Publications

2008

• Multi-level fast multipole multi-region method for 3D seismic response of alluvial basins
  
  • Chaillat Stéphanie
  • Bonnet Marc
  • Semblat Jean-François
  , 2008.
• Slip-shakedown analysis of a system of circular beams in frictional contact
  
  • Antoni Nicolas
  • Nguyen Quoc Son
  • Ragot Patrick
  Int. J. Solids & Structures, 2008, 45, pp.5189-5203. In automotive components, the cumulative microslip phenomenon is often observed for engine assemblies. This phenomenon results in an accumulation of the relative slips in a preferred tangential direction on the contact interface of two solids under cyclic loadings. A significant relative displacement may occur and leads to the assembly failure. In particular, a global rotation of the bearing shell may result from this mechanism of cumulated slips in conrod systems. To discuss this rotation problem, a model of two circular beams in frictional contact and submitted to a periodical rotating load is considered here. The aim is to give some simplified estimates of the critical rotation load based on a slip-shakedown analysis. The discussion holds for Tresca friction and can be extended to Coulomb friction under the assumption of small coupling. The static and kinematic slip-shakedown approaches are discussed. The obtained analytical results are shown to be in agreement with the finite element computations. (10.1016/j.ijsolstrr.2008.05.021)
  DOI : 10.1016/j.ijsolstrr.2008.05.021
• Fast multipole method applied to 3D frequency domain elastodynamics
  
  • Sanz Jose Antonio
  • Bonnet Marc
  • Dominguez Jose
  Engineering Analysis with Boundary Elements, Elsevier, 2008, 32, pp.787-795. This article is concerned with the formulation and implementation of a fast multipole-accelerated BEM for 3-D elastodynamics in the frequency domain, based on the so-called diagonal form for the expansion of the elastodynamic fundamental solution, a multi-level strategy. As usual with the FM-BEM, the linear system of BEM equations is solved by GMRES, and the matrix is never explicitly formed. The truncation parameter in the multipole expansion is adjusted to the level, a feature known from recent published studies for the Maxwell equations. A preconditioning strategy based on the concept of sparse approximate inverse (SPAI) is presented and implemented. The proposed formulation is assessed on numerical examples involving $O(10^{5})$ BEM unknowns, which show in particular that, as expected, the proposed FM-BEM is much faster than the traditional BEM, and that the GMRES iteration count is significantly reduced when the SPAI preconditioner is used. (10.1016/j.enganabound.2008.03.002)
  DOI : 10.1016/j.enganabound.2008.03.002
• A multi-level fast-multipole multi-region method for 3-D elastodynamics in the frequency domain
  
  • Chaillat Stéphanie
  • Semblat Jean-François
  • Bonnet Marc
  , 2008.
• Méthodologies pour l'identification de comportements mécaniques
  
  • Bonnet Marc
  , 2008.
• MR fluid linear actuators: a novel interaction mode
  
  • Lozada José
  • Hafez Moustapha
  • Boutillon Xavier
  , 2008, pp.6 p.. A novel linear actuator based on magneto-rheological (MR) fluid is presented. The linear actuator is composed of two coils and two magnetic cores leaving a 1 mm gap filled of MR-fluid. A magnetic or non-magnetic thin plate translates into the gap and shears the fluid. A controlled magnetic field, applied by the coils, changes the apparent viscosity of the fluid thereby the force opposed to the displacement of the plate is controlled. In order to study the MR-fluid behavior sheared by a thin plate, we present an experimental device able to measure the plate displacement and the force applied by the fluid on the plate. Experimental observations, modeling and parameters fitting are presented for both cases: magnetic plate and non-magnetic plate.
• Sur le problème d'évolution de fissure en élastoplasticité : approches primale et duale
  
  • Stolz Claude
  Comptes Rendus. Mécanique, Académie des sciences (Paris), 2008 (336), pp.500-505. Abstract We study the rate boundary value problem concerning crack propagation in an elastoplastic material. The formulation is given when the criterium of propagation is based on a energy release rate. Primal and dual approaches of the boundary value problem of evolution are proposed. To cite this article: C. Stolz, C. R. Mecanique 336 (2008). Résumé La formulation du problème en vitesse de fissure et de déplacement est discutée lorsque le critère de propagation est fondé sur l'analyse de la dissipation. On se place alors dnas le cas de critère énergétique comme proposé (Nguyen, 1985) et généralisé récemment au cas des matériaux élastoplastiques (Stolz, 2008). On obtient alors les formulations primale et duale du problème d'évolution de la propagation de la fissure en élastoplasticité. Pour citer cet article : C. Stolz, C. R. Mecanique 336 (2008). Mots-clés: (10.1016/j.crme.2008.03.005)
  DOI : 10.1016/j.crme.2008.03.005
• Inversion of probabilistic structural models using measured transfer functions
  
  • Arnst Maarten
  • Clouteau Didier
  • Bonnet Marc
  Computer Methods in Applied Mechanics and Engineering, Elsevier, 2008, 197, pp.589-608. This paper addresses the inversion of probabilistic models for the dynamical behaviour of structures using experimental data sets of measured frequency-domain transfer functions. The inversion is formulated as the minimization, with respect to the unknown parameters to be identified, of an objective function that measures a distance between the data and the model. Two such distances are proposed, based on either the loglikelihood function, or the relative entropy. As a comprehensive example, a probabilistic model for the dynamical behaviour of a slender beam is inverted using simulated data. The methodology is then applied to a civil and environmental engineering case history involving the identification of a probabilistic model for ground-borne vibrations from real experimental data. (10.1016/j.cma.2007.08.011)
  DOI : 10.1016/j.cma.2007.08.011
• Mise au point d'un nouveau modèle de comportement élasto-viscoplastique. Application au dimensionnement à la fatigue d'un collecteur d'échappement de moteur Diesel en fonte
  
  • Szmytka Fabien
  • Bourgeois Myriam
  • Mac Lan Nguyen-Tajan T.
  • Rémy Luc
  • Köster Alain
  • Maitournam Habibou
  Revue de Métallurgie, EDP Sciences, 2008, pp.341-346. Fatigue design of structures for high temperature service resorts to modelling based on elasto-viscoplasticity constitutive laws. The new model describes complex anisothermal cyclic loadings, accounting for viscosity on a large range of strain. The new constitutive law that has been developed for nodular cast iron, is intended for the design of automotive parts for high temperature service. (10.1051/metal:2008050)
  DOI : 10.1051/metal:2008050
• Intégrale duale en mécanique de la rupture.
  
  • Stolz Claude
  Comptes Rendus. Mécanique, Académie des sciences (Paris), 2008 (336), pp.434-439. We propose a dual approach in fracture mechanics based on complementary energy. The analysis of the dissipation shows that the thermodynamical force associated with the evolution of a crack is an energy release rate, form of which depends on the presence or not of mechanical discontinuities. This energy release rate is given as an integral based on free or complementary energy. We analyse the invariance of such integrals and we discuss the obtained results in elastoplasticity. Résumé On propose une intégrale duale en mécanique de la rupture ductile fondée sur l'énergie complémentaire. L'analyse de la dissipation mécanique en présence ou non de discontinuités mobiles montre que le paramètre énergétique associé à la vitesse de propagation est représenté par une intégrale de contour appropriée exprimée en terme d'énergie libre ou d'énergie complémentaire. On étudie alors l'invariance par rapport au contour de ces intégrales et on interpréte les résultats obtenus. (10.1016/j.crme.2008.02.002)
  DOI : 10.1016/j.crme.2008.02.002
• Refined finite element modelling for the vibration analysis of large rotating machines
  
  • Combescure Didier
  • Lazarus Arnaud
  Journal of Sound and Vibration, Elsevier, 2008, 318. This paper is aimed at presenting refined finite element modelling used for dynamic analysis of large rotating machines. The first part shows an equivalence between several levels of modelling: firstly, models made of beam elements and rigid disc with gyroscopic coupling representing the position of the rotating shaft in an inertial frame; secondly full three-dimensional (3D) or 3D shell models of the rotor and the blades represented in the rotating frame and finally two-dimensional (2D) Fourier model for both rotor and stator. Simple cases are studied to better understand the results given by analysis performed using a rotating frame and the equivalence with the standard calculations with beam elements. Complete analysis of rotating machines can be performed with models in the frames best adapted for each part of the structure. The effects of several defects are analysed and compared with this approach. In the last part of the paper, the modelling approach is applied to the analysis of the large rotating shaft part of the power conversion unit of the GT-MHR nuclear reactor. (10.1016/j.jsv.2008.04.025)
  DOI : 10.1016/j.jsv.2008.04.025
• Éléments d'acoustique linéaire
  
  • Boutillon Xavier
  , 2008.
• A homogenization-based constitutive model for isotropic viscoplastic porous media
  
  • Danas Kostas
  • Idiart Martin I.
  • Ponte Castañeda Pedro
  International Journal of Solids and Structures, Elsevier, 2008, 45, pp.3392-3409. An approximate model based on the "second-order" nonlinear homogenization method is proposed to estimate the effective behavior of isotropic, viscoplastic, porous materials. The model is constructed in such a way that it reproduces exactly the behavior of a "composite-sphere assemblage" in the limit of hydrostatic loadings, and therefore coincides with the hydrostatic limit of Gurson's criterion in the special case of ideal plasticity. As a consequence, the new model improves on earlier homogenization estimates, which have been found to be quite accurate for low triaxialities but overly stiff for sufficiently high triaxialities and nonlinearities. Additionally, the estimates delivered by the model exhibit a dependence on the third invariant of the macroscopic stress tensor, which has a nontrivial effect on the effective response of the material at moderate triaxialities. The proposed model is compared with exact results obtained for a special class of porous materials with sequentially laminated microstructures. The agreement is found to be quite good for the entire range of stress triaxialities, and all values of the porosity and nonlinearity considered. (10.1016/j.ijsolstr.2008.02.007)
  DOI : 10.1016/j.ijsolstr.2008.02.007
• A fast multipole accelerated BEM for 3-D elastic wave computation
  
  • Chaillat Stéphanie
  • Bonnet Marc
  • Semblat Jean-François
  Revue Européenne de Mécanique Numérique/European Journal of Computational Mechanics, Hermès / Paris : Lavoisier, 2008, 17, pp.701-712. 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 $N \log_{2}N$ per GMRES iteration. The present article addresses the extension of the FM-BEM strategy to 3D elastodynamics in the frequency domain. Efficiency and accuracy are demonstrated on numerical examples involving up to $N=O(10^{6})$ boundary nodal unknowns. (10.3166/remn.17.701-712)
  DOI : 10.3166/remn.17.701-712
• Optimal control approach in non linear mechanics
  
  • Stolz Claude
  Comptes Rendus. Mécanique, Académie des sciences (Paris), 2008, 336, pp.238-244. The purpose of this article is to present some applications of optimal control theory for non linear mechanical problems. In particular we consider some inverse problems dealing with the determination of unknown boundary conditions, the determination of internal state resulting of unknown loading history. Extensions to asymptotic behavior due to cyclic loading are also presented. (10.1016/j.crme.2007.11.015)
  DOI : 10.1016/j.crme.2007.11.015
• Instruments à cordes frottées
  
  • Boutillon Xavier
  , 2008, pp.511-532 et 132-135.
• Subsidence, sinkholes and craters above salt caverns
  
  • Berest Pierre
  • Bérest P.
  , 2008, pp.269-278.
• Dynamic fracture: an example of convergence towards a discontinuous quasi-static solution
  
  • Dumouchel Pierre-Emmanuel
  • Marigo Jean-Jacques
  • Charlotte M.
  Continuum Mechanics and Thermodynamics, Springer Verlag, 2008, 20, pp.1-19. Considering a one-dimensional problem of debonding of a thin film in the context of Griffith's theory, we show that the dynamical solution converges, when the speed of loading goes down to 0, to a quasistatic solution including an unstable phase of propagation. In particular, the jump of the debonding induced by this instability is governed by a principle of conservation of the total quasistatic energy, the kinetic energy being negligible. (10.1007/s00161-008-0071-3)
  DOI : 10.1007/s00161-008-0071-3
• A homogenization-based constitutive model for two-dimensional viscoplastic porous media
  
  • Danas Kostas
  • Idiart Martin I.
  • Ponte Castañeda Pedro
  Comptes Rendus. Mécanique, Académie des sciences (Paris), 2008, 336, pp.79-90. An approximate model based on the so-called "second-order" nonlinear homogenization method is proposed to estimate the effective behavior of viscoplastic porous materials exhibiting transversely isotropic symmetry. The model is constructed in such a way that it reproduces exactly the behavior of a "composite-cylinder assemblage" in the limit of in-plane hydrostatic loading, and therefore coincides with the hydrostatic limit of Gurson's criterion for plastic porous materials. As a consequence, the new model improves on earlier "second-order" homogenization estimates, which have been found to be overly stiff at sufficiently high triaxialities and nonlinearities. The proposed model is compared with exact results obtained for a special class of porous materials with sequentially laminated microstructures. The agreement is found to be excellent for the entire range of stress triaxialities, and all values of the porosity and nonlinearity considered. (10.1016/j.crme.2007.10.017)
  DOI : 10.1016/j.crme.2007.10.017
• Travelling interface waves in a brake-like system under unilateral contact and Coulomb friction
  
  • Nguyen Quoc Son
  • Oueslati Abdelbacet
  • Steindl Alois
  • Teufel Andreas
  • Troger Hans
  Comptes Rendus. Mécanique, Académie des sciences (Paris), 2008, 336 (1-2), pp.203-209. This article considers the frictional interface waves generated by the flutter instability of the sliding steady state for an elastic tube in frictional contact with a rigid and rotating shaft. According to the values of the contact pressure, the rotation velocity and the friction coefficient, several periodic dynamical responses can be found under the form of travelling surface waves. Examples of stick-slip, stick-slip-separation and stick-slip-separation-reverse-slip waves are reported here. Some discussions on the stability of these waves are also given. (10.1016/j.crme.2007.11.011)
  DOI : 10.1016/j.crme.2007.11.011
• Large Deformation of Anisotropic Austenitic Stainless Steel Sheets at Room Temperature: Multi-axial Experiments and Phenomenological Modeling
  
  • Mohr Dirk
  • Jacquemin Johan
  Journal of the Mechanics and Physics of Solids, Elsevier, 2008, pp.2935-2956.
• Combined shape-material sensitivity for elastic-wave identification of penetrable inclusions
  
  • Bonnet Marc
  • Guzina B. B.
  , 2008.
• A New Experimental Technique for the Multi-axial Testing of Advanced High Strength Steel
  
  • Mohr Dirk
  • Oswald M.
  Experimental Mechanics, Society for Experimental Mechanics, 2008, pp.65-77.
• Topological sensitivity and FMM-accelerated BEM applied to 3D acoustic inverse scattering
  
  • Nemitz Nicolas
  • Bonnet Marc
  Engineering Analysis with Boundary Elements, Elsevier, 2008, 32, pp.957-970. This study is set in the framework of inverse scattering of scalar (e.g. acoustic) waves. A qualitative probing technique based on the distribution of topological sensitivity of the cost functional associated with the inverse problem with respect to the nucleation of an infinitesimally-small hard obstacle is formulated. The sensitivity distribution is expressed as a bilinear formula involving the free field and an adjoint field associated with the cost function. These fields are computed by means of a boundary element formulation accelerated by the Fast Multipole method. A computationally fast approach for performing a global preliminary search based on the available overspecified boundary data is thus defined. Its usefulness is demonstrated through results of numerical experiments on the qualitative identification of a hard obstacle in a bounded acoustic domain, for configurations featuring $O(10^{5})$ nodal unknowns and O(10^{6})$ sampling points. (10.1016/j.enganabound.2007.02.006)
  DOI : 10.1016/j.enganabound.2007.02.006
• Discussion of "Second order topological sensitivity analysis" by J. Rocha de Faria et al
  
  • Bonnet Marc
  International Journal of Solids and Structures, Elsevier, 2008, 45, pp.705-707. The article by J. Rocha de Faria et al. under discussion is concerned with the evaluation of the perturbation undergone by the potential energy of a domain $\Omega$ (in a 2-D, scalar Laplace equation setting) when a disk $B_{\epsilon}$ of small radius $\epsilon$ centered at a given location $\hat{\boldsymbol{x}\in\Omega$ is removed from $\Omega$, assuming either Neumann or Dirichlet conditions on the boundary of the small `hole' thus created. In each case, the potential energy $\psi(\Omega_{\epsilon})$ of the punctured domain $\Omega_{\epsilon}=\Omega\setminus\B_{\epsilon}$ is expanded about $\epsilon=0$ so that the first two terms of the perturbation are given. The first (leading) term is the well-documented topological derivative of $\psi$. The article under discussion places, logically, its main focus on the next term of the expansion. However, it contains incorrrect results, as shown in this discussion. In what follows, equations referenced with Arabic numbers refer to those of the article under discussion.