiaux. L'approche se confirme être un moyen puissant pour modéliser l'anisotropie initiale et induite du comportement mécanique et du comportement hydraulique. Pour la modélisation du comportement de l'argilite du Callovo-Oxfordien, des VER sont construits en tenant compte des travaux de caractérisation de la géométrie des inclusions microscopiques et des résultats expérimentaux d'essais macroscopiques.La loi de comportement homogénéisée numériquement ainsi calibrée est utilisée dans des simulations de creusement de galerie jusqu'à des niveaux d'endommagement générant une localisation de la déformation.Ces calculs montrent à la fois la pertinence et l'applicabilité du concept double échelle pour l'évaluation du comportement hydromécanique des EDZ dans un contexte du stockage des déchets radioactifs.

International audience; Various forms of the plastic deformation in single crystals are studied in pure and hydrogen-containing nickel and nickel alloys oriented for single slip [1 3 5] and strained in the stage III regime (shear strain, gamma = 0.8). The heterogeneity of deformation is investigated at two distinct scales: slip bands and dislocation structures, using atomic force microscopy (AFM) and transmission electronic microscopy (TEM). Size and distribution of slip band thicknesses and geometrically necessary boundary (GNB) spacing are comparable. GNB structures both screen the long-range stress fields and decrease the mean free path of mobile dislocations, whereas equiaxed cells only impede dislocation motion through their role as obstacles. Consequently, GNB formation localizes deformation in specific slip bands. Additionally, the observed similarity between GNB spacing and equiaxed cell size suggests a correlation between these microstructural features. The impact of solid solution atoms on the inter-wall spacing is established for chromium and hydrogen. Both decrease the GNB spacing because of a decrease of the cross-slip probability and stacking fault energy, combined to a shielding effect for the later. The effect of GNB spacing on strain hardening is discussed in terms of the length scale associated with GNBs and the effect of solute content. (C) 2015 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.