Publications

2010

• Micromechanical Investigation of the Hydromechanical Behaviors of Carbonates Contribution of In-Situ Strain Field Measurement By Means of SEM And Optic Digital Image Correlation
  
  • Dautriat Jérémie
  • Bornert Michel
  • Gland Nicolas
  • Dimanov Alexandre
  • Raphanel Jean
  • Vizika Olga
  Petrophysics – The SPWLA Journal of Formation Evaluation and Reservoir Description, The Society of Petrophysicists and Well Log Analysts (SPWLA), 2010, 51 (6), pp.388-398. In a previous study (Dautriat et al., 2008), we have studied the macroscopic hydro-mechanical behavior of a moderately heterogeneous carbonate reservoir analogue, undergoing triaxial testing along several proportional stress paths, ranging from hydrostatic compression -to-axial compression. Evolutions of permeabilities and compressibilities during loading have been measured and correlated and the yield envelope has been determined. Structural heterogeneities have been shown to strongly affect the initiation of brittle and plastic damages. There is a trend to interpret the macroscopic response in term of micro-mechanisms without actual observation and identification. While post-mortem characterization techniques (HPMI, SEM and XR CT / μ-CT images) inform qualitatively on the damage mechanisms activated at the grain and aggregate scales, a quantitative and continuous micromechanical investigation is needed to follow the history of the deformation and the localization during compression. We have therefore performed in-situ observations during loading at different scales. First, small samples have been deformed by simple compression inside a SEM, in order to identify the physical deformation and damage micro-mechanisms responsible for the evolutions of the transport properties. Then, larger samples have been subjected to axial compression in a hydraulic press and have been observed by optical methods, in order to better understand the complex interactions governing the macroscopic behavior. Observations of the micro-mechanisms during mechanical tests are difficult for geomaterials because the levels of deformation are low (below the percent), but feasible with some care and appropriate recording devices; different regions of small parallelipipedic samples have been imaged using different magnifications to focus either on grain or contact, or to visualize the aggregates. Direct optical observations on bigger cylindrical samples, mechanically loaded on conventional UCS testing machines, have also been performed at two different scales by means of high resolution digital cameras. On one side, the full sample is imaged (≈20μm resolution) in order to characterize the overall response. On the opposite spot side, a centimetric area has been considered (≈3μm resolution), at which scale the composite nature of the rock made of microporous and dense calcite grains is revealed. Those two scales imaging experiments have been combined with efficient Digital Image Correlation (DIC) post-treatments, able to detect very small displacements and evolutions of the microstructures (strain accuracy better than 10-3). The comparisons of SEM images taken stepwise, reveal deformations hardly detectable by conventional observations, such as: opening or closure of pre-existing microcracks, nucleation of new microcracks and relative movements at grain interfaces. Different strain accommodation regimes are also observed in dense and microporous grains, respectively brittle and diffuse. The movies at sample scale show that the heterogeneity of strain is correlated to the local distribution of the aggregates, which confirms the post-mortem observations.
• Muscle contraction: a mechanical perspective
  
  • Marcucci Lorenzo
  • Truskinovsky Lev
  European Physical Journal E: Soft matter and biological physics, EDP Sciences: EPJ / Springer Nature, 2010, 32 (4), pp.411-418. In this paper we present a purely mechanical analog of the conventional chemo-mechanical modeling of muscle contraction. We abandon the description of kinetics of the power stroke in terms of jump processes and instead resolve the continuous stochastic evolution on an appropriate energy landscape. In general physical terms, we replace hard spin chemical variables by soft spin variables representing mechanical snap-springs. This allows us to treat the case of small and even disappearing barriers and, more importantly, to incorporate the mechanical representation of the power stroke into the theory of Brownian ratchets. The model provides the simplest non-chemical description for the main stages of the biochemical Lymn-Taylor cycle and may be used as a basis for the artificial micro-mechanical reproduction of the muscle contraction mechanism. (10.1140/epje/i2010-10641-0)
  DOI : 10.1140/epje/i2010-10641-0
• Multiscale Full-Field Strain Measurements for Micromechanical Investigations of the Hydromechanical Behaviour of Clayey Rocks
  
  • Bornert Michel
  • Valès Frédéric
  • Gharbi Houria
  • Nguyen Minh D.
  Strain, Wiley-Blackwell, 2010, 46 (1), pp.33–46. Digital image correlation techniques (DIC) are applied to sequences of optical images of argillaceous rock samples submitted to uniaxial compression at various saturation states at both the global centimetric scale of the samples and the local scale of their composite microstructure, made of a water-sensitive clay matrix and other mineral inclusions with a typical size of 50 μm. Various scales of heterogeneities are revealed by the optical technique. Not only is it confirmed that the clay matrix deforms much more than the other mineral inclusions, but it also appears that the deformation is very inhomogeneous in the matrix, with some areas almost not deformed, while others exhibit deformation twice the average overall strain (for a gauge length of 45 μm), depending on the local distribution of the inclusions. In almost-saturated rocks, overall heterogeneities are also linked to the presence of a network of cracks, induced by the preliminary hydric load. On such wet samples, DIC analysis shows that the overall strain results both from the bulk deformation of the sound rock, with deformation levels similar to those in dry samples, and the closing or opening of these mesoscopic cracks. (10.1111/j.1475-1305.2008.00590.x)
  DOI : 10.1111/j.1475-1305.2008.00590.x
• Hybrid Experimental-numerical Analysis of Basic Ductile Fracture Experiments for Sheet Metals
  
  • Mohr Dirk
  • Dunand M.
  International Journal of Solids and Structures, Elsevier, 2010, 47 (9), pp.1130-1143. A basic ductile fracture testing program is carried out on specimens extracted from TRIP780 steel sheets including tensile specimens with a central hole and circular notches. In addition, equi-biaxial punch tests are performed. The surface strain fields are measured using two- and three-dimensional digital image correlation. Due to the localization of plastic deformation during the testing of the tensile specimens, finite element simulations are performed of each test to obtain the stress and strain histories at the material point where fracture initiates. Error estimates are made based on the differences between the predicted and measured local strains. The results from the testing of tensile specimens with a central hole as well as from punch tests show that equivalent strains of more than 0.8 can be achieved at approximately constant stress triaxialities to fracture of about 0.3 and 0.66, respectively. The error analysis demonstrates that both the equivalent plastic strain and the stress triaxiality are very sensitive to uncertainties in the experimental measurements and the numerical model assumptions. The results from computations with very fine solid element meshes agree well with the experiments when the strain hardening is identified from experiments up to very large strains (10.1016/j.ijsolstr.2009.12.011)
  DOI : 10.1016/j.ijsolstr.2009.12.011
• Comparison of Fully Coupled Modeling and Experiments for Electromagnetic Forming Processes in Finitely Strained Solids
  
  • Thomas Jesse D.
  • Triantafyllidis Nicolas
  • Vivek A.
  • Daehn Glenn S.
  • Bradley John R.
  International Journal of Fracture, Springer Verlag, 2010, 163, pp.pp. 67-83. In fracture and fragmentation research the technique of electromagnetic forming, which uses electromagnetic (Lorentz) body forces to shape metallic parts, is finding significant use due to the high velocity, high strain rate loading it can impart without contact on workpieces. The same process is also becoming increasingly relevant formanufacturing processes in sheet metal forming, where this technique offers several advantages: speed, repeatability, non-contact loading, reduced springback and considerable ductility increase in several metals. Current modeling techniques for these coupled electromagnetic and thermomechanical processes are not based on coupled variational principles that can simultaneously account for electromagnetic and mechanical effects. Typically, separate solutions to the electromagnetic (Maxwell) and motion (Newton) equations are combined in staggered or lock-step methods, sequentially solving the mechanical and electromagnetic problems. To address this issue, Thomas and Triantafyllidis (J Mech Phys Solids 57:1391-1416, 2009) have recently introduced a fully coupled Lagrangian (reference configuration) variational principle, involving the magnetic field potential and the displacement field as independent variables. The corresponding Euler-Lagrange equations areMaxwell's and Newton's equations in the reference configuration under the eddy current approximation. This novel approach is used here to simulate free expansion experiments of AA6063-T6 aluminum tubes. A viscoplastic constitutive model, developed independently by the authors (Thomas et al. Acta Mater 55:2863-2873, 2007) for necking experiments in tubes of the same aluminum alloy, is used in the simulations. The measured electric currents and tube deformation--the latter obtained by Photon Doppler Velocimetry--show reasonably good agreement with the corresponding simulations, which are obtained using a variational integration numerical scheme that results in an efficient staggered solution algorithm.
• A fast approximate global search methodology for defect identification based on small-inclusion asymptotics of misfit functionals
  
  • Bonnet Marc
  , 2010.
• X-ray tomographic characterization of the macroscopic porosity of chemical vapor infiltration SIC/SIC composites: effects on the elastic behavior
  
  • Gelebart Lionel
  • Chateau Camille
  • Bornert Michel
  • Crépin Jérôme
  • Boller Elodie
  International Journal of Applied Ceramic Technology, Wiley, 2010, 7, pp.348-360. This paper focuses on the characterization of the macroporosity, the porosity among the tows, observed in chemical vapor infiltration composites and on its effect on the thermo-mechanical behavior. The experimental characterization of macroporosity is performed using an X-ray tomography technique. Numerical 3D images are used to describe the distribution of macroporosity with respect to the position of the plies. It is clearly established that the stacking of the plies has a significant effect on the porosity distribution. As a consequence for the micromechanical modelling, a unique element that contains only one ply is not representative of the porosity distribution and is not sufficient to evaluate the "effective" mechanical properties; several volume elements (VE), called "statistical volume elements (SVE)," with at least two plies per VE have to be used in order to account for the variability of the stacking of the plies. Finally, such SVE are directly extracted from the tomographic image and the "effective" elastic behavior is evaluated from the average of the "apparent" behavior evaluated on each SVE. In spite of their quite important size, the "apparent" behaviors evaluated for each SVE exhibit important fluctuations. (10.1111/j.1744-7402.2009.02470.x)
  DOI : 10.1111/j.1744-7402.2009.02470.x
• On the stick-slip waves under unilateral contact and Coulomb friction
  
  • Bui Hui Duong
  • Oueslati Abdelbacet
  Annals of Solid and Structural Mechanics, Springer Berlin Heidelberg, 2010, 1 (3-4), pp.159-172. In this paper, the construction of analytic solution of stick-slip waves propagating along the interface between an elastic half-space and a moving rigid one is investigated. The contact between the solids is governed by unilateral constraints and Coulomb friction law and the deformable body is loaded by remote uniform stresses t*yy<0, t*xy>0. The method of solution is based on the continuation of Radok's complex potentials within the framework of steady state elastodynamical problems. The governing equation combined with the boundary conditions are reduced to a Riemann-Hilbert problem with discontinuous coefficient. This approach for the stick-slip study is novel and differs from those in the literature, namely the series method and the Weertmann's dislocation formulation. We present the closed form solution of the Riemann-Hilbert problem and show that the principal unknowns are of number two: the wave celerity and the ratio of the slip length by the stick one. The considered loading introduces an additional velocity V* related to the elongation e*xx due to the normal stress t*yy. We show that if V* vanishes there is no solution. When V* is taken into account, it is possible to construct weakly singular solutions satisfying all stick-slip conditions except over a narrow zone at transition points: The shear stress is singular over a small zone and the normal stress exhibits a positive singularity over a very small zone in the slip region which implies a separation near the singular transition. (10.1007/s12356-010-0012-2)
  DOI : 10.1007/s12356-010-0012-2
• Weak variations of Lipschitz graphs and stability of phase boundaries
  
  • Grabovsky Yury
  • Kucher Vladislav
  • Truskinovsky Lev
  Cont. Mech. Therm., 2010, 23, pp.87-123. In the case of Lipschitz extremals of vectorial variational problems, an important class of strong variations originates from smooth deformations of the corresponding non-smooth graphs. These seemingly singular variations, which can be viewed as combinations of weak inner and outer variations, produce directions of differentiability of the functional and lead to singularity-centered necessary conditions on strong local minima: an equality, arising from stationarity, and an inequality, implying configurational stability of the singularity set. To illustrate the underlying coupling between inner and outer variations, we study in detail the case of smooth surfaces of gradient discontinuity representing, for instance, martensitic phase boundaries in non-linear elasticity. (10.1007/s00161-010-0171-8)
  DOI : 10.1007/s00161-010-0171-8
• Special Issue of European Journal of Computational Mechanics, vol 19, N° 1-2-3
  
  • Rey Christian
  • Raous Michel
  • Pasquet Philippe
  • Bonnet Marc
  • Feyel Frédéric
  , 2010, pp.328.
• Evaluation of Associated and Non-associated Quadratic Plasticity Models For Advanced High Strength Steel Sheets under Multi-axial Loading
  
  • Mohr Dirk
  • Dunand M.
  • Kim K.-H.
  International Journal of Plasticity, Elsevier, 2010, 26 (7), pp.939-956.
• A 3D finite element model for the vibration analysis of asymmetric rotating machines
  
  • Lazarus Arnaud
  • Prabel Benoit
  • Combescure Didier
  Journal of Sound and Vibration, Elsevier, 2010, 329. This paper suggests a 3D finite element method based on the modal theory in order to analyse linear periodically time-varying systems. Presentation of the method is given through the particular case of asymmetric rotating machines. First, Hill governing equations of asymmetric rotating oscillators with two degrees of freedom are investigated. These differential equations with periodic coefficients are solved with classic Floquet theory leading to parametric quasimodes. These mathematical entities are found to have the same fundamental properties as classic eigenmodes, but contain several harmonics possibly responsible for parametric instabilities. Extension to the vibration analysis (stability, frequency spectrum) of asymmetric rotating machines with multiple degrees of freedom is achieved with a fully 3D finite element model including stator and rotor coupling. Due to Hill expansion, the usual degrees of freedom are duplicated and associated with the relevant harmonic of the Floquet solutions in the frequency domain. Parametric quasimodes as well as steady-state response of the whole system are ingeniously computed with a component-mode synthesis method. Finally, experimental investigations are performed on a test rig composed of an asymmetric rotor running on nonisotropic supports. Numerical and experimental results are compared to highlight the potential of the numerical method. (10.1016/j.jsv.2010.03.029)
  DOI : 10.1016/j.jsv.2010.03.029
• Milieux Continus en transformations finies : Hyperélasticité, Rupture, Elastoplasticité
  
  • Stolz Claude
  , 2010, pp.1-270. L'ouvrage propose une introduction à la mécanique des milieux continus en transformations finies. Les premiers chapitres étudient les aspects cinématiques et statiques de la mécanique des milieux continus et donnent un éclairage sur les notions de transport des quantités mécaniques en suivant le mouvement de la matière. On analyse le cas des matériaux hyperélastiques incompressibles, dont les applications industrielles sont nombreuses. Cette modélisation des polymères est développée selon plusieurs aspects : une introduction statistique du comportement à partir de chaînes de monomères, puis une étude de l'équilibre du corps hyperélastique. L'introduction de la classe des déformations universelles éclaire les couplages non linéaires dus au comportement d'une part et à la géométrie d'autre part. L'étude et les conditions d'unicité de la réponse à un trajet d'équilibre sont présentées dans une approche de stabilité bifurcation. Les coques et membranes élastiques sont abordées succinctement et montre la multiplicité des modèles de description de la cinématique et de la statique de ces objets. La mécanique de la rupture en transformations finies est abordée selon deux points de vue : d'une part l'analyse des singularités potentielles en front de fissure, avec comme illustration la rupture en mode antiplan, et d'autre part au travers une modélisation d'un endommagement local de la matière défini par une élongation limite critique. Les problèmes d'évolution d'un ensemble de fissures ou de zones endommagées sont analysés. Enfin, les lois de comportement élastoplastiques sont décrites après avoir introduit la cinématique du monocristal. La loi de comportement du polycristal est alors étudiée dans une approche macroscopique utilisant la notion de configuration relâchée. Cette approche est justifiée par l'établissement de relations entre les grandeurs microscopiques, celles du monocristal, et macroscopiques. Enfin, la formulation du problème d'évolution obtenue permet d'étendre au cas élastoplastique les arguments utilisés en hyperélasticité pour l'étude de l'évolution d'un système de fissures. Quelques annexes apportent des compléments de modélisation pour les chargements thermomécaniques et cycliques, par l'introduction d'orientations privilégiées et l'existence d'élongations limites.
• Diffusion in Pyroxenes, Mica and Amphibole
  
  • Cherniak Daniele J
  • Dimanov Alexandre
  , 2010, 72 (1), pp.641-690. This chapter presents an overview of diffusion data for pyroxenes, amphiboles and micas. These minerals are grouped together since amphiboles and micas are closely related in structure to pyroxenes, with amphiboles essentially constructed of alternating layers with structures of mica and pyroxene. We begin with discussion of diffusion in pyroxenes, for which an extensive literature exists, with diffusion studies of major, minor and trace elements. We consider diffusion mechanisms in light of present understanding of defect chemistry, and discuss various crystal-chemical factors that may affect cation diffusion. The last section of the chapter presents a review of diffusion data for amphiboles and micas. Selected Arrhenius relations for these all these mineral phases are summarized in the Appendix Tables A1, A2, A3 and A4. This chapter focuses primarily on cation diffusion, since oxygen, hydrogen and noble gas diffusion are discussed in other chapters; readers interested in more detailed discussion of diffusion of these species in pyroxene, amphibole and mica are directed to Chapters 10 (Farver 2010, this volume) and 11 (Baxter 2010, this volume). (10.2138/rmg.2010.72.14)
  DOI : 10.2138/rmg.2010.72.14
• Identifying constitutive parameters from full-field measurements: a challenging issue in computational mechanics
  
  • Grediac Michel
  • Bonnet Marc
  , 2010.
• L'effondrement de 1873 à la mine de Varangéville
  
  • Berest Pierre
  • Bérest P.
  • Karimi-Jafari Mehdi
  • Brouard Benoît
  • Feuga Bernard
  Revue française de Géotechnique, edp sciences, 2010 (131-132), pp.105-118. On relate l’effondrement d’un quartier de la mine de sel de Varangéville survenu en 1873. Les descriptions de l’époque montrent que la partie centrale du recouvrement de la mine est descendue en bloc, entraînant une couronne intensément déformée. Les piliers ont poinçonné précocement le mur imbibé de saumure, mais le toit les a retenus tant que l’extension de la mine, et donc sa raideur à la flexion restaient modérées. Le calcul numérique montre que le caractère brutal de l’effondrement peut être relié au développement d’une zone dilatante, traversant toute la couche de sel, et engendrée par le report sur le contour de la mine d’une part du poids des terrains surincombants. (10.1051/geotech/2010131105)
  DOI : 10.1051/geotech/2010131105
• Multi-scale viscoplastic behavior of Halite : In-situ SEM full field measurements, a micromechanical approach
  
  • Bourcier M.
  • Dimanov A.
  • Héripré E.
  • Bornert Michel
  • Raphanel J.
  , 2010.
• Identification of a planar crack in Zener type viscoelasticity
  
  • Bui Hui Duong
  • Chaillat Stéphanie
  • Constantinescu Andrei
  • Grasso Eva
  Annals of Solid and Structural Mechanics, Springer Berlin Heidelberg, 2010, 1 (1), pp.3-8. The paper addresses the identification of a planar crack for Zener type linear viscoelastic solids. Under the condition of low frequency, the Zener model of viscoelasticity establishes the equivalence between viscoelasticity and elasticity and the equations are reduced to a Helmholtz type problem for time harmonic loadings. The solutions to the crack identification problems are then obtained from the corresponding solutions in elasticity, using only one frequency. (10.1007/s12356-009-0003-3)
  DOI : 10.1007/s12356-009-0003-3
• On the application of the Fast Multipole Method to Helmholtz-like problems with complex wavenumber
  
  • Frangi Attilio
  • Bonnet Marc
  Computer Modeling in Engineering and Sciences, Tech Science Press, 2010, 58, pp.271-296. This paper presents an empirical study of the accuracy of multipole expansions of Helmholtz-like kernels with complex wavenumbers of the form $k=(\alpha+\beta)\vartheta$, with $\alpha=0,\pm1$ and $\beta>0$, which, the paucity of available studies notwithstanding, arise for a wealth of different physical problems. It is suggested that a simple point-wise error indicator can provide an a priori indication on the number $N$ of terms to be employed in the Gegenbauer addition formula in order to achieve a prescribed accuracy when integrating single layer potentials over surfaces. For $\beta\geq 1$ it is observed that the value of $N$ is independent of $\beta$ and of the size of the octree cells employed while, for $\beta<1$, simple empirical formulas are proposed yielding the required $N$ in terms of $\beta$. (10.3970/cmes.2010.058.271)
  DOI : 10.3970/cmes.2010.058.271
• Beyond kinetic relations
  
  • Vainchtein Anna
  • Truskinovsky Lev
  Cont. Mech. Therm., 2010, 22, pp.485-504. We introduce the concept of kinetic or rate equations for moving defects representing a natural extension of the more conventional notion of a kinetic relation. Algebraic kinetic relations, widely used to model dynamics of dislocations, cracks and phase boundaries, link the instantaneous value of the velocity of a defect with an instantaneous value of the driving force. The new approach generalizes kinetic relations by implying a relation between the velocity and the driving force which is nonlocal in time. To make this relation explicit one may need to integrate a system of kinetic equations. We illustrate the difference between kinetic relation and kinetic equations by working out in full detail a prototypical model of an overdamped defect in a one-dimensional discrete lattice. We show that the minimal nonlocal kinetic description, containing now an internal time scale, is furnished by a system of two ordinary differential equations coupling the spatial location of defect with another internal parameter that describes configuration of the core region. (10.1007/s00161-010-0167-4)
  DOI : 10.1007/s00161-010-0167-4
• Inverse Problems
  
  • Bonnet Marc
  , 2010.
• Fracture Mechanics
  
  • Bui Huy Duong
  , 2010, pp.400.
• High temperature rheology of synthetic two−phase gabbroic aggregates: microstructural heterogeneities and local deformation mechanism
  
  • Raphanel Jean
  • Dimanov Alexandre
  • Nazarova L.A.
  • Nazarov L.A.
  • Artemova A.I.
  Fiziko-Tekhnicheskie Problemy Razrabotki Poleznykh Iskopaemykh / Journal of Mining Science, Springer Verlag, 2010, 46 (5), pp.495-502. The high-temperature rheology of heterogeneous anorthite — diopside aggregates has been investigated numerically, in support to experimental data obtained by triaxial torsion tests, performed at high pressure (400 MPa) and temperature (1150° C). The mechanical data exhibited linear viscous flow. Accordingly, scanning electron microscopy revealed grain sliding mechanisms, but also crystal slip plasticity, recrystallization and micro-fracturing. Finite element computations at the aggregate scale aimed at the understanding of the sequence of active mechanisms and their link to the macroscopic behavior. For instance, we show that the presence of coarser and stronger diopside inclusions in weaker and fine grained anorthite matrix results in very heterogeneous local stress fields, allowing for the activation of multiple deformation mechanisms. Our study indicates that shear zones in the lower crust should be dominated by Newtonian rheology in relation with grain sliding mechanisms, even though complementary accommodation mechanisms such as crystal plasticity and damage may be necessary at the local scale, due to the heterogeneous microstructures. (10.1007/s10913-010-0062-1)
  DOI : 10.1007/s10913-010-0062-1
• Vortex-induced vibration of a square cylinder in wind tunnel
  
  • Amandolèse Xavier
  • Hémon Pascal
  Comptes Rendus. Mécanique, Académie des sciences (Paris), 2010, 338 (1), pp.12-17. An experimental study of the vortex-induced-vibration of a flexibly mounted rigid square cylinder in a uniform airflow is presented. For this high mass ratio configuration, transverse oscillations are measured in detail for reduced velocities ranging from 5 to 20. In the lock-in region and starting from rest, the cylinder motion exhibits a transient regime followed by a limit cycle oscillation regime. New experimental data are provided in term of amplitudes and frequencies of the limit cycle oscillations. The transient behaviour is also characterized by measuring the growth rate of the oscillations amplitude. © 2009 Académie des sciences. (10.1016/j.crme.2009.12.001)
  DOI : 10.1016/j.crme.2009.12.001
• Symmetric FEM-driven BEM-FEM coupling for 3D linear fracture mechanics
  
  • Hu Heng
  • Chambon Laurent
  • Crozes Damien
  • Frangi A.
  • Bonnet Marc
  , 2010. see pdf file