Publications

2011

• Dynamical study of cell motility by simultaneous microscopy and surface plasmon resonance imagery
  
  • Moreau Julien
  • Allain Jean-Marc
  • Gulvady R.
  • Canva Michael
  , 2011.
• Modélisation multi-échelles de nappes fibrées en compression
  
  • Lignon Eric
  , 2011. Les nappes en matériau flexible renforcées par des câbles apparaissent dans de nombreux systèmes industriels. Le rôle essentiel des renforts fibrés est d'apporter à la structure une rigidité plus importante en extension et en flexion. Mais il peut arriver qu'ils subissent une compression axiale importante, éventuellement couplée à de la flexion, conduisant à des instabilités de type flambement dans le plan de nappe. La thèse introduit une modélisation mécanique et numérique originale de ces nappes permettant de décrire ces instabilités afin de mieux les comprendre, d'en contrôler les effets et de dimensionner ce type de structures par calcul. Il prend en compte la flexion globale des fibres, ainsi la gestion des effets locaux induits dans la matrice. La modélisation a été développée à deux échelles : - une échelle macroscopique, introduisant une cinématique enrichie de milieu continu, reposant sur une densité surfacique de poutres résistant aux flexions (dans le plan et hors plan). Un modèle d'éléments finis spécifique a été développé. On vérifie que ce modèle de structure mince n'est pas sujet au phénomène de verrouillage numérique grâce à une analyse théorique ainsi qu'à une série de tests numériques ; - une échelle microscopique décrit par un modèle de cellule local construit et justifié par analyse asymptotique, et résolu par éléments finis. La modélisation a été analysée sous trois aspects - l'aptitude à prendre en compte l'incompressibilité de la matrice sans verrouillage numérique. - l'étude de flambement sous compression par analyse de stabilité multi-échelles calculant la charge critique et le mode de flambement attendu, - la pertinence numérique des résultats obtenus par rapport aux simulations expérimentales disponibles.
• Reversible stress-induced martensitic phase transformations in a bi-atomic crystal
  
  • Elliott Ryan
  • Triantafyllidis Nicolas
  • Shaw John A.
  Journal of the Mechanics and Physics of Solids, Elsevier, 2011, pp.pp. 216-236.. In an earlier work, Elliott et al. (JMPS 54(1):161--192, 2006), the authors used temperature-dependent atomic potentials and path-following bifurcation techniques to solve the nonlinear equilibrium equations and find the temperature-induced martensitic phase transformations in stress-free, perfect, equi-atomic binary B2 crystals. Using the same theoretical framework, the current work adds the influence of stress to study the model's stress-induced martensitic phase transformations. The imposition of a uniaxial Biot stress on the austenite (B2) crystal, lowers the symmetry of the problem, compared to the stress-free case, and leads to a large number of stable equilibrium paths. To determine which ones are possible reversible martensitic transformations, we use the (kinematic) concept of the maximal Ericksen-Pitteri neighborhood (max EPN) to select those equilibrium paths with lattice deformations that are closest, with respect to lattice-invariant shear, to the austenite phase and thus capable of a reversible transformation. It turns out that for our chosen parameters only one stable structure (distorted aIrV) is found within the max EPN of the austenite in an appropriate stress window. The energy density of the corresponding configurations shows features of a stress-induced phase transformation between the higher symmetry austenite and lower symmetry martensite paths and suggests the existence of hysteretic stress-strain loops under isothermal load-unload conditions. Although the perfect crystal model developed in this work over-predicts many key material properties, such as the transformation stress and the Clausious-Clapeyron slope, when compared to real experimental values (based on actual polycrystalline specimens with defects), it is---to the authors' knowledge---the first atomistic model that has been demonstrated to capture all essential trends and behaviorobserved in shape memory alloys. (10.1016/j.jmps.2010.10.011)
  DOI : 10.1016/j.jmps.2010.10.011
• Roughening instability of broken extremals
  
  • Grabovsky Yury
  • Truskinovsky Lev
  Archive for Rational Mechanics and Analysis, Springer Verlag, 2011, 200, pp.183-202. We derive a new general jump condition on a broken Weierstrass–Erdmann extremal of a vectorial variational problem. Such extremals, containing surfaces of gradient discontinuity, are ubiquitous in shape optimization and in the theory of elastic phase transformations. The new condition, which does not have a one dimensional analog, reflects the stationarity of the singular surface with respect to two-scale variations that are nontrivial generalizations of Weierstrass needles. The over-determinacy of the ensuing free boundary problem suggests that typical stable solutions must involve microstructures or chattering controls. (10.1007/s00205-010-0377-8)
  DOI : 10.1007/s00205-010-0377-8
• DETERMINATION OF ROCK MASS STRENGTH PROPERTIES BY HOMOGENIZATION
  
  • Pouya Ahmad
  • Ghoreychi Mehdi
  International Journal for Numerical and Analytical Methods in Geomechanics, Wiley, 2011, 25, pp.1285-1303. A method for determining fractured rock mass properties is presented here on the basis of homogenisation approach. The rock mass is considered to be a heterogeneous medium composed of intact rock and of fractures. Its constitutive model is studied numerically using Finite Element Method and assimilating the fractures to joint elements (Coste1). The method has been applied to a granite formation in France. Geological data on different families of fractures have been used for the statistical representation of the fractures. A mesh-generating tool for the medium with high density of fractures has been developed. The mechanical behaviour of the rock mass (elasticity, ultimate strength and hardening law) has been determined assuming linear elasticity and Mohr-Coulomb strength criterion both for the intact rock and the fractures. Evolution of the mechanical strength in different directions has been determined as a function of the mean stress, thanks to various numerical simulations. The mechanical strength appears to be anisotropic due to the preferential orientation of the fractures. The numerical results allowed us to determine an oriented strength criterion for the homogenized rock mass. A 2D constitutive law for the homogenized medium has been deduced from numerical data. A 3D extension of this model is also presented. (10.1002/nag.176)
  DOI : 10.1002/nag.176
• Gradient damage models and their use to approximate brittle fracture
  
  • Pham Kim
  • Amor Hanen
  • Marigo Jean-Jacques
  • Maurini Corrado
  International Journal of Damage Mechanics, SAGE Publications, 2011, 20 (4), pp.618-652. In its numerical implementation, the variational approach to brittle fracture approximates the crack evolution in an elastic solid through the use of gradient damage models. In this article, we first formulate the quasi-static evolution problem for a general class of such damage models. Then, we introduce a stability criterion in terms of the positivity of the second derivative of the total energy under the unilateral constraint induced by the irreversibility of damage. These concepts are applied in the particular setting of a one-dimensional traction test. We construct homogeneous as well as localized damage solutions in a closed form and illustrate the concepts of loss of stability, of scale effects, of damage localization, and of structural failure. Considering several specific constitutive models, stress (10.1177/1056789510386852)
  DOI : 10.1177/1056789510386852
• Optimized butterfly specimen for the fracture testing of sheet materials under combined normal and shear loading
  
  • Dunand M.
  • Mohr Dirk
  Engineering Fracture Mechanics, Elsevier, 2011, pp.2919-2934.
• On some nonlinear inverse problems in elasticity
  
  • Andrieux Stephane
  • Bui Huy Duong
  Theoret. Appl. Mech., 2011, 38 (2), pp.pp. 125-154,. In this paper, we make a review of some inverse problems in elasticity, in statics and dynamics, in acoustics, thermoelasticity and viscoelasticity. Crack inverse problems have been solved in closed form, by considering a nonlinear variational equation provided by the reciprocity gap functional. This equation involves the unknown geometry of the crack and the boundary data. It results from the symmetry lost between current fields and adjoint fields which is related to their support. The nonlinear equation is solved step by step by considering linear inverse problems. The normal to the crack plane, then the crack plane and finally the geometry of the crack, defined by the support of the crack displacement discontinuity, are determined explicitly. We also consider the problem of a volumetric defect viewed as the perturbation of a material constant in elastic solids which satisfies the nonlinear Calderon's equation. The nonlinear problem reduces to two successive ones: a source inverse problem and a Volterra integral equation of the first kind. The first problem provides information on the inclusion geometry. The second one provides the magnitude of the perturbation. The geometry of the defect in the nonlinear case is obtained in closed form and compared to the linearized Calderon's solution. Both geometries, in linearized and nonlinear cases, are found to be the same.
• Simulation by classical molecular dynamics of the influence of radiation effects on the fracture behaviour of simplified nuclear glasses
  
  • Kieu Le-Hai
  • Delaye Jean-Marc
  • Stolz Claude
  , 2011.
• Localized deformation induced by heterogeneities in porous carbonate analysed by multi−scale digital image correlation
  
  • Dautriat Jérémie
  • Bornert Michel
  • Gland Nicolas
  • Dimanov Alexandre
  • Raphanel Jean
  Tectonophysics, Elsevier, 2011, 503 (1-2), pp.100-116. The understanding and the prevention of damage mechanisms, which have an impact on the hydrocarbon production and recovery rates, are of paramount interest for reservoir engineers. The modelling of such coupled processes relies essentially on experimentally obtained data, which characterize the macroscopic mechanical and transport properties. This approach however cannot account for the multi-scale structural heterogeneities of the considered rocks, in spite of their fundamental importance. The microstructural characterization of damage is usually based on ‘post-mortem’ observations of the samples, which provide both qualitative and quantitative information about the effects of the mechanisms activated at the grain scale and at intermediate scales, at a pervasive stage of damage after sample unloading. New techniques provide more quantitative and direct methods to follow the deformation history and the eventual development of localization and damage. In this study, the 2D Digital Image Correlation (DIC) technique has been applied to sequences of images taken from carbonate samples during uniaxial compression tests. Several scales have been considered, ranging from the centimetric scale of the samples to the local scale of their microstructure. For this purpose both optical observations and Scanning Electron Microscopy (SEM) were used. Although the macroscopic strain at failure was very small (< 0.2%), the DIC technique has proven to be reliable, provided one selects carefully image acquisition conditions and DIC parameters, as highlighted in our discussion on the uncertainties and the evaluation of errors. This technique has allowed us to quantify both the global and local strain fields during the deformation process. We have thus been able to precisely identify the localizations of damage and the local compaction mechanisms, and to relate them to the characteristic structural heterogeneities of the tested carbonate. (10.1016/j.tecto.2010.09.025)
  DOI : 10.1016/j.tecto.2010.09.025
• Cyclic behaviour of short glass fiber reinforced polyamide: experimental study and constitutive equations
  
  • Launay Antoine
  • Maitournam Habibou
  • Marco Yann
  • Szmytka Fabien
  International Journal of Plasticity, Elsevier, 2011, 27 (8), pp.1267-1293. Polymer matrix composites are widely used in the automotive industry and undergo fatigue loadings. The investigation of the nonlinear cyclic behaviour of such materials is a required preliminary work for a confident fatigue design, but has not involved many publications in the literature. This paper presents an extensive experimental study conducted on a polyamide 66 reinforced with 35 wt% of short glass fibres (PA66 GF35), at room temperature. The material was tested in two conditions: dry-as-moulded (DAM) and at the equilibrium with air containing 50% of relative humidity (RH50). An exhaustive experimental campaign in tensile mode has been carried out, including various strain or stress rates, complex mechanical histories and local thermo-mechanical recordings. Such an extended database allowed us to highlight several complex physical phenomena: viscoelastic effects at different time scales, irrecoverable mechanisms, non-linear kinematic hardening, non-linear viscous flow rule, cyclic softening. Taking into account this advanced analysis, a constitutive model describing the cyclic behaviour is proposed. As the experimental database only includes uniaxial tensile tests, the general 3D anisotropic frame is reduced to an uniaxial model valid for a specific orientation distribution. The robust identification process is based on tests which enable the uncoupling between the underlined mechanical features. This strategy leads to a model which accurately predicts the cyclic behaviour of conditioned as well as dry materials under complex tensile loadings. (10.1016/j.ijplas.2011.02.005)
  DOI : 10.1016/j.ijplas.2011.02.005
• Identification of the Direction-Dependency of the Martensitic Transformation in Stainless Steel Using In-Situ Magnetic Permeability Measurements
  
  • Beese A.M.
  • Mohr Dirk
  Experimental Mechanics, Society for Experimental Mechanics, 2011, pp.667-676.
• Fast identification of cracks using higher-order topological sensitivity for 2-D potential problems
  
  • Bonnet Marc
  Engineering Analysis with Boundary Elements, Elsevier, 2011, 35, pp.223-235. This article concerns an extension of the topological sensitivity (TS) concept for 2D potential problems involving insulated cracks, whereby a misfit functional $J$ is expanded in powers of the characteristic size $a$ of a crack. Going beyond the standard TS, which evaluates (in the present context) the leading $O(a^{2})$ approximation of $J$, the higher-order TS established here for a small crack of arbitrarily given location and shape embedded in a 2-D region of arbitrary shape and conductivity yields the $O(a^{4})$ approximation of $J$. Simpler and more explicit versions of this formulation are obtained for a centrally-symmetric crack and a straight crack. A simple approximate global procedure for crack identification, based on minimizing the $O(a^{4})$ expansion of $J$ over a dense search grid, is proposed and demonstrated on a synthetic numerical example. BIE formulations are prominently used in both the mathematical treatment leading to the $O(a^{4})$ approximation of $J$ and the subsequent numerical experiments. (10.1016/j.enganabound.2010.08.007)
  DOI : 10.1016/j.enganabound.2010.08.007
• Développement des potentiels empiriques pour les systèmes SiO2 B203 Na20
  
  • Kieu Le-Hai
  • Delaye Jean-Marc
  • Stolz Claude
  , 2011.
• Modeling radiation effects on the fracture process in simplified nuclear glass
  
  • Kieu Le-Hai
  • Delaye Jean-Marc
  • Stolz Claude
  , 2011.
• Minimal Integer Automaton behind Crystal Plasticity
  
  • Salman Umut
  • Truskinovsky Lev
  Physical Review Letters, American Physical Society, 2011, 106, pp.175503. Power law fluctuations and scale-free spatial patterns are known to characterize steady state plastic flow in crystalline materials. In this Letter we study the emergence of correlations in a simple Frenkel-Kontorova-type model of 2D plasticity which is largely free of arbitrariness, amenable to analytical study, and is capable of generating critical exponents matching experiments. Our main observation concerns the possibility to reduce continuum plasticity to an integer-valued automaton revealing inherent discreteness of the plastic flow. (10.1103/PhysRevLett.106.175503)
  DOI : 10.1103/PhysRevLett.106.175503
• Experimental investigation of the delayed behaviour of unsaturated argillaceous rocks by means of Digital Image Correlation techniques
  
  • Yang Diansen
  • Bornert Michel
  • Chanchole Serge
  • Wang Linlin
  • Valli Pierre
  • Gatmiri Behrouz
  Applied Clay Science, Elsevier, 2011, 54 (1), pp.53-62. We present an experimental study on the delayed behavior of unsaturated argillaceous rocks, including shrinkage, swelling, and creep, by means of Digital Image Correlation (DIC) techniques. In order to measure the very low strain rate of the argillaceous rocks at various scales (100 μm-cm) under uniaxial compression and various environmental conditions, a specific optimized optical setup was used. The natural argillaceous rocks were hydrated or dehydrated by controlling the ambient humidity around the samples, and the obtained unsaturated samples were then subjected to creep tests at different stress levels. The mechanical response to hydration and dehydration strongly depended on the mechanical loading, which induced an additional deformation. During creep, the strain rate increased when the moisture or the applied stress increased. The strain rate at a relative humidity of 75% was about one order of magnitude larger than at a dried state (relative humidity = 25%). The anisotropy of the strain induced by the moisture and mechanical loading was enhanced over time. The time dependent behavior as observed at different scales (100 μm-cm) is discussed. (10.1016/j.clay.2011.07.012)
  DOI : 10.1016/j.clay.2011.07.012
• Twelve-year monitoring of the idle Etrez salt cavern
  
  • Berest Pierre
  • Bérest P.
  • Brouard Benoît
  • Hévin Grégoire
  International Journal of Rock Mechanics and Mining Sciences, Pergamon and Elsevier, 2011, Volume 48 (1), pp.168-173. (10.1016/j.ijrmms.2010.07.004)
  DOI : 10.1016/j.ijrmms.2010.07.004
• Variational Principles in the Theory of Gradient Plasticity
  
  • Nguyen Quoc Son
  Comptes Rendus. Mécanique, Académie des sciences (Paris), 2011, 000 (000), pp.000. Gradient models have been intensively discussed in the literature for the study of time- dependent or time-independent processes such as visco-plasticity, plasticity and damage. This paper is devoted to the theory of Gradient Plasticity. A general and consistent math- ematical description available for common time-independent behaviours is presented. Our attention is focussed on the derivation of general results such as the description of the gov- erning equations for the global response, for the rate response, the expression of the associ- ated variational principles and the question of uniquenness in terms of the energy potential ́ and the dissipation potential. (10.1016/j.crme.2011.08.002)
  DOI : 10.1016/j.crme.2011.08.002
• Multiscale viscoplastic behaviour of halite : micromechanical approaches by full field measurements
  
  • Bourcier M.
  • Dimanov A.
  • Bornert Michel
  • Héripré E.
  • Charrier B.
  • Ludwig Wolfgang
  • Raphanel J. L.
  , 2011.
• Advances in the constitutive equation parameter identification procedure why experiments should discuss with numerical simulations
  
  • Crépin Jérôme
  • Geoffroy Dominique
  • Héripré Eva
  • Roos Arjen
  , 2011.
• Stress field in deformed polycrystals at the micron scale.
  
  • Castelnau O.
  • Bornert Michel
  • Robach O.
  • Micha J.-S.
  • Ulrich O.
  • Chiron R.
  • Le Bourlot Christophe
  , 2010, 6, pp.35005. (10.1051/epjconf/20100635005)
  DOI : 10.1051/epjconf/20100635005
• STABILITY OF SOLIDS: FROM STRUCTURES TO MATERIALS
  
  • Triantafyllidis Nicolas
  , 2011, pp.1-105. Stability is a fascinating topic in solid mechanics that has its roots in the celebrated Euler column buckling problem, which first appeared in 1744. Over the years advances in technology have led to the study of ever more complicated structures first in civil and subsequently in mechanical engineering applications. Aerospace applications, most notably failure of solid propellant rockets, led the way in the 1950s. Problems associated with materials and electronics industries came on stage in the 1970s and 1980s, starting with instabilities associated with thin films and phase transformations in shape memory alloys (SMA's), just to name some of the most preeminent examples. In a parallel path, starting in the late 19th century, mathematicians studying nonlinear differential equations, developed the concept of a bifurcation (term coined by Poincare) and created powerful techniques to study the associated singularities. They have also recognized the close association between bifurcation and symmetry in structures. It was for Koiter, beginning with his famous thesis in 1945, to connect the two communities. Amazing progress has been made since the early days of structural buckling problems and continues to be made in this field, with applications ranging from atomistic to geological scales. With the advent of new materials, the number of applications in this area continues to progress with an ever increasing pace, making it a challenge to present a first course in this topic within the short time available in one semester. The notes that follow are the first attempt to present a comprehensive, modern introduction to the subject of stability of solids. Given the time constraints, only equilibrium configurations of conservative systems will be considered here. These notes start with the introduction of the concepts of stability and bifurcation for conservative elastic systems through finite degree of freedom examples. They continue with the general theory of Lyapunov-Schmidt-Koiter (LSK) asymptotics, followed by examples from continuum mechanics. The presentation subsequently addresses the issue of scale in the stability of solids. In particular the relation between instability at the microstructural level and macroscopic properties of the solid is studied for several types of applications involving different scales: composites (fiber and particle-reinforced), cellular solids and finally SMA's, where temperature- or stress-induced instabilities at the atomic level have macroscopic manifestations visible to the naked eye.
• Introduction aux techniques d'identification
  
  • Bonnet Marc
  , 2011, pp.243-266.
• Effects of chemical alteration on mechanical and flow properties of a limestone, a multi-scale approach.
  
  • Zinsmeister L.
  • Dautriat J.
  • Bornert Michel
  • Dimanov A.
  • Gland N.
  • Raphanel J.
  , 2011.