ORBi Collection: Mechanical engineering
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A Stochastic Multi-scale Model For Predicting MEMS Stiction Failure
http://hdl.handle.net/2268/200451
Title: A Stochastic Multi-scale Model For Predicting MEMS Stiction Failure
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<br/>Author, co-author: Hoang Truong, Vinh; Wu, Ling; Paquay, Stéphane; Golinval, Jean-Claude; Arnst, Maarten; Noels, Ludovic
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<br/>Abstract: Adhesion is an important phenomenon in the context of MEMS for which the surface forces become dominant in comparison with the body forces. Because the magnitudes of the adhesive forces strongly depend on the surface interaction distances, which in turn evolve with the roughness of the contacting surfaces, the adhesive forces cannot be determined in a deterministic way. To quantify the uncertainties on the structural stiction behavior of a MEMS, this work proposes a “stochastic multi-scale methodology”. The key ingredient of the method is the evaluation of the random meso-scale apparent contact forces, which homogenize the effect of the nano-scale roughness and are integrated into a numerical model of the studied structure as a random contact law. To obtain the probabilistic behavior at the structural MEMS scale, a direct method needs to evaluate explicitly the meso-scale apparent contact forces in a concurrent way with the stochastic multi-scale approach. To reduce the computational cost, a stochastic model is constructed to generate the random meso-scale apparent contact forces. To this end, the apparent contact forces are parameterized by a vector of parameters before applying a polynomial chaos expansion in order to construct a mathematical model representing the probability of the random parameters vector. The problem of micro-beam stiction is then studied in a probabilistic way.Mean-Field-Homogenization-based stochastic multiscale methods for composite materials
http://hdl.handle.net/2268/200450
Title: Mean-Field-Homogenization-based stochastic multiscale methods for composite materials
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<br/>Author, co-author: Wu, Ling; Lucas, Vincent; Adam, Laurent; Noels, Ludovic
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<br/>Abstract: When considering a homogenization-based multiscale approach, at each integration-point of the macro-structure, the material properties are obtained from the resolution of a micro-scale boundary value problem. At the micro-level, the macro-point is viewed as the center of a Representative Volume Element (RVE). However, to be representative, the micro-volume-element should have a size much bigger than the micro-structure size. For composite materials which suffer from a large property and geometrical dispersion, either this requires RVE of sizes which cannot usually be obtained numerically, or simply the structural properties exhibit a scatter at the macro-scale. In both cases, the representativity of the micro-scale volume element is lost and Statistical Volume Elements (SVE) [1] should be considered in order to account for the micro-structural uncertainties, which should in turn be propagated to the macro-scale in order to predict the structural properties in a probabilistic way.
In this work we propose a non-deterministic multi-scale approach for composite materials following the methodology set in [2].
Uncertainties on the meso-scale properties and their (spatial) correlations are first evaluated through the homogenization of SVEs. This homogenization combines both mean-field method in order to gain efficiency and computational homogenization to evaluate the spatial correlation. A generator of the meso-scale material tensor is then implemented using the spectral method [3]. As a result, a meso-scale random field can be generated, paving the way to the use of stochastic finite elements to study the probabilistic behavior of macro-scale structures.
[1] M. Ostoja-Starzewski, X.Wang, Stochastic finite elements as a bridge between random material microstructure and global response, Computer Methods in Applied Mechanics and Engineering, 168, 35–49, 1999.
[2] V. Lucas, J.-C. Golinval, S. Paquay, V.-D. Nguyen, L. Noels, L. Wu, A stochastic computational multiscale approach; Application to MEMS resonators. Computer Methods in Applied Mechanics and Engineering, 294, 141–167, 2015.
[3] Shinozuka, M., Deodatis, G. Simulation of stochastic processes by spectral representation. Appl. Mech. Rev., 1991: 44(4): 191-204, 1991.Failure multiscale simulations of composite laminates based on a non-local mean-field damage-enhanced homogenization
http://hdl.handle.net/2268/200449
Title: Failure multiscale simulations of composite laminates based on a non-local mean-field damage-enhanced homogenization
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<br/>Author, co-author: Wu, Ling; Adam, Laurent; Doghri, Issam; Noels, Ludovic
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<br/>Abstract: A multiscale method is developed to study the failure of carbon fiber reinforced composites.
In order to capture the intra-laminar failure, a non-local mean-field homogenization (MFH) method accounting for the damage evolution of the matrix phase of the composite material [1] is considered. In that formulation, an incremental-secant MFH approach is used to account for the elastic unloading of the fibers during the strain softening of the matrix. In order to avoid the strain/damage localization caused by the matrix material softening, an implicit non-local method [2] was reformulated to account for the composite material anisotropy. As a result, accurate predictions of the composite softening behavior and of the different phases response is possible, even for volume ratios of inclusions around 60%. In particular it is shown that the damage propagation direction in each ply follows the fiber orientation in agreement with experimental data.
The delamination process is modeled by recourse to a hybrid discontinuous Galerkin (DG)/ extrinsic cohesive law approach. As for the extrinsic cohesive law (ECL), which represents the fracturing response only, and for which cohesive elements are inserted at failure onset, the method does not suffer from a mesh-dependent effect. However, because of the underlying discontinuous Galerkin method, interface elements are present since the very beginning of the simulation avoiding the need to propagate topological changes in the mesh with the propagation of the delamination. Moreover, the pre-failure response is accurately captured by the material law though the DG implementation, by contrast to usual intrinsic cohesive laws.
As a demonstration of the efficiency and accuracy of the method, a composite laminate with a quasi-isotropic sequence ([90/45/-45/90/0]S) and an open-hole geometry is studied using the multiscale method [3] and the results are compared to experimental data. The numerical model is found to predict the damage bands along the fiber directions as observed in the experimental samples inspected by X-ray computed tomography (XCT). Moreover, the predicted delamination pattern is found to match the experimental observations.
REFERENCES
[1] L. Wu, L. Noels, L. Adam, I. Doghri, An implicit-gradient-enhanced incremental-secant mean- field homogenization scheme for elasto-plastic composites with damage, International Journal of Solids and Structures, 50, 3843-3860, 2013.
[2] R. Peerlings, R. de Borst, W. Brekelmans, S. Ayyapureddi, Gradient-enhanced damage for quasi-brittle materials. International Journal for Numerical Methods in Engineering, 39, 3391-3403, 1996.
[3] L. Wu, F. Sket, J.M. Molina-Aldareguia, A. Makradi, L. Adam, I. Doghri, L. Noels, A study of composite laminates failure using an anisotropic gradient-enhanced damage mean-field homogenization model, Composite Structures, 126, 246–264, 2015.A Stochastic Multi-scale Model For Predicting MEMS Stiction Failure
http://hdl.handle.net/2268/200354
Title: A Stochastic Multi-scale Model For Predicting MEMS Stiction Failure
<br/>
<br/>Author, co-author: Hoang Truong, Vinh; Paquay, Stéphane; Golinval, Jean-Claude; Wu, Ling; Arnst, Maarten; Noels, Ludovic
<br/>
<br/>Abstract: Adhesion is an important phenomenon in the context of MEMS for which the surface forces become dominant in comparison with the body forces. Because the magnitudes of the adhesive
forces strongly depend on the surface interaction distances, which in turn evolve with the roughness of the contacting surfaces, the adhesive forces cannot be determined in a deterministic way.
To quantify the uncertainties on the structural stiction behavior of a MEMS, this work proposes a “stochastic multi-scale methodology”. The key ingredient of the method is the evaluation of the random meso-scale apparent contact forces, which homogenize the effect of the nano-scale roughness and are integrated into a numerical model of the studied structure as a random contact
law. To obtain the probabilistic behavior at the structural MEMS scale, a direct method needs to evaluate explicitly the meso-scale apparent contact forces in a concurrent way with the stochastic multi-scale approach. To reduce the computational cost, a stochastic model is constructed to generate the random meso-scale apparent contact forces. To this end, the apparent contact forces are parameterized by a vector of parameters before applying a polynomial chaos expansion in order to construct a mathematical model representing the probability of the random parameters vector. The problem of miro-beam stiction is then studied in a probabilistic way.Numerical Properties of a Discontinuous Galerkin formulation for electro-thermal coupled problems
http://hdl.handle.net/2268/200352
Title: Numerical Properties of a Discontinuous Galerkin formulation for electro-thermal coupled problems
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<br/>Author, co-author: Homsi, Lina; Geuzaine, Christophe; Noels, Ludovic
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<br/>Abstract: Discontinuous Galerkin (DG) methods are attractive tools to integrate several PDEs in engineering sciences, due to their high order accuracy and their high scalability in parallel simulations. The main interest of this work is to derive a constant and stable Discontinuous Galerkin method for two-way electro-thermal coupling analyses.
A fully coupled nonlinear weak formulation for electro-thermal problems is developed based on continuum mechanics equations which are discretized using the Discontinuous Galerkin method. Toward this end, the weak form is written in terms of energetically conjugated fields gradients and fluxes.
In order to validate the effectiveness of the formulation and illustrate the algorithmic properties, a numerical test for composite materials is performed.Nonlinear analysis of compliant mechanisms: application to tape springs
http://hdl.handle.net/2268/200302
Title: Nonlinear analysis of compliant mechanisms: application to tape springs
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<br/>Author, co-author: Dewalque, Florence; Bruls, Olivier
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<br/>Abstract: Brief summary of the mechanical behaviour of tape springs. Main results obtained by the means of finite element models. Description of the experimental set-up and results. See the extended abstract for more details.Inverse dynamics of a flexible 3D robotic arm for a trajectory tracking task
http://hdl.handle.net/2268/200182
Title: Inverse dynamics of a flexible 3D robotic arm for a trajectory tracking task
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<br/>Author, co-author: Lismonde, Arthur; Sonneville, Valentin; Bruls, OlivierModelling of multibody systems in the local frame
http://hdl.handle.net/2268/200140
Title: Modelling of multibody systems in the local frame
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<br/>Author, co-author: Bruls, Olivier; Sonneville, Valentin
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<br/>Abstract: A local frame finite element approach is proposed to describe the kinematics of a flexible multibody system, derive the equations of motion and solve them numerically. It is argued that this approach leads to reduced geometric nonlinearities and improved computational efficiency.Optimal design of flexible mechanisms using a generalized equivalent static load method
http://hdl.handle.net/2268/200139
Title: Optimal design of flexible mechanisms using a generalized equivalent static load method
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<br/>Author, co-author: Tromme, Emmanuel; Sonneville, Valentin; Guest, James K.; Bruls, Olivier; DUYSINX, Pierre
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<br/>Abstract: The equivalent static load (ESL) method is a powerful approach to solve dynamic response structural optimization problems. The method transforms the dynamic response optimization into a static response optimization under multiple load cases. The ESLs are defined based on the transient analysis response whereupon all the standard techniques of static response optimization can be used. In the last decade, the ESL method has been applied to perform structural optimization of flexible components of mechanical systems modeled as multibody systems. This method considers the optimization of isolated component during the static response optimization. The present research proposes a generalized ESL method accounting for the entire system during the static response optimization, which enables to formulate the constraints with respect to the mechanism and not restricted to the individual components. The proposed method relies on a Lie group formalism which has appealing properties to derive efficiently the ESL. Examples validate the method.On the compatibility equations in geometrically exact beam finite element
http://hdl.handle.net/2268/200138
Title: On the compatibility equations in geometrically exact beam finite element
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<br/>Author, co-author: Sonneville; Bruls, Olivier; Bauchau, Olivier A.
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<br/>Abstract: This paper discusses the compatibility equations which relate the velocity field and the strain field in geometrically exact beam theory. The analysis is carried out in the context of intrinsic equations, namely the dynamic equilibrium equations are formulated in terms of velocity and strain only. In addition to the well established objectivity and path-independence requirements of the spatial discretization, these compatibility equations show that a consistent spatial interpolation of the velocity field should depend on the curvature of the beam, including initial curvature and curvature from the deformation, and it is shown that this consistency is connected to the ability of the element to represent rigid body motion velocity. A two node interpolation scheme is studied and it appears that, as the element gets smaller under mesh refinement, the effect of this dependency reduces, leading eventually to the classical linear shape functions.An integrated control-structure design for manipulators with flexible links
http://hdl.handle.net/2268/200022
Title: An integrated control-structure design for manipulators with flexible links
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<br/>Author, co-author: Bastos Jr., Guaraci; Bruls, Olivier
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<br/>Abstract: Integrated optimization techniques for mechatronic systems aim at designing simultaneously the trajectory, the control system and the mechanical structure in order to minimize a performance index. The key advantage of such an integrated approach is the capability to search in a wide design space, to account for many dynamic couplings in an early design stage and to avoid simplifying assumptions which would induce a suboptimal design. This work considers that technique for robotic manipulators with flexible links. It is known that a exible multibody system is often non-minimum phase, here, no restriction is imposed to avoid it. This allows a free choice of the optimization process to select a lighter weight controlled system. Furthermore, the amplitudes of the non-actuated degrees-of-freedom should be reduced in order to limit bodies deformation. The mechanical model is derived using a nonlinear finite element method, which is a useful approach to represent systems with elastic bodies. An optimal control problem is considered to perform that integrated analysis and its time dicretization relies the direct transcription method.A Lie algebra approach to Lie group time integration of constrained systems
http://hdl.handle.net/2268/200020
Title: A Lie algebra approach to Lie group time integration of constrained systems
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<br/>Author, co-author: Arnold, Martin; Cardona, Alberto; Bruls, Olivier
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<br/>Abstract: Lie group integrators preserve by construction the Lie group structure of a nonlinear configuration space. In multibody dynamics, they support a representation of (large) rotations in a Lie group setting that is free of singularities. The resulting equations of motion are differential equations on a manifold with tangent spaces being parametrized by the corresponding Lie algebra. In the present paper, we discuss the time discretization of these equations of motion by a generalized-alpha Lie group integrator for constrained systems and show how to exploit in this context the linear structure of the Lie algebra. This linear structure allows a very natural definition of the generalized-alpha Lie group integrator, an efficient practical implementation and a very detailed error analysis. Furthermore, the Lie algebra approach may be combined with analytical transformations that help to avoid an undesired order reduction phenomenon in generalized-alpha time integration. After a tutorial-like step-by-step introduction to the generalized-alpha Lie group integrator, we investigate its convergence behaviour and develop a novel initialization scheme to achieve second-order accuracy in the application to constrained systems. The theoretical results are illustrated by a comprehensive set of numerical tests for two Lie group formulations of a rotating heavy top.Unilateral contact condition enhanced with squeeze film modelling in automotive differentials
http://hdl.handle.net/2268/200018
Title: Unilateral contact condition enhanced with squeeze film modelling in automotive differentials
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<br/>Author, co-author: Virlez, Geoffrey; Bruls, Olivier; Duysinx, Pierre; Géradin, Michel; Cardona, Alberto
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<br/>Abstract: The dynamic behaviour of automotive drivetrains is significantly influenced by contacts occurring between the various parts. In this paper, a three-dimensional formulation is proposed to model unilateral and frictional contact conditions between two rigid planar rings. The magnitude of the contact force is determined by a penalty method. In a second step, a simple squeeze film model is developed to account for the damping effect produced by the lubricating oil filling the gap between the two contacting bodies. The relevance and the accuracy of these models are illustrated through the global multibody modelling of a TORSEN differential.Variable thickness scroll compressor performance analysis—Part II: Dynamic modeling and model validation
http://hdl.handle.net/2268/199658
Title: Variable thickness scroll compressor performance analysis—Part II: Dynamic modeling and model validation
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<br/>Author, co-author: Bin, Peng; Lemort, Vincent; Legros, Arnaud; Hongsheng, Zhang; Haifeng, Gong
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<br/>Abstract: In order to investigate the performance of variable thickness scroll compressor, a detail mathematical modeling based on energy and mass balances is established in this two-part. In part II, dynamic modeling and model validation are developed. Temperature, pressure, mass flow of working chambers, friction loss power of moving parts, efficiency, and shaft power are investigated by solving the mathematical modeling. The experimental rig for variable thickness scroll compressor based on involute of circle, high order curve and arc is set up. From the comparison of the simulated and measured data, it can be seen that the compressor model predicts the mass flow, discharge temperature, and shaft power very well. So the proposed mathematical modeling can accurately describe all the suction, compression, and discharge processes for variable thickness scroll compressor.Variable thickness scroll compressor performance analysis—Part I: Geometric and thermodynamic modeling
http://hdl.handle.net/2268/199652
Title: Variable thickness scroll compressor performance analysis—Part I: Geometric and thermodynamic modeling
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<br/>Author, co-author: Bin, Peng; Lemort, Vincent; Legros, Arnaud; Hongsheng, Zhang; Haifeng, Gong
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<br/>Abstract: In order to investigate the performance of variable thickness scroll compressors, a detail mathematical modeling based on energy and mass balances is established in this two-part. In part I, the geometric modeling and thermodynamic modeling are developed. The profile based on circle involute, high order curve, and arc is built up using the base line method. The volume of working chambers from suction to discharge is defined. Thereafter, the evolution and derivative of the working chamber volume with respect to the orbiting angle are discussed. The energy and the mass balance for working chamber are described. Suction gas heating, radial and flank leakage, heat transfer between the working fluid, scroll wraps and plates are considered in the thermodynamic modeling. The established geometric modeling and thermodynamic modeling can provide better understanding of the variable thickness scroll compressor working process. The dynamical modeling and model validation are reported in part II.Recent Advances on the Oil-Free Scroll Compressor
http://hdl.handle.net/2268/199648
Title: Recent Advances on the Oil-Free Scroll Compressor
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<br/>Author, co-author: Bin, Peng; Legros, Arnaud; Lemort, Vincent; Xiaozheng, Xie; Haifeng, Gong
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<br/>Abstract: Traditionally, scroll compressors are mainly made of metallic parts and oil is used to lubricate the friction surfaces and reduce discharge temperature and leakage. But for the food processing, medical systems, textile manufacturing, fuel cell system, and other super-clean fields, the oil-less operation is critical. The oil is strictly forbidden in the working chambers of the scroll compressor in order to get the oil-free compressed air. So it is very important to develop the oil-free scroll compressor (OFSC). In this paper, the working principle and structure characteristics of the OFSC are investigated. Some of research works and the recent patents in this area are described and analyzed in detail, especially the water injection and air cooling OFSC. The future development on an OFSC is also presented. The analysis results demonstrated that there is dramatic growth potential in OFSC field.A numerical study of hypoelastic and hyperelastic large strain viscoplastic Perzyna type models
http://hdl.handle.net/2268/199412
Title: A numerical study of hypoelastic and hyperelastic large strain viscoplastic Perzyna type models
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<br/>Author, co-author: Careglio, Claudio; Canales Cardenas, Cristian; García Garino, Carlos; Mirasso, Anibal; Ponthot, Jean-Philippe
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<br/>Abstract: For the case ofmetalswith large viscoplastic strains, it is necessary to define appropriate constitutive models in order to obtain reliable results from the simulations. In this paper, two large strain viscoplastic Perzyna type models are considered. The first constitutive model has been proposed by Ponthot, and the elastic response is based on hypoelasticity. In this case, the kinematics of the constitutive model is based on the additive decomposition of the rate deformation tensor. The second constitutive model has been proposed by García Garino et al., and the elastic response is based on hyperelasticity. In this case, the kinematics of the constitutive model is based on the multiplicative decomposition of the deformation gradient tensor. In both cases, the resultant numerical models have been implemented in updated Lagrangian formulation. In this work, global and local numerical results of the mechanical response of both constitutive models are analyzed and discussed. To this end, numerical experiments are performed and different parameters of the constitutive models are tested in order to study the sensitivity of the resultant algorithms. In particular, the evolution of the reaction forces, the effective plastic strain, the deformed shapes and the sensitivity of the numerical results to the finite element mesh discretization have been compared and analyzed. The obtained results show that both models have a very good agreement and represent very well the characteristic of the viscoplastic constitutive model.On the numerical simulation of sheet metal blanking process
http://hdl.handle.net/2268/199411
Title: On the numerical simulation of sheet metal blanking process
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<br/>Author, co-author: Canales Cardenas, Cristian; Bussetta, Philippe; Ponthot, Jean-Philippe
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<br/>Abstract: The use of the blanking process has been widely spread in mass production industries. In this technique, the quality of the final product is directly related to the setting parameters of the process and the material response of the sheet. In the present work, a general framework based on the finite element method for the simulation of the sheet metal blanking process is presented. The proposed approach properly addresses all the numerical challenges related to blanking. First, an extension of elasto-viscoplastic constitutive equations for the large strain regime is used to take into account the material strain-rate sensitivity. Then, the inertial effects coming from high velocity operations are considered by means of an implicit time integration scheme. Moreover, the frictional contact interactions are simulated with the classical Coulomb law and an energetically consistent formulation of area regularization. Finally, ductile fracture is modeled thanks to the element deletion method coupled with a fracture criterion. The blanking process is then simulated for different setting parameters. The accuracy of this approach is evaluated by comparing the numerical predictions to experimental results for both quasi-static and dynamic conditions. Good agreement is found between experimental and numerical results for all cases.Thermomechanical simulation of blanking operated at high punch velocities
http://hdl.handle.net/2268/199410
Title: Thermomechanical simulation of blanking operated at high punch velocities
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<br/>Author, co-author: Canales Cardenas, Cristian; Boman, Romain; Ponthot, Jean-PhilippeComparison of moving boundary and finite-volume heat exchanger models in Modelica language
http://hdl.handle.net/2268/199251
Title: Comparison of moving boundary and finite-volume heat exchanger models in Modelica language
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<br/>Author, co-author: Desideri, Adriano; Dechesne, Bertrand; Wronski, Jorrit; Quoilin, Sylvain; Lemort, Vincent