Publications

2007

• A thermodynamical approach to contact wear as application of moving discontinuities
  
  • Stolz Claude
  Archive of Applied Mechanics, Springer Verlag, 2007, 77 (2-3), pp.165-175. The propagation of a moving surface inside a body is analysed within the framework of thermomechanical couplings when the moving surface is associated with an irreversible change in mechanical properties. The moving surface is a surface of heat sources and of entropy production whose intensities are related to particular energy release rates defined in terms of Hamiltonian gradients. For example, we analyse the wear process. Wear phenomena due to contact and relative motion between two solids depend on the loading conditions and material mechanical properties. Friction between contacting bodies induces damage of materials, producing surface and subsurface cracks. Particles are detached from sound solids when some local criteria are satisfied at the boundary. As wear occurs, geometrical changes take place and contact conditions are modified, and the particle induces a specific layer with particular properties. Then the interface between the bodies is a complex medium made of detached particles, eventually a lubricant fluid, and damaged zones. We propose to describe the evolution of the interface using a framework developed earlier for inducing the general form of a wear law. (10.1007/s00419-006-0057-1)
  DOI : 10.1007/s00419-006-0057-1
• Modélisations mécaniques de la touche de piano et de son imitation haptique
  
  • Lozada José
  • Boutillon Xavier
  • Hafez Moustapha
  , 2007, pp.6 p.. Le toucher d'un piano est une information sensorielle essentielle pour le contrôle de la nuance de jeu. Elle provient de la dynamique complexe du mécanisme d'actionnement qui transmet l'énergie mécanique du doigt au marteau. Les pianos numériques mettent en oeuvre des claviers qui ne reproduisent pas les finesses du toucher d'un piano traditionnel. Afin de palier cette défaillance, nous avons réalisé une interface haptique semi-active capable de reproduire le toucher du piano traditionnel. Ceci nécessite une modélisation fine du comportement dynamique du système traditionnel. Nous présentons le modèle dynamique de la touche de piano ; ses simulations sont comparées aux mesures de la réponse du système sous l'action du doigt. L'interface haptique est composée d'un levier auquel est appliqué un système d'amortissement actif à base de fluide magnéto-rhéologique (MRF). Nous présentons le modèle de l'interface ; ses simulations sont comparées à la réponse du système sous l'action du doigt.
• Estimating the parameters of a generalized lambda distribution
  
  • Fournier Benjamin
  • Rupin Nicolas
  • Bigerelle Maxence
  • Najjar Denis
  • Iost Alain
  • Wilcox R
  Computational Statistics and Data Analysis, Elsevier, 2007, 51 (6), pp.2813-2835. The method of moments is a popular technique for estimating the parameters of a generalized lambda distribution (GLD), but published results suggest that the percentile method gives superior results. However, the percentile method cannot be implemented in an automatic fashion, and automatic methods, like the starship method, can lead to prohibitive execution time with large sample sizes. A new estimation method is proposed that is automatic (it does not require the use of special tables or graphs), and it reduces the computational time. Based partly on the usual percentile method, this new method also requires choosing which quantile u to use when fitting a GLD to data. The choice for u is studied and it is found that the best choice depends on the final goal of the modeling process. The sampling distribution of the new estimator is studied and compared to the sampling distribution of estimators that have been proposed. Naturally, all estimators are biased and here it is found that the bias becomes negligible with sample sizes n⩾2×103. The .025 and .975 quantiles of the sampling distribution are investigated, and the difference between these quantiles is found to decrease proportionally to View the MathML source. The same results hold for the moment and percentile estimates. Finally, the influence of the sample size is studied when a normal distribution is modeled by a GLD. Both bounded and unbounded GLDs are used and the bounded GLD turns out to be the most accurate. Indeed it is shown that, up to n=106, bounded GLD modeling cannot be rejected by usual goodness-of-fit tests. (10.1016/j.csda.2006.09.043)
  DOI : 10.1016/j.csda.2006.09.043
• Resolution of linear viscoelastic equations in the frequency domain using real Helmholtz boundary integral equations
  
  • Chaillat Stéphanie
  • Bui Hui Duong
  Comptes Rendus. Mécanique, Académie des sciences (Paris), 2007, 335, pp.746-750. Boundary integral equations are well suitable for the analysis of seismic waves propagation in unbounded domains. Formulations in elastodynamics are well developed. In contrast, for the dynamic analysis of viscoelastic media, there are very seldom formulations by boundary integral equations. In this Note, we propose a new and simple formulation of time harmonic viscoelasticity with the Zener model, which reduces to classical elastodynamics if a compatibility condition is satisfied by boundary conditions. Intermediate variables which satisfy the classical elastodynamic equations are introduced. It makes it possible to utilize existing numerical tools of time harmonic elastodynamics.
• A numerical evaluation of various scale transition rules for uniform field models
  
  • Bouteleux Simon
  • Gérard Céline
  • Bacroix Brigitte
  • Bornert Michel
  • Brenner Renald
  • Cailletaud Georges
  • Crépin Jérôme
  • Leclercq Sylvain
  , 2007.
• A Fast Multipole Method formulation for 3D elastodynamics in the frequency domain
  
  • Chaillat Stéphanie
  • Bonnet Marc
  • Semblat J. F.
  Comptes Rendus. Mécanique, Académie des sciences (Paris), 2007, 335, pp.709-714. The solution of the elastodynamic equations using boundary element methods (BEMs) gives rise to fully-populated matrix equations. Earlier investigations on the Helmholtz and Maxwell equations have established that the Fast Multipole (FM) method reduces the complexity of a BEM solution to $N \mbox{log}_{2}N$ per GMRES teration. The present Note address the extension of the FM-BEM strategy to 3D elastodynamics in the frequency domain. Its efficiency and accuracy are demonstrated on numerical examples involving up to $N=O(10^{6})$ nodal unknowns. (10.1016/j.crme.2007.07.001)
  DOI : 10.1016/j.crme.2007.07.001
• Second order homogenization of the elastic wave equation for non-periodic layered media
  
  • Capdeville Yann
  • Marigo J.-J
  Geophysical Journal International, Oxford University Press (OUP), 2007, 170 (2), pp.823 - 838. In many cases, in the seismic wave propagation modelling context, scales much smaller than the minimum wavelength are present in the earth model in which we wish to compute seismograms. For many numerical methods these small scales are a challenge leading to high numerical cost. The purpose of this paper is to understand and to build the effective medium and equations allowing to average the small scales of the original medium without losing the accuracy of the wavefield computation. In this paper, only the simple layered medium case is studied, leaving the general 3-D medium case for future work. To obtain such an effective medium and equations, we use high order two scale homogenization applied to the wave equation for layered media with rapid variation of elastic properties and density compared to the smallest wavelength of the wavefield. We show that the order 0 homogenization gives the result that was obtained by Backus in 1962. Order 0 homogenized models are transversely isotropic even though the original model is isotropic. It appears that order 0 is not enough to obtain surface waves with correct group and phase velocities and higher order homogenization terms up to two are often required. In many cases, the order one and two simply require to correct the boundary conditions of the wave equation to obtain an accurate solution, even for surface waves. We show how to extend the theory from the periodic case to the non-periodic case. Examples in periodic and non-periodic media are shown. The accuracy of the results obtained by homogenization is checked against the normal mode solution computed in the original medium and shows good agreement. (10.1111/j.1365-246X.2007.03462.x)
  DOI : 10.1111/j.1365-246X.2007.03462.x
• Stokes Instability in Inhomogeneous Membranes: Application to Lipoprotein Suction of Cholesterol-Enriched Domains
  
  • Ben Amar Martine
  • Allain Jean-Marc
  • Puff N.
  • Angelova M.
  Physical Review Letters, American Physical Society, 2007, 99 (4), pp.044503. We examine the time-dependent distortion of a nearly circular viscous domain in an infinite viscous sheet when suction occurs. Suction, the driving force of the instability, can occur everywhere in the two phases separated by an interface. The model assumes a two-dimensional Stokes flow; the selection of the wavelength at short times is determined by a variational procedure. Contrary to the viscous fingering instability, undulations of the boundary may be observed for enough pumping, whatever the sign of the viscosity contrast between the two fluids involved. We apply our model to the suction by lipoproteins of cholesterol-enriched domains in giant unilamellar vesicles. Comparison of the number of undulations given by the model and by the experiments gives reasonable values of physical quantities such as the viscosities of the domains. (10.1103/PhysRevLett.99.044503)
  DOI : 10.1103/PhysRevLett.99.044503
• Homogenization-based constitutive models for porous elastomers and implications for macroscopic instabilities: I-Analysis
  
  • Lopez-Pamies Oscar
  • Ponte Castañeda Pedro
  Journal of the Mechanics and Physics of Solids, Elsevier, 2007, 55 (8), pp.1677-1701. The purpose of this paper is to provide homogenization-based constitutive models for the overall, finite-deformation response of isotropic porous rubbers with random microstructures. The proposed model is generated by means of the “second-order” homogenization method, which makes use of suitably designed variational principles utilizing the idea of a “linear comparison composite.” The constitutive model takes into account the evolution of the size, shape, orientation, and distribution of the underlying pores in the material, resulting from the finite changes in geometry that are induced by the applied loading. This point is key, as the evolution of the microstructure provides geometric softening/stiffening mechanisms that can have a very significant effect on the overall behavior and stability of porous rubbers. In this work, explicit results are generated for porous elastomers with isotropic, (in)compressible, strongly elliptic matrix phases. In spite of the strong ellipticity of the matrix phases, the derived constitutive model may lose strong ellipticity, indicating the possible development of shear/compaction band-type instabilities. The general model developed in this paper will be applied in Part II of this work to a special, but representative, class of isotropic porous elastomers with the objective of exploring the complex interplay between geometric and constitutive softening/stiffening in these materials. (10.1016/j.jmps.2007.01.007)
  DOI : 10.1016/j.jmps.2007.01.007
• Objective evaluation of linearization procedures in nonlinear homogenization: a methodology and some implications on the accuracy of micromechanical schemes
  
  • Rekik Amna
  • Auslender François
  • Bornert Michel
  • Zaoui André
  International Journal of Solids and Structures, Elsevier, 2007, 44 (10), pp.3468-3496. A systematic methodology for an accurate evaluation of various existing linearization procedures sustaining mean fields theories for nonlinear composites is proposed and applied to recent homogenization methods. It relies on the analysis of a periodic composite for which an exact resolution of both the original nonlinear homogenization problem and the linear homogenization problems associated with the chosen linear comparison composite (LCC) with an identical microstructure is possible. The effects of the sole linearization scheme can then be evaluated without ambiguity. This methodology is applied to three different two-phase materials in which the constitutive behavior of at least one constituent is nonlinear elastic (or viscoplastic): a reinforced composite, a material in which both phases are nonlinear and a porous material. Comparisons performed on these three materials between the considered homogenization schemes and the reference solution bear out the relevance and the performances of the modified second-order procedure introduced by Ponte Castañeda in terms of prediction of the effective responses. However, under the assumption that the field statistics (first and second moments) are given by the local fields in the LCC, all the recent nonlinear homogenization procedures still fail to provide an accurate enough estimate of the strain statistics, especially for composites with high contrast. (10.1016/j.ijsolstr.2006.10.001)
  DOI : 10.1016/j.ijsolstr.2006.10.001
• Volumetric digital image correlation applied to X-Ray microtomography images form triaxial compression tests on argillaceaous rocks
  
  • Lenoir Nicolas
  • Bornert Michel
  • Desrues Jacques
  • Bésuelle Pierre
  • Viggiani Gioacchino Cinno
  Strain, Wiley-Blackwell, 2007, 43 (3), pp.193–205. A set of triaxial compression tests on specimens of argillaceous rock were performed under tomographic monitoring at the European Synchrotron Radiation Facility in Grenoble, France, using an original experimental set-up developed at Laboratoire 3S, Grenoble. Complete 3D images of the specimens were recorded throughout each test using X-ray microtomography. Such images were subsequently analysed using a Volumetric Digital Image Correlation software developed at the Laboratoire de Me?canique des Solides in Palaiseau, France. Full-field incremental strain measurements were obtained, which allow to detect the onset of shear strain localisation and to characterise its development in a 3D complex pattern. Volumetric Digital Image Correlation revealed patterns which could not be directly observed from the original tomographic images, because the deformation process in the zones of localised deformation was essentially isochoric (i.e. without volumetric strain), hence not associated to density changes. (10.1111/j.1475-1305.2007.00348.x)
  DOI : 10.1111/j.1475-1305.2007.00348.x
• A quasi-static stability analysis for Biot’s equation and standard dissipative systems
  
  • Abed-Meraim Farid
  • Nguyen Quoc Son
  European Journal of Mechanics - A/Solids, Elsevier, 2007, 26 (3), pp.383-393. In this paper, an extended version of Biot's differential equation is considered in order to discuss the quasi-static stability of a response for a solid in the framework of generalized standard materials. The same equation also holds for gradient theories since the gradients of arbitrary order of the state variables and of their rates can be introduced in the expression of the energy and of the dissipation potentials. The stability of a quasi-static response of a system governed by Biot's equations is discussed. Two approaches are considered, by direct estimates and by linearizations. The approach by direct estimates can be applied in visco-plasticity as well as in plasticity. A sufficient condition of stability is proposed and based upon the positivity of the second variation of energy along the considered response. This is an extension of the criterion of second variation, well known in elastic buckling, into the study of the stability of a response. The linearization approach is available only for smooth dissipation potentials, i.e. for the study of visco-elastic solids and leads to a result on asymptotic stability. The paper is illustrated by a simple example. (10.1016/j.euromechsol.2006.06.005)
  DOI : 10.1016/j.euromechsol.2006.06.005
• Variational linear comparison bounds for nonlinear composites with anisotropic phases. I. General results
  
  • Idiart Martin I
  • Ponte Castañeda Pedro
  Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Royal Society, 2007, 463, pp.907-924. This work is concerned with the development of bounds for nonlinear composites with anisotropic phases by means of an appropriate generalization of the ‘linear comparison’ variational method, introduced by Ponte Castañeda for composites with isotropic phases. The bounds can be expressed in terms of a convex (concave) optimization problem, requiring the computation of certain ‘error’ functions that, in turn, depend on the solution of a non-concave/non-convex optimization problem. A simple formula is derived for the overall stress–strain relation of the composite associated with the bound, and special, simpler forms are provided for power-law materials, as well as for ideally plastic materials, where the computation of the error functions simplifies dramatically. As will be seen in part II of this work in the specific context of composites with crystalline phases (e.g. polycrystals), the new bounds have the capability of improving on earlier bounds, such as the ones proposed by deBotton and Ponte Castañeda for these specific material systems. (10.1098/rspa.2006.1797)
  DOI : 10.1098/rspa.2006.1797
• A novel approach to the heat build up problem of rubber
  
  • Le Chenadec Yohan
  • Stolz Claude
  • Raoult Ida
  • Nguyen Mac Lan
  • Charrier Pierre
  • Delattre Benoit
  , 2008, V, pp.345-350. Rubber is well-known to have a hysteretic behavior and a low thermal conductibility. The main consequences are the heat generation and heat build-up phenomena which occur in a rubber structure when submitted to repeated deformations. The purpose of our work is to estimate the steady-state temperature reached in elastomer structures when submitted to cyclic loadings. A decoupled strategy of the cyclic thermomechanical problem resolution is adopted. First a mechanical analysis is performed with a hyperelastic stabilized behavior of rubber. Then an estimation of the energy converted into heat is given. It is based on an energetic measure of a mechanical cycle and links the hysteretic loss energy to the elastic mechanical variables. It accounts for mean strains. An experimental investigation has been carried out in order to identify the estimation of the heat sources at various temperatures and mean strains. The influence of the Mullins effect on the dissipation is discussed. Finally, the thermal problem is solved and the influence of the geometry deformation on the heat equation in finite strains is taken into account with an approximation based on average values over a cycle. The heat build-up law is validated: heat build-up experiments have been carried out and comparisons with FE calculations have shown the ability of the law to estimate the transient and stationary temperature of an inhomogeneous structure submitted to cyclic loadings.
• Introducing infrared thermography in soil dynamics
  
  • Luong Minh-Phong
  Infrared Physics and Technology, Elsevier, 2007 (49), pp.306-311. The paper introduces infrared thermography as a non-contact and non-destructive technique that conveniently offers the possibility of evaluating the energy-dissipating ability of soil, generally difficult to be determined using traditional techniques. It allows records and observations in real time of heat patterns produced by the dissipation of energy caused by friction between grains. Such dissipative heat occurs when soil is subjected to vibratory loading exceeding the characteristic threshold, and it evidences the distortion mechanism. This energy dissipation mechanisminfluences the wave propagation, intergranular attenuation, and dispersion through particles contacts. The infrared thermographic technique, which couples mechanical and thermal energy, offers the potential of directly monitoring the stress state of particle rearrangement and predicting the macroscopic mechanical response of soils subjected to cyclic, dynamic or vibratory loading. In addition, infrared thermography evidences the fuse effect of soil, capable to mitigate significantly the earthquake loading on engineering structures. 2006 Elsevier B.V. All rights reserved. (10.1016/j.infrared.2006.06.025)
  DOI : 10.1016/j.infrared.2006.06.025
• Ultrasonic measurement of anisotropy and temperature dependence of elastic parameters by a dry coupling method applied to a 6061-T6 alloy
  
  • Augereau F.
  • Laux D.
  • Allais L.
  • Mottot M.
  • Caes C.
  Ultrasonics, Elsevier, 2007, 46 (1), pp.34-41. A pulse-echo ultrasonic method is presented to measure elastic parameter variations during thermal loading with high accuracy. Using a dry coupling configuration dedicated to high temperature investigation, this technique has been applied on 6061-T6 aluminium samples up to 220 °C. Experimental settings are described to assess the measurement reproducibility estimated at a value of 0.2%. Consequently, the anisotropy of this aluminium between the rolling direction and two orthogonal axes has been clearly detected and also measured versus temperature. As regards the temperature dependence of these elastic parameters, these results are compared with the estimations of the Young's modulus obtained during mechanical tests in conditions of low cycle fatigue (LCF). The same linear variation versus temperature is found but with a shift of 7 GPa. This difference has been classically attributed to systematic experimental error sources and to the distinction existing between dynamic and static elastic modulus. (10.1016/j.ultras.2006.10.002)
  DOI : 10.1016/j.ultras.2006.10.002
• Fast multipole boundary integral equation method for 3D seismic wave propagation in alluvial basins
  
  • Chaillat Stéphanie
  • Bonnet Marc
  • Semblat Jean-François
  , 2007.
• A Novel Haptic Interface for Musical Keyboards
  
  • Lozada José
  • Hafez Moustapha
  • Boutillon Xavier
  , 2007, pp.6 p.. A novel haptic interface for musical keyboards is presented. The piano key has an embedded active damping system based on magneto-rheological (MR) fluids that allows to reproduce the dynamic behavior of traditional pianos. The MR fluid is encapsulated into a mechanical sealing to avoid leakage. A slider is attached to the back of the key and shears the MR fluid. When a magnetic field is applied across the MR fluid, chains of particles are aligned along the magnetic field lines. The strain of the chains will create a resistant force that can be controlled on real time. An analytical model of the whole system is presented and compared to experimental results.
• MODELING COUPLING EFFECTS IN CORD-RUBBER COMPOSITE STRUCTURES
  
  • Hassis H.
  • El Arem Saber
  • Pidaparti Ramana
  JP Journal of Solids and Structures, 2007, 1 (3), pp.http://pphmj.com/abstract/2966.htm. An analytical model is developed to study the coupling effects in cordrubber composite materials. The analytical model takes into account the mismatch of stiffness between the cords and the rubber matrix material, and the twist-extension coupling. The transverse deformation, i.e., normal to the cords direction is based on the normal modes of a special system which describes the orthotropic and the coupling behaviour of cord-rubber composites. The equations of motion for the cord-composite plates are derived using the principle of virtual work. Results of deformation and stresses are obtained for some typical cord-rubber composite plates and are compared to the existing solutions. The results presented illustrate that the coupling effects are significant for nonsymmetrical cord orientations.
• Dérivées de l'énergie potentielle pour la propagation de fissure en 3D : Prise en compte de contraintes résiduelles
  
  • Edeline Gwenael
  • Bonnet Marc
  , 2007.
• Couplings in salt and salt caverns
  
  • Berest Pierre
  • Bérest P.
  , 2007.
• Bounds and estimates for the effective yield surface of porous media with a uniform or a nonuniform distribution of voids
  
  • Bilger Nicolas
  • Auslender François
  • Bornert Michel
  • Moulinec Hervé
  • Zaoui André
  European Journal of Mechanics - A/Solids, Elsevier, 2007, 26 (5), pp.810-836. (10.1016/j.euromechsol.2007.01.004)
  DOI : 10.1016/j.euromechsol.2007.01.004
• A discontinuous stabilized mortar method for general 3D elastic problems
  
  • Le Tallec Patrick
  • Hauret Patrice
  Computer Methods in Applied Mechanics and Engineering, Elsevier, 2007, 196 (49-52), pp.4881-4900. First, the present paper is concerned with the extension to linearized elastodynamics of the optimal results known in statics for the mortar method. It also analyzes and tests a new couple of displacements/Lagrange multipliers for the method, as proposed independently by Ben Belgacem [F. Ben Belgacem, A stabilized domain decomposition method with non-matching grids for the Stokes problem in three dimensions, SIAM J. Numer. Anal. 42 (2) (2004) 667–685] and the authors [P. Hauret, Méthodes numériques pour la dynamique des structures non-linéaires incompressibles à deux échelles (Numerical methods for the dynamic analysis of two-scale incompressible nonlinear structures), Ph.D. thesis, Ecole Polytechnique, 2004]. Finally, questions of practical implementation in the presence of curved interfaces are addressed and validated from the numerical point of view. (10.1016/j.cma.2007.06.014)
  DOI : 10.1016/j.cma.2007.06.014
• Transient behaviour of salt caverns
  
  • Berest Pierre
  • Karimi-Jafari Mehdi
  • Brouard Benoît
  • van Sambeek Leo
  , 2007, pp.383-390.
• Higher-order topological sensitivity for acoustic and elastodynamic inverse scattering
  
  • Bonnet Marc
  , 2007.