Publications

2023

• Moving layers and damage coupling with elasto-plasticity
  
  • Stolz Claude
  , 2023.
• Reduced order modeling of rotating structures featuring geometric nonlinearity with the direct parametrisation of invariant manifolds method
  
  • Martin Adrien
  • Opreni Andrea
  • Vizzaccaro Alessandra
  • Salles Loic
  • Thomas Olivier
  • Frangi Attilio
  • Touzé Cyril
  , 2023. The direct parametrisation method for invariant manifolds (DPIM) is applied to rotating structures. Reduced- order models of arbitrary order expansion can be derived for non-autonomous systems of nonlinear differential equations stemming from finite element models of continuous structures. The method is applied to a rotating simplified fan blade with comparisons to full order model simulations.
• A reduced model for conical contact dedicated to flexible multi-body dynamics
  
  • Serre Matthieu
  • Prabel Benoit
  • Maitournam Habibou
  , 2023. An efficient time integration scheme for flexible multi-body dynamics with frictional impacts dedicated to finite element simulations is presented. Considering bulky compact components the linear theory of elastodynamics may be applied and two separate explicit Newmark integration schemes coupled only by non-linear forces are used for elastic vibration and rigid body dynamics respectively. After a brief study focused on conservation properties, a dedicated rigid-body integration scheme is selected. To avoid contact detection and classical mesh to mesh computation a parameteric study based on static computations is performed to express the reaction forces as analytical functions of few positional arguments. The penalty method is applied and combined with the Coulomb law to modelize impacts between the two colliding bodies. The results are then illustrated on a use case with configuration dependent contact geometry. Finally the global model aims at interpreting experiments on such configurations.
• On evolution of irreversible systems: computing analysis results
  
  • León Baldelli Andrés
  • Neukirch Sébastien
  , 2023, pp.15-16. What happens to the stability of critical equilibrium states, as time goes by? In evolutionary problems, structural effects play a key role. We study evolving systems, singularly perturbed and under constraints. Picture fracture as a process: as a phenomenon of natural evolution, it offers an instance of a particularly complex natural system showing pattern formation and jumps, unknown both in time and space.
• Propagation effects in the synthesis of wind turbine aerodynamic noise
  
  • Mascarenhas David
  • Cotté Benjamin
  • Doaré Olivier
  Acta Acustica, EDP Sciences, 2023, 7, pp.23. The sound field radiated by a wind turbine changes significantly with propagation distance, depending on the meteorological conditions and on the type of ground. In this article, we present a wind turbine noise synthesis model which is based on theoretical source and propagation models. The source model is based on Amietâ’s theory for the prediction of the trailing edge noise and the turbulent inflow noise. The trailing edge noise uses the wall pressure spectrum calculated with Leeâ’s model for the suction side and Goodyâ’s model for the pressure side. The Kolmogorov spectrum is used for the prediction of the turbulent inflow noise. To account for the propagation effects associated with atmospheric refraction and ground reflection, a wide angle parabolic equation in inhomogeneous moving medium is considered. The scattering due to the turbulence in the atmosphere is accounted for using the Harmonoise model. The synthesis method is based on the moving monopole model to accurately predict the amplitude modulations at the receiver, and uses cross-fading between overlapping grains to obtain the time signals from the frequency-domain prediction model. Finally, audio signals are provided for a few test cases to emphasize various propagation phenomena associated with wind turbine noise. (10.1051/aacus/2023018)
  DOI : 10.1051/aacus/2023018
• Finite element simulation of high cycle fretting wear using an implicit adaptive cycle jump
  
  • Caradec Quentin
  • Breuzé Matthieu
  • Maitournam Habibou
  • Prabel Benoit
  • Fayard Jean-Luc
  Wear, Elsevier, 2023, 522, pp.204703. Fretting motion between two contacting solids can, under gross slip conditions, induce wear. A finite element model and a simulation strategy aiming at predicting wear under fretting motion are presented. The numerical results obtained are compared with experimental data from the literature. The proposed simulation process is particularly suitable for computing high numbers of cycles. To this end, a cycle jump technique is used, and different integration schemes are investigated. Results show that instabilities may arise when an explicit scheme is used, which limits the size of the cycle jump. On the other hand, using an implicit scheme involves a trade-off between the possibility of considering a larger cycle jump and the number of iterations required for convergence. It is shown that the more cycles we perform, the faster the implicit scheme converges. Therefore, the implicit scheme is especially appropriate for high-cycle computations. Moreover, an adaptive cycle jump is used with the implicit scheme, enabling to accelerate the computations for high numbers of cycles. (10.1016/j.wear.2023.204703)
  DOI : 10.1016/j.wear.2023.204703
• Reduced-order modeling of geometrically nonlinear rotating structures using the direct parametrisation of invariant manifolds
  
  • Martin Adrien
  • Opreni Andrea
  • Vizzaccaro Alessandra
  • Debeurre Marielle
  • Salles Loic
  • Frangi Attilio
  • Thomas Olivier
  • Touzé Cyril
  Journal of Theoretical, Computational and Applied Mechanics, INRIA, 2023, pp.1-31. The direct parametrisation method for invariant manifolds is a nonlinear reduction technique which derives nonlinear mappings and reduced-order dynamics that describe the evolution of dynamical systems along a low-dimensional invariant-based span of the phase space. It can be directly applied to finite element problems. When the development is performed using an arbitrary order asymptotic expansion, it provides an efficient reduced-order modeling strategy for geometrically nonlinear structures. It is here applied to the case of rotating structures featuring centrifugal effect. A rotating cantilever beam with large amplitude vibrations is first selected in order to highlight the main features of the method. Numerical results show that the method provides accurate reduced-order models (ROMs) for any rotation speed and vibration amplitude of interest with a single master mode, thus offering remarkable reduction in the computational burden. The hardening/softening transition of the fundamental flexural mode with increasing rotation speed is then investigated in detail and a ROM parametrised with respect to rotation speed and forcing frequencies is detailed. The method is then applied to a twisted plate model representative of a fan blade, showing how the technique can handle more complex structures. Hardening/softening transition is also investigated as well as interpolation of ROMs, highlighting the efficacy of the method. (10.46298/jtcam.10430)
  DOI : 10.46298/jtcam.10430
• Mécanique de la rupture et chargement cyclique en transformations finies
  
  • Stolz Claude
  , 2023. On présente quelques aspects de la mécanique de la rupture des milieux hyperélastiques, on montre en particulier que les champs asymptotiques de contraintes et de déformations n’ont pas les mêmes singularités que ceux des champs en petite transformation, on montre par ailleurs les difficultés inhérentes à la détermination des caractéristiques associées à la rupture. On présente une approche globale de l’effet Müllins et l’implication d’une déformation rémanente à la décharge. On présente quelques conséquences de ces déformations sur la réponse d’une structure précédemment déformée. On propose un modèle simple pour caractériser la réponse cyclique des élastomères
• A hyperbolic conservative one-velocity one-pressure barotropic three-component model for fast-transient fluid-structure interaction problems
  
  • Daude F.
  • Galon P.
  • Potapov S.
  • Beccantini A.
  • Mianné G.
  Applied Mathematics and Computation, Elsevier, 2023, 447, pp.127919. The present paper focuses on the simulation of compressible three-component flows interacting with surrounding deformable and immersed structures. For this purpose, a barotropic three-component model assuming instantaneous kinematic and mechanical equilibria is discussed. The mathematical properties of the system, the structure of the waves, the expression of the Riemann invariants and the existence of a mathematical entropy are thus examined. The link between the present model and the extension to three components of the Kapila model is discussed. An HLLC-type solver for the present three-component model based on the mathematical structure of the system is then described. The multi-fluid solver used is coupled with an updated Lagrangian approach used for the structural domain. Arbitrary Lagrangian-Eulerian (ALE) approach and Immersed Boundary Method (IBM) are here considered and compared for their capability to account for fluid-structure interactions (FSI). A series of Riemann problems with available analytical solutions are regarded to assess the used numerical approaches: Eulerian on fixed grids, ALE on moving grids and IBM with independent fluid and structure meshes. Finally, ALE and IBM methods are used to simulate an experimental configuration involving complex FSI problems with a multi-material flow and structural plastic deformations. The numerical results presented show a good agreement with the experimental data. (10.1016/j.amc.2023.127919)
  DOI : 10.1016/j.amc.2023.127919
• Interface propagation and energy dissipation in Shape Memory Alloys
  
  • He Y.J.
  Scripta Materialia, Elsevier, 2023, 230, pp.115420. (10.1016/j.scriptamat.2023.115420)
  DOI : 10.1016/j.scriptamat.2023.115420
• Modélisation, simulation et synthèse sonore de sources de bruit d'origine aérodynamique et vibratoire
  
  • Cotté Benjamin
  , 2023.
• Review of “Reduced-order modeling of geometrically nonlinear rotating structures using the direct parametrisation of invariant manifolds”
  
  • Martin Adrien
  • Opreni Andrea
  • Vizzaccaro Alessandra
  • Debeurre Marielle
  • Salles Loic
  • Frangi Attilio Alberto
  • Thomas Olivier
  • Touzé Cyril
  , 2023.
• A stochastic volume approach based on tailored Green’s functions for airfoil noise prediction at low Mach number
  
  • Trafny Nicolas
  • Serre Gilles
  • Cotté Benjamin
  • Mercier Jean-François
  Journal of Sound and Vibration, Elsevier, 2023, 551, pp.117603. The presence of boundary surfaces in a turbulent flow can result in the enhancement of the radiated acoustic field especially for eddies close to any geometrical singularity. At low Mach number, the best suited prediction methods consist in using an acoustic analogy solved with an integral formulation. In the present study, we focus on the Lighthill's wave equation combined with a tailored Green's function and a new semi-analytical model for the turbulence statistics in the space-frequency domain to extend acoustic analogies to geometries of arbitrary shapes. To validate the model predictions for the leading edge noise and the trailing edge noise, a NACA 0012 airfoil at zero angle of attack is considered and predictions are compared to experimental data. The volume integral approach introduced in this study allows us to study the spatial distribution of the noise sources inside the turbulence volume. In addition, the direct noise radiation associated with the turbulent boundary layer is investigated. (10.1016/j.jsv.2023.117603)
  DOI : 10.1016/j.jsv.2023.117603
• A stochastic volume approach based on tailored Green’s functions for airfoil noise prediction at low Mach number
  
  • Trafny Nicolas
  • Serre Gilles
  • Cotté Benjamin
  • Mercier Jean-François
  Journal of Sound and Vibration, Elsevier, 2023, 551, pp.117603. (10.1016/j.jsv.2023.117603)
  DOI : 10.1016/j.jsv.2023.117603
• Negative refraction of water waves by hyperbolic metamaterials
  
  • Euvé Leo-Paul
  • Pham Kim
  • Maurel Agnès
  Journal of Fluid Mechanics, Cambridge University Press (CUP), 2023, 961, pp.A16. We study the propagation of water waves in a three-dimensional device alternating open canals and resonant canals with subwavelength resonances. The dispersion of water waves in such a medium is obtained by analysing the full three-dimensional problem and combining Bloch–Floquet analysis with an asymptotic technique. We obtain the closed forms of the dispersions for resonant canals containing one or two resonators, which depend on only two functions associated with symmetric and antisymmetric modes, and on a geometric parameter analogous to the hopping parameter in topological systems. The analysis of the complete band structure reveals frequency ranges alternating between elliptical and hyperbolic dispersions; in particular, the hyperbolic regime gives rise to a negative effective water depth with a consequent negative refraction. Throughout the course of our study, our theoretical results are validated by comparison with numerical calculations of the full three-dimensional problem. (10.1017/jfm.2023.220)
  DOI : 10.1017/jfm.2023.220
• Finite element simulation of high cycle fretting wear using an implicit integration scheme and an adaptive cycle jump
  
  • Caradec Quentin
  • Breuze Matthieu
  • Maitournam Habibou
  • Prabel Benoit
  • Fayard Jean-Luc
  , 2023. Among the various mechanical and chemical processes that can generate wear, fretting refers to small amplitude cyclic tangential motion between two contacting solids. Wear under fretting motion happens in different industrial contexts and can significantly reduce the lifetime of components. For example, such damage mode could occur in pressurized water nuclear reactors between guide cards and control rods. Due to the diversity of mechanisms at stake, modeling wear is complex, and predicting fretting wear by numerical approaches raises some issues, especially due to non-linearities and the need to compute a very large number of time steps. This explains why investigations still mainly rely on experimental approaches. In the present study, a finite element model and a simulation strategy aiming at predicting fretting wear are presented. The model represents a stainless steels cylinder/plane cyclic contact and the numerical results obtained are compared with experimental data from the literature. The proposed simulation process is particularly suitable for computing a high number of fretting cycles. To this end, a cycle jump technique is used in association with different integration schemes. Results show that instabilities may arise on the computed pressure when an explicit scheme is used, which limits the cycle jump. On the other hand, an implicit scheme ensures stable computations but involves a trade-off between the possibility of considering a higher cycle jump and the number of iterations required for convergence. Results show that the more cycles we perform, the faster the implicit scheme converges. Therefore, the implicit scheme is especially appropriate for high-cycle computations. In addition, an adaptive cycle jump is used with the implicit scheme, enabling to accelerate the computations with a high number of cycles. The adaptive acceleration factor is obtained from an estimate of the wear profile enlargement rate.
• Asymptotic methods for resonant acoustical metamaterials
  
  • Zhou Hagström Carl
  , 2023. In this thesis, we are interested in effective asymptotic models to describe resonant acoustic metamaterials.The first part of the thesis is devoted to the study of dual-period array, sometimes referred to as compound gratings. When dealing with a dual-period grating, composed of a periodic unit cell with two slits, we are interested in the configuration where some symmetry is broken. By doing so, the evanescent field along the structure can couple with the propagating continuum. The perfect resonances becomes quasi-resonance, or leaky modes, and this leads to some striking behaviour in the transmission spectra, where asymmetric Fano like peaks are observed.In the first chapter, we present the problem setting. We will consider in this work the propagation a scalar wave, corresponding to solving the Helmholtz equation in two dimensions. We recall some properties of a regular subwavelegnth gratings and the a semi analytical modelling. We recall some fundamental properties, and establish the homogenization setting for the rest of the manuscript.In the second chapter, we present the physical properties of the dual period metagrating. We illustrate numerically the occurrences of trapped modes and the branch folding of guided wave, which allow the presence of the Fano resonance. The derivation of the homogenized effective model of a dual period metagrating is then presented, and we show the importance of the analysis at the edges of the array. The results show that the model is accurate up to surprisingly high frequencies. Furthermore, the obtained model allows for the derivation of closed form solutions and an analytical study of resonances exhibited by theThe second part focuses on space-coiled materials in the acoustic setting. As mentioned, these space-coiled or labyrinthine materials rely on the idea that the acoustic wave are forced to follow the path of the coiled slot. Spiral geometries and folding of the slot has allowed for compact design when dealing with surface waves. It has also stimulated a lot of research in terms of wave front manipulation. This can result in possibly large phase shift of the transmitted wave compared to the thickness of the structure. By varying the coiling from a cell to another, one can tune the phase shift and thus obtain beam steering. From a theoretical point of view, few attempts of deriving effective coefficient have been made. The question of effective length, i.e. the equivalent length of its uncoiled analogue, has been of great interest, and the few results rely on some heuristic definition of the uncoiled analogue. We tackle this problem through a more rigorous homogenization approach, and show that through some rearrangement of the coiling, one can obtain a richer response.In the third chapter, we revisit the classical space-coiled materials through classical homogenization and show that, although previous results have shown good results through intuition, the homogenization approach gives a more accurate equivalent effective index. The result are illustrated with numerical examples, and results from the existing literature are compared.The fourth chapter concerns the study of what we refer to as a meta-crystal. It consists of a space-coiled material, with straight slots of the order of the wavelength. Through some careful scaling, we derive an effective model which allows for one dimensional propagation inside each slot and where each turn distanced at the ordered of the wavelength acts as a scatterer. This can be interpreted as a one dimensional phononic crystal embedded in a subwavelength grating, which now benefits from two length-scales. The structure benefits from band gaps due to Bragg scattering, that is coupled with the Fabry-Pérot resonances. The total sample size stays however small thanks to the folding of the slots. Thanks to the derived effective model, the dispersion of the embedded crystal can be obtained, giving insight on the underlying mechanism.
• Validity of the effective sound speed approximation in parabolic equation models for wind turbine noise propagation
  
  • Kayser Bill
  • Mascarenhas David
  • Cotté Benjamin
  • Ecotière David
  • Gauvreau Benoit
  Journal of the Acoustical Society of America, Acoustical Society of America, 2023, 153 (3), pp.1846-1854. Parabolic equation (PE) based methods are widely used in outdoor acoustics because they can solve acoustic propagation problems above a mixed ground in a refractive and scattering atmosphere. However, recent research has shown phase error due to the effective sound speed approximation (ESSA). To overcome these limitations, a new PE formulation derived without the ESSA has been proposed recently. We investigate the impact of such phase error on wind turbine noise modeling, as the classical wide-angle parabolic equation (WAPE) with ESSA is widely used in the research community. We propose a comparison between the classical WAPE with ESSA and the new WAPE derived without the ESSA in the context of wind turbine noise. We highlight large phase error (several dB) on monochromatic calculations with a point source. Using an extended sound source representative of a wind turbine, we show small phase error (<1 dB) in a wind turbine noise context where sound level variability far from the source is of several dB. The validity of previous works using WAPE with ESSA is, thus, not questioned, although we do recommend the use of the new WAPE derived without the ESSA to accurately model the effect of wind speed on sound propagation. (10.1121/10.0017653)
  DOI : 10.1121/10.0017653
• Rupture et chargement cyclique
  
  • Stolz Claude
  , 2023. On présente des aspects de la mécanique de la rupture en élasticité non-linéaire. On étudie le ces de chargement cyclique pour étudier la fatigue des élastomères
• Modélisation de la tenue en fatigue à haute température d'aciers moulés austénitiques : Application au dimensionnement des turbocompresseurs
  
  • Meskine Zeineb
  , 2023. Les turbocompresseurs, composants des moteurs à combustion interne, sont couramment fabriqués en acier inoxydable austénitique comme la nuance 1.4837. Le respect des réglementations ayant trait aux émissions polluantes des véhicules induit des chargements thermomécaniques de plus en plus sévères qui influence notamment la résistance à la fatigue oligocyclique de ces pièces. Les critères de fatigue relavant de l'amorçage de fissure conduisent à des analyses numériques qui ne sont pas cohérentes avec les durées de vie mesurées à l'essai. La prise en compte de la propagation de fissure devient alors un enjeu majeur de conception. Il s'agit donc ici de proposer un modèle comprenant à la fois les éléments utiles à la définition d'un amorçage de fissure dans un cadre de fatigue sous conditions anisothermes mais aussi ceux nécessaires pour décrire la propagation de fissures en condition de viscoplasticité généralisée.Après avoir détaillé la problématique industrielle et les thématiques scientifiques associées, une caractérisation métallurgique est menée sur l'acier inoxydable 1.4837 où la composition chimique, les phases en présence et la taille de grains sont analysés, mettant en évidence une microstructure grossière et une dispersion importante des modules de Young. Les critères existants sont alors analysés et les faiblesses quant à l'estimation du nombre de cycles à amorçage des essais de fatigue et des durées de vie de la structure industrielle sont identifiées. Une reformulation du critère est alors proposée en intégrant tout d'abord une dépendance à la température d'essai puis la contribution mutuelle de l'énergie plastique dissipée par cycle stabilisé et l'énergie d'ouverture élastique, ce qui permet de prendre en compte les effets de fermeture et de contrainte moyenne. Des essais de fissuration uniaxiale sur éprouvettes entaillées et sous chargements isothermes et anisothermes pour une plage de température entre 300 °C et 950 °C sont ensuite menés afin d'analyser les vitesses de propagation de fissure en fonction de la température, l'amplitude et le rapport du chargement. Pour l'acier considéré, les fissures se propagent en mode transgranulaire tandis que les chemins de propagation observés sont perpendiculaires à la direction de sollicitation même si des interactions entre microstructure et fissures induisent des oscillations. Les effets de fermeture macroscopique et locale en lien avec la viscoplasticité cyclique et la température sont finement analysés. Les courbes de propagation de fissure ont été établies d'abord dans le cadre simplifié de la mécanique linéaire de la rupture. Elles apparaissent décorrélées de la microstructure locale du matériau étudié, mettant en évidence une bonne répétabilité du comportement. Ensuite, une approche basée sur une loi de micro-propagation est également proposée afin d'estimer les vitesses de propagation à partir d'une formulation énergétique. Ce modèle a été validé pour différents niveaux de chargements et est facilement utilisable en bureau d'étude.Enfin, les courbes de propagation ont enfin été établies dans le cadre de la mécanique non-linéaire de la rupture par l'intermédiaire des simulations par éléments finis élasto-viscoplastiques de la propagation de fissure et de la méthode G-Theta dans l'outil Z-cracks. Une étude approfondie de l'évolution des forces motrices de la propagation a été effectuée afin d'évaluer la variation des facteurs d'intensité de contrainte et de la taille de la zone plastique en fonction du chargement et de la longueur de fissure. Une attention particulière est accordée à la description de la fermeture de fissure macroscopique et locale avec la viscoplasticité cyclique et la température. Une étude de corrélation essais/calcul a enfin permis de conclure sur la pertinence de l'ensemble des résultats.
• Sur les effets d'inertie en flambement dynamique de colonnes sous impact longitudinal : expériences et modélisations
  
  • Alaoui-Tahiri Amine
  , 2023. Les objectifs de ce travail de thèse concernent principalement la compréhension des phénomènes mis en jeu dans la réponse dynamique des grilles d'assemblages combustibles en cas d'impact. Dans un premier temps, on se propose de concevoir et de réaliser une maquette de grille à échelle augmentée. Cette étape de conception s'accompagnera de la construction d'un modèle numérique paramétrique fondée sur une approche unidimensionnelle de type poutre avec masses ajoutées. Dans un second temps, des essais, à travers sur une instrumentation fine de la maquette, permettent de mieux identifier les comportements dominants pendant les phases de contact, de hiérarchiser et de caractériser les paramètres de la modélisation, dont l'influence a déjà été démontrée dans les approches théoriques et numériques.
• A hybrid shell-beam element for straight thin-walled tubular structures
  
  • Pascal-Abdellaoui Y.
  • Daude F.
  • Stolz Claude
  • Lafon P.
  • Galon P.
  Computers & Structures, Elsevier, 2023, 285, pp.107083. A novel beam model is proposed in order to consider deformations of its cross-section in the context of straight thin-walled tubes. For this purpose, the straight beam kinematics is enriched by addition of orthogonal shell-type displacement field of the tube section. The considered displacement field is composed of three contributions: classical linear beam and linear shell terms in conjunction with the non-linear coupling between local deformation of the section and its global rotation. Both Euler-Bernoulli and Love-Kirchhoff hypotheses for beam and shell kinematics, respectively, are adopted as well as the thin-walled assumption. First-order shear deformation for the radial variable and Fourier expansion in terms of the circumferential variable are also considered for the mid-surface displacement field. Then, the stress tensor is obtained under plane stress conditions. The virtual power principle is finally used to obtain the equations of motion satisfied by the corresponding generalized forces. Afterwards, an explicit updated Lagrangian Finite-Element approach using a lumped mass matrix is proposed for solving the tube governing equations and the stability condition of the time integration is given. Test-cases are then chosen to assess the present tube finiteelement. Both static and dynamic problems are considered. First, the proposed model is compared to analytical solutions. Finally, a tube subjected to a distributed patch loading is studied. The influence of the number of Fourier modes, of warping and coupling terms is examined. The proposed model makes it possible to retrieve classical shell solution of the cross-section deformation with significant computational savings. (10.1016/j.compstruc.2023.107083)
  DOI : 10.1016/j.compstruc.2023.107083
• Revisiting facet nucleation under mixed mode I+III loading with T-stress and mode-dependent fracture properties
  
  • Doitrand Aurélien
  • Leguillon Dominique
  • Molnár Gergely
  • Lazarus Veronique
  International Journal of Fracture, Springer Verlag, 2023. We study the problem of crack front segmentation into facets under mixed mode I+III loading. Discrete facet network nucleation is determined based on the match asymptotic expansion approach of the coupled criterion considering both the influence of T-stress (parallel to the initial crack front) and modedependent fracture properties. We show that considering exclusively either T-stress or mode dependent properties, facet nucleation may be more favorable than straight crack propagation but in conditions that are incompatible with experimental observations. It is only by coupling mode-dependent fracture properties with T-stress that we are able to determine configurations compatible with experimental observations for which facet nucleation is more likely to occur than straight crack propagation. These configurations depend on the T-stress magnitude and critical shear energy release rate. We thus highlight that crack front segmentation into facets is material and loading dependent phenomenon that is not related to a sole mode mixity threshold but also to T-stress magnitude and shear critical energy release rate. (10.1007/s10704-023-00703-0)
  DOI : 10.1007/s10704-023-00703-0
• Homogenized transition conditions for plasmonic metasurfaces
  
  • Lebbe Nicolas
  • Maurel Agnes
  • Pham Kim
  Physical Review B, American Physical Society, 2023, 107 (8), pp.085124. The present study aims to model the optical response of plasmonic metasurfaces made of a periodic arrangement of metallic particles with arbitrary shape and subwavelength dimensions. By combining homogenization with quasistatic plasmonic eigenmode expansion, the metasurface is replaced by a zero-thickness interface associated with frequency-dependent effective susceptibilities. The resulting discontinuities of the fields are responsible for strong interaction with the incoming light at the resonances when the complex permittivity of the metal passes close to the real permittivity of an eigenmode. Our modeling provides a physical picture of resonances in plasmonic metasurfaces, and it allows for a huge decrease in the numerical cost of their computations. In addition, comparisons with direct numerics in two dimensions evidence its predictive force at any incidence, particle shape, and arrangement. (10.1103/PhysRevB.107.085124)
  DOI : 10.1103/PhysRevB.107.085124
• Key role of boundary conditions for the 2D modeling of crack propagation in linear elastic Compact Tension tests
  
  • Triclot J.
  • Corre T.
  • Gravouil A.
  • Lazarus V.
  Engineering Fracture Mechanics, Elsevier, 2023, 277, pp.109012. In fracture mechanics, the use of experimental tests are fundamental to characterize the material properties in terms of crack initiation and propagation behavior. When modeled in boundary value problems, simplifications need to be made. Notably, the loading has to be reduced to a set of boundary conditions and the choice between plane stress and plane strain has to be done in the 2D case. Here we focus on the Compact Tension (CT) test which is a fracture setup commonly used to measure the fracture toughness at crack propagation onset and we question the possibility to use it to study crack propagation. For this, the tests are monitored by digital image correlation and compared to finite element method simulations. Three ways to guide the choice between plane stress and plane strain hypotheses are proposed. They lead to the same conclusion that the plane stress conditions are the most relevant for the geometry of the samples used here. The key role of boundary conditions is highlighted by testing several models, with imposed force or displacement boundary conditions, against the experimental data. Imposed force boundary conditions on the pin are shown to be able to reproduce the experiments before crack propagation and to be insensitive to the way this force is applied, in line with Saint Venant principle. The results with imposed displacement are in contrary very sensitive to their distribution along the pin. While the stage before propagation is accurately predicted by imposed forces, we show that for the propagation phase, Saint Venant is put in default and accurate results can only be obtained by imposing the displacement fields issued from the digital image correlation. These results can be extended to other fracture experiments, involving pin loading, like the Compact Tension Shear (CTS) or the (Tappered) Double Cantilever Beam ((T)DCB) tests. (10.1016/j.engfracmech.2022.109012)
  DOI : 10.1016/j.engfracmech.2022.109012