Publications

2010

• 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
• 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.
• 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
• 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
• 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
• Crack identification in elasticity using 3d time-domain topological derivative
  
  • Bellis Cédric
  • Bonnet Marc
  , 2010.
• Structural dynamics monitoring via a coupled data assimilation and modified error in constitutive relation technique
  
  • Alarcon Albert
  • Bodel Charles
  • Bonnet Marc
  , 2010.
• Linear non-normal energy amplification of harmonic and stochastic forcing in the turbulent channel flow
  
  • Hwang Yongyun
  • Cossu Carlo
  Journal of Fluid Mechanics, Cambridge University Press (CUP), 2010, 664 (December), pp.51-73. The linear response to stochastic and optimal harmonic forcing of small coherent perturbations to the turbulent channel mean flow is computed for Reynolds numbers ranging from Re-tau = 500 to 20 000. Even though the turbulent mean flow is linearly stable, it is nevertheless able to sustain large amplifications by the forcing. The most amplified structures consist of streamwise-elongated streaks that are optimally forced by streamwise-elongated vortices. For streamwise-elongated structures, the mean energy amplification of the stochastic forcing is found to be, to a first approximation, inversely proportional to the forced spanwise wavenumber while it is inversely proportional to its square for optimal harmonic forcing in an intermediate spanwise wavenumber range. This scaling can be explicitly derived from the linearized equations under the assumptions of geometric similarity of the coherent perturbations and of logarithmic base flow. Deviations from this approximate power-law regime are apparent in the pre-multiplied energy amplification curves that reveal a strong influence of two different peaks. The dominant peak scales in outer units with the most amplified spanwise wavelength of lambda(z) approximate to 3.5h, while the secondary peak scales in wall units with the most amplified lambda(+)(z) approximate to 80. The associated optimal perturbations are almost independent of the Reynolds number when, respectively, scaled in outer and inner units. In the intermediate wavenumber range, the optimal perturbations are approximatively geometrically similar. Furthermore, the shape of the optimal perturbations issued from the initial value, the harmonic forcing and the stochastic forcing analyses are almost indistinguishable. The optimal streaks corresponding to the large-scale peak strongly penetrate into the inner layer, where their amplitude is proportional to the mean-flow profile. At the wavenumbers corresponding to the large-scale peak, the optimal amplifications of harmonic forcing are at least two orders of magnitude larger than the amplifications of the variance of stochastic forcing and both increase with the Reynolds number. This confirms the potential of the artificial forcing of optimal large-scale streaks for the flow control of wall-bounded turbulent flows. (10.1017/s0022112010003629)
  DOI : 10.1017/s0022112010003629
• Inverse Problems
  
  • Bonnet Marc
  , 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
• 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
• Fracture Mechanics
  
  • Bui Huy Duong
  , 2010, pp.400.
• 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.
• 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
• Topological sensitivity of energy cost functional for wave-based defect identication
  
  • Bonnet Marc
  Comptes Rendus. Mécanique, Académie des sciences (Paris), 2010, 338, pp.377-389. This article is concerned with establishing the topological sensitivity (TS) against the nucleation of small trial inclusions of an energy-like cost function. The latter measures the discrepancy between two time-harmonic elastodynamic states (respectively defined, for cases where overdetermined boundary data is available for identification purposes, in terms of Dirichlet or Neumann boundary data for the same reference solid) as the strain energy of their difference. Such cost function constitutes a particular form of error in constitutive relation and may be used for e.g. defect identification. The TS is expressed in terms of four elastodynamic fields, namely the free and adjoint solutions for Dirichlet or Neumann data. A similar result is also given for the linear acoustic scalar case. A synthetic numerical example where the TS result is used for the qualitative identification of an inclusion is presented for a simple 2D acoustic configuration. (10.1016/j.crme.2010.07.016)
  DOI : 10.1016/j.crme.2010.07.016
• 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
• New flow rules in elasto-viscoplastic constitutive models for spheroidal graphite cast-iron
  
  • Szmytka Fabien
  • Rémy Luc
  • Maitournam Habibou
  • Köster Alain
  • Bourgeois Myriam
  International Journal of Plasticity, Elsevier, 2010, 26, pp.905-924. A specific flow rules and the corresponding constitutive elasto-viscoplastic model combined with new experimental strategy are introduced in order to represent a spheroidal graphite cast-iron behaviour on a wide range of strain, strain rate and temperature. A “full model” is first proposed to correctly reproduce the alloy behaviour even for very small strain levels. A “light model” with a bit poorer experimental agreement but a simpler formulation is also proposed. These macroscopic models, whose equations are based on physical phenomena observed at the dislocation scale, are able to cope with the various load conditions tested – progressive straining and cyclic hardening tests – and to correctly describe anisothermal evolution. The accuracy of these two models and the experimental databases to which they are linked is estimated on different types of experimental tests and compared with the accuracy of more standard Chaboche-type constitutive models. Each test leads to the superiority of the “full model”, particularly for slow strain rates regimes. After developing a material user subroutine, FEM simulations are performed on Abaqus for a car engine exhaust manifold and confirm the good results obtained from the experimental basis. We obtain more accurate results than those given by more traditional laws. A very good correlation is observed between the simulations and the engine bench tests. (10.1016/j.ijplas.2009.11.007)
  DOI : 10.1016/j.ijplas.2009.11.007
• Fast Multipole Method for 3D Electromagnetic Boundary Integral Equations. Application to Nondestructive Testing on Complex 3D Geometries
  
  • Lim Tekoing
  • Pichenot G.
  • Bonnet Marc
  , 2010.
• Multi-scale viscoplastic behaviour of Halite : In-situ SEM full field measurements, a micro-mechanical approach, Experimental mineralogy, petrology and geochemistry
  
  • Bourcier M.
  • Dimanov A.
  • Héripré E.
  • Bornert Michel
  • Raphanel J.
  , 2010.
• On the existence and uniqueness of a solution to the interior transmission problem for piecewise-homogeneous solids
  
  • Bellis Cédric
  • Guzina B. B.
  Journal of Elasticity, Springer Verlag, 2010, pp.in press. The interior transmission problem (ITP), which plays a fundamental role in inverse scattering theories involving penetrable defects, is investigated within the framework of mechanical waves scattered by piecewise-homogeneous, elastic or viscoelastic obstacles in a likewise heterogeneous background solid. For generality, the obstacle is allowed to be multiply connected, having both penetrable components (inclusions) and impenetrable parts (cavities). A variational formulation is employed to establish \emph{sufficient} conditions for the existence and uniqueness of a solution to the ITP, provided that the excitation frequency does not belong to (at most) countable spectrum of transmission eigenvalues. The featured sufficient conditions, expressed in terms of the mass density and elasticity parameters of the problem, represent an advancement over earlier works on the subject in that i) they pose a precise, previously unavailable provision for the well-posedness of the ITP in situations when both the obstacle and the background solid are heterogeneous, and ii) they are dimensionally consistent i.e. invariant under the choice of physical units. For the case of a viscoelastic scatterer in an elastic solid it is further shown, consistent with earlier studies in acoustics, electromagnetism, and elasticity that the uniqueness of a solution to the ITP is maintained irrespective of the vibration frequency. When applied to the situation where \emph{both} the scatterer and the background medium are viscoelastic i.e. dissipative, on the other hand, the same type of analysis shows that the analogous claim of uniqueness does not hold. Physically, such anomalous behavior of the ``viscoelastic-viscoelastic'' case (that has eluded previous studies) has its origins in a lesser known fact that the homogeneous ITP is not mechanically insulated from its surroundings -- a feature that is particularly cloaked in situations when either the background medium or the scatterer are dissipative. A set of numerical results, computed for ITP configurations that meet the sufficient conditions for the existence of a solution, is included to illustrate the problem. Consistent with the preceding analysis, the results indicate that the set of transmission values is indeed empty in the ``elastic-viscoelastic'' case, and countable for ``elastic-elastic'' and ``viscoelastic-viscoelastic'' configurations.
• Defect identification using elastodynamic topological sensitivity
  
  • Bonnet Marc
  , 2010.