Publications

2012

• An adaptive algorithm for cohesive zone model and arbitrary crack propagation
  
  • Chiaruttini Vincent
  • Geoffroy Dominique
  • Riolo Vincent
  • Bonnet Marc
  Revue Européenne de Mécanique Numérique/European Journal of Computational Mechanics, Hermès / Paris : Lavoisier, 2012, 21, pp.208-218. This paper presents an approach to the numerical simulation of crack propagation with cohesive models for the case of structures subjected to mixed mode loadings. The evolution of the crack path is followed by using an adaptive method: with the help of a macroscopic branching criterion based on the calculation of an energetic integral, the evolving crack path is remeshed as the crack evolves in the simulation. Special attention is paid to the unknown fields transfer approach that is crucial for the success of the computational treatment. This approach has been implemented in the finite element code Z-Set (jointly developed by Onera and Ecole des Mines) and is tested on two examples, one featuring a straight crack path and the other involving a complex crack propagation under critical monotonous loading monotonous. (10.1080/17797179.2012.744544)
  DOI : 10.1080/17797179.2012.744544
• Solving dynamic contact problems with local refinement in space and time
  
  • Hager Corinna I
  • Hauret Patrice
  • Le Tallec Patrick
  • Wohlmuth Barbara I
  Computer Methods in Applied Mechanics and Engineering, Elsevier, 2012, 201, pp.25 - 41. Frictional dynamic contact problems with complex geometries are a challenging task from the compu tational as well as from the analytical point of view since they generally involve space and time multi scale aspects. To be able to reduce the complexity of this kind of contact problem, we employ a non conforming domain decomposition method in space, consisting of a coarse global mesh not resolving the local struc ture and an overlapping fine patch for the contact computation. This leads to several benefits: First, we resolve the details of the surface only where it is needed, i.e., in the vicinity of the actual contact zone. Second, the subproblems can be discretized independently of each other which enables us to choose a much finer time scale on the contact zone than on the coarse domain. Here, we propose a set of interface conditions that yield optimal a priori error estimates on the fine meshed subdomain without any artificial dissipation. Further, we develop an efficient iterative solution scheme for the coupled problem that is robust with respect to jumps in the material parameters. Several complex numerical examples illustrate the performance of the new scheme. (10.1016/j.cma.2011.09.006)
  DOI : 10.1016/j.cma.2011.09.006
• Error estimates for 1D asymptotic models in coaxial cables with non-homogeneous cross-section
  
  • Imperiale Sébastien
  • Joly Patrick
  Advances in Applied Mechanics, New York ; London ; Paris [etc] : Academic Press, 2012, xx. This paper is the first contribution towards the rigorous justification of asymptotic 1D models for the time-domain simulation of the propagation of electromagnetic waves in coaxial cables. Our general objective is to derive error estimates between the "exact" solution of the full 3D model and the "approximate" solution of the 1D model known as the Telegraphist's equation. (10.4208/aamm.12-12S06)
  DOI : 10.4208/aamm.12-12S06
• Experiments and Modeling of Iron-Particle-Filled Magnetorheological Elastomers
  
  • Danas Kostas
  • Kankanala Sunny
  • Triantafyllidis Nicolas
  Journal of the Mechanics and Physics of Solids, Elsevier, 2012, 60, pp.120 - 138.
• Perfectly Matched Layer with Mixed Spectral Elements for the Propagation of Linearized Water Waves
  
  • Cohen Gary
  • Imperiale Sébastien
  Communications in Computational Physics, Global Science Press, 2012, 11 (2), pp.285-302. After setting a mixed formulation for the propagation of linearized water waves problem, we define its spectral element approximation. Then, in order to take into account unbounded domains, we construct absorbing perfectly matched layer for the problem. We approximate these perfectly matched layer by mixed spectral elements and show their stability using the 'frozen coefficient' technique. Finally, numerical results will prove the efficiency of the perfectly matched layer compared to classical absorbing boundary conditions. (10.4208/cicp.201109.261110s)
  DOI : 10.4208/cicp.201109.261110s
• Stick-slip waves between elastic and rigid half-spaces
  
  • Bui Huy Duong
  • Oueslati Abdelbacet
  Journal of Applied Mathematics and Mechanics, Elsevier, 2012, 76 (5), pp.pages 611-620. The construction of an analytic solution of the problem of stick-slip waves crossing the interface between an elastic half-space and a tigid one under unilateral contact and Coulomb friction is considered. The method of solution is based on the analytic continuation method of Radok's complex potentials within the framework of steady elastodynamic problems. The governing equations combined with the boundary conditions are reduced to a Riemann-Hilbert problem with discontinuous coefficient, and closed-form expressions of the solution are derived. It is found that the existence of solutions depends on the additional velocity, which is related to the longitudinal elongation. If this velocity is ignored, there is no solution, if not, it is possible to construct weakly singular solutions satisfying all stick-slip conditions except over a narrow zone where the waves exhibit a crack-like behaviour. (10.1016/j.jappmathmech.2012.11.003)
  DOI : 10.1016/j.jappmathmech.2012.11.003
• Variational convergences of dual energy functionals for elastic materials with a ε thin strong inclusion
  
  • Bessoud Anne-Laure
  • Geymonat Giuseppe
  • Krasucki Francoise
  • Michaille Gérard
  Journal of Elasticity, Springer Verlag, 2012, 109, pp.51-65. We give a new derivation, based on the complementary energy formulation, of a simplified model for a multi-structure made up of two anisotropic hyper-elastic bodies connected by a thin strong material layer. The model is obtained by identifying the Mosco limit of the stored complementary energy functional when the thickness is of order ε and the stiffness of order 1/ε where ε is a positive real adimensional parameter. In order to prove the existence of the displacement associated with the stress we use a suitable weak version of the Saint-Venant compatibility condition also known as Donati's theorem. (10.1007/s10659-011-9368-8)
  DOI : 10.1007/s10659-011-9368-8
• Influence of prestrain on mechanical properties of highly-filled elastomers: Measurements and modeling
  
  • Thorin Anders
  • Azoug Aurélie
  • Constantinescu Andrei
  Polymer Testing, Elsevier, 2012, 31, pp.978-986. The prestrain influence on viscoelastic properties $|E^\star|$ and $\tan \delta$ of four different HTPB composite propellants was measured using Dynamic Mechanical Analyses (DMA). A nonlinear behaviour in terms of prestrain was observed and then modelled using a modified generalized Maxwell model. Prestrain was introduced as a variable of the stiffness of each Maxwell element using simple relations with two parameters. An algorithm was proposed and numerically implemented to identify the model parameters from the measurements. The performance of the identification method is discussed in terms of accuracy of predictions when compared with measurements and in terms of robustness of the involved parameters. The good match with experimental measurements shows that the dependence on the uniaxial prestrain of the complex modulus of the studied composite propellants can be described with few Maxwell elements and yet good accuracy, for small prestrains. (10.1016/j.polymertesting.2012.07.014)
  DOI : 10.1016/j.polymertesting.2012.07.014
• On the role of kinetic energy during unstable propagation in a heterogeneous peeling test
  
  • Lazzaroni Giuliano
  • Bargellini R.
  • Dumouchel P.E.
  • Marigo Jean-Jacques
  International Journal of Fracture, Springer Verlag, 2012, 175, pp.127-150. We study the dynamic debonding of a one-dimensional inextensible film, subject to a monotonic loading and under the hypothesis that the toughness of the glue can take only two values. We first consider the case of a single defect of small length in the glue where the toughness is lower than in the remaining part. The dynamic solution is obtained in a closed form and we prove that it does not converge to the expected quasi-static one when the loading speed tends to zero. The gap is due to a kinetic energy which appears when the debonding propagates across the defect at a velocity which is of the same order as the sound velocity. The kinetic energy becomes negligible again only when the debonding has reached a critical distance beyond the defect. The case of many defects is then considered and solved using an exact numerical solution of the wave equation and the Griffith law of propagation. The numerical results highlight the effects of the time evolution of the kinetic energy which induce alternate phases of rapid and slow debonding, these oscillations depending essentially on the volume fraction of the greater toughness. (10.1007/s10704-012-9708-0)
  DOI : 10.1007/s10704-012-9708-0
• Boiling Crisis as a Critical Phenomenon
  
  • Lloveras Pol
  • Salvat-Pujol Frederick
  • Truskinovsky Lev
  • Vives Eduard
  Physical Review Letters, American Physical Society, 2012, pp.215701. We present the first experimental study of intermittency and avalanche distribution during a boiling crisis. To understand the emergence of power law statistics we propose a simple spin model capturing the measured critical exponent. The model suggests that behind the critical heat flux is a percolation phenomenon involving drying-rewetting competition close to the hot surface. (10.1103/PhysRevLett.108.215701)
  DOI : 10.1103/PhysRevLett.108.215701
• Reciprocity gap method
  
  • Andrieux Stéphane
  • Bui Hui Duong
  • Constantinescu Andrei
  , 2012, pp.368-378. (10.1002/9781118578469.ch13)
  DOI : 10.1002/9781118578469.ch13
• From Discrete Visco-Elasticity to Continuum Rate-Independent Plasticity: Rigorous Results
  
  • Mielke A.
  • Truskinovsky Lev
  Archive for Rational Mechanics and Analysis, Springer Verlag, 2012, 203, pp.577-619. We show that continuum models for ideal plasticity can be obtained as a rigorous mathematical limit starting from a discrete microscopic model describing a visco-elastic crystal lattice with quenched disorder. The constitutive structure changes as a result of two concurrent limiting procedures: the vanishing-viscosity limit and the discrete-to-continuum limit. In the course of these limits a non-convex elastic problem transforms into a convex elastic problem while the quadratic rate-dependent dissipation of visco-elastic lattice transforms into a singular rate-independent dissipation of an ideally plastic solid. In order to emphasize our ideas we employ in our proofs the simplest prototypical system mimicking the phenomenology of transformational plasticity in shape-memory alloys. The approach, however, is sufficiently general that it can be used for similar reductions in the cases of more general plasticity and damage models. (10.1007/s00205-011-0460-9)
  DOI : 10.1007/s00205-011-0460-9
• Experiments and Modeling of Anisotropic Aluminum Extrusions under Multi-axial Loading - Part I: Plasticity
  
  • Dunand M.
  • Maertens A.
  • Luo Meng
  • Mohr Dirk
  International Journal of Plasticity, Elsevier, 2012, pp.34-49.
• Audio, visual, and audio-visual egocentric distance perception by moving participants in virtual environments
  
  • Rébillat Marc
  • Boutillon Xavier
  • Corteel Étienne
  • Katz Brian F. G.
  ACM Transactions on Applied Perception, Association for Computing Machinery, 2012, 9 (4), pp.19 (p. 1-17). A study on audio, visual, and audio-visual egocentric distance perception by moving participants in virtual environments is presented. Audio-visual rendering is provided using tracked passive visual stereoscopy and acoustic wave fi eld synthesis (WFS). Distances are estimated using indirect blind-walking (triangulation) under each rendering condition. Experimental results show that distances perceived in the virtual environment are accurately estimated or overestimated for rendered distances closer than the position of the audio-visual rendering system and underestimated for distances farther. Interestingly, participants perceived each virtual object at a modality-independent distance when using the audio modality, the visual modality, or the combination of both. Results show WFS capable of synthesizing perceptually meaningful sound fields in terms of distance. Dynamic audio-visual cues were used by participants when estimating the distances in the virtual world. Moving may have provided participants with a better visual distance perception of close distances than if they were static. No correlation between the feeling of presence and the visual distance underestimation has been found. To explain the observed perceptual distance compression, it is proposed that, due to con flicting distance cues, the audio-visual rendering system physically anchors the virtual world to the real world. Virtual objects are thus attracted by the physical audio-visual rendering system. (10.1145/2355598.2355602)
  DOI : 10.1145/2355598.2355602
• Macroscopic plasticity modeling of anisotropic aluminum extrusions using a Reduced Texture Methodology
  
  • Rousselier Gilles
  • Luo Meng
  • Mohr Dirk
  International Journal of Plasticity, Elsevier, 2012, 30-31, pp.144-165. This paper deals with the modeling of the plasticity of extruded aluminum 6260-T6 at the macroscopic level. The model is based on the framework of classical polycrystalline plasticity. A Reduced Texture Methodology (RTM) is used to provide the computational efficiency needed for industrial applications. The RTM approach involves a significant reduction of the number of representative crystallographic orientations. Furthermore, a special hybrid experimental-numerical procedure is used to identify all model parameters (including texture) from mechanical experiments. The experimental program includes uniaxial tensile experiments for different material orientations. Due to the heterogeneity in texture and grain size along the thickness direction of the 2 mm thick extruded material, specimens of full- and reduced thickness are prepared. Uniaxial compression-tension experiments are completed with the help of an anti-buckling device. The mechanical response of full-thickness specimens is modeled using 12 crystallographic orientations. Only eight distinct grain orientations are required to obtain satisfactory predictions for the reduced-thickness specimens with the same set of hardening parameters. The models describe well the stress-strain curves and Lankford ratios for all directions. It is found that the computed reduced textures are in good agreement with EBSD measurements. The 8-grain model is also validated for non-proportional loading paths in the space of tension and shear. Simulations of punch experiments are performed to further validate the model and to demonstrate the computational efficiency of the RTM based polycrystalline plasticity model in structural applications. (10.1016/j.ijplas.2011.10.004)
  DOI : 10.1016/j.ijplas.2011.10.004
• Cyclic behaviour of structures under thermomechanical loadings: Application to exhaust manifolds
  
  • Benoit À La Guillaume Aurélie
  • Maitournam Habibou
  • Rémy Luc
  • Oger F.
  International Journal of Fatigue, Elsevier, 2012, 38, pp.65-74. A structure subjected to thermomechanical cyclic loadings may exhibit various cyclic behaviours: perfect elasticity, elastic shakedown, plastic shakedown and ratchetting. The quantitative characterization of these different asymptotic states is addressed in this paper, in the context of the Generalized Standard Materials (GSM). Criteria are established to identify them and capture the trend line of their evolution, in the context of numerical simulation. The definitions are extended to the case of temperature dependent mechanical properties. Simple strain paths are first considered to illustrate the relevancy of the proposition. Finally, as an application, the example of an exhaust manifold subjected to a classical thermomechanical fatigue test is analyzed. (10.1016/j.ijfatigue.2011.11.012)
  DOI : 10.1016/j.ijfatigue.2011.11.012
• An energy-preserving muscle tissue model: formulation and compatible discretizations
  
  • Chapelle Dominique
  • Le Tallec Patrick
  • Moireau Philippe
  • Sorine Michel
  International Journal for Multiscale Computational Engineering, Begell House, 2012, 10 (2), pp.189-211. In this paper we propose a muscle tissue model -- valid for striated muscles in general, and for the myocardium in particular -- based on a multi-scale physiological description. This model extends and refines an earlier-proposed formulation by allowing to account for all major energy exchanges and balances, from the chemical activity coupled with oxygen supply to the production of actual mechanical work, namely, the biological function of the tissue. We thus perform a thorough analysis of the energy mechanisms prevailing at the various scales, and we proceed to propose a complete discretization strategy -- in time and space -- respecting the same balance laws. This will be crucial in future works to adequately model the many important physiological -- normal and pathological -- phenomena associated with these energy considerations. (10.1615/IntJMultCompEng.2011002360)
  DOI : 10.1615/IntJMultCompEng.2011002360
• On the critical nature of plastic flow: One and two dimensional models
  
  • Salman Umut
  • Truskinovsky Lev
  International Journal of Engineering Science, Elsevier, 2012, 59, pp.219-254. Steady plastic flows have been compared to developed turbulence because the two phenomena share the inherent complexity of particle trajectories, the scale free spatial patterns and the power law statistics of fluctuations. The origin of the apparently chaotic and at the same time highly correlated microscopic response in plasticity remains hidden behind conventional engineering models which are based on smooth fitting functions. To regain access to fluctuations, we study in this paper a minimal mesoscopic model whose goal is to elucidate the origin of scale free behavior in plasticity. We limit our description to fcc type crystals and leave out both temperature and rate effects. We provide simple illustrations of the fact that complexity in rate independent athermal plastic flows is due to marginal stability of the underlying elastic system. Our conclusions are based on a reduction of an over-damped visco-elasticity problem for a system with a rugged elastic energy landscape to an integer valued automaton. We start with a one dimensional model and show that it reproduces the main macroscopic phenomenology of rate independent plastic behavior but falls short of generating self similar structure of fluctuations. We then provide evidence that a two dimensional model is already adequate for describing power law statistics of avalanches and fractal character of dislocation patterning. In addition to capturing experimentally measured critical exponents, the proposed minimal model shows finite size scaling collapse and generates realistic shape functions in the scaling laws. (10.1016/j.ijengsci.2012.03.012)
  DOI : 10.1016/j.ijengsci.2012.03.012
• Modelling radiation effects on the fracture process in simplified nuclear glass.
  
  • Kieu Le-Hai
  • Delaye Jean-Marc
  • Stolz Claude
  Key Engineering Materials, Trans Tech Publications, 2012, 488-489, pp.154-157.
• Application of the multi-level time-harmonic fast multipole BEM to 3-D visco-elastodynamics
  
  • Grasso Eva
  • Chaillat Stéphanie
  • Bonnet Marc
  • Semblat Jean-François
  Engineering Analysis with Boundary Elements, Elsevier, 2012, 36, pp.744-758. This article extends previous work by the authors on the single- and multi-domain time-harmonic elastodynamic multi-level fast multipole BEM formulations to the case of weakly dissipative viscoelastic media. The underlying boundary integral equation and fast multipole formulations are formally identical to that of elastodynamics, except that the wavenumbers are complex-valued due to attenuation. Attention is focused on evaluating the multipole decomposition of the viscoelastodynamic fundamental solution. A damping-dependent modification of the selection rule for the multipole truncation parameter, required by the presence of complex wavenumbers, is proposed. It is empirically adjusted so as to maintain a constant accuracy over the damping range of interest in the approximation of the fundamental solution, and validated on numerical tests focusing on the evaluation of the latter. The proposed modification is then assessed on 3D single-region and multi-region visco-elastodynamic examples for which exact solutions are known. Finally, the multi-region formulation is applied to the problem of a wave propagating in a semi-infinite medium with a lossy semi-spherical inclusion (seismic wave in alluvial basin). These examples involve problem sizes of up to about $3\,10^{5}$ boundary unknowns. (10.1016/j.enganabound.2011.11.015)
  DOI : 10.1016/j.enganabound.2011.11.015
• A new model of damage: a moving thick layer approach
  
  • Stolz Claude
  • Moes Nicolas
  International Journal of Fracture, Springer Verlag, 2012, 174 (1), pp.49-60. A new formulation of a damage law is proposed based on a continuous transition between a sound material and a totally or partially broken material. The evolution of damage is then associated with a moving layer. This point of view permits the description of initiation and propagation of defects in an unified framework. The motion of the thick layer is defined in the frame of the moving surface I" (o) separating the sound material and the damaged material. When the damage parameters are continuous functions of the distance to I" (o) , they satisfy the conditions of transport. For particular geometries and loadings the evolution of the system is discussed. Comparison with description of damage with discontinuities and sharp interface is also presented. (10.1007/s10704-012-9693-3)
  DOI : 10.1007/s10704-012-9693-3
• Dehydration-induced damage and deformation in gypsum and implications for subduction zone processes
  
  • Brantut Nicolas
  • Shubnel Alexandre
  • David Christian
  • Héripré Eva
  • Gueguen Yves
  • Dimanov Alexandre
  Journal of Geophysical Research, American Geophysical Union, 2012, 117 (B3). Experimental heating tests were performed on Volterra gypsum to study the micromechanical consequences of the dehydration reaction. The experimental conditions were drained, at 5~MPa fluid pressure, and confining pressures ranging from 15 to 55 MPa. One test was performed with a constant applied differential stress of 30~MPa. The reaction is marked by (1) a porosity increase and homogeneous compaction, (2) a swarm of acoustic emissions, (3) a large decrease in P- and S-wave velocities, and (4) a decrease in VP/VS ratio. Wave velocity data are interpreted in terms of crack density and pore aspect ratio, which, modeling pores as spheroids, is estimated at around 0.05 (crack-like spheroid). Complementary tests performed in an environmental scanning electron microscope indicate that cracks first form inside the gypsum grains, and are oriented preferentially along the crystal structure of gypsum. Most of the visible porosity appears at later stages when grains shrink and grain boundaries open. Extrapolation of our data to serpentinites in subduction zones suggest that the signature of dehydrating rocks in seismic tomography could be a low apparent Poisson's ratio, although this interpretation may be masked by anisotropy development due to preexisting crystal preferred orientation and/or deformation-induced cracking. The large compaction and the absence of strain localization in the deformation test suggests that dehydrating rocks may be seen as soft inclusions and could thus induce ruptures in the surrounding, nonreacting rocks. (10.1029/2011JB008730)
  DOI : 10.1029/2011JB008730
• Experiments and Modeling of Anisotropic Aluminum Extrusions under Multi-axial Loading - Part II: Fracture
  
  • Dunand M.
  • Luo Meng
  • Mohr Dirk
  International Journal of Plasticity, Elsevier, 2012, pp.36-58.
• Various estimates of Representative Volume Element sizes based on a statistical analysis of the apparent behavior of random linear composites
  
  • Salmi Moncef
  • Auslender François
  • Bornert Michel
  • Fogli Michel
  Comptes Rendus. Mécanique, Académie des sciences (Paris), 2012, 340 (4-5), pp.230-246. This article aims at proposing various estimates of the size of the Representative Volume Element (RVE) of random linear elastic matrix-inclusion composites. These estimates are derived from the computation of the apparent behavior of finite size volume elements (VE) by a new procedure presented in . [18] by Salmi et al. (2012) and briefly recalled. Two different points of view to define an RVE are considered: the RVE is defined as being the smallest VE required either to evaluate numerically the considered effective property of the composite by appropriate statistical averaging of apparent ones, or to be allowed to replace any instance of the heterogeneous material by a unique homogeneous equivalent one in structural mechanics problems. In order to introduce the fluctuations of the apparent properties within such definitions of the RVE size, we first study the statistics of the apparent properties. Then, relying on the results of this statistical study, several proposals of RVE criteria are presented and applied to random linear elastic fiber-matrix composites for several contrasts and inclusion (or pore) volume fractions. © 2012 Académie des sciences. (10.1016/j.crme.2012.02.007)
  DOI : 10.1016/j.crme.2012.02.007
• Fast multipole method applied to Symmetric Galerkin boundary element method for 3D elasticity and fracture problems
  
  • Pham Anh Duc
  • Mouhoubi Saida
  • Bonnet Marc
  • Chazallon Cyrille
  Engineering Analysis with Boundary Elements, Elsevier, 2012, 36, pp.1838-1847. The solution of three-dimensional elastostatic problems using the Symmetric Galerkin Boundary Element Method (SGBEM) gives rise to fully-populated (albeit symmetric) matrix equations, entailing high solution times for large models. This article is concerned with the formulation and implementation of a multi-level fast multipole SGBEM (FM-SGBEM) for elastic solid with cracks. Arbitrary geometries and boundary conditions may be considered. Numerical results on test problems involving a cube, single or multiple cracks in an unbounded medium, and a cracked cylindrical solid are presented. BEM models involving up to $10^{6}$ BEM unknowns are considered, and the desirable predicted trends of the elastostatic FM-SGBEM, such as a $O(N)$ complexity per iteration, are verified. (10.1016/j.enganabound.2012.07.004)
  DOI : 10.1016/j.enganabound.2012.07.004