Publications

2014

• Determination of the effect of stress state on the onset of ductile fracture through tension torsion experiments
  
  • Papasidero Jessica
  • Doquet Véronique
  • Mohr Dirk
  Experimental Mechanics, Society for Experimental Mechanics, 2014, 54 (2), pp.137-151. A tubular tension-torsion specimen is proposed to characterize the onset of ductile fracturein bulk materials at low stress triaxialities. The specimen features a stocky gage section of reduced thickness. The specimen geometry is optimized such that the stress and strain fields within the gage section are approximately uniform prior to necking. The stress state is plane stress while circumferential strain is approximately zero. By applying different combianations of tension and torsion, the material response can be determined for stress triaxialities ranging from zero (pure shear) to about 0.58 (transverse plane strain tension) and Lode angle parameters ranging from 0 to 1. The relative displacement and rotation of the specimens shoulder as well as the surface strain field witing the gage section are determined through stereo digital image correlation. Multiaxial fracture experiments are performed on a 36CrNiMO16 high strenght steel. A finite element model is built to determine the evolution of the local stress and strain fields all the way to fracture. Furthermore the newly-proposed Hosford-Coulomb fracture initiation model is used to describe the effect of stress state on the onset of fracture.
• Etude expérimentale et numérique de la rupture ductile sous chargement multiaxial
  
  • Papasidero Jessica
  , 2014. Une géométrie d'éprouvette tubulaire de traction-torsion entaillée a été optimisée pour caractériser l'effet de l'état des contraintes (triaxialité et paramètre de Lode) sur la ductilité des métaux à faible taux de triaxialité. Des essais biaxiaux proportionnels ou non, accompagnés de mesures des champs cinématiques par stéréo-corrélation d'images ont été réalisés sur un acier 36NiCrMo16 revenu et un alliage d'aluminium 2024-T351. Les trajets de chargement à rupture (évolution au point critique de la déformation plastique équivalente, de la triaxialité des contraintes et du paramètre de Lode) ont été obtenus. L'évolution de la ductilité de l'alliage d'aluminium en fonction de la triaxialité obtenue en traction-torsion diffère notablement de celle obtenue par Bao et Wierbicki en 2004 qui suggérait une ductilité minimale en cisaillement, tandis que la technique de traction-torsion révèle une ductilité maximale en cisaillement. Un effet notable des trajets de chargement non monotones ou non proportionnels sur la ductilité a été mis en évidence au moyen d'essais séquentiels composés d'un pré-chargement en compression, torsion ou traction, suivi d'une séquence de chargement proportionnel en traction-torsion combinées. Des observations au MEB de coupes métallographiques à l'issue d'essais biaxiaux interrompus, ainsi qu'un suivi en temps réel de la déformation et de l'endommagement en surface, lors d'essais de torsion dans le MEB et un essai de fissuration couplé à un suivi 3D de l'endommagement par laminographie sous rayonnement synchrotron ont mis en évidence des phénomènes de localisation à de multiples échelles ainsi que la croissance de certaines cavités, même en cisaillement pur, qui contraste avec l'affaissement total prédit par les modèles de cellule élémentaire. Ceci semble lié à l'allongement axial significatif mesuré en torsion pure (effet Swift). La localisation par cisaillement apparaît comme le mécanisme prédominant de coalescence des cavités, ce qui justifie l'adoption d'un critère d'initiation de la rupture de type Hosford-Coulomb. Utilisé en conjonction avec un indicateur non-linéaire d'endommagement il permet de rendre compte des ductilités mesurées, y compris sous chargement potentiellement non-proportionnel.
• Mathematical modelling of multi conductor cables
  
  • Beck Geoffrey
  • Imperiale Sebastien
  • Joly Patrick
  Discrete and Continuous Dynamical Systems - Series S, American Institute of Mathematical Sciences, 2014, pp.26. This paper proposes a formal justification of simplified 1D models for the propagation of electromagnetic waves in thin non-homogeneous lossy conductor cables. Our approach consists in deriving these models from an asymptotic analysis of 3D Maxwell’s equations. In essence, we extend and complete previous results to the multi-wires case. (10.3934/dcdss.2015.8.521)
  DOI : 10.3934/dcdss.2015.8.521
• Statistical inverse method for the multiscale identification of the apparent random elasticity field of heterogeneous microstructures
  
  • Soize Christian
  • Desceliers Christophe
  • Guilleminot Johann
  • Nguyen M. T.
  • Allain Jean-Marc
  • Gharbi H.
  , 2014.
• Editorial
  
  • Bérest Pierre
  Oil & Gas Science and Technology - Revue d'IFP Energies nouvelles, Institut Français du Pétrole (IFP), 2014, 69 (7), pp.1135-1141. No abstract available (10.2516/ogst/2014049)
  DOI : 10.2516/ogst/2014049
• Multi-scale mechanical characterization of sound dentin
  
  • Wang Wenlong
  • Vennat Elsa
  • Puel Guillaume
  • Roubier Nicolas
  • Allain Jean-Marc
  • Attal Jean-Pierre
  , 2014.
• Modelling the dynamics of the piano action: is apparent success real?
  
  • Thorin Anders
  • Boutillon Xavier
  • Lozada José
  Acta Acustica united with Acustica, Hirzel Verlag, 2014, pp.10. The kinematics and the dynamics of the piano action mechanism have been much studied in the last 50 years and fairly sophisticated models have been proposed in the last decade. Surprisingly, simple as well as sophisticated models seem to yield very valuable simulations when compared to measurements. We propose here a very simple model, with only 1-degree of freedom, and compare its outcome with force and motion measurements obtained by playing a real piano mechanism. The model, purposely chosen as obviously too simple to be predictive of the dynamics of the grand piano action, appears either as very good or as very bad, depending on which physical quantities are used as the input and output. We discuss the sensitivity of the simulation results to the initial conditions and to noise and the sensitivity of the experimental/simulation comparisons to the chosen dynamical model. It is shown that force-driven simulations with position comparisons, as they are proposed in the literature, do not validate the dynamical models of the piano action. It is suggested that these models be validated with position-driven simulations and force comparisons. (10.3813/AAA.918795)
  DOI : 10.3813/AAA.918795
• Direct finite element computation of non-linear modal coupling coefficients for reduced-order shell models
  
  • Touzé Cyril
  • Vidrascu Marina
  • Chapelle Dominique
  Computational Mechanics, Springer Verlag, 2014, 54, pp.567-580. We propose a direct method for computing modal coupling coefficients - due to geometrically nonlinear effects - for thin shells vibrating at large amplitude and discretized by a finite element (FE) procedure. These coupling coefficients arise when considering a discrete expansion of the unknown displacement onto the eigenmodes of the linear operator. The evolution problem is thus projected onto the eigenmodes basis and expressed as an assembly of oscillators with quadratic and cubic nonlinearities. The nonlinear coupling coefficients are directly derived from the finite element formulation, with specificities pertaining to the shell elements considered, namely, here elements of the ''Mixed Interpolation of Tensorial Components'' family (MITC). Therefore, the computation of coupling coefficients, combined with an adequate selection of the significant eigenmodes, allows the derivation of effective reduced-order models for computing - with a continuation procedure - the stable and unstable vibratory states of any vibrating shell, up to large amplitudes. The procedure is illustrated on a hyperbolic paraboloid panel. Bifurcation diagrams in free and forced vibrations are obtained. Comparisons with direct time simulations of the full FE model are given. Finally, the computed coefficients are used for a maximal reduction based on asymptotic nonlinear normal modes (NNMs), and we find that the most important part of the dynamics can be predicted with a single oscillator equation. (10.1007/s00466-014-1006-4)
  DOI : 10.1007/s00466-014-1006-4
• Foundation, analysis, and numerical investigation of a variational network-based model for rubber
  
  • Gloria Antoine
  • Le Tallec Patrick
  • Vidrascu Marina
  Continuum Mechanics and Thermodynamics, Springer Verlag, 2014, 26 (1), pp.1--31. Since the pioneering work by Treloar, many models based on polymer chain statistics have been proposed to describe rubber elasticity. Recently, Alicandro, Cicalese, and the first author have rigorously derived a continuum theory of rubber elasticity from a discrete model by variational convergence. The aim of this paper is twofold. First we further physically motivate this model, and complete the analysis by numerical simulations. Second, in order to compare this model to the literature, we present in a common language two other representative types of models, specify their underlying assumptions, check their mathematical properties, and compare them to Treloar's experiments. (10.1007/s00161-012-0281-6)
  DOI : 10.1007/s00161-012-0281-6
• Numerical validation of an Homogenized Interface Model
  
  • Geymonat Giuseppe
  • Hendili Sofiane
  • Krasucki Françoise
  • Vidrascu Marina
  Computer Methods in Applied Mechanics and Engineering, Elsevier, 2014, 269, pp.356-380. The aim of this paper is to numerically validate the effectiveness of a matched asymptotic expansion formal method introduced in a pioneering paper by Nguetseng and Sànchez Palencia [1] and extended in [2], [3]. Using this method a simplified model for the influence of small identical heterogeneities periodically distributed on an internal surface to the overall response of a linearly elastic body is derived. In order to validate this formal method a careful numerical study compares the solution obtained by a standard method on a fine mesh to the one obtained by asymptotic expansion. We compute both the zero and the first order terms in the expansion. To efficiently compute the first order term we introduce a suitable domain decomposition method. (10.1016/j.cma.2013.11.009)
  DOI : 10.1016/j.cma.2013.11.009
• Experimental study and modeling of the mechanical behavior of SiC/SiC composite tubes
  
  • Gélébart L.
  • Bernachy-Barbe Fabien
  • Bornert Michel
  • Crépin Jérôme
  , 2014.
• Reconstruction of constitutive parameters in isotropic linear elasticity from noisy full-field measurements
  
  • Bal Guillaume
  • Bellis Cédric
  • Imperiale Sébastien
  • Monard François
  Inverse Problems, IOP Publishing, 2014, 30, pp.125004. Within the framework of linear elasticity we assume the availability of internal full-field measurements of the continuum deformations of a non-homogeneous isotropic solid. The aim is the quantitative reconstruction of the associated moduli. A simple gradient system for the sought constitutive parameters is derived algebraically from the momentum equation, whose coefficients are expressed in terms of the measured displacement fields and their spatial derivatives. Direct integration of this system is discussed to finally demonstrate the inexpediency of such an approach when dealing with noisy data. Upon using polluted measurements, an alternative variational formulation is deployed to invert for the physical parameters. Analysis of this latter inversion procedure provides existence and uniqueness results while the reconstruction stability with respect to the measurements is investigated. As the inversion procedure requires differentiating the measurements twice, a numerical differentiation scheme based on an ad hoc regularization then allows an optimally stable reconstruction of the sought moduli. Numerical results are included to illustrate and assess the performance of the overall approach. (10.1088/0266-5611/30/12/125004)
  DOI : 10.1088/0266-5611/30/12/125004
• Characterization of mechanical damage in granite
  
  • Luong Minh-Phong
  • Emami Mehrdad
  Array, Elsevier, 2014, 8 (27), pp.38-42. This paper aims to illustrate the use of infrared thermography as a non-destructive and non-contact technique to observe the phenomenological manifestation of damage in granite under unconfined compression. It allows records and observations in real time of heat patterns produced by the dissipation of energy generated by plasticity. The experimental results show that this technique, which couples mechanical and thermal energy, can be used for illustrating the onset of damage mechanism by stress concentration in weakness zones. (10.3221/IGF-ESIS.27.05)
  DOI : 10.3221/IGF-ESIS.27.05
• Measuring local and global vibration modes in model plants
  
  • Der Loughian Christelle C.
  • Tadrist Loïc
  • Allain Jean-Marc
  • Diener Julien
  • Moulia Bruno B.
  • de Langre Emmanuel
  Comptes rendus de l’Académie des sciences. Série IIb, Mécanique, Elsevier, 2014, 342 (1), pp.1-7. Model plants are extensively used in biological studies, and their mechanical behaviour needs to be better understood, in relation to studies in mechanoperception for instance. We present here the first approach to derive experimentally the modal parameters of two of these plants, Arabidopsis thaliana and Populus tremula alba. A classical sinusoidal sweep excitation is used, with a measurement of displacements based on LKT optical flow tracking, followed by a Bi-Orthogonal decomposition (BOD). This allows to estimate several modal frequencies for each plant, as well as the corresponding spatial localizations of deformation. Analyzing the modal frequencies, we show that global and local modes correspond to distinct ranges of frequencies and depend differently on plant size. Possible phenotyping applications are then discussed. (10.1016/j.crme.2013.10.010)
  DOI : 10.1016/j.crme.2013.10.010
• Voxel-based path planning for 3D scanning of mechanical parts
  
  • Lartigue Claire
  • Quinsat Yann
  • Mehdi-Souzani Charyar
  • Zuquete Guarato Alexandre
  • Tabibian Shadan
  Computer-Aided Design and Applications, CAD Solutions LLC (imprimé) and Taylor & Francis Online (en ligne), 2014, pp.220-227. The paper deals with an original approach to scan path planning that applies for any type of sensors. The approach relies on the representation of the part surface as a voxel map. The size of each voxel is defined according to the sensor FOV. To each voxel, a unique point of view is associated in function of visibility and quality criteria. Whatever the sensor, the method provides a set of admissible points of view to ensure the surface digitizing with a given quality.
• Influence of interfacial adhesion on the mechanical response of magneto‑rheological elastomers at high strain
  
  • Pössinger T
  • Bolzmacher Christian
  • Bodelot Laurence
  • Triantafyllidis Nicolas
  Microsystem Technologies, Springer Verlag, 2014, 20, pp.803-814. macroscopic behavior of the composite only after 80 % deformation in the case of the 30 % volume fraction Mre. (10.1007/s00542-013-2036-0)
  DOI : 10.1007/s00542-013-2036-0
• The homogenized behavior of unidirectional fiber-reinforced composite materials in the case of debonded fibers
  
  • Berrehili Yahya
  • Marigo Jean-Jacques
  Mathematics and Mechanics of Complex Systems, International Research Center for Mathematics & Mechanics of Complex Systems (M&MoCS),University of L’Aquila in Italy, 2014, 2 (2), pp.181-207. This paper is devoted to the analysis of the homogenized behavior of unidirectional composite materials once the fibers are debonded from (but still in contact with) the matrix. This homogenized behavior is built by an asymptotic method in the framework of the homogenization theory. The main result is that the homogenized behavior of the debonded composite is that of a generalized continuous medium with an enriched kinematics. Indeed, besides the usual macroscopic displacement field, the macroscopic kinematics contains two other scalar fields. The former one corresponds to the displacement of the matrix whereas the two latter ones correspond to the sliding and the rotation of the debonded fibers with respect to the matrix. Accordingly, new homogenized coefficients and new coupled equilibrium equations appear. This problem is addressed in a linear elastic three-dimensional setting.
• Bipotential versus return mapping algorithms: Implementation of non associated flow rules
  
  • Magnier Vincent
  • Charkaluk Eric
  • de Saxcé Géry
  International Journal of Solids and Structures, Elsevier, 2014, 51 (15-16), pp.2857-2864. Numerical implementation of constitutive laws involves specific incremental methods. The "return mapping" (Simo and Hughes, 1998) and the "bipotential" (de Saxcé, 1992) are one of those, associated respectively to two different classes of materials: the General Standard Materials (GSM) for the return mapping and the Implicit Standard Materials (ISM) for the bipotential. The objective of this paper is then to compare the implementation of those both methods in the case of non associated flow rules in plasticity. In the first section, the properties of the different previous material classes will be recalled and the methods of "return mapping" and "bipotential" will be detailed. The comparison of both methods is realised on the non linear kinematic hardening rule of Armstrong-Frederick (Armstrong and Frederick, 1966) in a second section and the details are given in a third part. The numerical implementation is realised in Abaqus/Standard 6.11 by the means of a UMat subroutine and the practical simple case of tension-compression is analysed in a last section. (10.1016/j.ijsolstr.2014.04.004)
  DOI : 10.1016/j.ijsolstr.2014.04.004
• A three-dimensional analysis of fatigue crack paths in thin metallic sheets
  
  • Esnault Jean-Baptiste
  • Doquet Véronique
  • Massin Patrick
  International Journal of Fatigue, Elsevier, 2014, 62, pp.119-132. Fatigue crack growth in thin sheets of 7075 T651 aluminium alloy and S355 steel were characterised in 3D, using crack front markings and topographic reconstructions of fracture surfaces. Tests performed in air or in salt water produced different crack paths for similar mechanical condit ions, shear lips being reduced by corrosive environment, in the aluminium alloy as well as in the steel. Before the onset of shear lips development, tunnelling crack fronts were observed, due to the difference in closure effects at mid-thickness and near free surfaces. Tunnelling was progressively reduced and cancelled as slanted crack growth developed, even though DK I was reduced locally by crack twisting. This indicates a significant contribution of shear modes to the crack driving force, even though mode I striations are present in slanted zones. Elastic three-dimensional X-FEM computations were performed to analyse the observed crack growth kinetics, based on ΔKI , ΔKII and ΔKIII. The crack growth rates correlated much better to ΔKeq = √(ΔKI^2 + ΔKII^2 + (ΔKIII^2/(1-ν))) than to ΔKI. Elastic–plastic finite element simulations and the local application of a fatigue criterion with an amplitude-dependent critical plane were found to capture qualitatively the transition in fracture mode and its inhibition by side grooves. (10.1016/j.ijfatigue.2013.03.015)
  DOI : 10.1016/j.ijfatigue.2013.03.015
• Strong convergence results for the asymptotic behavior of the 3D-shell model
  
  • Chapelle Dominique
  • Collin Annabelle
  Journal of Elasticity, Springer Verlag, 2014, 115 (2), pp.173-192. We revisit the asymptotic convergence properties - with respect to the thickness parameter - of the earlier-proposed 3D-shell model. This shell model is very attractive for engineering applications, in particular due to the possibility of directly using a general 3D constitutive law in the corresponding finite element formulations. We establish strong convergence results for the 3D-shell model in the two main types of asymptotic regimes, namely, bending- and membrane-dominated behavior. This is an important achievement, as it completely substantiates the asymptotic consistency of the 3D-shell model with 3D linearized isotropic elasticity. (10.1007/s10659-013-9452-3)
  DOI : 10.1007/s10659-013-9452-3
• General coupling of porous flows and hyperelastic formulations -- From thermodynamics principles to energy balance and compatible time schemes
  
  • Chapelle Dominique
  • Moireau Philippe
  European Journal of Mechanics - B/Fluids, Elsevier, 2014, 46, pp.82-96. We formulate a general poromechanics model -- within the framework of a two-phase mixture theory -- compatible with large strains and without any simplification in the momentum expressions, in particular concerning the fluid flows. The only specific assumptions made are fluid incompressibility and isothermal conditions. Our formulation is based on fundamental physical principles -- namely, essential conservation and thermodynamics laws -- and we thus obtain a Clausius-Duhem inequality which is crucial for devising compatible constitutive laws. We then propose to model the solid behavior based on a generalized hyperelastic free energy potential -- with additional viscous effects -- which allows to represent a wide range of mechanical behaviors. The resulting formulation takes the form of a coupled system similar to a fluid-structure interaction problem written in an Arbitrary Lagrangian-Eulerian formalism, with additional volume-distributed interaction forces. We achieve another important objective by identifying the essential energy balance prevailing in the model, and this paves the way for further works on mathematical analyses, and time and space discretizations of the formulation. (10.1016/j.euromechflu.2014.02.009)
  DOI : 10.1016/j.euromechflu.2014.02.009
• Probability density functions: From porosities to fatigue lifetime
  
  • Charkaluk Eric
  • Constantinescu Andrei
  • Szmytka Fabien
  • Tabibian Shadan
  International Journal of Fatigue, Elsevier, 2014, 63, pp.127-136. This paper proposes a novel method to establish and identify a probability density function characterizing the fatigue lifetime. The method is initiated with a quantitative analysis of the microstructure of the material, which provides the initial probability distribution of defects. After identifying a given probability density function of defects, one can transport it into a lifetime probability density function using a growth law involving a measure of the loading over a cycle. Several parameters of the growth law are finally estimated from a given set of fatigue experiments on specimens and several techniques are discussed. The method is applied on real defect observations and lifetime data. The estimated lifetimes using the novel technique is of similar quality with standard estimation providing the probability density function of lifetime as an additional output. This output can be used directly as an input in a stress-strength interference method. (10.1016/j.ijfatigue.2014.01.017)
  DOI : 10.1016/j.ijfatigue.2014.01.017
• Modeling of damage in unidirectional ceramic matrix composites and multi-scale experimental validation on third generation SiC/SiC minicomposites
  
  • Chateau Camille
  • Gélébart Lionel
  • Bornert Michel
  • Crépin Jérôme
  • Caldemaison Daniel
  • Sauder Cédric
  Journal of the Mechanics and Physics of Solids, Elsevier, 2014, 63, pp.298-319. The purpose of this paper is to experimentally validate a 1D probabilistic model of damage evolution in unidirectional SiC/SiC composites. The key point of this approach lies in the identification and validation at both local and macroscopic scales. Thus, in addition to macroscopic tensile tests, the evolution of microscopic damage mechanisms - in the form of matrix cracks and fiber breaks - is experimentally analyzed and quantified through in-situ scanning electron microscope and computed tomography tensile tests. A complete model, including both matrix cracking and fiber breaking, is proposed on the basis of existing modeling tools separately addressing these mechanisms. It is based on matrix and fiber failure probability laws and a stress redistribution assumption in the vicinity of matrix cracks or fiber breaks. The identification of interfacial parameters is conducted to fit the experimental characterization, and shows that conventional assumptions of 1D probabilistic models can adequately describe matrix cracking at both macro- and microscopic scales. However, it is necessary to enrich them to get a proper prediction of ultimate failure and fiber break density for Hi-Nicalon type S fiber-reinforced SiC/SiC minicomposites. (10.1016/j.jmps.2013.09.001)
  DOI : 10.1016/j.jmps.2013.09.001
• Soft beams: when capillarity induces axial compression
  
  • Neukirch Sébastien
  • Antkowiak Arnaud
  • Marigo Jean-Jacques
  Physical Review E, American Physical Society (APS), 2014, 89 (1), pp.012401. We study the interaction of an elastic beam with a liquid drop in the case where bending and extensional effects are both present. We use a variational approach to derive equilibrium equations and constitutive relation for the beam. This relation is shown to include a term due to surface energy in addition of the classical Young's modulus term, leading to a modification of Hooke's law. At the triple point where solid, liquid, and vapor phases meet we find that the external force applied on the beam is parallel to the liquid-vapor interface. Moreover, in the case where solid-vapor and solid-liquid interface energies do not depend on the extension state of the beam, we show that the extension in the beam is continuous at the triple point and that the wetting angle satisfy the classical Young-Dupré relation. (10.1103/PhysRevE.89.012401)
  DOI : 10.1103/PhysRevE.89.012401
• The Mechanisms of Deformation and Damage of Mudstones: A Micro-scale Study Combining ESEM and DIC
  
  • Wang L. L.
  • Bornert Michel
  • Héripré E.
  • Chanchole S.
  • Pouya Ahmad
  • Halphen B.
  Rock Mechanics and Rock Engineering, Springer Verlag, 2014, pp.s.p.. Combining environmental scanning electron microscopy (ESEM) and digital image correlation techniques, the mechanical behaviour of mudstones is studied at the scale of their composite microstructure (that is, grains of carbonate and quartz embedded in a clay matrix). A specially designed apparatus is developed to allow in-situ uniaxial compression tests on samples with controlled humidity states in the ESEM chamber. As the mechanical behavior of mudstones is sensitive to water content, two tests on samples with contrasting water contents (3.8 and 7.4 %) are performed to identify the unified mechanisms of deformation and damage. We illustrate heterogeneous local strain fields that well correlate with the microstructure of mudstones. Three types of deformation bands involving different mechanisms have been classified: orthogonal (compaction of macro-pores and closure of pre-existing cracks), parallel (micro-cracking) and inclined (shear deformation) to the uniaxial compression direction. These deformation modes are activated at different stress levels, and they strongly interact: for instance, a high-strained shear band may result in tensile micro-cracks at its tip. We also illustrate damage phenomena, particularly at the inclusion-matrix interface, which is found to be a hazardous position for nucleation of micro-cracks. (10.1007/s00603-014-0670-1)
  DOI : 10.1007/s00603-014-0670-1