Publications

2026

• Analytical and experimental study of turbulence-induced vibrations in a cantilever-mounted coaxial cylinder
  
  • Plado Costante Loucas
  • Lagrange Romain
  • Kocher Maud
  • Puscas Maria Adela
  Journal of Fluids and Structures, Elsevier, 2026, 147, pp.104678. This paper investigates turbulence-induced vibrations in a confined annular flow configuration representative of pressurized water reactor internals. The experimental setup consists of a rigid inner cylinder mounted on two flexible rectangular plates inside a cylindrical vessel. Building on our previous work, analytical expressions for the fluid-elastic forces in quiescent fluid are derived, accounting for added mass, damping, partial immersion, viscous, and confinement effects. Theoretical predictions of the natural frequencies for various filling heights are obtained and systematically validated against experimental measurements. A new nondimensional formulation of the governing equations further yields an analytical expression for the root mean square displacement under turbulent forcing. The root mean square prediction is based on an effective homogeneous turbulence model characterized by a prescribed pressure power spectral density and correlation lengths drawn from the literature. Although dedicated measurements indicate that the turbulence in the present configuration is not strictly homogeneous, introducing a calibrated cut-off reduced frequency in the pressure spectrum yields a consistent and quantitatively accurate description of the root mean square response as a function of reduced velocity. (10.1016/j.jfluidstructs.2026.104678)
  DOI : 10.1016/j.jfluidstructs.2026.104678
• Internal combination resonance in a Micro Electro-Mechanical three-axis gyroscope: Experimental results and reduced-order modelling via invariant manifolds
  
  • Colombo Alessio
  • Villa Marco
  • Morelli Federico
  • Fedeli Patrick
  • Touzé Cyril
  • Frangi Attilio
  Mechanical Systems and Signal Processing, Elsevier, 2026, 260, pp.114933. This work investigates internal combination resonance in a Micro-Electro-Mechanical System (MEMS) three-axis gyroscope, where energy couples among three vibrational modes via the relationship ω1 + ω2 ≈ ω3 . The phenomenon is first characterised experimentally through frequency response measurements and spectrograms, revealing paired resonance peaks that emerge only under dual-frequency excitation. A theoretical framework grounded in complex normal form theory is then developed, deriving analytical expressions for the frequency-response curves which are shown to replicate the experimental findings. A reduced-order model of the fully coupled electromechanical problem is constructed via Direct Parametrisation of Invariant Manifolds applied to the full finite element mesh (1.3 million degrees of freedom), demonstrating quantitative agreement with experiments and validating the predicted mechanisms. By combining invariant manifold parametrisation with complex normal form theory, the methodology bridges the gap between analytical understanding and practical finite element reduction, yielding explicit solutions for nonlinear phenomena whilst maintaining computational efficiency for large-scale systems. The results validate invariant manifold methods as a robust tool for MEMS design and control applications. (10.1016/j.ymssp.2026.114933)
  DOI : 10.1016/j.ymssp.2026.114933
• Numerical benchmark to assess sensitivity to spatial discretization in quasi-static fracture simulations : Application to phase-field models
  
  • Zembra Edgar
  • Loiseau Flavien
  • Lazarus Véronique
  • Henry Hervé
  , 2026. Numerous numerical methods based on Linear Elastic Fracture Mechanics (LEFM), such as phase-field fracture models, enable the solution of crack propagation problems. Despite established mathematical properties (e.g., Γ-convergence), their numerical discretization can introduce systematic biases that persist even with spatial mesh refinement, such as artificial anisotropy in fracture properties at the element scale. Although acknowledged, these biases remain underexplored in practice. To address this gap, this work introduces a numerical benchmark for quantitatively evaluating discretization-induced biases. The benchmark focuses on the propagation of an off-centered crack in a band subjected to a sliding tensile load, where the crack follows an exponentially decaying trajectory toward the band center. This path is verified against a sharp crack LEFM reference solution. This non-trivial yet well-characterized crack path offers a robust basis for the quantitative assessment and the comparison of different crack propagation solvers. To illustrate this benchmark, we assess two phase-field implementations: one based on the finite element method and another on the finite difference method. These simulations reveal that discretization indeed introduces local artificial anisotropy. For structured meshes, crack path curvature is not captured, even for element sizes considered small enough in classical practice. For unstructured meshes, while the path is well-captured at smaller sizes, oscillations in the predicted trajectory are observed. Used here to assess the discretization biases of two specific numerical methods, this benchmark test is intended to evaluate other numerical methods for simulating crack propagation.
• Développement d’un modèle prédictif de l’usure pour les composants REP
  
  • Fayard Jean-Luc
  • Bentivegna Filippo
  • Breuze Matthieu
  • Prabel Benoit
  • Maitournam Habibou
  • Stolz Claude
  , 2026. Les composants internes des réacteurs à eau pressurisée sont soumis à des sollicitations mécaniques et thermohydrauliques répétées, conduisant à des contacts de type impact-glissement, glissement ou fretting. Ces sollicitations peuvent entraîner une usure progressive des matériaux, caractérisée par une perte de matière et une modification de la géométrie des surfaces en contact. La prédiction de cette évolution constitue un enjeu important pour l’analyse de la durée de vie des composants, la maintenance et la sûreté des installations. Les modèles classiques d’usure, tels que la loi d’Archard ou les lois fondées sur l’énergie dissipée par frottement à la surface de contact, permettent de corréler certains résultats expérimentaux. Cependant, les coefficients associés à ces approches dépendent fortement de la géométrie, du chargement, du couple de matériaux et de l’environnement. Cette dépendance limite leur portée prédictive lorsque les conditions d’application changent. Pour dépasser ces limitations, des approches plus physiques peuvent être envisagées, notamment le modèle fondé sur l’endommagement proposé par Caradec et al., dans lequel la perte de matière est associée à l’accumulation progressive d’un endommagement local. Ce travail s’inscrit dans le développement d’une méthodologie numérique de prédiction de l’usure par fretting, appliquée à une configuration cylindre/plan modélisée en déformations planes sous Cast3M. Le chargement considéré consiste en une mise en contact sous effort normal constant, suivie d’un déplacement tangentiel cyclique imposé. Avant les calculs d’usure, le cadre numérique est validé à partir de la solution analytique de Hertz, en comparant la pression de contact et les contraintes en profondeur. Cette étape permet de préciser les choix de maillage, de type d’éléments et de post-traitement des champs mécaniques. Une nouvelle stratégie de maillage est ensuite mise en place afin de conserver un raffinement suffisant dans la zone de contact et de glissement, tout en réduisant le coût numérique des calculs multi-cycles. Le raffinement local est piloté par le nombre d’éléments dans la demi-largeur de contact hertzienne. Des études de sensibilité sont également réalisées afin de fixer les paramètres numériques nécessaires aux simulations d’usure, notamment la discrétisation du cycle de fretting et le facteur d’accélération utilisé pour réduire le coût des calculs multi-cycles. La contribution présente la comparaison de deux approches de simulation de l’usure : l’approche énergétique et l’approche fondée sur l’endommagement. Ces deux approches sont appliquées à un essai de fretting simple issu des travaux de Marc et al., pour lequel la mesure expérimentale disponible est le volume usé final. Enfin, une troisième approche est introduite. Elle se fonde sur l’exploitation des champs de contraintes et de déformations sous la zone de contact. L’objectif est d’identifier une grandeur mécanique caractéristique de l’usure dans le volume de matière, puis de définir un critère permettant de déterminer les zones usées. La pertinence de cette approche est évaluée en comparant ses prédictions à celles des approches fondées sur l’énergie dissipée par frottement à la surface de contact et sur l’endommagement local.
• On the validity limits of the parametrisation method for invariant manifolds: an assessment of practical criteria for vibrating systems
  
  • de Figueiredo Stabile A.
  • Grolet A.
  • Vizzaccaro A.
  • Touzé Cyril
  Nonlinear Dynamics, Springer Verlag, 2026, 114 (16), pp.1058. The parametrisation method for invariant manifolds is a powerful technique for deriving reducedorder models in the context of nonlinear vibrating systems with geometric nonlinearities, allowing accurate computations of nonlinear normal modes. Thanks to arbitrary order asymptotic expansions, converged results are within reach and directly applicable to finite element structures. However, since it relies on a local theory and asymptotic expansions, the results are only valid up to a given amplitude, which defines the convergence radius of the approximation. The aim of this contribution is to investigate the validity limits of the approach and review the existing error estimates, with the concrete objective of proposing a practical approach to estimate the validity range during the computation, thus producing safe bounds within which the reduced-order model can be used. Three different criteria are assessed. The first one uses the error in the invariance equation as the distance to the fixed point increases. The second one is adapted from an upper bound criterion derived for normal form transforms and based on the potential singularities of the homological operator. The third one uses validity limits of series expansion through Cauchy and d'Alembert rules, which can be tested either on the reduced dynamics coefficients or those of the nonlinear mappings. The criteria are tested on a number of different examples that are representative of the situations encountered when dealing with nonlinear vibrations. The Duffing equation serves as a first benchmark that allows considering conservative oscillations, forced systems at primary resonance, and superharmonic resonance. The investigations are then extended to a vibrating system with two degrees of freedom. Finally, the different criteria are assessed on a finite element beam structure, and guidelines are formulated to generalise their practical use and produce accurate and easy-to-use error bounds in the context of model order reduction for nonlinear vibrating structures. (10.1007/s11071-026-12956-0)
  DOI : 10.1007/s11071-026-12956-0
• Magnetic and electromagnetic vibration absorbers
  
  • Lo Feudo Stefania
  • Li Haiqin
  • Cumunel Gwendal
  • Li Ang
  • Touzé Cyril
  , 2026, 254, pp.171-202. In this chapter, two different devices that use magnetic and electromagnetic forces for the purpose of vibration mitigation, are presented. First, a magnetic vibration absorber, solely relying on magnetic forces to create a nonlinear restoring force, is studied. Thanks to an accurate representation of the magnetic field and together with geometric design rules, the device is capable of displaying different kind of linear and nonlinear forces and can be thus easily adjusted to create either a nonlinear tuned vibration absorber (with positive linear stiffness), a nonlinear energy sink (NES with vanishing linear stiffness and thus only nonlinear restoring force), or a bistable NES with negative linear restoring force. The performance of the different absorber choices is analysed to mitigate the vibration of a three-storey structure. Second, an electromagnetic vibro-impact NES is investigated. The system consists of a linear oscillator equipped with multiple turns of coil, coupled to a magnet attachment that undergoes two-sided inelastic impacts. The device is analysed in terms of vibration mitigation, and it is shown that the addition of the electromagnetic forces enhances the robustness of the device as compared to its counterparts that use only mechanical forces. (10.1007/978-3-032-23215-1_7)
  DOI : 10.1007/978-3-032-23215-1_7
• Coupled CFD–DEM modelling of damage to a breakwater armour layer made of Antifer cubes exposed to regular waves
  
  • Barcet Matthieu
  • Benguigui William
  • Laviéville Jérome
  • Benoit Michel
  • Fede Pascal
  • Bonometti Thomas
  Ocean Engineering, Elsevier, 2026, 363, pp.126525. The study aims to demonstrate the capabilities of a CFD-DEM (Computational Fluid Dynamics -Discrete Element Method) to predict wave-structure interactions and armour units motions in a breakwater composed of Antifer cubes. To do so, the fluids (air and water) are simulated using a Eulerian-Eulerian CFD solver and the contacts between the blocks and the slope are solved using a DEM code. The codes were coupled and validated in a previous study, using idealised configurations that did not reflect actual coastal structures. This work extends the previous study to a semi-realistic configuration where the blocks are positioned along a inclined wall to represent the armour layer of a rubble-mound breakwater. Both experiments and simulations are performed, and the results are compared to evaluate the accuracy of the model. The comparisons are made on the number of displaced armour units and on the amplitude of their displacement.<p>Two regular configurations are studied: a one-layer configuration and a two-layers configuration which improves the stability and better represents realistic breakwaters. Finally, simulations are performed on a randomly generated armour layer which the goal of improving the realism of the breakwater.</p> (10.1016/j.oceaneng.2026.126525)
  DOI : 10.1016/j.oceaneng.2026.126525
• Modal experimental continuation of an aircraft during ground vibration test
  
  • Chukwu Augustus
  • Stephan Cyrille
  • Touzé Cyril
  • Doaré Olivier
  , 2026. Phase-locked loop experimental continuation method is extended to multi-input multi-output testing, for the identification of the nonlinear dynamics of an aircraft during ground vibration test. More specifically, backbone curve tracking in moderately nonlinear regimes is investigated. Force appropriation and phase control over multiple excitation points are presented, and particular attention is devoted to introduce weighted mode purity indices, to robustly assess the nonlinear mode isolation. A full-scale aircraft is used to illustrate the methods, revealing the benefits that can be obtained for the identification of nonlinear characteristics. (10.2514/6.2026-4777)
  DOI : 10.2514/6.2026-4777
• Path-following methods for quasi-static crack propagation: Application to phase-field fracture
  
  • Loiseau Flavien
  • Lazarus Véronique
  , 2026. Numerical simulations of quasi-static crack propagation in brittle materials often suffer from numerical instabilities, such as snapback events, due to structural softening. In variational phase-field fracture models, these instabilities manifest as abrupt crack jumps, thereby impeding physical validity, as the energy minimization is performed over a significant crack increment. Moreover, they often prevent incremental force boundary conditions, as they may lead to a loss of force balance as soon as the crack starts propagating. This study introduces path-following methods to mitigate such instabilities in quasi-static phase-field fracture simulations. We evaluate existing methods alongside a novel approach, Control by Maximum Strain Increment Outside the Crack (CMSIOC), which enforces stable crack growth by constraining strain increments in the uncracked region. All studied methods rely on a single scalar control equation that depends solely on displacement fields, enabling integration into classical staggered solvers without major changes. Performance is assessed via three benchmark problems of increasing complexity, with results compared against Linear Elastic Fracture Mechanics (LEFM) references based on Griffith's criterion and the G-max criterion. Our findings show that CMSIOC: 1. Accurately follows the equilibrium path, avoiding abrupt crack jumps while preserving physical validity; 2. Supports force-controlled boundary conditions without loss of force balance during propagation; 3. Ensures uniform incremental crack growth, properly distributing the computational efforts across load steps. These results highlight CMSIOC's robustness as a model- and problem-independent solution for stable phase-field fracture simulations.
• Path-following methods for phase-field simulation of quasi-static crack propagation
  
  • Loiseau Flavien
  • Lazarus Véronique
  International Journal of Solids and Structures, Elsevier, 2026, 334, pp.113974. The variational approach to fracture, particularly through its regularization as a phase-field model, has become a widely used tool for simulating the quasi-static propagation of cracks in structures. However, classic incremental loading can induce unstable crack growth, violating the quasi-static assumption, and in some cases, leads to a loss of force balance, preventing self-consistency and the estimation of dissipated energy during snapback instabilities. To address this challenge, path-following methods are investigated. Their aim is to adjust the applied load so that it stays at the propagation threshold, thereby preserving the quasi-static assumption and ensuring equilibrium solutions. In this work, we apply and evaluate multiple path-following methods within the framework of variational phase-field fracture models, which are developed to regularize linear elastic variational sharp crack evolution problems. Our study pursues two objectives. First, we review several existing path-following methods, with a focus on partitioned strategies based on the displacement field, which decouple the path-following control equation from the rest of the system, facilitating easier integration with staggered solvers. In addition, we introduce a new path-following method whose particularity is to limit the maximum strain increment outside the cracked regions. Second, we use the Γ-convergence to the sharp crack model to evaluate these methods across three crack propagation problems of increasing complexity. The comparison demonstrates that the proposed path-following method offers a simple yet highly effective approach to capture the equilibrium path in phase-field fracture simulations. This method robustly maintains the quasi-static assumption, ensuring physically meaningful results. By enabling accurate estimation of the energy dissipated during snapback instabilities, it paves the way for the rational design of more resistant heterogeneous materials. (10.1016/j.ijsolstr.2026.113974)
  DOI : 10.1016/j.ijsolstr.2026.113974
• Path-Following Methods for Quasi-Static Crack Propagation in Phase-Field Fracture Models
  
  • Loiseau Flavien
  • Lazarus Véronique
  , 2026. Quasi-static crack propagation simulations in brittle materials often suffer from numerical instabilities, such as snapback events, due to structural softening. In phase-field fracture models, these instabilities manifest as abrupt crack jumps, impeding the physical validity as the energy minimization is performed over a significant crack increment. Moreover, they often prevent the imposition of incremental force boundary conditions, as they may lead to a loss of force balance as soon as the crack starts to propagate. This study explores the application of path-following methods to variational phase-field fracture simulation. It aims to identify a method that is robust, model- and problem-independent, and easy to implement in a classic staggered solver. To this aim, we evaluate existing path-following techniques alongside a novel proposition: Control by Maximum Strain Increment Outside the Crack (CMSIOC), which ensures stable crack propagation by limiting strain increments in the uncracked region. All studied methods introduce a single scalar control equation dependent solely on displacement fields, enabling seamless integration into classic staggered solvers without requiring significant modifications. To assess the performance of these methods, we compare them across three numerical benchmark problems of increasing complexity. For reference, we employ a sharp crack model from Linear Elastic Fracture Mechanics (LEFM) based on Griffith's theory and the G-max criterion. Our findings demonstrate that CMSIOC reliably follows the equilibrium path and closely replicates LEFM benchmark solutions. Hence, it enables the capture of snapback instabilities without abrupt crack jumps, also allowing for force-controlled boundary conditions without loss of force balance. Another advantage is that it provides nearly uniform crack growth per increment, thereby balancing the computational cost across load steps. This presentation will: (1) recall the concept of equilibrium paths in fracture mechanics, (2) introduce the CMSIOC, detailing its theoretical foundation and implementation, (3) present the results of the benchmark problems, and (4) conclude on this work with practical recommendations for integrating path-following methods into phase-field fracture simulations.
• Experimental and Numerical Investigation of Aeroacoustic Installation Effects on Small-Scale Multi-Rotor Systems in Hover
  
  • El Ouni Khalil
  • Simiao Pitta Vinicius
  • Cotté Benjamin
  , 2026. This paper investigates aeroacoustic installation effects in small-scale multi-rotor systems in hover through a combined experimental and numerical approach. Measurements were conducted in an anechoic chamber for three configurations: an isolated propeller, a propeller with its supporting arm, and a tandem propeller arrangement representative of a quadcopter layout. The propellers operate at very low Reynolds numbers, around 3 × 10 4 , where transitional flow and viscous effects are important. A mid-fidelity aerodynamic model based on a NonLinear Vortex Lattice Method is considered to predict the aerodynamic forces used as input to Hanson's tonal noise model. The aerodynamic simulation is shown to be very sensitive to airfoil polar data. In the tandem configuration, unsteady loading noise plays a significant role. The results show that a small variation of rotational speed of rotors induces a change of directivity for the unsteady loading noise and the total noise. (10.2514/6.2026-3349)
  DOI : 10.2514/6.2026-3349
• Theoretical Study of Turbulence Ingestion Noise for Propellers in Nonuniform Flows
  
  • Lavanant Romain
  • Cotté Benjamin
  • Serre Gilles
  • Mercier Jean-François
  , 2026. This paper presents an analytical model for predicting the broadband noise radiated by a propeller ingesting a spatially nonuniform turbulent flow. The formulation, derived from Goldstein's acoustic analogy, expresses the far-field power spectral density through azimuthal Fourier decompositions of the incident heterogeneous turbulence spectrum, thereby retaining inter-strip and blade-to-blade correlations along the blade span. The spatially varying turbulence parameters (integral length scale and turbulence intensity) that serve as inputs to the spectrum models are derived analytically from Prandtl's mixing-length shear-production approach. Two turbulence spectrum formulations are considered: a heterogeneous isotropic von Kármán spectrum and a heterogeneous anisotropic Kerschen-Gliebe spectrum. A comparison with experimental data for a rotor ingesting a turbulent boundary layer highlights the respective roles of anisotropy and heterogeneity. On the one hand, an isotropic turbulence description fails to reproduce the measured spectral humps (haystacks) at blade passing frequency harmonics; anisotropy with a stretched streamwise length scale is required. On the other hand, the heterogeneous model captures the progressive attenuation of higher-order haystacks through destructive interference between contributions of varying eddy sizes across the propeller disk, an effect that homogeneous models systematically overpredict. (10.2514/6.2026-3517)
  DOI : 10.2514/6.2026-3517
• Extension du domaine de validité des modèles réduits fondés sur la méthode de paramétrisation de variétés invariantes : continuation analytique automatisée de cycles limites
  
  • de Figueiredo Stabile André
  • Grolet Aurélien
  • Touzé Cyril
  , 2026. Extension du domaine de validité des modèles réduits fondés sur la méthode de paramétrisation de variétés invariantes : continuation analytique automatisée de cycles limites
• Accounting for grain crushing and pore collapse for strain localization in rocks
  
  • Collins-Craft Nicholas Anton
  • Sulem Jean
  • Stefanou Ioannis
  • Einav Itai
  , 2026. We present a model for crushable granular rocks by embedding breakage mechanics in the Cosserat continuum. This model features a dependence on an enriched set of state variables (the elastic strains and curvatures, the density, the solid fraction, and the breakage state variable), demonstrates a dependence of the yield surface on the Lode angle, breakage and solid fraction, and evolution laws that tightly couple the competing processes. We then outline the notion of linear stability analysis and how we use this technique to obtain both the thickness and orientation of any shear bands that may form in the system. The model is then calibrated from data available in the literature on Fontainebleau sandstone and other similar granular rocks. We compare the model predictions with experimental measures of both the stress-strain response, and the width and angle of shear bands, and find good agreement with the results that have been previously reported.
• Bubble rise dynamics in a quiescent liquid and impact on a cylinder
  
  • Beltran F.
  • Benguigui W.
  • Merigoux N.
  • Bonometti T.
  • Colin C.
  International Journal of Multiphase Flow, Elsevier, 2026, 199 (May), pp.105672. This study investigates the dynamics of a single bubble rising in a quiescent liquid and impacting a fixed cylinder using a resolved two-fluid approach. The resolved two-fluid approach is validated against experimental data and compared with a one-fluid approach through 2D axisymmetric and 3D simulations across a wide range of Reynolds and E &amp; ouml;tvos numbers, and density ratios. The two-fluid model accurately reproduces the bubble shape, terminal velocity, and impact dynamics, showing agreement with both experimental observations and the one-fluid approach. A detailed analysis on the impact force coefficient exerted by the bubble on the cylinder is conducted with the two-fluid approach by varying the bubble's Reynolds and E &amp; ouml;tvos numbers and the density, viscosity, and bubble-to-cylinder diameter ratios (Reb is an element of [1, 80],Eo is an element of [10, 116], rho l/rho g is an element of [25, 1000], mu l/mu g is an element of [10, 100], and db/Dc is an element of [0.5, 1.0]). This study reveals that, when varying one dimensionless number at a time, the bubble Reynolds number has the most significant influence on the impact force coefficient, followed by the bubble-to-cylinder diameter ratio and the E &amp; ouml;tv &amp; ouml;s number, while the effects of viscosity and density ratios are weaker. A correlation on the impact force coefficient (associated to the force applied by the bubble on the cylinder at impact) is proposed and may be useful for Euler-Lagrange point-particle methods. (10.1016/j.ijmultiphaseflow.2026.105672)
  DOI : 10.1016/j.ijmultiphaseflow.2026.105672
• An augmented lagrangian XFEM formulation for stabilizing near-tip singularities in fluid-driven fractures modeling
  
  • Faivre Maxime
  • Martin Alexandre
  • Massin P.
  • Giot Richard
  • Golfier Fabrice
  Computer Methods in Applied Mechanics and Engineering, Elsevier, 2026, 451, pp.118649. This paper enhances a fully-coupled hydromechanical model developed in the XFEM by introducing a new augmented Lagrangian formulation to stabilize the hydrodynamical behavior at interfaces. While the original model stabilized the mechanical part, it inadequately represented pressure fields near high gradients, particularly at the tip. The new formulation projects fields into an appropriate function space, enabling the use of a standard lumping technique on the mass matrix from the discretized time derivative in Reynolds’ lubrication equation. It also incorporates a lumping approach tailored to parabolic PDEs to stabilize the bulk behavior. Since Reynolds’ equation becomes singular near the tip in impermeable porous media, a virtual opening is introduced to regularize the fluid flow. The improved model is validated with analytical solutions, demonstrating its effectiveness in eliminating spurious pressure oscillations near discontinuities. (10.1016/j.cma.2025.118649)
  DOI : 10.1016/j.cma.2025.118649
• Un modèle filaire hybride poutre-coque pour la rupture de tuyauteries à haute énergie
  
  • Coron Amalio
  , 2026. Les entreprises du secteur de l'énergie exploitent des installations comportant de vastes réseaux de tuyauteries. La compréhension et la modélisation du comportement de ces systèmes, aussi bien en fonctionnement nominal qu'en situation accidentelle, sont cruciales. Cette thèse présente le développement d'un modèle filaire haute fidélité pour la modélisation de réseaux de tuyauteries industriels en situation accidentelle.Des modélisations filaires enrichies de tuyauterie ont été développées dans la littérature. Depuis les travaux de von Kármán en 1911, ces modèles ont suscité un intérêt particulier, notamment dans les contributions de Wood, Bathe et Almeida, Militello et Huespe, Weicker, Karamanos et Arbind. Contrairement aux modèles de poutre classique, le point commun des modèles enrichis réside dans la prise en compte des déformations des sections. Celles-ci sont décrites par une modélisation en coque cylindrique de la tuyauterie, dont la cinématique est développée en série de Fourier sur la section circulaire. La cinématique ainsi proposée est donc plus riche et plus complète qu'un modèle de poutre simple.Un tel modèle a été développé à EDF R&D lors de travaux antérieurs à cette thèse. Il combine un comportement de poutre et de coque pour décrire la déformation globale de la tuyauterie ainsi que la déformation des sections transverses. Les hypothèses d'Euler-Bernoulli sont utilisées pour le modèle poutre et les hypothèses de Kirchhoff-Love sont retenues pour la cinématique de coque. De plus, les déplacements de la coque sont développés en série de Fourier en fonction de la coordonnée angulaire de la section. Les coefficients de la série de Fourier constituent alors les inconnues cinématiques du modèle, en complément de ceux du modèle de poutre. Ce modèle de tube sain a été discrétisé par la méthode des éléments finis et implémenté dans un code de calcul en dynamique explicite.Dans cette thèse, l'élément hybride poutre-coque pour les tuyauteries saines est étendu pour l'étude des fissures progressives. La cinématique de la tuyauterie saine est donc complétée pour représenter une tuyauterie fendue. Dans cette perspective, des inconnues cinématiques supplémentaires sont incorporées au modèle pour permettre l'ouverture des sections transverses.Cette nouvelle cinématique est construite en étudiant un tube fendu sur toute sa longueur sous des chargements dans chaque direction de l'espace. Ce tube est modélisé comme un anneau fendu. La réponse mécanique de cet anneau fendu est exprimée en fonction de la coordonnée angulaire de la section de manière cohérente avec la formulation coque développée en série de Fourier. Les nouveaux termes sont ajoutés à ceux de la coque, avec les nouvelles composantes du déplacement associé. Les résultats de cette nouvelle cinématique sont ensuite analysés. Un nouvel élément fini, appelé tube fendu, a été développé sur la base de cette cinématique enrichie.Dans un premier temps, la capacité de la nouvelle cinématique à représenter le comportement d'une tuyauterie fissurée est évaluée. Les champs de déplacement d'une simulation éléments finis de coque sont projetés sur les composantes de la cinématique de tube fendu. Chaque champ et sa projection associée sont comparés.Les résultats de simulations numériques du modèle de tube fendu sont ensuite comparés avec des solutions de référence. Ces solutions sont soit analytiques, soit numériques obtenues par des simulations en éléments de coque. Les cas de comparaisons sont d'abord des cas uniformes de tuyau fendu sous plusieurs chargements (pression, force linéique). Le modèle est ensuite utilisé pour la représentation d'un tuyau qui comporte une partie saine et une partie fissurée reliées.
• Steady-State Algorithm with Structural Periodicity: Application to Computation of Railways’ Ballast Plastic Strains
  
  • Badinier Thibault
  • Maiolino Siegfried
  • Maitournam Habibou
  Geotechnics, MDPI, 2026, 6 (1), pp.29. The geometry of ballasted railway tracks is crucial for ensuring railway safety and efficiency. This paper introduces the use of innovative steady-state algorithms designed to compute plastic strains in linear geotechnical structures like railway ballast layers, within Finite Element Methods (FEMs). Facing the specificities of moving loads, traditional step-by-step algorithms, while simple and adaptable, are computationally expensive and time-consuming. In contrast, the proposed steady-state algorithms leverage an Eulerian approach to describe the movement of loads significantly reducing computational time while maintaining accuracy. This paper proposes these algorithms as a methodological improvement and demonstrates the applicability and efficiency of the method for non-periodic structures, as well as for periodic structures, such as railway tracks with evenly spaced sleepers. This paper demonstrates the applicability and efficiency of theses algorithms through comparative studies with traditional methods on typical railway structures. The results show that the presented algorithm not only matches the accuracy of step-by-step methods but also drastically reduces computation time and data storage requirements. This advancement has practical applications for railway infrastructure managers, enabling more efficient and accurate predictions of track geometry evolution and preventing incidents through improved maintenance strategies. (10.3390/geotechnics6010029)
  DOI : 10.3390/geotechnics6010029
• Determination of the Effective Permeabilities in Partially Saturated Porous Media, Using the Periodic Homogenization Technique
  
  • Bouchard Raphaël
  • Bourbatache Mohamed-Khaled
  • Le Tien Dung
  • Millet Olivier
  • Stefanou Ioannis
  Transport in Porous Media, Springer Verlag, 2026, 153 (4), pp.47. Abstract In this study, we address determination of the effective permeabilities in rigid, partially saturated porous media for an immiscible two-phase Newtonian fluid flow. The periodic homogenization technique is applied to derive macroscopic flow laws for two-phase systems from the pore-scale Navier–Stokes equations governing immiscible fluids. Two distinguished cases are considered: two incompressible fluids (case 1) and an incompressible fluid with a compressible one (case 2). In both cases, the homogenized result shows the independence of the macroscopic laws and the closure problems on the fluid compressibility, except for the macroscopic mass conservation equation. Finally, numerical simulations are performed by solving the closure problems for a given interface position determined from the phase-field simulations, in order to analyze the role of each effective permeability in the generalized Darcy’s law for several fluid mixtures and different porosity. The numerical results offer insights into the influence of microstructure, fluid properties, and capillary bridge distribution on the effective permeabilities. (10.1007/s11242-025-02265-2)
  DOI : 10.1007/s11242-025-02265-2
• Characterization of static and dynamic stall noise of a NACA0012 airfoil using the Lattice Boltzmann Method
  
  • Grimberg Milo
  • Cotté Benjamin
  • Jondeau Emmanuel
  • Vienne Lucien
  • Clair Vincent
  • Pestana Miguel
  • Boudet Jérôme
  , 2026. The prediction of aerodynamic and aeroacoustic phenomena associated with airfoil stall remains a challenging task due to the strong flow unsteadiness, large-scale separation, and broadband noise generation involved. In this study, the Lattice Boltzmann Method (LBM) is assessed for the simulation of static and dynamic stall noise of a NACA0012 airfoil by direct comparison with experimental data obtained during a dedicated measurement campaign [1]. Numerical simulations are performed at a Reynolds number of Re_c = 6.25 × 10 5 and a Mach number of Ma = 0.21 for both fixed and periodically pitching configurations. Static simulations cover angles of attack from 0° to 24° , while the dynamic case consists of a sinusoidal pitching motion at 4 Hz at a mean angles of 15° with an amplitude of ±7° . The numerical results are compared to experimental measurements of pressure coefficient distributions, lift coefficients, wall-pressure spectra, and farfield noise spectra. For the static configuration, the LBM simulations reproduce the main aerodynamic trends observed experimentally across pre-stall and post-stall regimes. A systematic offset between numerical and experimental results is identified and attributed to a difference between the nominal geometric angle of attack and the effective aerodynamic incidence. Once this offset is taken into account, good agreement is obtained in terms of pressure distributions, lift polar evolution, and far-field noise levels. In the dynamic configuration, the LBM captures the characteristic lift hysteresis associated with dynamic stall, as well as the temporal modulation of aerodynamic and acoustic quantities throughout the pitching cycle. In addition to integral metrics, the analysis of instantaneous fields provides qualitative insight into the spatial localization of dominant acoustic source regions, highlighting the role of the boundary layer and the trailing edge in noise radiation. Overall, the results demonstrate that the Lattice Boltzmann Method constitutes a reliable approach for predicting the aerodynamic and aeroacoustic response of airfoils under static and dynamic stall conditions at moderate Mach numbers.
• Reduced order modelling for shell finite element structures using the direct parametrisation of invariant manifolds: Hardening/softening transition, resonant dynamics and mode selection
  
  • Xia Zixu
  • Touzé Cyril
  • Cong Yu
  • Gu Shuitao
  • Feng Zhi-Qiang
  Thin-Walled Structures, Elsevier, 2026, 220, pp.114329. The accurate simulation of the nonlinear dynamics of thin-walled structures is a critical but computationally demanding task. In this contribution, a 7-parameter solid-shell finite element formulation is combined with the direct parametrisation method for invariant manifolds (DPIM), in order to derive accurate and efficient reduced-order models (ROM) accounting for geometric nonlinearity. The method is illustrated in its ability to be used with different yet complementary purposes. On the one hand, low-order tractable models can be obtained, providing simple ROMs that are amenable to giving physical insights and understanding. On the other hand, higher-order solutions are available within the same framework, hence providing accurate and converged solutions. This scheme is carried out on examples with increasing complexity. First, the transition from hardening to softening behaviour for thin shells with shape imperfections is investigated. The 1:2 resonance as a driver of the change of type of nonlinearity is analysed, and a full understanding of the smooth transition is illustrated. Then, shells with varying thicknesses are investigated, and the case of 1:2 internal resonance is further investigated, showing the emergence of isolated solution branches (isola). In the course of the numerical simulations, it is shown how the reduced basis needs to be enlarged to take into account more and more complex resonance scenarios, and some guidelines are provided in order to help the analyst in selecting the master modes. The numerical results highlight the ability of the reduced-order models to provide a fully comprehensive and integrated framework for the understanding and accurate prediction of thin shells' nonlinear dynamics. (10.1016/j.tws.2025.114329)
  DOI : 10.1016/j.tws.2025.114329
• A harmonic balance normal form parametrisation for single mode reduction of nonlinear vibrating systems
  
  • Grolet Aurélien
  • Touzé Cyril
  • de Figueiredo Stabile André
  • Thomas Olivier
  Communications in Nonlinear Science and Numerical Simulation, Elsevier, 2026, 157, pp.109708. This paper introduces a model-order reduction technique for lightly damped nonlinear vibrating systems. By combining calculation details that are specific to the harmonic balance method, the asymptotic numerical method, and the normal form style parametrisation for invariant manifolds, a complete procedure that can cope with single-mode reduction is detailed. Introducing harmonic decomposition in the process allows for a different treatment of the temporal information of the solution, which comes with advantages as compared to normal form expansions based on polynomial expansions. The computation proceeds with two nested loops on both the harmonics and the polynomial degree expansion. A decisive advantage of the procedure is its ability to compute a new expansion from a known solution, which allows the derivation of amplitudedependent piecewise reduced order models (ROMs), together with an integrated procedure that can switch from the invariant manifolds computation attached to either fixed points or limit cycles. Once the validity limit of a first expansion is met, the procedure can restart from a point where convergence is reached and produce a new ROM. This feature has the potential to overcome the well-known limitations of asymptotic expansions associated with the parametrisation method for invariant manifolds, and is derived here only for conservative systems. The whole analysis also clearly establishes the links existing between the normal form approach and computations based on the harmonic balance combined with the asymptotic numerical method. Examples of increasing complexity, starting from a Duffing equation, a two-degree-of-freedom system and a finite element beam model, are analysed, and comparisons with existing techniques are provided. (10.1016/j.cnsns.2026.109708)
  DOI : 10.1016/j.cnsns.2026.109708
• Review of "Asymptotic approaches for dealing with distorted crack geometries
  
  • Lazarus Véronique
  , 2026.
• Normal form computation of nonlinear dispersion relationship for locally resonant metamaterial
  
  • Wang Tao
  • Touzé Cyril
  • Li Haiqin
  • Ding Qian
  Physica D: Nonlinear Phenomena, Elsevier, 2026, 488, pp.135115. This article is devoted to the application of the parametrisation method for invariant manifold with a complex normal form style (CNF), for the derivation of higher-order approximations of underdamped nonlinear dispersion relationships for periodic structures, more specifically by considering the case of a locally resonant metamaterial chain incorporating damping and various nonlinear stiffnesses. Two different strategies are proposed to solve the problem. In the first one, Bloch's assumption is first applied to the equations of motion. The nonlinear change of coordinates provided by the complex normal form style in the parametrisation method is applied. This direct procedure, which applies first the wave dependency to the original physical coordinates of the problem, is referred to as CNF-BP (for CNF applied with Bloch's assumption on physical coordinates). In the second strategy, the nonlinear change of coordinates provided by the parametrisation method, which relates the physical coordinates to the so-called normal coordinates, is first applied. Then the periodic assumption is used, thus imposing a Bloch wave ansatz on the normal coordinates. This method will be referred to as CNF-PN (for CNF with a periodic assumption on normal coordinates). In the conservative case, the two CNF calculation strategies are first verified by comparing with the results from existing literature. Subsequently, two carefully selected examples demonstrate that the CNF-PN strategy exhibits superior capability in capturing complex wave propagation phenomena, whereas the CNF-BP strategy encounters limitations in handling non-fundamental harmonics and the nonlinear interactions between host oscillators. The influence of truncation order on the accuracy of CNF-PN is further examined, demonstrating its effectiveness in extending the validity limit. For underdamped systems, the CNF-PN is systematically compared against numerical techniques, a classical analytical perturbation technique (the method of multiple scales), and direct numerical time integration of annular chain structures. The results confirm the exceptional accuracy of the CNF-PN in predicting nonlinear dispersion relationships, damping ratios, invariant manifolds, and wave attenuation characteristics, as long as the validity limit of the asymptotic expansion is not reached. This advancement provides a novel and efficient analytical and numerical tool for studying nonlinear metamaterials. (10.1016/j.physd.2026.135115)
  DOI : 10.1016/j.physd.2026.135115