Publications

2013

• Solid Drops: Large Capillary Deformations of Immersed Elastic Rods
  
  • Mora Serge
  • Maurini Corrado
  • Phou Ty
  • Fromental Jean-Marc
  • Audoly Basile
  • Pomeau Yves
  Physical Review Letters, American Physical Society, 2013, 111 (11). Under the effect of surface tension a blob of liquid adopts a spherical shape when immersed in another fluid. We demonstrate experimentally that soft, centimeter-size elastic solids can exhibit a similar behavior: when immersed into a liquid, a gel having a low elastic modulus undergoes large, reversible deformations. We analyze three fundamental types of deformations of a slender elastic solid driven by surface stress, depending on the shape of its cross-section: a circular elastic cylinder shortens in the longitudinal direction and stretches transversally; the sharp edges of a square based prism get rounded off as its cross-sections tend to become circular; a slender, triangular based prism bends. These experimental results are compared to analysis and non-linear simulations of neo-Hookean solids deformed by surface tension, and are found to be in good agreement with each other. (10.1103/PhysRevLett.111.114301)
  DOI : 10.1103/PhysRevLett.111.114301
• Identification of transient heat sources using the reciprocity gap
  
  • Auffray Nicolas
  • Bonnet Marc
  • Pagano Stéphane
  Inverse Problems in Science and Engineering, Taylor & Francis, 2013, 21, pp.721-738. The deformation of solid materials is nearly always accompanied with temperature variations, induced by intrinsic dissipation and thermomechanical coupling. Heat sources give precious information on the thermomechanical behavior of materials. They can be indirectly observed from thermal measurements on the specimen boundary, obtained e.g. via infrared thermography. To solve the inverse problem of identifying heat sources from such observations, a non-iterative algebraical method based on the Reciprocity Gap Method is proposed. This approach, used elsewhere mainly for time-independent identification, is applied here to transient measurements. Under appropriate modelling assumptions the number of heat sources, their spatial locations and energies are retrieved, as demonstrated on numerical experiments where the robustness of the method to measurement noise is also studied. (10.1080/17415977.2012.731597)
  DOI : 10.1080/17415977.2012.731597
• From gradient damage laws to Griffith's theory of crack propagation
  
  • Sicsic Paul
  • Marigo Jean-Jacques
  Journal of Elasticity, Springer Verlag, 2013, 113 (1), pp.55-74. This paper is devoted to the comparison of the evolution of damage governed by a gradient damage model with the evolution of a crack predicted by Griffith's law. The analysis is made in a two-dimensional setting, assuming that damage is concentrated inside thin bands whose width is proportional to the internal length of the material. Taking advantage of the variational formulation based on the three principles of irreversibility, stability and energy balance, one introduces a generalized Rice path integral which contains terms involving the gradient of damage. Assuming that the internal length of the material is small by comparison with the dimension of the body, a separation of scales is achieved. Owing to the energy balance and the stability condition, one first proves some properties of this path integral with respect to the path. Then, one shows that the evolution of the damage zone is governed by Griffith's law, the dissipated surface energy being given by the energy dissipated in the damage process zone.
• Noise-Corrected Estimation of Complex Modulus in Accord With Causality and Thermodynamics: Application to an Impact Test.
  
  • Collet Pierre
  • Gary Gérard
  • Lundberg Bengt
  Journal of Applied Mechanics, American Society of Mechanical Engineers, 2013, 80 (011018-1), pp.JANUARY 2013. Methods for estimation of the complex modulus generally produce data from which discrete results can be obtained for a set of frequencies. As these results are normally afflicted by noise, they are not necessarily consistent with the principle of causality and requirements of thermodynamics. A method is established for noise-corrected estimation of the complex modulus, subject to the constraints of causality, positivity of dissipation rate and reality of relaxation function, given a finite set of angular frequencies and corresponding complex moduli obtained experimentally. Noise reduction is achieved by requiring that two self-adjoint matrices formed from the experimental data should be positive semidefinite. The method provides a rheological model that corresponds to a specific configuration of springs and dashpots. The poles of the complex modulus on the positive imaginary frequency axis are determined by a subset of parameters obtained as the common positive zeros of certain rational functions, while the remaining parameters are obtained from a least squares fit. If the set of experimental data is sufficiently large, the level of refinement of the rheological model is in accordance with the material behavior and the quality of the experimental data. The method was applied to an impact test with a Nylon bar specimen. In this case, data at the 29 lowest resonance frequencies resulted in a rheological model with 14 parameters. The method has added improvements to the identification of rheological models as follows: (1) Noise reduction is fully integrated. (2) A rheological model is provided with a number of elements in accordance with the complexity of the material behavior and the quality of the experimental data. (3) Parameters determining poles of the complex modulus are obtained without use of a least squares fit. (10.1115/1.4007081)
  DOI : 10.1115/1.4007081
• Micro-scale experimental investigation of the swelling anisotropy of the Callovo-Oxfordian argillaceous rock
  
  • Wang Linlin
  • Bornert Michel
  • Chanchole Serge
  • Yang Diansen
  • Héripré Eva
  • Tanguy Arnaud
  • Caldemaison Daniel
  Clay Minerals, Mineralogical Society, 2013, 48 (2), pp.391-402. An experimental study of the swelling anisotropy of the Callovo-Oxfordian argillaceous rock under hydration is presented. The investigation, which combines environmental scanning electron microscopy (ESEM) and digital image correlation techniques, has been carried out at the micrometric scale of the composite microstructure of the rock. Specimens were hydrated in the ESEM over a wide range of relative humidity and observations conducted on two planes: plane 1 parallel to the bedding plane, and plane 2 perpendicular to it. The observations reveal that the local swelling (which can be quantified at a local gauge length of about 5 µm) is strongly anisotropic in both planes. The global swelling, measured over areas of about 500 µm in width, is also clearly anisotropic in plane 2 (with major swelling direction normal to the bedding plane), but not in plane 1. The global isotropy in plane 1 arises from the uniform distribution of the orientation of anisotropic local strains, while the anisotropic swelling in plane 2 is due to a preferred local orientation. (10.1180/claymin.2013.048.2.17)
  DOI : 10.1180/claymin.2013.048.2.17
• Modified Kolsky Formulas for an Increased Measurement Duration of SHPB Systems
  
  • Gary Gérard
  • Mohr Dirk
  Experimental Mechanics, Society for Experimental Mechanics, 2013, 53 (4), pp.713-717. The so-called incident, reflected and transmitted strain histories are typically recorded during standard Split Hopkinson Pressure Bar (SHPB) experiments. Subsequently, the stress-strain curve for the specimen material is determined based on these recordings. Unless wave deconvolution techniques are employed, the reliable measurement of the reflected wave requires an input bar which is at least twice as long as the striker bar (of equal impedance). The present brief technical note elucidates the advantages of a simple alternative configuration which has only been seldom used in the past. Based on the assumption of quasi-static equilibrium at the specimen level, we present a modification of Kolsky's formulas such that the stress-strain curve for the specimen material can be obtained from the measurement of the incident and transmitted strain histories only. As a result, the measurement of the reflected wave may be omitted and a much shorter input bar can be chosen. Conversely, a much longer striker bar may be used for a given input bar length, thereby increasing the valid duration of standard SHPB experiments by up to 100% through the use of the modified Kolky formulas. An example experiment is shown where the duration of valid measurements has been increased by more than 70%.
• Parallel measurements of reaction kinetics using ultralow-volumes
  
  • Fradet Etienne
  • Abbyad Paul
  • Vos Marten H.
  • Baroud Charles N.
  Lab on a Chip, Royal Society of Chemistry, 2013, 13 (22), pp.4326-4330. We present a new platform for the production and manipulation of microfluidic droplets in view of measuring the evolution of a chemical reaction. Contrary to existing approaches, our device uses gradients of confinement to produce a single drop on demand and guide it to a pre-determined location. In this way, two nanoliter drops containing different reagents can be placed in contact and merged together, in order to trigger a chemical reaction. The reaction rate is extracted from an analysis of the observed reaction-diffusion front. We show that the results obtained using this platform are in excellent agreement with stopped-flow measurements, while decreasing the sample consumption 5000 fold. We also show how the device operation can be parallelized in order to react an initial sample with a range of compounds or concentrations, on a single integrated chip. This integrated chip thus further reduces sample consumption while reducing the time required for the experimental runs from hours to minutes. (10.1039/c3lc50768h)
  DOI : 10.1039/c3lc50768h
• Oscillation damping in trees
  
  • Spatz Hanns-Christof
  • Theckes Benoit
  Plant Science, Elsevier, 2013, 207, pp.66-71. Oscillation damping is of vital importance for trees to withstand strong gusty winds. Tree adaptation to wind loading takes place over a long time and during a storm only passive damping mechanisms can reduce the impact of the wind on trunk and roots. Structural damping, a phenomenon, which is associated with the conspicuous movements of the branches relative to the trunk is of particular importance. Primary and higher order branches can be seen as multiple tuned mass dampers. Moreover, as the frequency bands overlap within branches and between primary branches and the entire tree, resonance energy transfer can distribute mechanical energy over the entire tree, such that it is dissipated more effectively than in a tree with stiff branches and not so much focused on the tree trunk and the roots. Theoretical studies using modal analysis and finite element methods have supported these assertions. Next to "multiple mass damping" and "multiple resonance damping", both characterized by linear coupling between the elements, a third non linear mode, operative at large amplitudes has been identified: "damping by branching". In all these not mutually exclusive concepts frequency tuning between the elements appears to be a fundamental requisite. (C) 2013 Elsevier Ireland Ltd. All rights reserved. (10.1016/j.plantsci.2013.02.015)
  DOI : 10.1016/j.plantsci.2013.02.015
• Multi-parameter Fatigue Equivalence Loadings for Specification Applications
  
  • Roux Clément
  • Lorang Xavier
  • Maitournam Habibou
  • Nguyen-Tajan Mac-Lan
  • Quesson Benoit
  Procedia Engineering, Elsevier, 2013, 66, pp.393-402. This paper deals with a method to define Equivalent Fatigue Loads (EFL) from in-service load measurement in the case of a structure subjected to multiple variable fatigue loadings. EFL can be used in order to define tests on full scale structures for an experimental validation approach. It can be also used for the evaluation of the severity of the in-service loads, useful step in a reliability approach, in order to optimize the geometry with respect to the fatigue damage. The aim of the paper is to define the mathematical and mechanical concept of the Equivalence Fatigue Method in the case of multi-parameters loading for specification application. This method uses fatigue damage evaluation from statistical in-service measurement data. The specificity of the method presented here is to use a fully multi-parameters equivalence method. Damages is evaluated using life prediction method based on multiaxial criteria. The method is used for rotating structures, applied to a specific family of structure: train wheels. Train wheels are critical safety railway components mainly subjected to random multiaxial fatigue induced by multi-parameters loading. In this paper an approach to evaluate damage from this measurement in order to find the EFL with a damage equivalence optimization is developed. (10.1016/j.proeng.2013.12.093)
  DOI : 10.1016/j.proeng.2013.12.093
• Influence of orthogonal prestrain on the viscoelastic behaviour of highly-filled elastomers
  
  • Azoug Aurélie
  • Thorin Anders
  • Nevière Robert
  • Pradeilles-Duval Rachel-Marie
  • Constantinescu Andrei
  Polymer Testing, Elsevier, 2013, 32 (2), pp.375-384. Highly filled elastomers exhibit a complex nonlinear mechanical behaviour that is difficult to characterize experimentally. This paper presents a Dynamic Mechanical Analysis (DMA) method coupled with orthogonal prestrains, applied in two distinct steps. A localization operator between measurements at the arms of a cross shaped specimen and the stress and strain fields at its center was determined using elastic small strain finite element computations. The operator makes estimating the storage and loss moduli at the center of the specimen possible. A mathematical model is then fitted to the moduli values. These results are compared to DMA measurements of highly filled elastomers under uniaxial prestrain. Although the storage and loss moduli increase with the prestrain under both loadings, the nonlinear behaviour is quantitatively modified by adding an orthogonal prestrain. In addition, the modification of the behaviour under a horizontal prestrain is cancelled out by an increase of the vertical prestrain, which may be explained by fillers aligning in the direction of the prestrain. (10.1016/j.polymertesting.2012.12.005)
  DOI : 10.1016/j.polymertesting.2012.12.005
• From the onset of damage to rupture: construction of responses with damage localization for a general class of gradient damage models
  
  • Pham Kim
  • Marigo Jean-Jacques
  Continuum Mechanics and Thermodynamics, Springer Verlag, 2013, 25 (2-4), pp.147--171. We propose a construction method of non homogeneous solutions for the traction problem of an elastic damaging bar. This bar has a softening behavior which obeys a gradient damaged model. The method is applicable for a wide range of brittle materials. For sufficiently long bars, we show that localization arises on sets whose length is proportional to the material internal length and with a profile which is also a material characteristic. From its onset until the rupture, the damage profile is obtained either in a closed form or after a simple numerical integration depending on the model. Thus, the proposed method provides definitions for the critical stress and fracture energy that can be compared with experimental results. We finally discuss some features of the global behavior of the bar such as the possibility of a snap-back at the onset of damage. We point out the sensitivity of the responses to the parameters of the damage law. All these theoretical considerations are illustrated by numerical examples. (10.1007/s00161-011-0228-3)
  DOI : 10.1007/s00161-011-0228-3
• Load-Inversion Device for the High Strain Rate Tensile Testing of Sheet Materials with Hopkinson Pressure Bars
  
  • Dunand Matthieu
  • Gérard Gary
  • Mohr Dirk
  Experimental Mechanics, Society for Experimental Mechanics, 2013, 53 (7), pp.1177-1188. A high strain rate tensile testing technique for sheet materials is presented which makes use of a split Hopkinson pressure bar system in conjunction with a load inversion device. With compressive loads applied to its boundaries, the load inversion device introduces tension into a sheet specimen. Two output bars are used to minimize the effect of bending waves on the output force measurement. A Digital Image Correlation (DIC) algorithm is used to determine the strain history in the specimen gage section based on high speed video imaging. Detailed finite element analysis of the experimental set-up is performed to validate the design of the load inversion device. It is shown that under the assumption of perfect alignment and slip-free attachment of the specimen, the measured stress-strain curve is free from spurious oscillations at a strain rate of 1,000 s(-1). Validation experiments are carried out using tensile specimens extracted from 1.4 thick TRIP780 steel sheets. The experimental results for uniaxial tension at strain rates ranging from 200 s(-1) to 1,000 s(-1) confirm the oscillation-free numerical results in an approximate manner. Dynamic tension experiments are also performed on notched specimens to illustrate the validity of the proposed experimental technique for characterizing the effect of strain rate on the onset of ductile fracture in sheet materials. (10.1007/s11340-013-9712-y)
  DOI : 10.1007/s11340-013-9712-y
• Characterization of the High Temperature Strain Partitioning in Duplex Steels
  
  • Martin Guilhem
  • Caldemaison Daniel
  • Bornert Michel
  • Pinna Christophe
  • Bréchet Yves
  • Véron Muriel
  • Mithieux Jean-Denis
  • Pardoen Thomas
  Experimental Mechanics, Society for Experimental Mechanics, 2013, 53 (2), pp.205-215. A microgrid technique has been developed for the analysis of the high-temperature micro-scale strain distribution between ferrite and austenite into duplex stainless steels. The local strain is measured by micro-extensometry using square microgrids engraved on flat specimens by electro-lithography. The sample with microgrids on the surface and preliminary imaged with high definition scanning electron microscope (SEM), is inserted in a plane strain compression specimen to be deformed under conditions representative of hot rolling. After deformation, the sample is extracted from the compressed block and the surface is again analyzed by SEM and image processing to determine the strain field. The strain is heterogeneously distributed with a strong localization of the deformation, in the form of shear bands located within the ferrite and at the vicinity of the austenite/ferrite interphase boundaries. These strain maps provide useful informations about the rheology of the phases as well as about the local conditions at the origin of the damage process (10.1007/s11340-012-9628-y)
  DOI : 10.1007/s11340-012-9628-y
• Improvement of thermomechanical full-field analysis of metallic polycrystals using crystallographic data
  
  • Seghir Rian
  • Witz Jean-Francois
  • Charkaluk Eric
  • Dufrenoy Philippe
  Mechanics & Industry, EDP Sciences, 2013, 13 (6), pp.395-403. This paper is based on additional treatments of the experimental results obtained by L. Bodelot, L. Sabatier, E. Charkaluk, P. Dufrénoy [Experimental setup for fully coupled kinematic and thermal measurements at the microstructure scale of an AISI 316l steel, Mater. Sci. Eng. A 501 (2009) 52-60]. In order to perform inter- and intragranular thermomechanical analyses in a metallic polycrystal at the grain scale, a crystallography-based projection technique of the thermal and displacement fields on a polynomial basis is proposed. It enables intragranular coupled analysis of strain and temperature full-field data consistent with the plastic slip activation observed on specimen surface after the test. (10.1051/meca/2012035)
  DOI : 10.1051/meca/2012035
• Creep closure rate of a shallow salt cavern at Gellenoncourt, France
  
  • Benoît Brouard
  • Berest Pierre
  • Vincent De Greef
  • Jean-François Béraud
  • Cédric Lheur
  International Journal of Rock Mechanics and Mining Sciences, Pergamon and Elsevier, 2013 (62), pp.42-50. Cavern creep closure rate was recorded in the SG13-SG14 salt cavern of the Gellenoncourt brine field operated by CSME at Gellenoncourt in Lorraine, France. Cavern compressibility and the evolution of cavern brine temperature first were measured. In this shallow cavern (250-m, or 800-ft, deep), which had been kept idle for 30 years, cavern-brine thermal expansion can be disregarded. To assess cavern closure rate, a 10-month brine-outflow test was performed, followed by a 6-month shut-in test. During the tests, brine outflow or pressure evolution is influenced by atmospheric pressure changes, ground temperature changes and Earth tides. From the average pressure-evolution rate, it can be inferred that the steady-state cavern closure rate is slower than 10−5/year or 3 10−13/s.
• Modelling the influence of temperature and relative humidity on the time-dependent mechanical behaviour of a short glass fibre reinforced polyamide
  
  • Launay Antoine
  • Marco Yann
  • Maitournam Habibou
  • Raoult Ida
  Mechanics of Materials, Elsevier, 2013, 56, pp.pp 1 - 10, issn = "0167-6636", url = "http://www.sciencedirect.com/science/article/pii/S016766361200. Polymer matrix composites, and especially short glass fibre reinforced polyamides, are widely used in the automotive industry. Their application on structural components requires a confident mechanical design taking into account the sensitivity of the mechanical response to both temperature T and relative humidity H. In this paper, the constitutive model already developed by the authors (Launay et al., 2011) is applied to describe the non-linear time-dependent behaviour of a PA66-GF35 under various hygrothermal conditions. The extensive experimental database involves testing conditions under and above the glass transition temperature Tg. An equivalence principle between temperature and relative humidity is applied and validated, since the non-linear mechanical response is shown to depend only on the temperature gap T-Tg(H). (10.1016/j.mechmat.2012.08.008)
  DOI : 10.1016/j.mechmat.2012.08.008
• Onset-of-instability in Axially Compressed Honeycomb under General Loading
  
  • Lopez-Jimenez F.
  • Triantafyllidis Nicolas
  International Journal of Solids and Structures, Elsevier, 2013, 50, pp.3934 - 3946.
• Fracture and debonding of a thin film on a stiff substrate: analytical and numerical solutions of a one-dimensional variational model
  
  • Baldelli Andrés Alessandro Leon
  • Bourdin Blaise
  • Marigo Jean-Jacques
  • Maurini Corrado
  Continuum Mechanics and Thermodynamics, Springer Verlag, 2013, 25 (2--4), pp.243--268. Westudymulti-fissurationanddebondingphenomenaofathinfilmbondedtoastiffsubstrateusing the variational approach to fracture mechanics. We consider a reduced one-dimensional membrane model where the loading is introduced through uniform inelastic (e.g., thermal) strains in the film or imposed dis- placements of the substrate. Fracture phenomena are accounted for by adopting a Griffith model for debonding and transverse fracture. On the basis of energy minimization arguments, we recover the key qualitative prop- erties of the experimental evidences, like the periodicity of transverse cracks and the peripheral debonding of each regular segment. Phase diagrams relate the maximum number of transverse cracks that may be created before debonding takes place, as a function of the material properties and the sample's geometry. The theo- retical results are illustrated with numerical simulations obtained through a finite element discretization and a regularized variational formulation of the Ambrosio-Tortorelli type, which is suited to further extensions in two-dimensional settings. (10.1007/s00161-012-0245-x)
  DOI : 10.1007/s00161-012-0245-x
• Yield Design
  
  • Salençon Jean
  , 2013, pp.240.
• Application of 2D and 3D Digital Image Correlation on CO2-like altered carbonate
  
  • Zinsmeister Louis
  • Dautriat Jérémie
  • Dimanov Alexandre
  • Raphanel Jean
  • Bornert Michel
  , 2013.
• Vibroacoustics of the piano soundboard: Reduced models, mobility synthesis, and acoustical radiation regime
  
  • Boutillon Xavier
  • Ege Kerem
  Journal of Sound and Vibration, Elsevier, 2013, 332 (18), pp.4261-4279. In string musical instruments, the sound is radiated by the soundboard, subject to the strings excitation. This vibration of this rather complex structure is described here with models which need only a small number of parameters. Predictions of the models are compared with results of experiments that have been presented in Ege et al. [Vibroacoustics of the piano soundboard: (Non)linearity and modal properties in the low- and mid- frequency ranges, Journal of Sound and Vibration 332 (5) (2013) 1288-1305]. The apparent modal density of the soundboard of an upright piano in playing condition, as seen from various points of the structure, exhibits two well-separated regimes, below and above a frequency flim that is determined by the wood characteristics and by the distance between ribs. Above flim, most modes appear to be localised, presumably due to the irregularity of the spacing and height of the ribs. The low-frequency regime is predicted by a model which consists of coupled sub-structures: the two ribbed areas split by the main bridge and, in most cases, one or two so-called cut-off corners. In order to assess the dynamical properties of each of the subplates (considered here as homogeneous plates), we propose a derivation of the (low-frequency) modal density of an orthotropic homogeneous plate which accounts for the boundary conditions on an arbitrary geometry. Above flim, the soundboard, as seen from a given excitation point, is modelled as a set of three structural wave-guides, namely the three inter-rib spacings surrounding the excitation point. Based on these low- and high-frequency models, computations of the point-mobility and of the apparent modal densities seen at several excitation points match published measurements. The dispersion curve of the wave-guide model displays an acoustical radiation scheme which differs significantly from that of a thin homogeneous plate. It appears that piano dimensioning is such that the subsonic regime of acoustical radiation extends over a much wider frequency range than it would be for a homogeneous plate with the same low-frequency vibration. One problem in piano manufacturing is examined in relationship with the possible radiation schemes induced by the models. (10.1016/j.jsv.2013.03.015)
  DOI : 10.1016/j.jsv.2013.03.015