Publications

2007

• 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 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
• 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
• 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.
• 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
• 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
• On the cumulative microslip phenomenon
  
  • Antoni Nicolas
  • Son Nguyen Quoc
  • Ligier Jean-Louis
  • Saffré Philippe
  • Pastor Joseph
  European Journal of Mechanics - A/Solids, Elsevier, 2007, 26 (4), pp.626-646. The cumulative microslip phenomenon is the accumulation of relative slips in a tangential direction on the contact interface of two solids under cyclic loadings. This lead to significant global relative displacement between components and can account for the failure of some assembly parts in mechanical structures. Practical examples from the automotive industry are presented in this paper to describe the cumulative microslip in real situations. The phenomenon is then discussed from a theoretical point of view as an asymptotic behaviour by analogy with the ratchetting effects in elastoplasticity. Accommodation and slip shakedown are introduced in the same spirit. A slip shakedown theorem is proposed and leads to the definition of a safety coefficient with respect to slips when a standard law of friction is assumed. The safety coefficient can be computed from two static and kinematic approches in min-max duality. A simple example is given.
• MR-fluid-based haptic interface
  
  • Lozada José
  • Boutillon Xavier
  • Hafez Moustapha
  , 2006, pp.4 p.. A haptic interface based on magneto-rheological (MR) fluids is presented. The device is aiming for low inertia and the possibility of emulating quasi free-space motion as well as moderate resistive forces. It is based on the direct shear operating mode of the MR fluid with a slider. Friction caused by the translation motion of the slider is highly reduced by the use of a membrane that ensures sealing for the fluid container. The first experimental results are reported.
• Experimental study of the quasi-static and dynamic behaviour of cork under compressive loading
  
  • Gameiro Celina Pires
  • Cirne José
  • Gary Gérard
  J. Matter Sci, 2007, 42 (12), pp.4316-4324. Cork is a natural cellular material with increasing industrial applications due to its remarkable combination of properties. Its mechanical behaviour explains why it is often used for applications like sealing, packaging, insulation, vibration control, weight reduction, flotation, sound damping, etc. However, the mechanical behaviour of cork when subjected to impact has not been well investigated yet since the studies described in the literature generally focus strain rates below 10−1 s−1. Understanding the behaviour of cork at high rates of deformation becomes imperative when considering applications such as crash protection. Hence, in the present work, the authors compare the quasi-static and dynamic response of four types of cork when compressed axially at strain rates from 10−3 s−1 to 600 s−1. Data from the Split-Hopkinson Pressure Bars are used to generate stress–strain curves for natural and agglomerate cork samples, and the results are discussed in terms of the cellular structure of cork. (10.1007/s10853-006-0675-6)
  DOI : 10.1007/s10853-006-0675-6
• A fast multipole accelerated BEM for 3-D seismic wave computation
  
  • Chaillat Stéphanie
  • Bonnet Marc
  • Semblat Jean-François
  , 2007.
• Nonlinear sequential laminates reproducing hollow sphere assemblages
  
  • Idiart Martín I.
  Comptes Rendus. Mécanique, Académie des sciences (Paris), 2007, 335 (7), pp.363-368. A special class of nonlinear porous materials with isotropic ‘sequentially laminated’ microstructures is found to reproduce exactly the hydrostatic behavior of ‘hollow sphere assemblages’. It is then argued that this result supports the conjecture that Gurson's approximate criterion for plastic porous materials, and its viscoplastic extension of Leblond et al. (1994), may actually yield rigorous upper bounds for the hydrostatic flow stress of porous materials containing an isotropic, but otherwise arbitrary, distribution of porosity. (10.1016/j.crme.2007.04.003)
  DOI : 10.1016/j.crme.2007.04.003
• 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.
• Couplings in salt and salt caverns
  
  • Berest Pierre
  • Bérest P.
  , 2007.
• Dérivées de l'énergie potentielle pour la propagation de fissure en 3D : Prise en compte de contraintes résiduelles
  
  • Edeline Gwenael
  • Bonnet Marc
  , 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
• 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.
• 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
• Higher-order topological sensitivity for acoustic and elastodynamic inverse scattering
  
  • Bonnet Marc
  , 2007.
• Inversion of random field models for heterogeneous media from spectral analysis of mechanical waves
  
  • Arnst Maarten
  • Bonnet Marc
  • Clouteau Didier
  • Ta Quang-Anh
  , 2007.