Publications

2007

• 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
• A fast multipole accelerated BEM for 3-D seismic wave computation
  
  • Chaillat Stéphanie
  • Bonnet Marc
  • Semblat Jean-François
  , 2007.
• 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.
• 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
• 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
• 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.
• Inverse acoustic scattering by generalized topological expansion
  
  • Bonnet Marc
  , 2007.
• A multiple fine-scale satellite-derived landscape approach: example of bluetongue modelling in Corsica.
  
  • Guis Hélène
  • Tran Annelise
  • Mauny Frédéric
  • Baldet Thierry
  • Barragué Bruno
  • Gerbier Guillaume
  • Viel Jean-François
  • Roger François
  • de La Rocque Stéphane
  Veterinaria Italiana, 2007, 43 (3), pp.669-683.
• Questions of Prediction of the Long-Term Behaviour of Underground Openings, KeyNote Lecture
  
  • Berest Pierre
  • Bérest P.
  , 2007, Vol. 3, pp.1413-1425.
• Two-scale Dirichlet-Neumann Preconditioners for Boundary Refinements
  
  • Hauret Patrice
  • Le Tallec Patrick
  , 2007, 55, pp.447-454. The present work introduces simple Dirichlet-Neumann preconditioners for the solution of elasticity problems in presence of numerous small disjoint geometric refinements on the boundary of the domain, situation which typically occurs in the tire industry. Moreover, the condition number of the preconditioned system is proved to be independent of the number and the size of the small details on the boundary. Finally, as an enhancement, a second proposed preconditioner makes use of a coarse space counterbalancing the effect of essential boundary conditions on the small details, and a simple numerical academic test illustrates the increased ef- ficiency. Further details on the motivation as well as complete proofs can be found in [4, 5]. (10.1007/978-3-540-34469-8_56)
  DOI : 10.1007/978-3-540-34469-8_56
• Variational linear comparison bounds for nonlinear composites with anisotropic phases. II. Crystalline materials
  
  • Idiart Martin
  • Ponte Castañeda Pedro
  Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Royal Society, The, 2007, 463, pp.925-943. In part I of this work, bounds were derived for the effective potentials of nonlinear composites with anisotropic constituents, making use of an appropriate generalization of the linear comparison variational method. In this second part, the special case of nonlinear composites with crystalline constituents is considered. First, it is shown that, for this special but very important class of materials, the ‘variational’ bounds of part I are at least as good as an earlier version of the bounds due to deBotton & Ponte Castañeda. Then, the relative merits of these two types of bounds are studied in the context of a model, two-dimensional, porous composite with a power-law crystalline matrix phase, under anti-plane loading conditions. The results show that, indeed, the variational bounds of part I improve, in general, on the earlier bounds, with the former becoming progressively sharper than the latter as the number of slip systems of the crystalline matrix phase increases. In particular, it is shown that, unlike the bounds of deBotton & Ponte Castañeda, the variational bounds of part I are able to recover the variational bound for composites with an isotropic matrix phase, as the number of slip systems, all having the same flow stress, tends to infinity. (10.1098/rspa.2006.1804)
  DOI : 10.1098/rspa.2006.1804
• Homogenization-based constitutive models for porous elastomers and implications for macroscopic instabilities: II-Results
  
  • Lopez-Pamies Oscar
  • Ponte Castañeda Pedro
  Journal of the Mechanics and Physics of Solids, Elsevier, 2007, 55 (8), pp.1702-1728. In Part I of this paper, we developed a homogenization-based constitutive model for the effective behavior of isotropic porous elastomers subjected to finite deformations. In this part, we make use of the proposed model to predict the overall response of porous elastomers with (compressible and incompressible) Gent matrix phases under a wide variety of loading conditions and initial values of porosity. The results indicate that the evolution of the underlying microstructure—which results from the finite changes in geometry that are induced by the applied loading—has a significant effect on the overall behavior of porous elastomers. Further, the model is in very good agreement with the exact and numerical results available from the literature for special loading conditions and generally improves on existing models for more general conditions. More specifically, we find that, in spite of the fact that Gent elastomers are strongly elliptic materials, the constitutive models for the porous elastomers are found to lose strong ellipticity at sufficiently large compressive deformations, corresponding to the possible onset of “macroscopic” (shear band-type) instabilities. This capability of the proposed model appears to be unique among theoretical models to date and is in agreement with numerical simulations and physical experience. The resulting elliptic and non-elliptic domains, which serve to define the macroscopic “failure surfaces” of these materials, are presented and discussed in both strain and stress space. (10.1016/j.jmps.2007.01.008)
  DOI : 10.1016/j.jmps.2007.01.008
• 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, The, 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.
• Fast multipole boundary integral equation method for 3D seismic wave propagation in alluvial basins
  
  • Chaillat Stéphanie
  • Bonnet Marc
  • Semblat Jean-François
  , 2007.
• 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
• 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
• 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.
• 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.
• Couplings in salt and salt caverns
  
  • Berest Pierre
  • Bérest P.
  , 2007.
• 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
• Field statistics in nonlinear composites. II. Applications
  
  • Idiart Martin
  • Ponte Castañeda Pedro
  Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Royal Society, The, 2007, 463, pp.203-222. Part I of this work provided a methodology for extracting the statistics of the local fields in nonlinear composites, from the effective potential of suitably perturbed composites. In particular, exact relations were given for the first and even moments of the fields in each constituent phase. In this part, use is made of these exact relations in the context of the ‘variational’, ‘tangent second-order’ and ‘second-order’ nonlinear homogenization methods to generate estimates for the phase averages and second moments of the fields for two-phase, power-law composites with isotropic and transversely isotropic microstructures. The accuracy of these estimates is assessed by confronting them against corresponding exact results for sequentially laminated composites. Among the nonlinear homogenization estimates considered in this work, the second-order estimates are found to be, in general, the most accurate, especially for large heterogeneity contrast and nonlinearity. Thus, these estimates are able to capture, for example, the strong anisotropy in the strain fluctuations that can develop inside nonlinear porous and rigidly reinforced composites. (10.1098/rspa.2006.1757)
  DOI : 10.1098/rspa.2006.1757
• Locking free matching of different three dimensional models in structural mechanics
  
  • Le Tallec Patrick
  • Mani Saloua
  ESAIM: Mathematical Modelling and Numerical Analysis, Société de Mathématiques Appliquées et Industrielles (SMAI) / EDP, 2007, 41 (1), pp.129-145. The present paper proposes and analyzes a general locking free mixed strategy for computing the deformation of incompressible three dimensional structures placed inside flexible membranes. The model involves as in Chapelle and Ferent [Math. Models Methods Appl. Sci. 13 (2003) 573-595] a bending dominated shell envelope and a quasi incompressible elastic body. The present work extends an earlier work of Arnold and Brezzi [Math Comp. 66 (1997) 1-14] treating the shell part and proposes a global stable finite element approximation by coupling optimal mixed finite element formulations of the different subproblems by mortar techniques. Examples of adequate finite elements are proposed. Convergence results are derived in two steps. First a global inf-sup condition is proved, deduced from the local conditions to be satisfied by the finite elements used for the external shell problem, the internal incompressible 3D problem, and the mortar coupling, respectively. Second, the analysis of Arnold and Brezzi [Math. Comp. 66 (1997) 1-14] is extended to the present problem and least to convergence results for the full coupled problem, with constants independent of the problem's small parameters. (10.1051/m2an:2007013)
  DOI : 10.1051/m2an:2007013