Publications

2008

• Duality and symmetry lost in solid mechanics
  
  • Bui Huy Duong
  Comptes Rendus. Mécanique, Académie des sciences (Paris), 2008, 336, pp.12-23. Some conservation laws in solid and fracture mechanics present a lack of symmetry between kinematic and dynamic variables. It is shown that Duality is the right tool to establish the symmetry between equations and variables and to provide conservation laws of the pure divergence type which provide true path independent integrals. The loss of symmetry of some energetic expressions is exploited to derive a new method for solving some inverse problems. In particular, the earthquake inverse problem is solved analytically.
• 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
• Inverse acoustic scattering by small-obstacle expansion of misfit function
  
  • Bonnet Marc
  Inverse Problems, IOP Publishing, 2008, 24, pp.035022. This article concerns an extension of the topological derivative concept for 3D inverse acoustic scattering problems, whereby the featured cost function $J$ is expanded in powers of the characteristic size $\epsilon$ of a sound-hard scatterer about $\epsilon=0$. The $O(\epsilon^{6})$ approximation of $J$ is established for a small scatterer of arbitrary shape of given location embedded in an arbitrary acoustic domain, and generalized to several such scatterers. Simpler and more explicit versions of this result are obtained for a centrally-symmetric scatterer and a spherical scatterer. An approximate and computationally fast global search procedure is proposed, where the location and size of the unknown scatterer is estimated by minimizing the $O(\epsilon^{6})$ approximation of $J$ over a search grid. Its usefulness is demonstrated on numerical experiments, where the identification of a spherical, ellipsoidal or banana-shaped scatterer embedded in a acoustic half-space from known acoustic pressure on the surface is considered. (10.1088/0266-5611/24/3/035022)
  DOI : 10.1088/0266-5611/24/3/035022
• Viscoelastic impact between a cylindrical striker and a long cylindrical bar
  
  • Bussac Marie-Noëlle
  • Collet Pierre
  • Gary Gérard
  • Lundberg Bengt
  • Mousavi Saed
  International Journal of Impact Engineering, Elsevier, 2008, 35 (4), pp.226-239. Axial impact between a cylindrical striker of finite length and a long cylindrical bar, both of linearly viscoelastic materials, is considered under uni-axial conditions. General results are derived for the impact force, the particle velocity and the strain in the bar in terms of closed-contour integrals suitable for numerical evaluation. Such results are derived also for the transfer of momentum and energy from the striker to the bar. Numerical results for elastic and viscoelastic impact of a striker and a bar with different cross-sectional areas are compared. In viscoelastic impact, unlike elastic impact, the duration of impact may be finite but larger than two transit times for a wave front through the striker due to the for-mation of a tail after the main pulse. Furthermore, repeated contacts and separations of the striker and the bar may occur within a range of striker-to bar characteristic impedance ratios smaller than one. In viscoelastic impact, the duration of impact is at least as long and the momentum and energy transferred are at most as large as in elastic impact. Strains measured at three locations of a PMMA bar impacted by PMMA strikers of three different lengths agree well with the theoretical results. (10.1016/j.ijimpeng.2007.02.003)
  DOI : 10.1016/j.ijimpeng.2007.02.003
• Magnetoelastic Buckling of a Rectangular Block in Plane Strain
  
  • Kankanala Sunny
  • Triantafyllidis Nicolas
  Journal of the Mechanics and Physics of Solids, Elsevier, 2008, 56, pp.1147 - 1169.
• Multi-level fast multipole multi-region method for 3D seismic response of alluvial basins
  
  • Chaillat Stéphanie
  • Bonnet Marc
  • Semblat Jean-François
  , 2008.
• Comportement mécanique à très long terme des mines et cavernes dans le sel gemme : loi de Norton-Hoff ou loi de Lemaître ?
  
  • Berest Pierre
  • Bérest P.
  • Karimi-Jafari Mehdi
  • Brouard Benoît
  Revue française de Géotechnique, edp sciences, 2008 (124), pp.45-59.
• Biaxial Testing of Sheet Materials at High Strain Rates Using Viscoelastic Bars
  
  • Grolleau Vincent
  • Gary Gérard
  • Mohr Dirk
  Experimental Mechanics, Society for Experimental Mechanics, 2008, 48 (3), pp.293-306. A dynamic bulge testing technique is developed to perform biaxial tests on metals at high strain rates. The main component of the dynamic testing device is a movable bulge cell which is directly mounted on the measuring end of the input bar of a conventional split Hopkinson pressure bar system. The input bar is used to apply and measure the bulging pressure. The experimental system is analyzed in detail and the measurement accuracy is discussed. It is found that bars made of low impedance materials must be used to achieve a satisfactory pressure measurement accuracy. A series of dynamic experiments is performed on aluminum 6111-T4 sheets using viscoelastic nylon bars to demonstrate the capabilities of the proposed experimental technique. The parameters of the rate-dependent Hollomon–Cowper–Symonds J2 plasticity model of the aluminum are determined using an inverse analysis method in conjunction with finite element simulations. (10.1007/s11340-007-9073-5)
  DOI : 10.1007/s11340-007-9073-5
• A multi-level fast-multipole multi-region method for 3-D frequency-domain elastodynamics
  
  • Chaillat Stéphanie
  • Semblat Jean-François
  • Bonnet Marc
  , 2008.
• Interpretation of Mechanical Integrity Tests
  
  • Berest Pierre
  • Bérest P.
  , 2008, pp.1263-1270.
• L'effondrement de 1873 à la mine de Varangéville
  
  • Berest Pierre
  • Bérest P.
  , 2008, pp.281-288.
• Conception d'un algorithme de calcul du risque de chute de la personne âgée
  
  • Thibaud Marie
  • Bloch Frédéric
  • Brèque Cyril
  • Kemoun Gilles
  , 2008.
• MECHANICAL PROPERTIES OF GLENOID CANCELLOUS BONE
  
  • Kalouche Ibrahim
  • Abdelmoumen Samir
  • Crepin Jerome
  • Mitton David
  • Guillot Geneviève
  • Gagey Olivier
  Journal of Biomechanics, Elsevier, 2008, 41, pp.S 324.
• Theoretical and numerical modeling of solid-solid phase change: Application to the description of the thermodynamical behaviour of shape memory alloys
  
  • Moumni Ziad
  • Zaki Wael
  • Nguyen Quoc Son
  International Journal of Plasticity, Elsevier, 2008, 24 (xx), pp.614-645. The mechanical behaviour of a solid capable of undergoing internal phase change is considered. Reversible and dissipative constitutive equations are established within the framework of generalized standard materials with internal constraints. The constraints are accounted for using Lagrange multipliers. The presented model is based upon a phenomenological configuration in series (Reuss model). In the case of reversible phase change, it is shown that the elastic energy of the material can be obtained by convexification the energy functions of existing phases. In the dissipative case, it is shown how the behaviour of the material can be made stable by developing evolving equations from a suitable dissipation potential. As an application, a description of the thermomechanical behaviour of shape memory alloys (SMAs). The obtained constitutive equations can be used to simulate the pseudoelastic response of SMAs as well as the one-way shape memory effect. Validation against experimental data is performed in the case of multiaxial thermomechanical loading for NiTi and Cu-based alloys. (10.1016/j.ijplas.2007.07.007)
  DOI : 10.1016/j.ijplas.2007.07.007
• 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
• 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
• 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
• Topological sensitivity and FMM-accelerated BEM applied to 3D acoustic inverse scattering
  
  • Nemitz N.
  • 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
• 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.
• 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.
• Instruments à cordes frottées
  
  • Boutillon Xavier
  , 2008, pp.511-532 et 132-135.
• 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
• 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