Publications

2005

• Inverse problems in elasticity
  
  • Bonnet Marc
  • Constantinescu Andrei
  Inverse Problems, IOP Publishing, 2005, 21, pp.R1-R50. This review is devoted to some inverse problems arising in the context of linear elasticity, namely the identification of distributions of elastic moduli, model parameters or buried objects such as cracks. These inverse problems are considered mainly for three-dimensional elastic media under equilibrium or dynamical conditions, and also for thin elastic plates. The main goal is to overview some recent results, in an effort to bridge the gap between studies of a mathematical nature and problems defined from engineering practice. Accordingly, emphasis is given to formulations and solution techniques which are well suited to general-purpose numerical methods for solving elasticity problems on complex configurations, in particular the finite element method and the boundary element method. An underlying thread of the discussion is the fact that useful tools for the formulation, analysis and solution of inverse problems arising in linear elasticity, namely the reciprocity gap and the error in constitutive equation, stem from variational and virtual work principles, i.e., fundamental principles governing the mechanics of deformable solid continua. In addition, the virtual work principle is shown to be instrumental for establishing computationally efficient formulae for parameter or geometrical sensitivity, based on the adjoint solution method. Sensitivity formulae are presented for various situations, especially in connection with contact mechanics, cavity and crack shape perturbations, thus enriching the already extensive known repertoire of such results. Finally, the concept of topological derivative and its implementation for the identification of cavities or inclusions are expounded. (10.1088/0266-5611/21/2/R01)
  DOI : 10.1088/0266-5611/21/2/R01
• Fast multipole method applied to the coupling of elastostatic BEM with FEM
  
  • Margonari M.
  • Bonnet Marc
  Computers & Structures, Elsevier, 2005, 83, pp.700-717. BEM–FEM coupling is desirable for three-dimensional problems involving specific features such as (i) large or unbounded media with linear constitutive properties, (ii) cracks, (iii) critical parts of complex geometry requiring accurate stress analyses. However, for cases with a BEM discretization involving a large number NBEM of degrees of freedom, setting up the BEM contribution to the coupled problem using conventional techniques is an expensive $O(NBEM^{2})$ task. Moreover, the fully-populated BEM block entails a $O(NBEM^{2})$ storage requirement and a $O(NBEM^{3})$ contribution to the solution time via usual direct solvers. To overcome these pitfalls, the BEM contribution is formulated using the fast multipole method (FMM) and the coupled equations are solved by means of an iterative GMRES solver. Both the storage requirements and the solution times are found to be close to O(NBEM). A preconditioner based on the sparse approximate inverse of the BEM block is shown to improve the convergence of the GMRES solver. Numerical examples involving NBEM = O(10^5 − 10^6) unknowns, run on a PC computer, are presented; they include the Eshelby inclusion (as a validation example), a many-inclusion configuration, and a dam structure. (10.1016/j.compstruc.2004.09.007)
  DOI : 10.1016/j.compstruc.2004.09.007
• Numerical approach in thermomechanical fatigue
  
  • Charkaluk Eric
  • Constantinescu Andrei
  • Thomas Jean-Jacques
  , 2005. This paper presents a global approach of thermomechanical design in the automotive industry based on four different aspects: the loading definition, the modelling of the constitutive law and of the damage and a failure criterion. This approach is applied on cylinder heads and on exhaust manifolds submitted to transient thermal loading and permits to predict the cracked area as well as the lifetime. The main hypothesis and the different aspects are detailed and results on automotive parts are presented.
• Multi-scale characterization and modelling of human cortical bone.
  
  • Ho Ba Tho M.C.
  • Stolz Claude
  • Vanleene M.
  • Bensamoun S.
  • Treutenaere J.M.
  • Rey C.
  , 2005.
• Thermodynamics of rate-independent plasticity
  
  • Puglisi Giuseppe
  • Truskinovsky Lev
  Journal of the Mechanics and Physics of Solids, Elsevier, 2005, 53, pp.655-679. We show that the singular dissipative potential of the phenomenological rate-independent plasticity can be obtained by homogenization of a micro-model with quadratic dissipation. The essential ingredient making this reduction possible is a rugged energy landscape at the micro-scale, generating under external loading a regular cascade of subcritical bifurcations. Such landscape may appear as a result of a sufficiently strong pinning or jamming of defects, leading to elastic micro-metastability. The rate-independent plastic deformation emerges in this description as a continuous succession of infinitesimal viscous events; the limiting procedure presumes the elimination of small time and length scales. We present an explicit example of a simple viscoelastic mass-spring system whose macroscopic dissipative behavior is plastic, rate independent. (10.1016/j.jmps.2004.08.004)
  DOI : 10.1016/j.jmps.2004.08.004
• Small-inclusion asymptotic for inverse problems in acoustics
  
  • Bonnet Marc
  , 2005.
• Identification d'obstacles en acoustique dans des domaines tridimensionnels bornés
  
  • Nemitz Nicolas
  • Bonnet Marc
  , 2005, pp.437-442. Cette communication concerne l’identification d’obstacles dans un domaine acoustique tridimensionnel borné. L’approche présentée repose sur deux ingrédients essentiels. Le premier est l’utilisation d’une méthode d’équations intégrales rapide fondée sur la fast multipole method, grâce à laquelle il est possible d’aborder ce type de problème d’inversion sur des configurations tridimensionnelles bornées de longueurs caractéristiques relativement grandes par rapport à la longueur d’onde acoustique. Le second est le gradient topologique de la function coût associée au problème inverse, permettant de déterminer les zones du domaine acoustique dans lesquelles l’introduction virtuelle d’un obstacle infinitésimal induit une diminution de la fonction coût. Cela permet par exemple de guider le choix de conditions initials pour la mise en oeuvre ultérieure d’un algorithme d’inversion reposant sur l’optimisation de la function coût. Ces deux aspects sont présentés et illustrés sur des exemples numériques. (10.3166/remn.15.307-318)
  DOI : 10.3166/remn.15.307-318
• Small-obstacle expansion in 3-d inverse scattering
  
  • Bonnet Marc
  , 2005.
• Evaluation précise des procédures de linéarisation en homogénéisation non linéaire
  
  • Rekik Amna
  • Bornert Michel
  • Auslender F.
  • Zaoui André
  , 2005.
• Topological sensitivity techniques for 3D elastic and acoustic inverse scattering
  
  • Bonnet Marc
  , 2005. (10.1016/j.cma.2005.10.026)
  DOI : 10.1016/j.cma.2005.10.026
• Overview of some mechanical investigations concerning polycrystals behavior in collaboration with Immpetus and LM3
  
  • Bornert Michel
  • Gilormini P.
  • Pinna C.
  • Rupin N.
  • Zaoui A.
  , 2005.
• Fluid structure interaction problems in large deformation
  
  • Le Tallec Patrick
  • Gerbeau Jean-Frédéric
  • Hauret Patrice
  • Vidrascu Marina
  Comptes Rendus. Mécanique, Académie des sciences (Paris), 2005, 333, pp.910-922. The present article deals with the simulation of fluid structure interaction problems in large deformation, and discusses two aspects of their numerical solution: (i) the derivation of energy conserving time integration schemes in presence of fluid structure coupling, moving grids, and nonlinear kinematic constraints such as incompressibility and contact, (ii) the introduction of adequate preconditioners efficiently chaining local fluid and structure solvers. Solutions are proposed, analyzed and tested using nonlinear energy correcting terms, and added mass based Dirichlet Neumann preconditioners. Numerical applications include nonlinear impact problems in elastodynamics and blood flows predictions within flexible arteries.
• Kinetics of martensitic phase transitions: lattice model
  
  • Truskinovsky Lev
  • Vainchtein Anna
  SIAM Journal on Applied Mathematics, Society for Industrial and Applied Mathematics, 2005, 66, pp.533-553. Martensitic phase transitions are often modeled by mixed-type hyperbolic-elliptic systems. Such systems lead to ill-posed initial-value problems unless they are supplemented by an additional kinetic relation. In this paper we explicitly compute an appropriate closing relation by replacing the continuum model with its natural discrete prototype. The procedure can be viewed as either regularization by discretization or a physically motivated account of underlying discrete microstructure. We model phase boundaries by traveling wave solutions of a fully inertial discrete model for a bi-stable lattice with harmonic long-range interactions. Although the microscopic model is Hamiltonian, it generates macroscopic dissipation which can be specified in the form of a relation between the velocity of the discontinuity and the conjugate configurational force. This kinetic relation respects entropy inequality but is not a consequence of the usual Rankine--Hugoniot jump conditions. According to the constructed solution, the dissipation at the macrolevel is due to the induced radiation of lattice waves carrying energy away from the propagating front. We show that sufficiently strong nonlocality of the lattice model may be responsible for the multivaluedness of the kinetic relation and can quantitatively affect kinetics in the near-sonic region. Direct numerical simulations of the transient dynamics suggest stability of at least some of the computed traveling waves. (10.1137/040616942)
  DOI : 10.1137/040616942
• Du quasi-statique au dynamique rapide avec un unique moyen d'essai
  
  • Gary Gérard
  , 2005.
• Simulations and microstructural effects on macroscopic mechanical behavior and local strain and stress field heterogeneities. Application to zirconium alloys
  
  • Bertolino G.
  • Bilger N.
  • Crépin Jérôme
  • Dexet M.
  • Héripré E.
  , 2005. No abstract provided
• El Método Multipolo Rápido para la Aceleración del Método de los Elementos de Contorno en Elastodinámica Isótropa 3D.
  
  • Sanz J. A.
  • Bonnet Marc
  • Saez A.
  , 2005. No abstract provided
• Contraintes résiduelles dans les éprouvettes cylindriques
  
  • Bérest Pierre
  • Vouille Gérard
  Revue française de Géotechnique, edp sciences, 2005, 110, pp.41-50. On attribue fréquemment aux « contraintes résiduelles » ou « contraintes internes » diverses manifestations anormales observées dans les massifs rocheux ou sur des carottes prélevées en profondeur. Pour décrire ces phénomènes on considère une loi de comportement élastique linéaire présentant des « déformations initiales » non compatibles. Les contraintes résiduelles ne dépendent alors que de la forme de l’objet considéré, des paramètres élastiques et du tenseur d’incompatibilité (ou tenseur de Ricci) associé aux déformations initiales. En supposant que ce tenseur est constant dans une petite éprouvette cylindrique prélevée dans le massif rocheux, on établit la forme générale des champs de contrainte résiduelle qui peuvent affecter l’éprouvette. (10.1051/geotech/2005110041)
  DOI : 10.1051/geotech/2005110041
• Quasicontinuum modelling of short-wave instabilities in crystal lattices
  
  • Truskinovsky Lev
  • Vainchtein Anna
  Philosophical Magazine, Taylor & Francis, 2005, 85, pp.4055-4065. We propose a hybrid quasicontinuum model which captures both long and short-wave instabilities of crystal lattices and combines the advantages of weakly non-local (higher gradient) and strongly non-local (integral) continuum models. To illustrate the idea, we study the simplest one-dimensional lattice exhibiting commensurate and incommensurate short-wave instabilities. We explicitly compute stability limits of the homogeneous states using both discrete and quasicontinuum models. The new quasicontinuum approximation is shown to be capable of reproducing a detailed structure of the discrete stability diagram. (10.1080/14786430500363270)
  DOI : 10.1080/14786430500363270
• Modelling's tyre's wear : a local approach
  
  • Delattre Benoit
  • Pradeilles-Duval Rachel-Marie
  • Stolz Claude
  , 2005.
• Proposition of a general yield function in geomechanics
  
  • Maïolino Siegfried
  Comptes Rendus. Mécanique, Académie des sciences (Paris), 2005, 333, pp.279-284. A general smooth and convex yield function is proposed, able to model the particular behavior of geomaterials, particularly rock materials that are characterized by a linear or parabolic Mohr's envelope, and a particular shape in the deviatoric plane. These characteristics are defined by two functions: the equation of the criterion in the meridian plane and the extension ratio, which are integrated in a general equation ensuring convexity and smoothness of the yield function, whatever the characteristic functions. This expression is interesting, because it allows a straightforward development of a constitutive model based on triaxial tests, in extension and compression. It also allows the development of smooth criteria corresponding to the Mohr–Coulomb criterion and the Hœk–Brown criterion, the latter typical of rock mechanics. (10.1016/j.crme.2004.11.008)
  DOI : 10.1016/j.crme.2004.11.008
• Giens 2005
  
  • Allix Olivier
  • Bonnet Marc
  • Grellier Jean-Paul
  • Ohayon Roger
  • Rassineux Alain
  , 2005. Le calcul des structures est un domaine de recherches et d’applications industrielles en perpétuel développement. Son objet est la modélisation et la simulation numérique des comportements, en espace et en temps, des structures interagissant avec un environnement passif ou actif. Du fait de la croissance rapide des performances des ordinateurs, des problèmes autrefois inabordables sont maintenant étudiés : variabilité, problèmes multiphysiques, multiéchelles.</br></br> Tous les deux ans, l’association CSMA organise un colloque national en calcul des structures et la prise en charge de cette septième édition a été confiée au Laboratoire Roberval de Mécanique de l’Université de Technologie de Compiègne.</br></br> Le Comité Scientifique a retenu 180 communications réparties sur quatre sessions parallèles, une session « poster » et une session logiciel. En outre, nous avons invité le groupe pour l'Avancement des Méthodes Numériques de l'Ingénieur (GAMNI), qui présentera ses travaux dédiés à l'optimisation.</br></br> Le Colloque de « Giens » est un événement majeur, quasi incontournable pour la communauté de la mécanique numérique, académique et industrielle, un lieu de rencontre et d’échanges privilégiés entre les chercheurs, jeunes et plus confirmés, et les ingénieurs de l’industrie. Nous souhaitons que cette septième édition du Colloque soit digne des précédentes.</br></br> Le Comité d'Organisation remercie tous les participants et exprime sa gratitude au Comité scientifique et aux membres des institutions, entreprises et organismes de recherche qui ont œuvré au succès de ce septième Colloque.</br></br> Il est possible de consulter la collection <a href="https://hal.science/CSMA2005">CSMA2005</a> correspondante.
• Ductile fracture of synthetic anorthite aggregates deformed to large strain in torsion.
  
  • Rybacki Erik
  • Dimanov Alexandre
  • Dresen Georg
  , 2005.
• On the Identification of multiscale crystal plasticity models of Titanium Aluminides
  
  • Roos A.
  • Thomas M.
  • Héripré E.
  • Crépin Jérôme
  • Chaboche J. L.
  , 2005. No abstract provided
• Experimental investigation of strain, damage and failure of hydrided zirconium alloys with various hydride orientations
  
  • Racine Aude
  • Bornert Michel
  • Sainte Catherine Claude
  • Cappelaere Chantal
  • Caldemaison Daniel
  , 2005.
• Mechanics and Materials: some aspects and trends of current research
  
  • Zaoui A.
  , 2005.