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The Eikonal non-local damage (ENL) approach models damage as a space-deforming phenomenon that affects the interaction distance between material points. As damage increases, interactions between points decrease, ultimately resulting in no interaction. In the integral version of such an approach, non-local interaction distances between material points are computed by solving a stationary Hamilton-Jacobi equation with a damage-dependent Riemannian metric. In the implicit gradient version of ENL models, the Riemannian metric figures in the Helmholtz equation to be solved for computing the non-local field controlling damage evolution. However, one of the main criticisms of such formulation is the lack of thermodynamics basis in its derivation. This paper presents a thermodynamics derivation of the Eikonal implicit gradient formulation based on differential geometry concepts to overcome this issue. A free-energy potential is defined considering the non-local strain as a morphological descriptor belonging to the abstract differentiable manifold (where the Riemannian metric is defined). Following a micromorphic media framework, the balance equations of the model are obtained. It is shown that the stress tensor and thermodynamic force associated with damage are the sum of standard and additional non-local contributions. It is also shown that the resulting energy dissipation is always positive, thus verifying the Clausium-Duhem inequality. After presenting all development considering second-order anisotropic continuum damage, the isotropic formulation is obtained as a particular case. Finally, a two-dimensional numerical implementation of an isotropic implicit Eikonal non-local gradient damage model is illustrated. Test cases are simulated to show the relocalization features of the considered formulation and its natural capability of naturally representing damage-to-fracture transition for high damage levels.

National audience

International audience; The design of reinforced concrete structures follows prescriptions of codes and standards (e.g., ACI and Eurocode). The strut-and-tie method is the only approach detailed in standards for the design of reinforcement of massive structures. Stut-and-tie methods are currently showing a strong interest and several techniques are based on automatic strategies and topological optimization. However, this method is based on a strong hypothesis associated with linear elastic analyses. In particular, the occurrence of pre-existing cracks is not considered when drawing the strut-and-tie model. This work aims to understand the role of an initially cracked state and, thus, the loading history in the design and choice of strut and tie directions. An experimental test is analyzed for a real size corbel loaded in two different inplane directions with forces not applied simultaneously. Hence, the specimen was cracked when the second force was applied. The corbel has minimal reinforcement to avoid brittle failure but should not affect the crack directions. The instrumentation used, combining digital image correlation and optical fiber sensing, allows for monitoring during the test and provides insight into the cracking history and the deformations in visible surfaces and in the bulk. Digital image correlation was used over the entire top surface of the corbel to measure displacement fields and thus strain fields, as well as information on cracking during the test. Optical fibers were installed within the specimen to measure strains in bulk. This measurement allows for the detection of cracks in the sample volume and thus complements digital image correlation measurements for fibers close to the surface. The results provide key data on the flow history of mechanical fields within the structure under different loads. This information helped clarify the domain of validity of strut-and-tie fundamental assumptions and may improve this design approach.

International audience; The 13th fib Symposium was to be held in Paris in 2020, following the previous symposium in Prague in 2018. Due the Covid-19 pandemic, we decided to split the symposium into two parts. In 2020 (26 to 28 August), we had an online symposium with the hope to be able to organise an in-person symposium in 2021. Unfortunately, the evolution of the pandemic did not allow us to envisage this. The second session of the 13th fib Symposium is therefore also be organised online on 21-22 July 2021.Two organisations are involved in the preparation of these events: The University Gustave Eiffel and the École normale supérieure Paris-Saclay, with the support of the French association of civil engineering (AFGC - representing the national fib group) and the University - Association of Civil Engineering (AUGC) and, of course, of the fib.After a classic review process, the 35 selected papers for 2021 are divided into four themes for the oral presentations with two parallel sessions over two days. Thirty minutes are allowed for each presentation in order to have the opportunity for a long discussion, which is a part of the spirit of these PhD symposia. The best papers will be rewarded by our sponsor (EFB-école française du béton) and by the fib. It is a great pleasure for us to express our gratitude to all the sponsors who contributed to the organisation of the symposium.For 2021, a keynote also enriches the program as in 2020. Magali Anderson (https://www.holcim.com/magali-anderson) will present a talk entitled: “Why concrete and cement are key for a net-zero world?” A topic close to the 2020 one and also very important, especially for the researchers of the future.Finally, let us wish to all participants – especially PhD students – an interesting event. We hope that this Symposium will help them to progress in scientific work and perhaps also in the fib activities.

International audience; A long-standing tradition of the fib, the PhD Symposia started in 1996. They were established by Prof. Balázs in Budapest to support young researchers and practitioners. Since then, the fib National Groups have already organised twelve symposia. The PhD symposia have become highly-recognised events, boasting the participation of international experts attending the symposia as PhD students' supervisors or keynote speakers. A two-year interval between each symposium allows for a thorough preparation of the event and for a sufficient amount of new information. The spirit of these symposia is to allow for a relaxed and friendly atmosphere, which befits the young generation.

International audience

International audience; The contribution of Reinforced Concrete (RC) wall-slab junctions to both dynamical behaviour and strength of nuclear buildings subjected to seismic loadings is investigated. An experimental program has been defined jointly by EDF and CEA, in order to improve the knowledge of the junctions' behaviour. As it has already been proposed in the literature for beam-column joints, our aim is to define a constitutive model of reinforced concrete wall-slab junctions fit to be integrated in a structural FE plate or shell model of a RC building. The objective is to represent the specific contribution of the junction to stiffness, forces redistribution and strength, under representative in-plane and out-of-plane seismic loading components. The experimental campaign, carried out on a series of 2 times 2 representative RC mockups, includes alternate static loading conditions and increasing seismic loading on Azalée shaking table, at CEA, up to high intensity ground motions. We discriminate the respective contributions of the slabs and the wall on one hand and of the junction on the other hand on the stiffness degradation and the dynamical response. We present the first steps achieved in the definition of the numerical model: kinematics, constitutive relation, by reference to experimental observations.

International audience; The embedding of anchoring systems in the retrofitting of Reinforced Concrete (RC) structures by means of Fiber Reinforced Polymers (FRP) often implies local failure modes associated to high stress concentrations. In order to account for such mechanical behaviours in standard finite element computations, an explicit representation of interfaces is required. This strategy presents, however , several limitations in terms of computational cost and mesh-related issues. On the other hand, implicit models may not be sufficiently accurate in order to reproduce the aforementioned localized phenomena. Specific finite elements for the simulation of pull-out mechanisms are here presented. The presence of interfaces is taken into account by enriching the displacement approximation by means of additional unknowns defined at the element level. Static-condensation, therefore, allows preserving the structure of the finite element procedure and limiting the computational effort.

International audience; Cette contribution présente la transition d'un modèle d'endommagement Eikonal Non Local (ENL) vers un modèle à discontinuité forte dans un cas unidimensionnel. En introduisant la formation d'une fissure cohésive dans les zones où l'endommagement est proche de l'unité, cette nouvelle formulation cherche à résoudre les problèmes d'objectivité des résultats par rapport au maillage des méthode de régularisation avec évolution des interactions non locales (e.g. la méthode ENL) à la localisation de l'endommagement dans un seul élément fini.

International audience; As part of the periodic reassessments of the safety of existing nuclear structures and the design of new ones, the contribution of wall-slab junctions to both behaviour and resistance of nuclear buildings subjected to seismic loadings is investigated. An experimental program has been defined jointly with the CEA [REF], in order to improve our knowledge of the junctions' behaviour. In parallel, work is underway in order to propose a model of the junctions, starting first from literature experimental observations and numerical detailed 3D computations results. Unlike previous global models for RC junctions in the literature, whose validity domain is generally limited either to out-of-plane or to in-plane stresses, our aim is to define a model fit to be integrated in a structural FE plate or shell model of a nuclear building. The purpose of this model is to represent the contribution of the junction to both stiffness and resistance when the building is subjected to seismic loads, that can include both in-plane and out-of-plane components. The purpose of this paper is to present the first steps achieved in the definition of this model, starting from the representation of the junctions in their elastic behaviour domain. Starting from the 3D kinematics in the joint area, a model of behaviour able to represent accurately the deformation modes of the elastic joint subjected to diverse loads has been selected. It is connected to plates elements which represent the behaviour of thin structural elements (walls, floors) in order to transmit the displacements and rotations at its interfaces. The boundary between the junction element and the plate elements representing walls and floors is set at the limit of the respective structural elements, thus increasing the representativeness of these FE models. The capacity of this model to effectively represent the joint stiffness is assessed in the elastic range, first considering a homogeneous material and then taking into account the presence of both concrete and reinforcement in the structure. A parametric study is carried out, in order to validate the model within the variation range of thicknesses, reinforcement ratio, etc. representative of nuclear buildings. The results are presented herein. In a second time, the framework of the non-linear model proposed to describe the junctions' behaviour beyond their elastic range is exposed.

International audience; Integral non-local (INL) formulations on the internal variables of the constitutive model [1] are widely used to regularize Continuum Damage computations, in the presence of stress softening for instance. According to this approach the thermodynamic variable driving the damage evolution process at a given material point is computed by weighted averaging of the corresponding local field over the entire domain. Averaging is performed through a non-local weighting function, such that the higher the Cartesian distance between two material points, the lower is their interaction. A main drawback of this assumption consists, however, in nonphysical interactions between material points across damaged bands, cracks and holes. From a numerical viewpoint, this induces some parasite effects, such as damage spreading over a large damaged band, damage diffusion near notches and free-edges, etc. Enhancements of the initial methods were proposed by allowing non-local interactions to evolve depending on mechanical fields (e.g. damage, stress, strain). The Eikonal Non-Local (ENL) formulation [2, 3] provides a novel interpretation of damage dependent evolving non-local interactions. According to this approach, one considers that damage induces a curvature of the Riemannian space in which interaction distances are computed. As a consequence, non-local interactions between material points are controlled by geodesic distances approximating the viscosity solution of an isotropic time-independent Eikonal equation with a damage dependent Riemannian metric function. Geodesic distances are then used to define the kernel of weighting function to be used in integral non-local averaging. This mathematical and physical framework allows for directly modeling evolving interactions throughout the damage process, from damage growth to strain local-ization. In this contribution, a simple isotropic ENL damage model and its numerical implementation [3] are presented first. Two-dimensional strain localization problems are then simulated in order to present the main features of the proposed formulation. Attention is mainly focused on non-local interactions across damaged bands and near notches and/or free-edges, to show that parasite effects classically associated with standard INL formulations are avoided, or at least strongly reduced.

International audience; The analysis and prediction of the degradation process and cracking of concrete structures with numerical models is an important issue in the field of civil engineering. In order to describe the global behavior of a structure composed of quasi-brittle material as well as local fields, a continuous approach using nonlinear constitutive law (e.g. damage, plasticity,…) remains the most efficient one regarding the computational time. However, one has to consider additional tools to extract discrete information about cracks like spacing and openings from these computations. The objective of this research is to propose tools capable of extracting local information such as cracking using two post-treatment methods of a global finite element analysis. First, in the proposed method, a global non-linear finite element analysis of the whole structure is performed. This analysis reveals the zones of degradation that are to be reanalyzed via a local analysis using two post-treatment methods. The first method combines a topological search method used to locate cracks developed by Bottoni et al. [1] and a continuous/discontinuous approach used to compute the crack opening initially proposed by Dufour et al. [2].. It consists in comparing the computed strain fields, with the analytical one derived from the displacement profile described as a strong disconti-nuity. Both strain fields are regularized using a Gaussian function. The crack opening can then be adjusted so as to reduce the gap between the regularized strain field and the regular-ized strong discontinuity strain field. Furthermore, a general formulation of these tools for 2D and 3D problem is proposed in this work. The direction of the mode I crack at a point is determined as the one which maximizes the crack opening along the associated 1D profile. The second method is a non-intrusive reanalysis at the local scale performed with a discrete model in order to extract fine information about crack opening. A region of interest (ROI) corresponding to the damaged area obtained from the global analysis is defined. Then, the loading steps corresponding to the steps of reanalysis are determined, where boundary conditions are extracted from the continuous displacement field and applied on the non-free surfaces of the ROI. The material is described with a discrete element approach based on an assembly of polyhedral particles linked by Euler-Bernoulli beams with brittle behaviour. Further details concerning the discrete model used at the local scale can be found in [3]. The displacement fields obtained from the FE analysis are compared to the experimental data provided from the post-processing of the actual test in order to analyze the concordance of the results on the global scale.

International audience; Cement-based materials undergo several types of deformations related to temperature, drying and hydration, namely, thermal, drying and autogeneous shrinkage. These strains may lead to tensile stresses, and sometimes to cracking, which can reduce the durability, limit mechanical material performance and reduce tightness (if required). The principal mechanisms of cracking by shrinkage restraint are presented, namely, self-restraint (gradients, strains incompatibilities due to the heterogeneity of cement-based materials) and external restraint (concrete lift, rendering mortar for instance). Then, 2 examples are given, including experimental results and numerical simulations. In the first one, shrinkage cracking in the case of a tunnel lining for a subway (40 cm thickness) is presented. Effects of autogeneous, drying and thermal (due to the heat release during hydration) are studied. After identification of material parameters, numerical simulations are performed. They show that thermal shrinkage at early-age is the main cause of snap-through cracks affected tightness. In the second example, the case of nuclear power plant construction is studied (1.2 m thickness). Cracking may occur because of thermal gradients and shrinkage restraint (by the previous lift or the raft foundation). Effect of creep is particularly unveiled. The numerical simulations show that differential creep in tension/compression leads to different results: no cracks or snap-through cracks. The evolutions of coefficient of thermal expansion and Poisson ratio are also addressed: their impact on the prediction of stresses is very limited, since they have a sharp evolution just before the setting of the material.

International audience; The prediction of concrete's long-term properties is of great importance for durability issues. The development of internal stresses generated by drying affect these latter especially the mechanical strength or the Young's modulus. In this paper, internal stresses due to drying are considered explicitly. In agreement with experimental results (not presented), the drying effects are modelled in a process taking into account the evaluation of the water state of the material, the modelling of the induced shrinkage strains and ending in mechanical computation. The evolution of the mechanical characteristics, the cracking induced by drying and the residual transport properties of the material can thus be determined.

International audience; Le processus de fissuration d’une poutre entaillée en béton fibré soumise à une sollicitation de flexion 1-point dynamique a été étudié. L’analyse est faite à partir de la réponse globale issue d’un calcul élément fini afin d’extraire localement de l’information fine concernant la fissure. Deux approches pour le post-traitement de l’analyse globale sont comparées : une méthode continue/discontinue ainsi qu’une analyse globale/locale. Les estimations d’ouverture de fissure obtenues numériquement sont alors comparées aux résultats expérimentaux.

International audience; This communication deals with the effect of drying on concrete’s mechanical properties. This study is conducted through experimental and numerical simulations with or without drying. A visco-elastic model with damage for concrete provides the state of stress and damage before loading due to drying shrinkage. The mechanical behavior of specimens, with or without drying, is then compared in terms of overall behavior. This investigation will thus allow to understand and to model the effects of drying on the mechanical behaviour of cementitious materials.

International audience

Dans les milieux hétérogènes, les mécanismes physiques et mécaniques ne peuvent être complètement analysés sans prendre en compte la présence d’interfaces au sein des matériaux. Ces frontières, d’épaisseur faible, voir nulle, présentent un défi en terme de modélisation et de caractérisation expérimentale. Dans les matériaux cimentaires comme le béton, les interfaces entre inclusions rocheuses et pâte de ciment sont particulièrement importantes de par leur épaisseur non négligeable, leur structure très poreuse et leur comportement mécanique plus faible. De par leur structure poreuse, une grande quantité d’eau libre est stockée dans ces zones. Une présence qui est associée par beaucoup à la variation des comportements mécaniques sous sollicitations dynamiques. Dans cette étude, une méthode expérimentale de caractérisation de l’interface entre une roche, le granite, et un mortier est présentée. Les méthodes de dépouillement permettant d’obtenir différents paramètres caractérisant le comportement à rupture de cette interface seront discutés., Academic Journal of Civil Engineering, Vol 34 No 1 (2016): Special Issue - RUGC 2016 Liège

International audience; no abstract

International audience; In this paper, a tool to evaluate meso-structures' quality is presented. This tool is modified to produce a local measurement of the element density in a matrix. From this local value , a prediction method is proposed for crack nucleation and propagation in concrete under dynamic loading. The predictions that can be obtain with this method are then compared to results from numerical simulmations of dynamic traction using Akantu Finite Elements code.; Dans ce papier, un outil d'analyse de la qualité des méso-structures est présenté. Il a été modifié pour obtenir une me-sure de la densité local d'éléments dans les mésostructures de béton. De cet mesure local, on propose une méthode de prédiction de la fissuration dans le béton, en terme de nucléa-tion et de propagation, lors de sollicitations dynamiques. Les prédictions que l'on peut faire sont comparées à des simulations de traction dynamique avec le code de calcul Akantu.

National audience; Dans le processus de conception d'une installation industrielle sensible, la sureté de la structure présente un aspect primordial. Le dimensionnement du génie-civil ainsi que la qualification des matériels aux sollicitations dynamiques doivent tenir compte des accélérations qu'ils subissent. Ces accélérations doivent intégrer les mouvements sismiques, mais également les mouvements d'ébranlement consécuti s l'impact d'avion de réquences de coupure plus élevées. Les méthodologies actuelles permettant d'évaluer cet ébranlement reposent sur des analyses, rarement non linéaires, par éléments finis en transitoires par intégration directe ou par projection sur base modale. Dans ces deu cas pour parvenir représenter de manière pertinente un contenu de moyenne fréquence, il convient de mettre en place un raffinement de maillage difficilement compatible avec la taille des modèles de ces structures de génie civil. A in d'enrichir les méthodologies industrielles employées et de permettre une meilleure représentation du comportement de la structure mo ennes réquences, une démarche couplant une analyse temporelle et non linéaire de la zone de choc avec une approche fréquentielle de traitement de l'ébranlement par l'utilisation de la TVRC (Théorie Variationnelle des Rayons Complexes) est proposée. L'objecti est ainsi d'utiliser l'e icacité numérique de la stratégie employée, notamment en moyennes fréquences, pour qualifier de grandes structures en béton armé soumises à un impact d'avion.

International audience; The strength variability of the concrete-like materials is usually represented, in pheno-menological macroscopic models, using stochastic tools that need to be identified with a large number of experimental tests. The variability phenomenon is then usually linked to the non-uniform characteristics of the material at the mesoscopic scale, due to the various phases of the concrete. An alternative to a macroscopic model with numerous parameters is to represent these phases explicitely. In this work, we intend to explore the influence of the heterogeneous meso-structure of the concrete (aggregates in a cement paste matrix) on its dynamic properties. For this purpose, we use FE simulations with a cohesive approach and an explicit representation of the meso-structure. A 2D geometrical model of concrete consisting of aggregates, in-terfacial transition zones and a matrix is used. That kind of approach has been previously been used to give a better understanding of the fracture mechanisms ([1], [2]) and gave relevant results on the Dynamic Increase Factor (DIF) experimentaly observed. However, if the scale of the numerical specimen is large enough, that means that the material can be seen as homogeneous, and we are not able to reproduce the experimental variability on the tensile strength [3]. The influence of the spatial disposition of the elements of the mesostructures is still open for discussion. Specifically, the impact of the clustering of aggregates on crack initiation and propagation. In our study, we propose to analyse the effect of such groups of aggregates later called clusters. In order to detect and mesure the clustering, we developped a statistical indicator inspired from a global estimator, Ripley's function [4]. Numerical results coupling the mesure of the clustering with its effect on the global fracture process will be presented.

International audience; This work aims to develop and identify a new model for reinforced concrete joint element subject to cyclic loadings. Based on experiments and 3D numerical modeling, a simplified model of RC beam-column joint is introduced (within the framework of macro-element). In a first experimental study, this joint will be tested under reverse cyclic loading applied at the beam tip to identify its behavior under this kind of loading in terms of strength, stiffness and ductility. In parallel of experiments, a finite elements model of the joint based on 3D finite elements is presented to highlight and define the nonlinear mechanisms involved in the ruin of the assembly. This step will confirm the experimentally observed phenomena: damage, friction, plasticity. Secondly, a simplified macro-element model for beam-column joint, associated to a nonlinear behavior, is introduced to reflect the response of the joint under cyclic loading loads. Model parameters will be identified from experimental results and analysis on a local scale via 3D finite element calculation. Finally, numerical analyses will be performed to validate the proposed approach in comparison with the experimental tests.