Publications

2010

• On standard dissipative gradient models
  
  • Nguyen Quoc Son
  Ann. Solid Struct. Mech., 2010, 1 (2), pp.59-75. A general presentation on gradient models for solids in thermo- mechanics is given in this paper. Firstly, it is shown that the introduction of the gradients of the internal variables can be conveniently done under the formalism of the generalized standard materials. The derivation of the governing equations and the associated boundary conditions of a solid can be derived in a straightforward manner from the basic assumption of existence of an energy potential and a dissipation potential. Secondly, the attention is focussed on the introduction of the temperature gradient. Two descriptions, respectively by Forest & al. and by Nguyen & Andrieux are discussed. The last one is based upon an interesting definition of the entropy and of the internal energy by Legendre transform of the free energy with respect to the temperature and the temperature gradient. The obtained results are justified in a simple example of micro-macro modeling of thermal conduction in a rigid composite. In particular, it is shown that the associated thermal equation removes the paradox of instantaneous propagation. (10.1007/s12356-010-0006-0)
  DOI : 10.1007/s12356-010-0006-0
• Cyclic behavior of short glass fiber reinforced polyamide for fatigue life prediction of automotive components
  
  • Launay Antoine
  • Marco Yann
  • Maitournam Habibou
  • Raoult Ida
  • Szmytka Fabien
  Procedia Engineering, Elsevier, 2010, 2 (1), pp.901-910. Fatigue life prediction of polymer matrix composites requires the investigation of the cyclic behavior. This paper deals with the experimental study conducted on a polyamide 66 reinforced with 35 wt% of short glass fibers (PA66 GF35), at room temperature. The material was tested dry-as-molded or at the equilibrium with an air containing 50% of relative humidity. The dynamic mechanical analysis leads us to focus on the material conditioned at RH=50%, which appears to exhibit the most complex mechanical effects, and is yet representative of the actual service life. An exhaustive experimental campaign in tensile mode has been carried out, including various strain or stress rates, complex mechanical histories and local thermo-mechanical recording. The material has thus been tested in static tension at stress rates ranging over four decades (from 2.5 to 2500 MPa/s), and also in cyclic tension with loading histories combining creep, stress relaxation or strain recovery steps at different strain/stress levels. Such an extended database allowed us to highlight several mechanical phenomena: at least two characteristic viscous times co-exist, and are independent of any irreversible mechanism. Residual strain appears above a stress threshold, and a kinematic hardening law is suggested to explain tension-relaxation-recovery tests. Eventually, hints of a non-linear viscous flow law and of a cyclic damage law are pointed out. (10.1016/j.proeng.2010.03.097)
  DOI : 10.1016/j.proeng.2010.03.097
• Approche variationnelle de l'endommagement : I. Les concepts fondamentaux
  
  • Marigo Jean-Jacques
  • Pham Kim
  Comptes Rendus. Mécanique, Académie des sciences (Paris), 2010, 338 (4), pp.191-198. This Note is devoted to the construction of local brittle damage laws. We first justify by the Drucker–Ilyushin postulate to set their formulation within the framework of Generalized Standard Materials. Accordingly, the strain work becomes a state function whose convexity properties are directly related to the hardening or softening properties of the material. Moreover, the evolution problem can be read as a variational problem which is reinforced so that it finally contains the concepts of stability and of energy conservation. (10.1016/j.crme.2010.03.009)
  DOI : 10.1016/j.crme.2010.03.009
• Approche variationnelle de l'endommagement : II. Les modèles à gradient
  
  • Pham Kim
  • Marigo Jean-Jacques
  Comptes Rendus. Mécanique, Académie des sciences (Paris), 2010, 338 (4), pp.199-206. This second part of the variational approach to damage is devoted to the construction of non-local gradient-enhanced models. That consists in extending to these regularized models the concepts introduced in the first part for local damage models. Specifically, once the gradient of damage has been inserted into the energy expression, the damage evolution problem is still based on the three physical principles of irreversibility, stability and energy balance. This new formulation is compared with that usually postulated and its merits are emphasized. (10.1016/j.crme.2010.03.012)
  DOI : 10.1016/j.crme.2010.03.012
• Elastic and nonlinear behaviour of argillaceous rocks under combined moisture and mechanical loads investigated by means of multiscale full full-field strain measurement techniques
  
  • Yang D.S.
  • Bornert Michel
  • Nguyen Minh D.
  • Chanchole S.
  • Gharbi H.
  • Valli P.
  , 2010.
• Déchets nucléaires : le stockage doit-il être réversible ?
  
  • Berest Pierre
  • Bérest P.
  , 2010, pp.82-83.
• Identification of Young's Modulus from Indentation Testing and Inverse Analysis
  
  • Prou Joris
  • Kishimoto Kikuo
  • Constantinescu Andrei
  Journal of Solid Mechanics and Materials Engineering, 2010, 4 (6), pp.781--795. In this study, a numerical method for the identification of the Young's modulus of linear elastic coated materials from continuous indentation test is first presented. The identification is based on an inverse analysis where the minimization of a cost functional is performed by a gradient descent algorithm. The main result is the computation of cost function gradient by using a direct differentiation technique, resulting in a time saving method compared to the widely used finite difference method. The validity and illustration of this approach is shown through several numerical examples. The second part of this article is dedicated to the identification of elasto-plastic thin films Young's modulus. A new method is proposed, where the inverse analysis relies only on finite element computations for elastic materials.
• Revisiting energy release rates in brittle fracture
  
  • Chambolle Antonin
  • Francfort Gilles A.
  • Marigo Jean-Jacques
  Journal of Nonlinear Science, Springer Verlag, 2010, 20 (4), pp.395-424. We revisit in a 2d setting the notion of energy release rate, which plays a pivotal role in brittle fracture. Through a blow-up method, we extend that notion to crack patterns which are merely closed sets connected to the crack tip. As an application, we demonstrate that, modulo a simple meta-stability principle, a moving crack cannot generically kink while growing continuously in time. This last result potentially renders obsolete in our opinion a longstanding debate in fracture mechanics on the correct criterion for kinking. (10.1007/s00332-010-9061-2)
  DOI : 10.1007/s00332-010-9061-2
• Evaluation of Stress-strain Curve Estimates in Dynamic Experiments
  
  • Mohr Dirk
  • Gary Gérard
  • Lundberg Bengt
  International Journal of Impact Engineering, Elsevier, 2010, 37, pp.161-169. Accurate measurements of the forces and velocities at the boundaries of a dynamically loaded specimen may be obtained using split Hopkinson pressure bars (SHPB) or other experimental devices. However, the determination of a representative stress-strain curve based on these measurements can be challenging. Due to transient effects, the stress and strain fields are not uniform within the specimen. Several formulas have been proposed in the past to estimate the stress-strain curve from dynamic experiments. Here, we make use of the theoretical solution for the waves in an elastic specimen to evaluate the accuracy of these estimates. It is found that it is important to avoid an artificial time shift in the processing of the experimental data. Moreover, it is concluded that the combination of the output force based stress estimate and the average strain provides the best of the commonly used stress-strain curve estimates in standard SHPB experiments. (10.1016/j.ijimpeng.2009.09.007)
  DOI : 10.1016/j.ijimpeng.2009.09.007
• Displacement correction for punching at a dynamically loaded bar end
  
  • Safa Kamal
  • Gary Gérard
  International Journal of Impact Engineering, Elsevier, 2010, 37, pp.371-384. The object of this work is to provide a 3-D displacement correction for local punching due to axial load at the end of a bar. For this purpose, an analytical calculation of the indentation at the end of an elastic isotropic bar subjected to a dynamic loading is carried out. It provides a first-order correction of the displacement obtained through the 1-D wave analysis commonly used in SHPB processing. This correction improves the results obtained for the dynamic behavior of the specimen, in particular at early instants of loading where its response is often purely elastic. Tabulated values are provided for easy use in SHPB testing. (10.1016/j.ijimpeng.2009.09.006)
  DOI : 10.1016/j.ijimpeng.2009.09.006
• Localisation de la déformation dans un milieu granulaire vue jusqu'à l'échelle du grain à l'aide de la tomographie à rayons X
  
  • Bésuelle Pierre
  • Hall S.
  • Viggiani Gioacchino Cinno
  • Lenoir Nicolas
  • Desrues J.
  • Pannier Y.
  • Bornert Michel
  , 2010.
• On micro-macro transition in non linear mechanics
  
  • Stolz Claude
  Materials, MDPI, 2010, 3 (1), pp.296-317. This paper is devoted to the description of the general relationships between microscopic and macroscopic mechanical quantities in non-linear mechanics. From a thermodynamical viewpoint, it is only necessary to know the two macroscopic potentials (macroscopic free energy and macroscopic potential of dissipation) to describe the state of the body and its quasistatic evolution. These global potentials are the averages of the local ones. We point out some particular cases of non-linearities, especially the case of damaged materials. (10.3390/ma3010296)
  DOI : 10.3390/ma3010296
• Crack identification in elasticity using 3d time-domain topological derivative
  
  • Bellis Cédric
  • 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
• Structural dynamics monitoring via a coupled data assimilation and modified error in constitutive relation technique
  
  • Alarcon Albert
  • Bodel Charles
  • Bonnet Marc
  , 2010.
• 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
• 12-year pressure monitoring in an idle salt cavern — The 1997-1998 Etrez abandonment test revisited.
  
  • Berest Pierre
  • Bérest P.
  , 2010, pp.233-244.
• 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
• Very slow creep tests on salt samples
  
  • Bérest Pierre
  • Béraud Jean-François
  • Brouard Benoit
  • Blum Pierre-Antoine
  • Charpentier Jean-Pierre
  • Greef Vincent De
  • Gharbi Hakim
  • Valès Frédéric
  EPJ Web of Conferences, EDP Sciences, 2010, 6. Long-term creep tests have been performed on rock-salt and argillite samples under very small uniaxial loadings (σ = 0.02 to 0.1 MPa) . To minimize the effects of temperature variations, testing devices were set in a mine where temperature fluctuations are of the order of one-hundredth of a degree Celsius. The mechanical loading was provided by dead weights. The deformations were measured through special displacement sensors with a resolution of ∆ε = 10-8. Strain rates as small as έ = 7 × 10-13s-1 were measured. These tests allow rock-sample creep to be investigated at very small strain rates. The tests also prove that extrapolation of constitutive laws at very small rates is often incorrect. (10.1051/epjconf/20100622002)
  DOI : 10.1051/epjconf/20100622002
• Mechanics of the power stroke in Myosin II
  
  • Marcucci Lorenzo
  • Truskinovsky Lev
  Physical Review E : Statistical, Nonlinear, and Soft Matter Physics [2001-2015], American Physical Society, 2010, 81, pp.051915. Power stroke in skeletal muscles is a result of a conformational change in the globular portion of the molecular motor myosin II. In this paper we show that the fast tension recovery data reflecting the inner working of the power stroke mechanism can be quantitatively reproduced by a Langevin dynamics of a simple mechanical system with only two structural states. The proposed model is a generalization of the two state model of Huxley and Simmons. The main idea is to replace the rigid bistable device of Huxley and Simmons with an elastic bistable snap spring. In this setting the attached configuration of a cross bridge is represented not only by the discrete energy minima but also by a continuum of intermediate states where the fluctuation induced dynamics of the system takes place. We show that such soft-spin approach explains the load dependence of the power stroke amplitude and removes the well-known contradiction inside the conventional two state model regarding the time scale of the power stroke. (10.1103/PhysRevE.81.051915)
  DOI : 10.1103/PhysRevE.81.051915
• 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.
• 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
• 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