Publications

2006

• Second-order theory for nonlinear composites and application to isotropic constituents
  
  • Idiart Martín I
  • Danas Kostas
  • Ponte Castañeda Pedro
  Comptes Rendus. Mécanique, Académie des sciences (Paris), 2006, 334 (10), pp.575-581. New prescriptions are proposed for the ‘reference’ fields in the context of the ‘second-order’ nonlinear homogenization method [P. Ponte Castañeda, Second-order homogenization estimates for nonlinear composites incorporating field fluctuations: I—Theory, J. Mech. Phys. Solids 50 (2002) 737–757], and are used to generate estimates for the effective behavior and first moments of the local fields in nonlinear composites. The new prescriptions yield simple, analytical expressions not only for the effective potentials, but also for the macroscopic stress-strain relation, as well as for the phase averages of the strain and stress fields. For illustrative purposes, ‘second-order’ estimates of the Hashin–Shtrikman type are provided for two-phase, transversely-isotropic composites with power-law phases, and are compared with exact results available for power-law, multiple-rank, sequential laminates. The agreement is found to be quite good for all ranges of nonlinearities and inclusion concentrations considered. (10.1016/j.crme.2006.06.006)
  DOI : 10.1016/j.crme.2006.06.006
• Identification of poroelastic constants of tight rocks from laboratory tests
  
  • Lecampion Brice
  • Constantinescu Andrei
  • Malinski Laurent
  International Journal of Geomechanics, American Society of Civil Engineers, 2006, 6, pp.201-208. This paper discusses the identification of poroelastic constants and hydraulic conductivity from two transient laboratory tests performed on cylindrical core: drained isotropic confinement and pulse test. The combination of the two tests allows us to estimate all poroelastic parameters with the exception of the shear modulus. Despite the lack of analytical solutions for the fully coupled case, closed form solutions of the forward problems are obtained for a slender specimen. The validity of these solutions for a realistic aspect ratio of the core is assessed by a comparison with a finite element model. The identification problem is solved by minimizing a least square functional using an explicit gradient computed using the direct differentiation of the closed form solution and a Levenberg–Marquardt algorithm. The uniqueness of this inverse problem as well as the effect of noise on input data are fully discussed. The identification procedure is then applied to tests performed on a deep argillaceous rock (argillite of Meuse Haute–Marne). (10.1061/(ASCE)1532-3641(2006)6:3(201))
  DOI : 10.1061/(ASCE)1532-3641(2006)6:3(201)
• Localisation dans les milieux poreux linéaires fortement anisotropes
  
  • Willot François
  • Pellegrini Yves-Patrick
  • Castañeda Pedro Ponte
  • Idiart Martin
  , 2006.
• On the overall behavior, microstructure evolution, and macroscopic stability in reinforced rubbers at large deformations: I-Theory
  
  • Lopez-Pamies Oscar
  • Ponte Castañeda Pedro
  Journal of the Mechanics and Physics of Solids, Elsevier, 2006, 54 (4), pp.807-830. This work presents an analytical framework for determining the overall constitutive response of elastomers that are reinforced by rigid or compliant fibers, and are subjected to finite deformations. The framework accounts for the evolution of the underlying microstructure, including particle rotation, which results from the finite changes in geometry that are induced by the applied loading. In turn, the evolution of the microstructure can have a significant geometric softening (or hardening) effect on the overall response, leading to the possible development of macroscopic instabilities through loss of strong ellipticity of the homogenized incremental moduli. The theory is based on a recently developed “second-order” homogenization method, which makes use of information on both the first and second moments of the fields in a suitably chosen “linear comparison composite,” and generates fairly explicit estimates—linearizing properly—for the large-deformation effective response of the reinforced elastomers. More specific applications of the results developed in this paper will be presented in Part II. (10.1016/j.jmps.2005.10.006)
  DOI : 10.1016/j.jmps.2005.10.006
• Identification d'obstacles en acoustique dans des domaines tridimensionnels bornés
  
  • Nemitz Nicolas
  • Bonnet Marc
  Revue Européenne de Mécanique Numérique/European Journal of Computational Mechanics, Hermès / Paris : Lavoisier, 2006, 15, pp.307-318. Cette communication concerne l'identification d'obstacles dans un domaine acoustique tridimensionnel borné. L'approche présentée repose sur deux ingrédients essentiels. Le premier est l'utilisation d'une méthode d'équations intégrales rapide fondée sur la fast multi-pole method, grâce à laquelle il est possible d'aborder ce type de problème d'inversion sur des configurations tridimensionnelles bornées de longueurs caractéristiques relativement grandes par rapport à la longueur d'onde acoustique. Le second est le gradient topologique de la fonction coût associée au problème inverse, permettant de déterminer les zones du domaine acoustique dans lesquelles l'introduction virtuelle d'un obstacle infinitésimal induit une diminution de la fonction coût. Cela permet par exemple de guider le choix de conditions initiales pour la mise en œuvre ultérieure d'un algorithme d'inversion reposant sur l'optimisation de la fonction coût. Ces deux aspects sont présentés et illustrés sur des exemples numériques. (10.3166/remn.15.307-318)
  DOI : 10.3166/remn.15.307-318
• Small-obstacle expansion for 3D acoustic and elastodynamic inverse scattering
  
  • Bonnet Marc
  , 2006. (10.1088/0266-5611/24/3/035022)
  DOI : 10.1088/0266-5611/24/3/035022
• A computational lifetime prediction of a thermal shock experiment. Part II: discussion on difference fatigue criteria
  
  • Amiable Sébastien
  • Chapuliot Sébastien
  • Constantinescu Andreï
  • Fissolo Antoine
  Fatigue and Fracture of Engineering Materials and Structures, Wiley-Blackwell, 2006, 29, pp.219-228. The SPLASH experiment has been designed in 1985 by the CEA to simulate thermal fatigue due to cooling shocks on steel specimens and is similar to the device reported by Marsh in Ref. [1]. The purpose of this paper is to discuss the application of different fatigue criteria in this case. The fatigue criteria: dissipated energy, Manson Coffin, Park and Nelson, dissipated energy with a pressure term, are determined for the experiment using results from FEM computations presented in the first part of the paper (Part I) and compared with results from uniaxial and multiaxial experiments from literature. The work emphasizes the evolution of the triaxiality ratio during the loading cycle. (10.1111/j.1460-2695.2006.0983.x)
  DOI : 10.1111/j.1460-2695.2006.0983.x
• Extensométrie surfacique et volumique pour l'analyse multi-échelle des matériaux
  
  • Bornert Michel
  , 2006.
• TGV disc brake squeal
  
  • Lorang Xavier
  • Foy-Margiocchi Florence
  • Son Nguyen Quoc
  • Gautier Pierre-Etienne
  Journal of Sound and Vibration, Elsevier, 2006, 293, pp.735-746. The discomfort generated by the noise emission of braking systems in train has aroused recently many studies on the mechanical modeling of brake noise in France. A theoretical and numerical discussion on the phenomenon of brake squeal is given here in relation with some experimental data. This study is based upon a flutter instability analysis giving the unstable modes of the TGV brake system. (10.1016/j.jsv.2005.12.006)
  DOI : 10.1016/j.jsv.2005.12.006
• Topological sensitivity and FMM-accelerated BEM applied to 3D acoustic inverse scattering
  
  • Nemitz Nicolas
  • Bonnet Marc
  , 2006. 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 hard obstacles in a bounded 3D acoustic domain, for configurations featuring nodal unknowns and sampling points, based on exact or noisy synthetic data. (10.1016/j.enganabound.2007.02.006)
  DOI : 10.1016/j.enganabound.2007.02.006
• Écart à la réciprocité et identification de fissures en thermoélasticité isotrope transitoire
  
  • Andrieux Stéphane
  • Bui Huy Duong
  Comptes Rendus. Mécanique, Académie des sciences (Paris), 2006, 334, pp.225-229. On s'intéresse à un solide élastique isotrope renfermant une ou plusieurs fissures planes, et soumis à un chargement d'origine thermique variable dans le temps. On relève la valeur du champ de déplacement et du champ des tractions surfaciques sur le bord du solide. On propose dans cette Note la définition et l'exploitation d'un écart à la réciprocité, formulé uniquement à partir des grandeurs mécaniques connues sur le bord du solide, qui permet de déterminer explicitement le plan renfermant la ou les fissures, les conditions régnant sur celles-ci étant quelconques dès lors qu'elles assurent la continuité du vecteur contrainte et du flux de chaleur normal. (10.1016/j.crme.2006.02.004)
  DOI : 10.1016/j.crme.2006.02.004
• Work of indentation approach to the analysis of hardness and modulus of thin coatings
  
  • Korsunsky Alexander
  • Constantinescu Andreï
  Materials Science and Engineering: A, Elsevier, 2006, 423, pp.28-35. The problem of accurate identification of mechanical properties, primarily hardness and modulus, invariably arises whenever very thin coatings are considered that consist of single or multiple layers, e.g. in the context of fitness-for-purpose characterisation of coated systems, monitoring in-service degradation, component lifetime prediction, etc. Rapid developments in the areas of nano-fabrication, nano-manipulation and nano-technology lead to the increased importance of reliable characterisation of mechanical properties of progressively thinner coatings. Instrumented small scale (nano-) indentation is particularly well-suited to surface-engineered and thin-coated systems. The present study presents a review and refinement of the interpretation techniques for instrumented (nano) indentation for reliable property de-convolution of coated systems. Particular attention is devoted to contact modulus and hardness, as the properties that play the key role in controlling the deformation response of any surface, and affect such service properties as impact and erosion resistance, wear and fretting fatigue resistance, resistance to crack initiation and propagation, etc. A flexible multi-scaling power law functional description is introduced and discussed, and its application to various example systems is illustrated. (10.1016/j.msea.2005.09.126)
  DOI : 10.1016/j.msea.2005.09.126
• Min-max Duality and Shakedown Theorems in Plasticity
  
  • Nguyen Quoc Son
  , 2006, pp.81-92. This paper gives an overall presentation of shakedown theorems in perfect and in hardening plasticity. General results on shakedown theorems are discussed in the framework of generalized standard materials. The starting point is a static shakedown theorem available for perfect and for hardening plasticity. It leads by min-max duality to the dual static and kinematic approaches to compute the safety coefficient with respect to shakedown. These approaches are discussed for common models of isotropic and of kinematic hardening. In particular, the kinematic approach leads to some new results on the expressions of the safety coefficient. (10.1000/ISBN-0387291962)
  DOI : 10.1000/ISBN-0387291962
• An integral-equation approach for small-obstacle approximation in 3D acoustic and elastodynamic inverse scattering
  
  • Bonnet Marc
  , 2006.
• A direct method for the solution of evolution problems
  
  • Comte François
  • Maitournam M.
  • Burry Pierre
  • Nguyen T. Mac Lan
  Comptes Rendus. Mécanique, Académie des sciences (Paris), 2006, 334 (5), pp.317-322. An alternative numerical method to solve structural evolution problems is presented. It belongs to the family of Large Time Increment Methods. The problem is solved on the whole time interval separating a global stage where a SA and KA solution is searched and a local stage where the constitutive law is satisfied. To solve the global stage, consuming the most CPU time, the mechanical fields are decomposed in a wavelet basis and the equilibrium is solved only for the largest coefficients. (10.1016/j.crme.2006.02.007)
  DOI : 10.1016/j.crme.2006.02.007
• White beam microdiffraction experiments for the determination of the local plastic behaviour of polycrystals
  
  • Castelnau Olivier
  • Goudeau Philippe
  • Geandier Guillaume
  • Tamura Nobumichi
  • Béchade Jean Luc
  • Bornert Michel
  • Caldemaison Daniel
  Materials Science Forum, Trans Tech Publications Inc., 2006, 524-525, pp.103-108. The overall plastic behavior of polycrystalline materials strongly depends on the microstructure and on the local rheology of individual grains. The characterization of the strain and stress heterogeneities within the specimen, which result from the intergranular mechanical interactions, is of particular interest since they largely control the microstructure evolutions such as texture development, work-hardening, damage, recrystallization, etc. The influence of microstructure on the effective behavior can be addressed by physical-based predictive models (homogenization schemes) based either on full-field or on mean-field approaches. But these models require the knowledge of the grain behavior, which in turn must be determined on the real specimen under investigation. The microextensometry technique allows the determination of the surface total (i.e. plastic + elastic) strain field with a micrometric spatial resolution. On the other hand, the white beam X-ray microdiffraction technique developed recently at the Advanced Light Source enables the determination of the elastic strain with the same spatial resolution. For polycrystalline materials with grain size of about 10 micrometers, a complete intragranular mechanical characterization can thus be performed by coupling these two techniques. The very first results obtained on plastically deformed copper and zirconium specimens are presented. (10.4028/www.scientific.net/MSF.524-525.103)
  DOI : 10.4028/www.scientific.net/MSF.524-525.103
• Modélisation numérique du Friction Stir Welding
  
  • Bastier Arnaud
  • Maitournam Habibou
  • Dang Van Ky
  • Roger Frédéric
  Revue Européenne de Mécanique Numérique/European Journal of Computational Mechanics, Hermès / Paris : Lavoisier, 2006, 15, pp.41-52. Le travail présenté dans cet article décrit une méthode de calcul destinée à la simulation d’un procédé de soudage appelé Friction Stir Welding. À partir d’une loi de comportement viscoplastique et d’une approche eulérienne, le champ de température est évalué en tenant compte de l’écoulement de matière autour de l’outil. Ce premier résultat, obtenu à l’aide d’une résolution par éléments finis mixtes, est validé par des données expérimentales issues de measures obtenues par thermographie infrarouge. La seconde étape du calcul a pour but de determiner les contraintes résiduelles de l’assemblage après soudage. Pour cela, un algorithme élastoplastique stationnaire est utilisé. Lors du calcul, l’histoire mécanique de la matière est prise en compte en intégrant le comportement le long des trajectoires suivies par les points matériels. Seule la phase stationnaire du procédé sera simulée dans l’ensemble de ce travail. (10.3166/remn.15.41-52)
  DOI : 10.3166/remn.15.41-52
• Introduction aux techniques d'homogénéisation
  
  • Zaoui A.
  , 2006.
• Rheology of the lower crust: laboratory data and field observations,
  
  • Dresen Georg
  • Dimanov A.
  • Rybacki E.
  • Xiaohui X.
  • Kenkmann T.
  • Wirth R.
  , 2006.
• Influence de la morphologie microstructurale sur la réponse mécanique de polycristaux biphasés
  
  • Rupin N.
  • Bornert Michel
  • Zaoui A.
  • Pinna C.
  • Gilormini P.
  , 2006.
• Multi-scale finite-strain plasticity model for stable metallic honeycombs incorporating microstructural evolution
  
  • Mohr Dirk
  International Journal of Plasticity, Elsevier, 2006, 22, pp.1899-1923. This paper deals with the development of a mechanism-based two-scale constitutive model for thick-walled metallic honeycombs in sandwich applications. The mechanical response of metallic honeycomb sandwich sheets subject to large in-plane normal loading and out-of-plane shear loading is investigated using a detailed finite element model of the honeycomb microstructure. Based on the simulation results, a simple micro-mechanical system is proposed and used to develop the macroscopic constitutive model. The finite-strain constitutive model accounts for microstructural evolution due to geometrical changes and strain hardening at the microscale. The macroscopic model has been validated for various loading conditions. Furthermore, the evolution of the macroscopic yield surface for pure out-of-plane shear is discussed in detail. (10.1016/j.ijplas.2006.01.004)
  DOI : 10.1016/j.ijplas.2006.01.004
• Identification of non-parametric probabilistic structural dynamics models from measured transfer functions
  
  • Arnst Maarten
  • Bonnet Marc
  • Clouteau Didier
  , 2006. 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
• Mesures de champs et identification de modèles de plasticité cristalline
  
  • Gérard Céline
  , 2006.
• Macroscopic behavior and field fluctuations in viscoplastic composites: Second-order estimates versus full-field simulations
  
  • Idiart Martin
  • Moulinec Hervé
  • Ponte Castañeda Pedro
  • Suquet Pierre
  Journal of the Mechanics and Physics of Solids, Elsevier, 2006, 6, pp.201-208. This work presents a combined numerical and theoretical study of the effective behavior and statistics of the local fields in random viscoplastic composites. The full-field numerical simulations are based on the fast Fourier transform (FFT) algorithm [Moulinec, H., Suquet, P., 1994. A fast numerical method for computing the linear and nonlinear properties of composites. C. R. Acad. Sci. Paris II 318, 1417–1423], while the theoretical estimates follow from the so-called “second-order” procedure [Ponte Castañeda, P., 2002a. Second-order homogenization estimates for nonlinear composites incorporating field fluctuations: I—Theory. J. Mech. Phys. Solids 50, 737–757]. Two-phase fiber composites with power-law phases are considered in detail, for two different heterogeneity contrasts corresponding to fiber-reinforced and fiber-weakened composites. Both the FFT simulations and the corresponding “second-order” estimates show that the strain-rate fluctuations in these systems increase significantly, becoming progressively more anisotropic, with increasing nonlinearity. In fact, the strain-rate fluctuations tend to become unbounded in the limiting case of ideally plastic composites. This phenomenon is shown to correspond to the localization of the strain field into bands running through the composite along certain preferred orientations determined by the loading conditions. The bands tend to avoid the fibers when they are stronger than the matrix, and to pass through the fibers when they are weaker than the matrix. In general, the “second-order” estimates are found to be in good agreement with the FFT simulations, even for high nonlinearities, and they improve, often in qualitative terms, on earlier nonlinear homogenization estimates. Thus, it is demonstrated that the “second-order” method can be used to extract accurate information not only for the macroscopic behavior, but also for the anisotropic distribution of the local fields in nonlinear composites. (10.1016/j.jmps.2005.11.004)
  DOI : 10.1016/j.jmps.2005.11.004
• Analyse des solides déformables par la méthode des éléments finis
  
  • Bonnet Marc
  • Frangi A.
  , 2006, pp.320.