Publications

2007

• 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
• Transient behaviour of salt caverns
  
  • Berest Pierre
  • Karimi-Jafari Mehdi
  • Brouard Benoît
  • van Sambeek Leo
  , 2007, pp.383-390.
• Testing aluminum alloy from quasi-static to dynamic strain rates with a modified Split Hopkinson Bar method
  
  • Othman Ramzi
  • Gary Gérard
  Experimental Mechanics, Society for Experimental Mechanics, 2007, 47 (2), pp.295-299. An aluminum alloy(1) was tested at quasi-static to dynamic strain-rates (from 10(-1) to 5 10(3) s(-1)), using a single measuring device, a modified Split Hopkinson Bar. A wave separation technique [Bussac et al., J Mech Phys Solids 50:321-350, 2002] based on the maximum likelihood method was applied to process the strain and velocity measurements recorded at various points on each bar. With this method, it is possible to compute the stress, strain, displacement and velocity at any point on the bar. Since the measurement time is unlimited, the maximum strain measured in a given specimen no longer decreases with the strain-rate, as occurs with the classical Split Hopkinson Bar method. (10.1007/s11340-006-9023-7)
  DOI : 10.1007/s11340-006-9023-7
• 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, 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
• Mise en 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
  • Rémy Luc
  • Maitournam Habibou
  • Köster Alain
  • Bourgeois Myriam
  • Mac Lan Nguyen-Tajan T.
  , 2007, pp.8 p..
• Transient Behaviour of salt caverns. Interpretation of Mechanical Integrityb Tests
  
  • Berest Pierre
  • Bérest P.
  • Karimi-Jafari Mehdi
  • Brouard Benoît
  • van Sambeek Leo
  International Journal Rock Mechanics & Mining Sciences, 2007 (44), pp.767-786.
• Elasticity with Mathematica
  
  • Constantinescu Andrei
  • Korsunsky Alexander
  , 2007, pp.255. This book gives a an introduction to the key ideas and principles in the theory of elasticity with the help of symbolic computation. Differential and integral operators on vector and tensor fields of displacements, strains and stresses are considered on a consistent and rigorous basis with respect to curvilinear orthogonal coordinate systems. As a consequence, vector and tensor objects can be manipulated readily, and fundamental concepts can be illustrated and problems solved with ease. The method is illustrated using a variety of plane and three-dimensional elastic problems. General theorems, fundamental solutions, displacements and stress potentials are presented and discussed. The Rayleigh-Ritz method for obtaining approximate solutions is introduced for elastostatic and spectral analysis problems. The book contains more than 60 exercises and solutions in the form of Mathematica notebooks that accompany every chapter. Once the reader learns and masters the techniques, they can be applied to a large range of practical and fundamental problems. (10.1017/CBO9780511546167)
  DOI : 10.1017/CBO9780511546167
• Bifurcation of equilibrium solutions and defects nucleation
  
  • Stolz Claude
  International Journal of Fracture, Springer Verlag, 2007, 147, pp.103-107. The purpose of this article is to revise some concepts on defects nucleation based on bifurcation of equilibrium solutions. Equilibrium solutions are obtained on a homogeneous body and on a body with an infinitesimal defect such as cavity under the same prescirbed dead load. First void formation and growth in non linear mechanics are examined. A branch of radial transformation bifurcates from the undeformed configuration in presence of a small cavity. Two cases of behaviour is examined. One case is the growth of cavity by only the deformation of the matrix. In another modelling the cavity evolves like a damaged zone. The transition between the sound part and the damaged one is governed by a local criterium. Each configuration leads to the definition of a nucleation criterium based on a presence of a bifurcation state, comman state of the homogeneous boby and a body with an infinitesimal defect. (10.1007/s10704-007-9147-5)
  DOI : 10.1007/s10704-007-9147-5
• Localization of elastic deformation in strongly anisotropic, porous, linear materials with periodic microstructures: exact solutions and dilute expansions
  
  • Willot François
  • Pellegrini Yves-Patrick
  • Ponte Castañeda Pedro
  Journal of the Mechanics and Physics of Solids, Elsevier, 2007, 56, pp.1245-1268. Exact solutions are derived for the problem of a two-dimensional, infinitely anisotropic, linear-elastic medium containing a periodic lattice of voids. The matrix material possesses either one infinitely soft, or one infinitely hard loading direction, which induces localized (singular) field configurations. The effective elastic moduli are computed as functions of the porosity in each case. Their dilute expansions feature half-integer powers of the porosity, which can be correlated to the localized field patterns. Statistical characterizations of the fields, such as their first moments and their histograms are provided, with particular emphasis on the singularities of the latter. The behavior of the system near the void close packing fraction is also investigated. The results of this work shed light on corresponding results for strongly nonlinear porous media, which have been obtained recently by means of the ``second-order'' homogenization method, and where the dilute estimates also exhibit fractional powers of the porosity. (10.1016/j.jmps.2007.10.002)
  DOI : 10.1016/j.jmps.2007.10.002
• Equations intégrales en mécanique de la rupture: aspects théoriques et numériques
  
  • Bonnet Marc
  , 2007.
• Field statistics in nonlinear composites. I. Theory
  
  • Idiart Martin
  • Ponte Castañeda Pedro
  Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Royal Society, 2007, 463 (2077), pp.183-202. This work presents a means for extracting the statistics of the local fields in nonlinear composites from the effective potential of suitably perturbed composites. The idea is to introduce a parameter in the local potentials, generally a tensor, such that differentiation of the corresponding effective potential with respect to the parameter yields the volume average of the desired quantity. In particular, this provides a generalization to the nonlinear case of well-known formulas in the context of linear composites, which express phase averages and second moments of the local fields in terms of derivatives of the effective potential. Such expressions are useful since they allow the generation of estimates for the field statistics in nonlinear composites, directly from homogenization estimates for appropriately defined effective potentials. Here, use is made of these expressions in the context of the ‘variational’, ‘tangent second-order’ and ‘second-order’ homogenization methods, to obtain rigorous estimates for the first and second moments of the fields in nonlinear composites. While the variational estimates for these quantities are found to be identical to those proposed in previous works, the tangent second-order and second-order estimates are found be different. In particular, the new estimates for the first moments given in this work are found to be entirely consistent with the corresponding estimates for the macroscopic behaviour. Sample results for two-phase, power-law composites are provided in part II of this work. (10.1098/rspa.2006.1756)
  DOI : 10.1098/rspa.2006.1756
• Deep salt-cavern abandonment
  
  • Berest Pierre
  • Karimi-Jafari Mehdi
  • Brouard Benoît
  , 2007, pp.445-452.
• FM-BEM and topological derivative applied to inverse acoustic scattering
  
  • Bonnet Marc
  • Nemitz Nicolas
  , 2007, pp.187-212. 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(10⁵) nodal unknowns and O(10⁶) sampling points. (10.1007/978-3-540-47533-0_8)
  DOI : 10.1007/978-3-540-47533-0_8
• Study of non-proportionnal loading paths : comparison between experimental results and simulations performed by finite element and homogenized models
  
  • Gérard Céline
  • Bacroix Brigitte
  • Bornert Michel
  • Brenner Renald
  • Cailletaud Georges
  • Caldemaison Daniel
  • Chauveau Thierry
  • Crépin Jérôme
  • Leclercq Sylvain
  • Mounoury Valérie
  , 2007. The plastic behavior of fcc materials is studied under complex loading path at room temperature. Multi-scale experimental results are compared to finite element computations of polycrystalline aggregates, and to simulation by homogenization techniques. Combinations of sequences of simple loading paths such as tension, simple shear, rolling, cyclic tension-compression, with different orientations with regard to rolling direction, are considered. The material used in the study has been cold rolled and annealed. Specimen are marked with several gold microgrids to measure local strain field by digital correlation of scanning electron microscope images, whereas global strains are measured by classical extensometry. A polycrystalline aggregate taking into account the material microstructure is used to perform finite element simulations corresponding to the experiments. The texture measured by X-ray diffraction is represented. Several single crystal models, using the 12 slip systems of the octahedral families, are introduced. Various assumptions are considered for the description of the self and latent hardening. The comparisons between the simulation and the experiments are made on three types of variables~: on a global level, with the description of the macroscopic stress-strain curve, on a local level, by considering the local fields, and in terms of phase averages. Informations about the consistency of the transition rules are deduced.
• Micromechanical modeling of packing and size effects in particulate composites
  
  • Marcadon V.
  • Herve E.
  • Zaoui A.
  International Journal of Solids and Structures, Elsevier, 2007, vol. 44, pp.pp. 8213−8228.
• Creep and strain-dependent microstructures of synthetic anorthite-diopside aggregates
  
  • Dimanov Alexandre
  • Rybacki Erik
  • Wirth Richard
  • Dresen Georg
  Journal of Structural Geology, Elsevier, 2007, 29 (6), pp.1049-1069. (10.1016/j.jsg.2007.02.010)
  DOI : 10.1016/j.jsg.2007.02.010