Publications

2016

• A coupled BEM-FEM method for finite strain magneto-elastic boundary-value problems
  
  • Nedjar Boumediene
  Computational Mechanics, Springer Verlag, 2016. The first objective of this contribution is the formulation of nonlinear problems in magneto-elasticity involving finite geometry of the surrounding free space. More specifically for the magnetic part of the problem, the surrounding free space is described by means of a boundary integral equation for which boundary elements are used that are appropriately coupled with the finite element discretization used inside the material. The second objective is to develop a numerical strategy to solve the strongly coupled magneto-mechanics problem at hand. Herein we provide a staggered scheme consisting of a magnetostatic resolution employing the above coupled BEM-FEM procedure at fixed deformation, followed by a mechanical resolution at fixed magnetic fields. This decoupled method renders the whole solution strategy very appealing since, among others, the first BEM-FEM resolution is linear for some prototype models, and the remaining mechanical resolution is analogous to nowadays classical nonlinear elastostatic problems in the finite strain range. Some nonlinear boundary-value problems are simulated to demonstrate the applicability of the proposed framework. (10.1007/s00466-016-1370-3)
  DOI : 10.1007/s00466-016-1370-3
• Inertial regimes in a curved electromagnetically forced flow
  
  • Boisson Jean
  • Monchaux Romain
  • Aumaître Sébastien
  , 2016. We investigated experimentally the flow driven by a Lorentz force induced by an axial magnetic field − → B and a radial electric current I applied between two fixed concentric copper cylinders. The gap geometry corresponds to a rectangular section with an aspect ratio of η = 4 and we probe the azimuthal and axial velocity profiles of the flow along the vertical axis by using ultrasonic Doppler velocimetry. We have performed several runs at moderate magnetic field strengths, corresponding to moderate Hartmann numbers M 300. At these forcing parameters and because of the geometry of our experimental device, we show that the inertial terms are not negligible. This induces the azimuthal velocity that depends on both I and B. From measurements of the vertical velocity we focus on the characteristics of the secondary flow: the time averaged velocity profiles are compatible with a secondary flow presenting two pairs of stable vortices as pointed out by previous numerical studies. We exhibited a transition between two dynamical modes, a high and a low frequency one. The high frequency mode, which emerges at low magnetic field forcing, corresponds to the propagation in the r-direction of tilted vortices. This mode is consistent with our previous experiments and with the instability described in Zhao et al. (2011) taking place in an elongated duct geometry. The low frequency mode, observed for high magnetic field forcing, consists in large excursions of the vortices. The dynamics of these modes matches the first axisymmetric instability described in Zhao & Zikanov (2012) taking place in an square duct geometry. We demonstrated that this transition is controlled by the inertial magnetic thickness H ′ which is the characteristic length we introduce as a balance between the advection and the Lorentz force. The key point here is that when the inertial magnetic thickness H ′ is comparable to one geometric characteristic length (H/2 in the vertical or △r in the radial direction) the corresponding mode is favored. Therefore, when H ′ /(H/2) ≈ 1 we observe the high frequency mode taking place in elongated duct geometry, and when H ′ /△r ≈ 1 we observe the low frequency mode taking place in square duct geometry and high magnetic field.
• On moving thick layer approach for graded damage modelling
  
  • Stolz Claude
  International Journal of Fracture, Springer Verlag, 2016, 202 (2), pp.195-205. We propose to examine analytical solutions of propagation of graded damage for particular geometries in the context of the formulation of a damage law based on a continuous transition between a sound material and a totally or partially broken material. The evolution of damage is associated with a moving layer of finite thickness, defined in the frame of a moving surface Γ0. The dissipation and the driven forces for the motion of the layer depend on the local shape, in particular on the curvature of the surface Γ0. This study is then focused on the effect of this curvature on the stability of the propagation of the layer. Comparison with description of damage with sharp interface is also presented. (10.1007/s10704-016-0154-2)
  DOI : 10.1007/s10704-016-0154-2
• High-frequency performance of ferromagnetic shape memory alloys
  
  • Pascan Oana-Zenaida
  • He Y. J.
  • Moumni Ziad
  • Zhang Weihong
  Annals of Solid and Structural Mechanics, Springer Berlin Heidelberg, 2016, 8 (1-2), pp.17 - 25. (10.1007/s12356-016-0045-2)
  DOI : 10.1007/s12356-016-0045-2
• Dynamique et stabilité d'une chaîne d'aimants. Application à la récupération d'énergie.
  
  • Lee Joosung
  , 2016. L'étude de la dynamique d'une chaîne d'aimants et l'application de ce type de système à la récupération d'énergie sont les objets de la thèse. Une chaîne d'aimants cylindriques aimantés selon le diamètre et soumise à la gravité et à un champ magnétique extérieur a d'abord été etudiée. Deux modèles linéaires décrivant la dynamique de la chaîne ont été développés : un modèle discret basée sur l'approche lagrangienne et un modèle continu en la considérant comme une poutre continue. Les prédictions des modèles ont été comparées aux expériences. La stabilité du système en fonction de la gravité et du champ magnétique a été ensuite caractérisée numériquement. Après cette première étude, nous avons proposé une utilisation de ce type de système à la récupération d'énergie. Un drapeau articulé constitué d'aimants rectangulaires très fins et aimantés selon l'épaisseur a été conçu. Ce drapeau a été placé dans un écoulement d'eau et une bobine a été positionnée dans l'environnement pour convertir le mouvement du drapeau en flottement en une force électromotrice (f.e.m). Cette dernière a été à la fois estimée numériquement et mesurée expérimentalement. Nous avons ensuite exploité le calcul numérique de la f.e.m pour chercher les géométries et les positions de la bobine maximisant le potentiel de récupération d'énergie.
• A fully coupled HM –XFEM method with cohesive zone model: application to fluid-driven fracture network
  
  • Faivre Maxime
  • Paul Bertrand
  • Golfier Fabrice
  • Giot Richard
  • Massin Patrick
  • Colombo Daniele
  , 2016. A fully coupled HM –XFEM method with cohesive zone model: application to fluid-driven fracture network
• Modélisation et simulation d'écoulements transitoires eau-vapeur en approche bifluide
  
  • Lochon Hippolyte
  , 2016. Cette thèse traite de la modélisation et de la simulation des écoulements diphasiques transitoires eau-vapeur. Dans de nombreuses installations industrielles, des écoulements monophasiques d'eau liquide sont susceptibles de devenir diphasiques lors de certaines situations transitoires. La modélisation de ces écoulements peut s'avérer délicate car deux phénomènes physiques interagissant fortement entre eux, le changement de phase et la propagation d'ondes de pression, sont alors à prendre en compte. Une approche bifluide statistique, ne supposant aucun équilibre entre les phases, est utilisée afin de modéliser de tels écoulements. Les modèles obtenus sont de type convection-source et s'apparentent au modèle de Baer-Nunziato. Différentes lois de fermeture pour ces modèles sont comparées sur des cas expérimentaux de transitoires eau-vapeur tels que les coups de bélier et la dépressurisation d'une tuyauterie d'eau liquide suite à une rupture. La simulation numérique des différents modèles est effectuée grâce à une méthode à pas fractionnaires. Un nouveau schéma de convection, robuste et efficace, capable de gérer toute equation d'état est utilisé dans la première étape de cette méthode. La seconde étape est dédiée au traitement des termes sources et requiert différents schémas implicites. Une grande attention est accordée à la vérification de tous les schémas numériques utilisés grâce à des études de convergence. Une nouvelle modélisation du transfert de masse est également proposée, sur la base de travaux dédiés à la brusque dépressurisation d'eau liquide en approche homogène. La validation du modèle est effectuée grâce de nombreuses comparaisons calcul-expérience.
• Multi-scale Analysis of the Fatigue of Shape Memory Alloys
  
  • Zheng Lin
  , 2016. Shape Memory Alloy (SMA) is a typical smart material having many applications from aerospace industry, mechanical and civil engineering, to biomedical devices, where the material’s fatigue is a big concern. One of the challenging issues in studying the fatigue behaviors of SMA polycrystals is the interaction between the material damage and the martensitic phase transformation which takes place in a macroscopic homogeneous mode or a heterogeneous mode (forming macroscopic patterns (Lüders-like bands) due to the localized deformations and localized heating/cooling). Such pattern formation and evolution imply the governing physical mechanisms in the material system such as the fatigue process, but there is still no fatigue study of SMAs by tracing the macro-band patterns and the local material responses. To bridge this gap, systematic tensile fatigue experiments are conducted on pseudoelastic NiTi polycrystalline strips by in-situ optical observation on the band-pattern evolutions and by tracing the deformation history of the cyclic phase transformation zones where fatigue failure occurs. These experimental results help to better understand the stress- and frequency-dependent fatigue behaviors. Particularly, it is found that the local residual strain rather than the structural nominal/global residual strain is a good indicator on the material’s damage leading to the fatigue failure, which is important for understanding and modeling the fatigue process in SMAs.
• An overview of the modelling of fracture by gradient damage models
  
  • Marigo Jean-Jacques
  • Maurini Corrado
  • Pham Kim
  Meccanica, Springer Verlag, 2016, 51 (12), pp.3107–3128. The paper is devoted to gradient damage models which allow us to describe all the process of degradation of a body including the nucleation of cracks and their propagation. The construction of such model follows the variational approach to fracture and proceeds into two stages: (i) definition of the energy; (ii) formulation of the damage evolution problem. The total energy of the body is defined in terms of the state variables which are the displacement field and the damage field in the case of quasi-brittle materials. That energy contains in particular gradient damage terms in order to avoid too strong damage localizations. The formulation of the damage evolution problem is then based on the concepts of irreversibility, stability and energy balance. That allows us to construct homogeneous as well as localized damage solutions in a closed form and to illustrate the concepts of loss of stability, of scale effects, of damage localization, and of structural failure. Moreover, the variational formulation leads to a natural numerical method based on an alternate minimization algorithm. Several numerical examples illustrate the ability of this approach to account for all the process of fracture including a 3D thermal shock problem where the crack evolution is very complex. (10.1007/s11012-016-0538-4)
  DOI : 10.1007/s11012-016-0538-4
• A MODAL APPROACH TO THE NUMERICAL SIMULATION OF A STRING VIBRATING AGAINST AN OBSTACLE: APPLICATIONS TO SOUND SYNTHESIS
  
  • Issanchou Clara
  • Le Carrou Jean-Loic
  • Bilbao Stefan
  • Touzé Cyril
  • Doaré Olivier
  , 2016. A number of musical instruments (electric basses, tanpuras, si-tars...) have a particular timbre due to the contact between a vibrating string and an obstacle. In order to simulate the motion of such a string with the purpose of sound synthesis, various technical issues have to be resolved. First, the contact phenomenon, inherently nonlinear and producing high frequency components, must be described in a numerical manner that ensures stability. Second, as a key ingredient for sound perception, a fine-grained frequency-dependent description of losses is necessary. In this study, a new conservative scheme based on a modal representation of the displacement is presented, allowing the simulation of a stiff, damped string vibrating against an obstacle with an arbitrary geometry. In this context, damping parameters together with eigenfrequencies of the system can be adjusted individually, allowing for complete control over loss characteristics. Two cases are then numerically investigated: a point obstacle located in the vicinity of the boundary , mimicking the sound of the tanpura, and then a parabolic obstacle for the sound synthesis of the sitar.
• Stable control for mixed-mode concrete fracture
  
  • Carpiuc A.
  • Jailin C
  • Poncelet M.
  • Kazymyrenko K.
  • Hild F.
  , 2016. The knowledge of the concrete behavior is essential when analyzing the aging and leakage phenomena of production facilities. On the industrial level the concrete fracture characterization is currently performed through standard experimental tests that are not sufficiently rich to determine in an optimized manner all the corresponding characteristics. First there is a general lack of mixed mode loading experiments that produce non trivial crack paths. Moreover, even for some well defined material properties (as for example critical shear stress) the corresponding loading tests are not sufficiently developed, as the results are too dependent on aggregate distribution and specimen sizes. It means that we are still not able to locally reproduce some specific me-chanical stresses distribution and repeatedly check it in order to attain necessary accuracy. Therefore an improvement in corresponding measurement technique is still needed. When studying concrete fracture behavior the main difficulty is related to instable crack propagation. In the past some relevant works in mixed mode fracture were conducted by Nooru-Mohamed. More recently the work was extended employing an up-to-date full-field measurement technique. In this work, we develop a stable crack path control technique that allows “customized” cracking tests creation for the characterization of various materials. Using this technique well instrumented and discriminating mixed–mode crack propagation tests performed on VERCORS concrete samples are presented. Finally we discuss the relevance of these tests for various pa-rameters identification and some possible extension of stable crack path control technique.
• Crack Tip Equation of Motion in Dynamic Gradient Damage Models
  
  • Li Tianyi
  • Marigo Jean-Jacques
  Journal of Elasticity, Springer Verlag, 2016. We propose in this contribution to investigate the link between the dynamic gradient damage model and the classical Griffith's theory of dynamic fracture during the crack propagation phase. To achieve this main objective, we first rigorously reformulate two-dimensional linear elastic dynamic fracture problems using variational methods and shape derivative techniques. The classical equation of motion governing a smoothly propagating crack tip follows by considering variations of a space-time action integral. We then give a variationally consistent framework of the dynamic gradient damage model. Owing to the analogies between the variational ingredients of these two models and under some basic assumptions concerning the damage band structuration, one obtains a generalized Griffith criterion which governs the crack tip evolution within the non-local damage model. Assuming further that the internal length is small compared to the dimension of the body, the previous criterion leads to the classical Griffith's law through a separation of scales between the outer linear elastic domain and the inner damage process zone. (10.1007/s10659-016-9595-0)
  DOI : 10.1007/s10659-016-9595-0
• Optimization of piezoelectric flags
  
  • Piñeirua Miguel
  • Doaré Olivier
  • Michelin Sébastien
  , 2016.
• A complete vibroacoustic model for the nonlinear response of imperfect circular plates : application to sound synthesis
  
  • Aragonès Àngels
  • Touzé Cyril
  • Bilbao Stefan
  • Ducceschi Michele
  , 2016. A complete vibroacoustic model is presented in order to compute numerically the sound pressure generated by a thin circular plate vibrating with large amplitude motions. The vibratory part relies on a modal approach for the von Kármán thin plate equations. A special emphasis is put in this paper on the inclusion of a geometrical imperfection describing the shape of the circular plate, hence extending previous results for perfect plates to the generic case of imperfect plates and shallow shells. A conservative scheme is used in order to integrate in time the modal equations of motion for the imperfect plate. The acoustic radiation is taken into account by using a finite difference approach for the sound field. The vibroacoustic coupling gives rise to a complete model which is applied for the purpose of sound synthesis of cymbals and gong-like instruments. Simulation results are shown in order to investigate the influence of the geometric imperfection on the sound produced. Plates with different profiles are compared and focus is set on the ability of the imperfection to favour the appearance of the turbulent regime.
• DYNAMIC BEHAVIOR OF A TUNABLE MAGNETIC VIBRATION ABSORBER
  
  • Benacchio Simon
  • Malher Arnaud
  • Lo Feudo Stefania
  • Boisson Jean
  • Touzé Cyril
  , 2016. A magnetic vibration absorber (MVA), completely relying on magnetic forces, is used to reduce the displacement of a vibrating structure. The distinctive feature of this absorber is the ability of tuning its linear stiffness together with its nonlinear cubic and quintic stiffnesses. Repulsive and corrective magnets are used to finely tune the values of these stiffness coefficients. A modelisation, relying on a multipolar expansion of the magnetic fields of each magnets, is used to predict the values of the stiffnesses from the geometry. Using only three geometrical parameters the MVA can be passively designed either as a nonlinear tuned vibration absorber (NLTVA), a nonlinear energy sink (NES), or a bi-stable absorber with negative linear stiffness.
• Effects of geometrical nonlinearities on the acoustic black hole effect
  
  • Denis V
  • Pelat A
  • Touzé Cyril
  • Gautier F
  , 2016. The Acoustic Black Hole effect (ABH) is a passive vibration damping technique without added mass based on flexural waves properties in thin structures with variable thickness. The usual implementation on plates is a region where the thickness is reduced with a power law profile, covered with a visco-elastic layer. The inhomogoneity induces a decrease of the wave speed and an increase of the amplitude in the small thickness region, which makes the energy dissipation more efficient due to the absorbing layer. The wave amplitude in the ABH easily reaches the plate thickness and is the origin of geometrical nonlinearities. These nonlin-earities can generate coupling between linear beam eigenmodes of the structure and induce energy transfer between low and high frequency regime. This phenomenon may be used to increase the efficiency of the ABH treatment in the low frequency regime where it is usually inefficient. An experimental investigation shows that the ABH termination displays a nonlinear behaviour and allows for modal coupling. A strongly nonlinear regime can also be observed, which is associated with Wave Turbulence. A model of nonlinear ABH beam as von Kármán plate of variable thickness and a modal resolution of the problem confirm the observed effects and gives more insights on these results.
• A phenomenological model for predicting the effect of damping on wave turbulence spectra in vibrating plates
  
  • Humbert Thomas
  • Josserand C
  • Touzé Cyril
  • Cadot Olivier
  , 2016. Thin plates vibrating at large amplitudes may exhibit a strongly nonlinear regime that has to be studied within the framework of wave turbulence. Experimental studies have revealed the importance of the damping on the spectra of wave turbulence , which precludes for a direct comparison with the theoretical results, that assumes a Hamiltonian dynamics. A phenomenological model is here introduced so as to predict the effect of the damping on the turbulence spectra. Self-similar solutions are found and the cutoff frequency is expressed as function of the damping rate and the injected power.
• PASSIVE CONTROL OF AIRFOIL FLUTTER USING A NONLINEAR TUNED VIBRATION ABSORBER
  
  • Malher Arnaud
  • Touzé Cyril
  • Doaré Olivier
  • Habib Giuseppe
  • Kerschen Gaëtan
  , 2016. The influence of a Nonlinear Tuned Vibration Absorber (NLTVA) on the airfoil flutter is investigated. In particular, its effect on the instability threshold and the potential subriticality of the bifurcation is analyzed. For that purpose, the airfoil is modeled using the classical pitch and plunge aeroelastic model together with a linear approach for the aerodynamic loads. To ensure limit cycle oscillation (LCO) to the airfoil in its post-critical regime, cubic nonlinearities are added to the structural model. The influence of each NLTVA parameter is studied and an optimum tuning of these parameters is found. The study reveals the ability of the NLTVA to both shift the instability and avoid its possible subcriticality.
• Electro-hydrodynamic synchronization of piezoelectric flags
  
  • Xia Yifan
  • Doaré Olivier
  • Michelin Sébastien
  Journal of Fluids and Structures, Elsevier, 2016, 65, pp.398 - 410. (10.1016/j.jfluidstructs.2016.06.011)
  DOI : 10.1016/j.jfluidstructs.2016.06.011
• Numerical investigation of dynamic brittle fracture via gradient damage models
  
  • Li Tianyi
  • Marigo Jean-Jacques
  • Guilbaud Daniel
  • Potapov Serguei
  Advanced Modeling and Simulation in Engineering Sciences, Springer, 2016, 3, pp.26. Background: Gradient damage models can be acknowledged as unified framework of dynamic brittle fracture. As a phase-field approach to fracture, they are gaining popularity over the last few years in the computational mechanics community. This paper concentrates on a better understanding of these models. We will highlight their properties during the initiation and propagation phases of defect evolution. Methods: The variational ingredients of the dynamic gradient damage model are recalled. Temporal discretization based on the Newmark-β scheme is performed. Several energy release rates in gradient damage models are introduced to bridge the link from damage to fracture. Results and discussion: An antiplane tearing numerical experiment is considered. It is found that the phase-field crack tip is governed by the asymptotic Griffith's law. In absence of unstable crack propagation, the dynamic gradient damage model converges to the quasi-static one. The defect evolution is in quantitative accordance with the linear elastic fracture mechanics predictions. Conclusion: These numerical experiments provide a justification of the dynamic gradient damage model along with its current implementation, when it is used as a phase-field model for complex real-world dynamic fracture problems. (10.1186/s40323-016-0080-x)
  DOI : 10.1186/s40323-016-0080-x
• Fluid-solid-electric couplings in piezoelectric flags
  
  • Xia Yifan
  • Doaré Olivier
  • Michelin Sébastien
  , 2016.
• Moving surfaces and interfaces : application to damage, fracture and wear contact
  
  • Stolz Claude
  AIMS Materials Science, AIMS Press, 2016, 3 (3), pp.881-907. The full scenario of the degradation of solids under mechanical loading is described by modelling the gradual loss of rigidity. This common approach is purely local. Another way to describe the damage evolution is to consider the propagation of the surface separating sound material and damaged material. When this surface is moving, a flux of matter is induced, that is useful for describing the loss of material during wear mechanisms or brittle fracture. The article proposes modelling of moving surface and interface in order to describe such behaviours. The problem of evolution is written, analysis of stability and bifurcation of the propagation is also presented. Applications to brittle fracture, transition from fracture to damage and wear contact are briefly investigated. (10.3934/matersci.2016.3.881)
  DOI : 10.3934/matersci.2016.3.881
• A finite strain modeling for electro-viscoelastic materials
  
  • Nedjar Boumediene
  International Journal of Solids and Structures, Elsevier, 2016. Of interest in this work is the multi-physics modeling of electrically sensitive materials known to have viscoelastic properties. We show how the current state of the art in the modeling of electro-mechanics in deformable media can easily be integrated within the unified framework of continuum thermodynamics, this latter being crucial in setting the convenient forms for the constitutive laws and evolution equations. The formulation is developed within the finite strain range and we adopt the nowadays well-accepted multiplicative decomposition of the deformation gradient into elastically relaxing and viscous parts giving rise to an intermediate configuration on which the electric field vectors can eventually be transported. The paper discusses in depth such a formulation. Among others, it is implicitly found that the electric displacement and polarization vectors can be split into equilibrium and non-equilibrium parts. A model example is proposed for the purpose of demonstration to study some phenomena qualitatively. The paper presents also the numerical design of a simplified version within the context of the finite element method to illustrate the effectiveness of the proposed framework for structural simulations. (10.1016/j.ijsolstr.2016.07.016)
  DOI : 10.1016/j.ijsolstr.2016.07.016
• Directional damage gradient modeling of fiber/matrix debonding in viscoelastic UD composites
  
  • Nedjar Boumediene
  Composite Structures, Elsevier, 2016 (153), pp.895-901. Delayed damage due fiber/matrix debonding can be observed in many unidirectional fiber-reinforced composites, for instance those made with Epoxy-based polymeric resins. As the role of the constitutive matrix is to deform and support stresses primarily in shear, adequate viscoelastic modeling must be adopted. We have recently shown that such a phenomenon can be described within the integrity-basis formulation of transverse isotropy that allows for a neat decomposition of the mechanical response into fiber-directional, transverse, and pure shear parts, the latter being used here to capture the aforementioned viscoelasticity. For the modeling of the degradation by debonding, we use in this work an approach based on continuum damage mechanics. More specifically, two ingredients are involved: (i) the use of the gradient of the damage quantity within a higher-order formulation and, (ii) the damage gradient is herein projected toward the direction of the fibers. Indeed, it is mainly observed that debonding paths mostly propagate along the reinforcements. One then speaks of a directional damage gradient formulation. (10.1016/j.compstruct.2016.07.012)
  DOI : 10.1016/j.compstruct.2016.07.012
• Effects of confinment in the buckling of a flexible plate in axial flow: experimental and numerical study
  
  • Adjiman Julie
  • Doaré Olivier
  • Moussou Pierre
  • de Buretel de Chassey Nicolas
  , 2016. Static instability of flexible structures forced by a parallel flow, a.k.a. divergence, has been the subject of a relatively small amount of studies, unlike flutter. In order to prepare future studies of the collective behaviour of several slender structures coupled by the fluid in axial flow, the canonical case of a flat flexible plate clamped at both ends is investigated numerically and experimentally. The onset of divergence is determined throughout a series of calculation of the fluid forces generated by a prescribed deformation of the plate. Using the Galerkin method, these fluid forces are expanded in the basis of the natural modes; they exactly balance the mechanical forces when the fluid velocity reaches the instability threshold. The instability velocity can be determined by an eigenvalue calculation involving the fluid force expansion and the modal stiffnesses of the plate. Comparisons are provided with 2D analytical calculations and with an experiment performed with a 0.3m×0.03m mylar plate at Reynolds numbers varying between 10 4 and 10 5. A fair agreement is observed between the 3D potential calculation and the experiments, whereas the 2D analytical solution underestimates the instability velocity.