Publications

2015

• Simulation numérique des phénomènes capillaires et de mouillage pour l'étude de la formation de macro/micro-porosités dans les procédés d'élaboration par infusion
  
  • Liu Yujie
  • Moulin Nicolas
  • Bruchon Julien
  • Liotier Pierre-Jacques
  • Drapier Sylvain
  , 2015. Cet article présente une stratégie numérique, basée sur une approche éléments finis pour la simulation du contact entre deux fluides et un solide, impliquant des effets capillaires et de mouillage, appliquée à la formation de macro/micro-porosités au cours des procédés d'élaboration des matériaux composites par infusion. Ce modèle s'appuie sur une description eulérienne des deux fluides non miscibles (la résine et l'air) avec des conditions aux bords qui décrivent les phénomènes de mouillage aux interfaces fluides/fibres. L'interface entre les deux fluides est décrite par une méthode level set, sur laquelle est prise en compte la force capillaire.
• Implémentation robuste pour maîtriser le conditionnement et la précision des modélisations X-FEM
  
  • Ndeffo Marcel
  • Massin Patrick
  • Moes Nicolas
  , 2015. Dans le cas général d'une discontinuité positionnée arbitrairement dans un maillage, la méthode X-FEM peut présenter une convergence sous-optimale. En effet, lorsque l'interface X-FEM se rapproche des nœuds du maillage, le conditionnement augmente exponentiellement, tandis qu'une erreur numérique notable, se propage dans toute la structure. Ces limitations sont intrinsèques à la formulation X-FEM. Nous discuterons de différents remèdes à cet état de fait.
• Réponse d'un matériau hyperélastique fragile : comparaison approches analytiques et numériques en mode anti-plan
  
  • Stolz Claude
  • Parilla Gomez Andrès
  , 2015. On étudie la forme des champs mécaniques autour d'une quasi-fissure pour une classe de matériau isotrope hyperélastique incompressible fragile. dont le critère de rupture est une déformation critique. La quasi-fissure est une zone endommagée où les contraintes sont nulles, la frontière entre zone saine et endommagée est obtenue analytiquement. Des simulations numériques fondées sur une optimisation de forme sont proposées pour résoudre le problème d'équilibre avec quasifissure pour des comportements fragiles plus généraux.
• Approche variationnelle de la rupture dynamique via les modèles d'endommagement à gradient
  
  • Li Tianyi
  • Marigo Jean-Jacques
  • Guilbaud Daniel
  • Potapov Serguei
  , 2015. Nous présentons une extension en dynamique des modèles d’endommagement à gradient qui peuvent être vus comme une régularisation de l’approche variationnelle de la rupture capable de prédire dans un cadre unifié l’initiation et le trajet spatio-temporel (propagation, bifurcation, branchement, arrêt) de fissures complexes dans des matériaux quasi-fragiles sous chargement dynamique. La formulation variationnelle précise ainsi que son implémentation numérique par éléments finis sont détaillées et illustrées par des simulations représentatives en accord avec les résultats théoriques et expérimentaux.
• Propagation 3D de fissures cohésives X-FEM
  
  • Massin Patrick
  • Ferté Guilhem
  • Moes Nicolas
  , 2015. Une stratégie innovante d'étude quasi-statique de problèmes de propagation de fissures a été proposée dans Code_Aster, couplant des modèles de zones cohésives et la méthode des éléments finis étendus (XFEM). Elle a été validée sur des benchmarks issus de la littérature, pour la plupart des expériences réalisées sur des éprouvettes de béton. La capacité de la méthode à prédire des trajets de fissurations complexes pour des problèmes tridimensionnels a ainsi été illustrée. Une extension à la dynamique a été réalisée et validée pour les trajets de fissurations droits, les premiers résultats sur trajets courbes étant prometteurs.
• Utilisation des schémas d'intégration classiques pour traiter la plasticité en X-FEM
  
  • Martin Alexandre
  • Massin Patrick
  , 2015. La subdivision de l'élément parent en sous-cellules d'intégration utilisée dans le cadre de la méthode X-FEM convient difficilement à l'étude de la propagation d'une fissure dans un milieu plastifié. Il est alors notamment nécessaire de réaliser la projection des variables internes aux points d'intégration des sous-éléments. Cette contribution étend au cas de la plasticité une méthode d'intégration utilisant les formules de quadrature de Gauss standards, initialement développée dans le cadre de l'élasticité linéaire. La méthode proposée se limite aux cas des interfaces et des éléments linéaires.
• Implantation de lois de comportement mécanique à l'aide de MFront: simplicité, efficacité, robustesse et portabilité
  
  • Helfer Thomas
  • Proix Jean-Michel
  • Fandeur Olivier
  , 2015. Ce papier est dédié au générateur de code open-source nommé MFront. Plusieurs langages dédiés (domain specific languages), basés sur le C++, permettent d'écrire de manière simple, compacte, efficace et robuste, l'implantation de lois de comportement mécanique. Après une vue d'ensemble, nous décrivons certaines des techniques de programmation utilisées. Nous présentons ensuite divers algorithmes permettant d'accroître la robustesse des schémas d'intégration implicites. Enfin, nous discutons certaines questions liées à la portabilité des implantations entre différents codes.
• Simulation numérique de l'influence de la porosité sur le comportement d'un alliage à mémoire de forme NiTi
  
  • Troufflard Julien
  • Rio Gérard
  • Liu Yujie
  , 2015. Ce travail propose une étude par éléments finis de l'évolution des propriétés d'un alliage à mémoire de forme à base Nickel-Titane en présence de porosité. Le but final est de remonter au comportement homogène équivalent. L'influence de la porosité est étudiée en réalisant des simulations avec des conditions périodiques en déplacement sur des motifs ayant une fraction de vide jusqu'à 20%. Le matériau est modélisé avec une loi d'élasto-hystérésis. L'évolution des propriétés macroscopiques est obtenue par une analyse graphique directe des moyennes des champs de contrainte et de déformation.
• Variational Approach to Dynamic Brittle Fracture via Gradient Damage Models
  
  • Li Tianyi
  • Marigo Jean-Jacques
  • Guilbaud Daniel
  • Potapov Serguei
  , 2015. In this paper we present a family of gradient-enhanced continuum damage models which can be viewed as a regularization of the variational approach to fracture capable of predicting in a unified framework the onset and space-time dynamic propagation (growth, kinking, branching, arrest) of complex cracks in quasi-brittle materials under severe dynamic loading. The dynamic evolution problem for a general class of such damage models is formulated as a variational inequality involving the action integral of a generalized Lagrangian and its physical interpretation is given. Finite-element based implementation is then detailed and mathematical optimization methods are directly used at the structural scale exploiting fully the variational nature of the formulation. Finally, the link with the classical dynamic Griffith theory and with the original quasi-static model as well as various dynamic fracture phenomena are illustrated by representative numerical examples in quantitative accordance with theoretical or experimental results.
• Shear wall mock up subjected to monotonic loading with concrete steel bond model
  
  • Mang C.
  • Jason Ludovic
  • Davenne L.
  , 2015. This paper presents a numerical simulation of a shear-wall mock-up subjected to monotonic loading with a new steel-concrete bond model. First, global responses (forcedisplacement curves) are compared to the experimental results and show a good agreement between simulation and experiment. In order to compare the local responses such as crack orientation, crack spacing and crack opening, a new post-processing method is presented. It is based on the definition of the crack path from the displacement field or the change in the sign of the bond slip. The crack opening is then obtained using the displacement in the normal direction of the crack. The method is applied on the shear wall and the results are compared to the experimental data obtained with digital image correlation. A good agreement is once again obtained.
• Modelling of ground and atmospheric effects on wind turbine noise
  
  • Tian Yuan
  • Cotté Benjamin
  , 2015. Amiet's analytical model for trailing edge noise is used to predict the noise radiated by a Siemens SWT 2.3-93 wind turbine. Good agreement with experiment is found for sound power level (SWL) spectrum for frequencies higher than 1kHz. The immission level is then calculated with an image source model and compared with point source calculation. Ground reflection and atmospheric absorption are considered for the propagation model. The effect of ground reflection is seen to modify the sound pressure level spectrum and the amplitude modulation strength. The point source approximation yields accurate results for the overall sound pressure level, but exaggerates interference dips in the spectrum and thus overestimates the strength of amplitude modulation.
• Prediction of variability in wind turbine noise calculations
  
  • Cotté Benjamin
  • Tian Yuan
  , 2015. We propose in this work a method to predict the variability in wind turbine noise calculations due to wind speed and direction fluctuations. First, wind lidar data measurements during a 24-hour period are analyzed, and four periods with different atmospheric stability conditions are selected. Then, a wind turbine noise model based on Amiet's theory for trailing edge noise is presented and used to predict the sound pressure level at a fixed receiver during the 24-hour period. Finally, a Monte Carlo sampling method is described that allows us to accurately predict the statistics of sound pressure level during each selected period. The variability is seen to be much more pronounced during the day than during the night, and statistical quantities are shown to depend on the period duration considered.
• On the application of the method of difference potentials to linear elastic fracture mechanics
  
  • Woodward W. H.
  • Utyuzhnikov S
  • Massin Patrick
  International Journal for Numerical Methods in Engineering, Wiley, 2015, 103, pp.703--736. The Difference Potential Method (DPM) proved to be a very efficient tool for solving boundary value problems (BVPs) in the case of complex geometries. It allows BVPs to be reduced to a boundary equation without the knowledge of Green's functions. The method has been successfully used for solving very different problems related to the solution of partial differential equations. However, it has mostly been considered in regular (Lipschitz) domains. In the current paper, for the first time, the method has been applied to a problem of linear elastic fracture mechanics. This problem requires solving BVPs in domains containing cracks. For the first time, DPM technology has been combined with the finite element method. Singular enrichment functions, such as those used within the extended finite element formulations, are introduced into the system in order to improve the approximation of the crack tip singularity. Near-optimal convergence rates are achieved with the application of these enrichment functions. For the DPM, the reduction of the BVP to a boundary equation is based on generalised surface projections. The projection is fully determined by the clear trace. In the current paper, for the first time, the minimal clear trace for such problems has been numerically realised for a domain with a cut. KEY WORDS: method of difference potentials; extended finite element method; fracture; rate of convergence (10.1002/nme.4903)
  DOI : 10.1002/nme.4903
• Adaptive zooming method for the analysis of large structures with localized nonlinearities
  
  • Llau Antoine
  • Jason Ludovic
  • Dufour Frédéric
  • Baroth Julien
  Finite Elements in Analysis and Design, Elsevier, 2015, 106, pp.73-84. Simulating concrete cracking requires nonlinear modelling applied on a refined mesh if a correct evaluation of crack properties needs to be achieved. Therefore, it is rather costly and even sometimes impossible when large reinforced concrete structures are considered. Alternative solutions have therefore to be proposed. This contribution presents a structural zooming method for the simulation of large reinforced concrete structures with localized nonlinearities. Our method is based on static condensation (Guyan 1965) and provides an adaptive framework for performance-oriented use of this method in nonlinear simulations. In particular, it only simulates the behavior of nonlinear interesting zones (detected by adapted criteria). The areas where refined modelling is not required are replaced by their equivalent stiffnesses. The linearity criteria, depending on the chosen mechanical models, are also used to activate new interesting zones during the simulation. This method substantially decreases the computational cost on both presented test cases (a two-dimensional concrete beam and a three-dimensional reinforced concrete building). (10.1016/j.finel.2015.07.011)
  DOI : 10.1016/j.finel.2015.07.011
• Pseudoelastic Shape Memory Alloys to Mitigate the Flutter Instability: A Numerical Study
  
  • Malher Arnaud
  • Doaré Olivier
  • Touzé Cyril
  , 2015, 168, pp.353-365. A passive control of aeroelastic instabilities on a two-degrees-of-freedom (dofs) system is considered here using shape memory alloys (SMA) springs in their pseudo-elastic regime. SMA present a solid-solid phase change that allow them to face strong deformations (∼10%) ; in the pseudo-elastic regime, an hysteresis loop appears in the stress-strain relationship which in turn gives rise to an important amount of dissipated energy. This property makes the SMA a natural candidate for mitigating undesired vibrations in a passive manner. A 2-dofs system is here used to model the classical flutter instability of a wing section in a uniform flow. The SMA spring is selected to act on the pitch in order to dissipate energy of the predominant motion. A simple phenomenological model for the SMA hysteresis loop is introduced, allowing for a quantitative study of the important parameters to optimize in view of an experimental design. Thanks to a simple phenomenological model for the SMA hysteresis loop, a quantitative numerical study is performed in order to exhibit the best tuning of the material parameters for controlling the flutter instability. (10.1007/978-3-319-19851-4_17)
  DOI : 10.1007/978-3-319-19851-4_17
• Multi-axial Fatigue Criteria with Length Scale and Gradient Effects
  
  • Zepeng Ma
  • Maitournam Habibou
  • Le Tallec Patrick
  Procedia Engineering, Elsevier, 2015, 133, pp.60 - 71. The objective of the work is first to extend some classic high cycle fatigue (HCF) criteria (as Crossland, Dang Van, Papadopoulos, ...) to take into account a sensitivity of the criteria to stress spatial variations occurring at length scale lg, and second to compare the performances of the extensions through numerical simulations of experimental fatigue tests. After an introduction of the basic criteria and their gradient based extensions proposed by Luu et al., we focus on the Crossland criterion to propose a more practical and simple expression taking into account the gradient of the stress amplitude and the maximum hydrostatic stress. The proposition is then tested and applied to different simple situations: 4-point bending and cantilever rotative bending. The relative errors between the exact solutions and the numerical simulations are estimated. Biaxial bending-torsion tests are also simulated to demonstrate the capabilities of the approach. The generalization of the approach to other multiaxial fatigue criteria is briefly shown through the case of Papadopoulos 2001 proposal. Finally, the present study develops a simple formulation of gradient multi-axial fatigue criteria extending the classical HCF criteria. In this work only stress gradient with a beneficial effect on fatigue have been considered. (10.1016/j.proeng.2015.12.624)
  DOI : 10.1016/j.proeng.2015.12.624
• Edge flutter of long beams under follower loads
  
  • de Langre Emmanuel
  • Doaré Olivier
  Journal of Mechanics of Materials and Structures, Mathematical Sciences Publishers, 2015, 10 (3), pp.283–297. The linear instability of a beam tensioned by its own weight is considered. It is shown that for long beams, in the sense of an adequate dimensionless parameter, the characteristics of the instability caused by a follower force do not depend on the length. The asymptotic regime significantly differs from that of short beams: flutter prevails for all types of follower loads, and flutter is localized at the edge of the beam. An approximate solution using matched assymptotic expansion is proposed for the case of a semi-infinite beam. Using a local criterion based on the stability of waves, the characteristics of this regime as well as its range of application can be well predicted. These results are finally discussed in relation with cases of flow-induced instabilities of slender structures. (10.2140/jomms.2015.10.283)
  DOI : 10.2140/jomms.2015.10.283
• Finite element modelling of the oxidation kinetics of Zircaloy-4 with a controlled metal-oxide interface and the influence of growth stress
  
  • Zumpicchiat Guillaume
  • Pascal Serge
  • Tupin Marc
  • Berdin Clotilde
  Corrosion Science, Elsevier, 2015, 100, pp.209-221. Experimentally, zirconium-based alloys oxidation kinetics is sub-parabolic, by contrast with the Wagner theory which predicts a parabolic kinetics. Two finite element models have been developed to simulate this phenomenon: the diffuse interface model and the sharp interface model. Both simulate parabolic oxidation kinetics. The growth stress effects on oxygen diffusion are studied to try to explain the gap between theory and experience. Taking into account the influence of the hydrostatic stress and its gradient into the oxygen flux expression, sub-parabolic oxidation kinetics have been simulated. The sub-parabolic behaviour of the oxidation kinetics can be explained by a non-uniform compressive stress level into the oxide layer.
• 3D numerical modeling of dynamic recrystallization under hot working: Application to Inconel 718
  
  • de Jaeger Julien
  • Solas Denis
  • Fandeur Olivier
  • Schmitt Jean-Hubert
  • Rey Colette
  Materials Science and Engineering: A, Elsevier, 2015, 646, pp.33-44. Hot forging of Inconel 718 is an essential process to give shape and in-use properties to final part design. Dynamic recrystallization is the main mechanism influencing the properties through a grain size control. It is then of crucial importance to be able to predict the mechanical behavior during forging and the microstructure evolution during and after the dynamic recrystallization. A coupling between a crystal plasticity finite element model and a recrystallization model using a 3D cellular automata approach is applied to a 3D polycrystalline aggregate deformed by compression. Beyond the prediction of the stress–strain curves at different strain rates, numerical simulations enable the visualization of stress, strain, energy, local orientation, dislocation density fields within the aggregate. Finally, the recrystallization kinetic and the grain size are recorded as a function of strain. The results are in a rather good agreement with experiments, even if the predicted grain size is slightly larger than the measured one. To improve the prediction, annealing twinning is accounted for. (10.1016/j.msea.2015.08.038)
  DOI : 10.1016/j.msea.2015.08.038
• A theory of finite strain magneto-poromechanics
  
  • Nedjar Boumediene
  Journal of the Mechanics and Physics of Solids, Elsevier, 2015, 84, pp.293-312. The main purpose of this paper is the multi-physics modeling of magnetically sensitive porous materials. We develop for this a magneto-poromechanics formulation suitable for the description of such a coupling. More specifically, we show how the current state of the art in the mathematical modeling of magneto-mechanics can easily be integrated within the unified framework of continuum thermodynamics of open media, which is crucial in setting the convenient forms of the state laws to fully characterize the behavior of porous materials. Moreover, due to the soft nature of these materials in general, the formulation is directly developed within the finite strain range. In a next step, a modeling example is proposed and detailed for the particular case of magneto-active foams with reversible deformations. In particular, due to their potentially high change in porosity, a nonlinear porosity law recently proposed is used to correctly describe the fluid flow through the interconnected pores when the solid skeleton is finitely strained causing fluid release or reabsorption. From the numerical point of view, the variational formulation together with an algorithmic design is described for an easy implementation within the context of the finite element method. Finally, a set of numerical simulations is presented to illustrate the effectiveness of the proposed framework. (10.1016/j.jmps.2015.08.003)
  DOI : 10.1016/j.jmps.2015.08.003
• Adaptive zooming method for the simulation of quasi-brittle materials
  
  • Llau Antoine
  • Jason Ludovic
  • Baroth Julien
  • Dufour Frédéric
  Applied Mechanics and Materials, Trans Tech Publications, 2015, 784, pp.284-291. A method to simulate concrete structures (quasi- brittle material) with localized nonlinearities is presented. Based on Guyan’s condensation, it consists in replacing the elastic zones of the structure by their equivalent rigidities (super-elements). The nonlinear computation is then performed only on the damaged zones of interest, i.e. damaged. As new damaged zones may appear, ourthe proposed method monitors the evolution of the system and re-integrates previously condensed areas if necessary. This method, applied on different tests cases, allows a substantial computation economy which allows the use of very fine description in nonlinear areas. (10.4028/www.scientific.net/AMM.784.284)
  DOI : 10.4028/www.scientific.net/AMM.784.284
• Asymptotic fields ahead a crack for a class of non linear materials under mode III
  
  • Stolz Claude
  Mechanics of Materials, Elsevier, 2015, 90, pp.102-110. The paper considers the mechanical fields near the tip of a crack deformed by an anti-plane shear at infinity for a class of non linear elastic materials. For brittle material rupture occurs when a maximal stretch is reached. Taking account of this critical value, the crack is replaced by a totally damaged zone of finite thickness named a quasicrack. Inside this domain, the stress is identically zero and the shape of the boundary between damaged and undamaged body is found analytically. (10.1016/j.mechmat.2015.04.005)
  DOI : 10.1016/j.mechmat.2015.04.005
• Antiplane shear field for a class of hyperelastic incompressible brittle material : analytical and numerical approaches
  
  • Parrilla-Gomez Andres
  • Stolz Claude
  Journal of Mechanics of Materials and Structures, Mathematical Sciences Publishers, 2015, 10 (3), pp.395-410. This paper reconsiders the problem of determining the elastostatics fields near the tip of a crack in a body deformed by an antiplane shear for a class of incompressible, homogeneous, isotropic materials. The study is generalized to the formation of a quasicrack under the same conditions of loading for brittle material that cannot support any further loading when a critical strength is reached. The crack is then replaced by a totally damaged zone where the stress is identically zero. The shape of the boundary between the damaged and undamaged body is found analytically. A numerical approach is proposed to address the problem for more general constitutive law. The analytical solution is recovered by a process of shape optimization. (10.2140/jomms.2015.10.395)
  DOI : 10.2140/jomms.2015.10.395
• Investigations into the cumulative fatigue life of an AISI 304L austenitic stainless steel used for pressure water reactors: Application of a double linear damage rule
  
  • Fissolo Antoine
  • Gourdin Cédric
  • Chen Yinqiang
  • Perez Grégory
  • Stelmaszyk J.M.
  International Journal of Fatigue, Elsevier, 2015, 77, pp.199-215. In order to investigate cumulative damage in fatigue, a multi-level fatigue programme has been carried out on an austenitic stainless steel AISI 304L. All the tests have been performed under controlled strain-amplitude conditions, with several changes of levels up to rupture; values of strain-amplitude were included between 0.20% and 0.80%. The present experimental programme shows that applying a linear damage rule (LDR), also referred to as Palmgren–Miner’s rule, has been demonstrated to be unreliable in some cases. A loading sequence (loading history) effect is clearly shown for the two-level sequence tests; application of the LDR leads to residual fatigue-life overestimation for high-to-low loading (H–L) sequences whereas residual fatigue-life is underestimated for low-to-high loading (L–H) sequences. The multi-level and block tests, undertaken in this campaign, confirm also a possible non-verification of the LDR. Within this framework, the double linear damage rule (DLDR) has been tested. Its application would seem to be promising as an additional approach in certain situations. However, complex sequences and random fatigue tests are still needed to draw a conclusion, and to more clearly evaluate the conditions where use of the LDR would not be sufficient. (10.1016/j.ijfatigue.2015.02.010)
  DOI : 10.1016/j.ijfatigue.2015.02.010
• From damage to fracture, a modelization based on moving discontinuities and layers
  
  • Stolz Claude
  Applied Mechanics and Materials, Trans Tech Publications, 2015, 784 (784), pp.325-333. A damage modelization is proposed based on a continuous transition from undamaged to damaged material. The evolution of damage is associated with a moving layer of finite thickness $l_c$, then initiation and propagation of damage can be unified in the same constitutive law. The driving force associated to the layer motion is a generalized release rate of energy. Using a normality rule based on this force the solution of the rate boundary value problem of propagation and displacement satisfies a variational inequation. Applications of the model are proposed. (10.4028/www.scientific.net/AMM.784.325)
  DOI : 10.4028/www.scientific.net/AMM.784.325