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Sheet metal forming processes generally involve large deformations together with complex loading sequences. In order to improve numerical simulation predictions of sheet parts forming, physically-based constitutive models are often required. The main objective of this paper is to analyze the strain localization phenomenon during the plastic deformation of sheet metals in the context of such advanced constitutive models. Most often, an accurate prediction of localization requires damage to be considered in the finite element simulation. For this purpose,an advanced, anisotropic elastic-plastic model, formulated within the large strain framework and taking strain-path changes into account, has been coupled with an isotropic damage model. This coupling is carried out within the framework of continuum damage mechanics.In order to detect the strain localization during sheet metal forming, Rice’s localizationcriterion has been considered, thus predicting the limit strains at the occurrence of shear bands as well as their orientation. The coupled elastic-plastic-damage model has been implemented in Abaqus/Implicit. The application of the model to the prediction of Forming Limit Diagrams (FLDs) provided results that are consistent with the literature and emphasized the impact of the hardening model on the strain-path dependency of the FLD. The fully threedimensional formulation adopted in the numerical development allowed for some new results – e.g. the out-of-plane orientation of the normal to the localization band, as well as more realistic values for its in-plane orientation.; International audience; Sheet metal forming processes generally involve large deformations together with complex loading sequences. In order to improve numerical simulation predictions of sheet parts forming, physically-based constitutive models are often required. The main objective of this paper is to analyze the strain localization phenomenon during the plastic deformation of sheet metals in the context of such advanced constitutive models. Most often, an accurate prediction of localization requires damage to be considered in the finite element simulation. For this purpose,an advanced, anisotropic elastic-plastic model, formulated within the large strain framework and taking strain-path changes into account, has been coupled with an isotropic damage model. This coupling is carried out within the framework of continuum damage mechanics.In order to detect the strain localization during sheet metal forming, Rice’s localizationcriterion has been considered, thus predicting the limit strains at the occurrence of shear bands as well as their orientation. The coupled elastic-plastic-damage model has been implemented in Abaqus/Implicit. The application of the model to the prediction of Forming Limit Diagrams (FLDs) provided results that are consistent with the literature and emphasized the impact of the hardening model on the strain-path dependency of the FLD. The fully threedimensional formulation adopted in the numerical development allowed for some new results – e.g. the out-of-plane orientation of the normal to the localization band, as well as more realistic values for its in-plane orientation.

International audience; In this paper, an extended version of Biot's differential equation is considered in order to discuss the quasi-static stability of a response for a solid in the framework of generalized standard materials. The same equation also holds for gradient theories since the gradients of arbitrary order of the state variables and of their rates can be introduced in the expression of the energy and of the dissipation potentials. The stability of a quasi-static response of a system governed by Biot's equations is discussed. Two approaches are considered, by direct estimates and by linearizations. The approach by direct estimates can be applied in visco-plasticity as well as in plasticity. A sufficient condition of stability is proposed and based upon the positivity of the second variation of energy along the considered response. This is an extension of the criterion of second variation, well known in elastic buckling, into the study of the stability of a response. The linearization approach is available only for smooth dissipation potentials, i.e. for the study of visco-elastic solids and leads to a result on asymptotic stability. The paper is illustrated by a simple example.

Two original algorithms are proposed for the computation of bifurcation points in fluid mechanics. These algorithms consist of finding the zero values of a specific indicator. To compute this indicator a perturbation method is used which leads to an analytical expression of this indicator. Two kinds of instability are considered: stationary and Hopf bifurcations. To prove the efficiency and advantages of such numerical methods several numerical tests are discussed.

The development of plastic creases, called wrinkles, during sheet metal conveying in processing lines is considered. Finite element analyses are carried out to model wrinkling when a sheet is passing over a roll. A description of this phenomenon is proposed. When a strip is stretched, small compressive stresses occur near the roll and cause the strip buckling. Simulations have shown that friction between sheet and roll accentuates the post-buckling patterns during strip displacement. In some cases, buckles evolve to create a wrinkle by a plastic cumulative mechanism., Cet article porte sur l'étude de la formation de défauts de forme, appelés plis, lors du transport en continu de bandes métalliques. Un modèle éléments finis a été mis au point pour simuler le passage d'une bande sur un rouleau. Il nous permet de préciser les mécanismes à l'origine du plissement. La traction appliquée à la bande afin de la guider, engendre l'apparition de contraintes compressives secondaires faisant flamber la bande. Nous avons observé que ces ondulations sont fortement accentuées lors du mouvement de la tôle. Ce phénomène est lié au frottement bande-rouleau. Dans certains cas, les plis se forment par l'action d'un mécanisme cumulatif plastique.

The formulation of a six-node solid-shell called SHB6, which is a linear, isoparametric element, is discussed. An eigenvalue analysis of the element stiffness matrix is first carried out. Several modifications are introduced into the formulation of the SHB6 element following the assumed strain method adopted by Belytschko and Bindeman. SHB6's coordinates and displacements are related to the nodal coordinates and displacements through the linear shape functions. Applying the simplified form of the Hu-Washizu nonlinear mixed variational principle, in which the assumed stress field is chosen to be orthogonal to the difference between the symmetric part of the displacement gradient and the assumed strain field, the formula is obtained. The newly developed SHB6 element was implemented into the finite element codes INCA and ASTER. It represents some improvement since it converges well and performs much better than the PRI6 six-node three-dimensional element in all of the benchmark problems tested.; International audience; The formulation of a six-node solid-shell called SHB6, which is a linear, isoparametric element, is discussed. An eigenvalue analysis of the element stiffness matrix is first carried out. Several modifications are introduced into the formulation of the SHB6 element following the assumed strain method adopted by Belytschko and Bindeman. SHB6's coordinates and displacements are related to the nodal coordinates and displacements through the linear shape functions. Applying the simplified form of the Hu-Washizu nonlinear mixed variational principle, in which the assumed stress field is chosen to be orthogonal to the difference between the symmetric part of the displacement gradient and the assumed strain field, the formula is obtained. The newly developed SHB6 element was implemented into the finite element codes INCA and ASTER. It represents some improvement since it converges well and performs much better than the PRI6 six-node three-dimensional element in all of the benchmark problems tested.

International audience; The present work deals with the use of asymptotic numerical methods (ANM) to manage crack onset and crack growth in the framework of Continuum Damage Mechanics (CDM). More specifically, an application of regularization techniques to a 1D cohesive model is proposed. The standard "triangle" damageable elastic model, often used in finite element codes to describe fracture of brittle materials, was chosen. Results associated with load-unload cycle showed that ANM is convenient to take numerically this specific non regular behaviour into account. Moreover, the present paper also shows that the chosen damageable interface model can be introduced in the generalized standard material formalism which unables us to define a complete energy balance associated with the damage process. In such a framework, the new damage state variable is a displacement. Finally, a 1D finite element application to a simple elastic damageable structure is shown to emphasize the potentialities of such an approach.

Within the framework of sheet metal forming, the importance of hardening models for springback predictions has been often emphasized. While some specific applications require very accurate models, in many common situations simpler (isotropic hardening) models may be sufficient. In these conditions, investigation of the impact of hardening models requires well defined test configurations and accurate measurements to generate the reference data. Specific draw-bend tests have been especially conceived for this purpose. In this work, such a draw-bending experimental device has been designed, for use on a biaxial tension machine. Three different steel sheets have been tested (one mild steel sheet and two HSS sheets) with thicknesses between 0.8 and 2 mm. Up to three different back-force levels were used for the tests. Wall curvatures and springback angles were measured. Finite element simulations of the tests were performed. A parameter sensitivity analysis has been carried out in order to determine the numerical parameters ensuring accurate springback results. The tests were simulated using an isotropic hardening model and a combined isotropic-kinematic hardening model. The impact of the hardening model is explored for the various test configurations and conclusions are drawn concerning their relative importance.; International audience; Within the framework of sheet metal forming, the importance of hardening models for springback predictions has been often emphasized. While some specific applications require very accurate models, in many common situations simpler (isotropic hardening) models may be sufficient. In these conditions, investigation of the impact of hardening models requires well defined test configurations and accurate measurements to generate the reference data. Specific draw-bend tests have been especially conceived for this purpose. In this work, such a draw-bending experimental device has been designed, for use on a biaxial tension machine. Three different steel sheets have been tested (one mild steel sheet and two HSS sheets) with thicknesses between 0.8 and 2 mm. Up to three different back-force levels were used for the tests. Wall curvatures and springback angles were measured. Finite element simulations of the tests were performed. A parameter sensitivity analysis has been carried out in order to determine the numerical parameters ensuring accurate springback results. The tests were simulated using an isotropic hardening model and a combined isotropic-kinematic hardening model. The impact of the hardening model is explored for the various test configurations and conclusions are drawn concerning their relative importance.

With a view to environmental, economic and safety concerns, car manufacturers need to design lighter and safer vehicles in ever shorter development times. In recent years, High Strength Steels (HSS) like Interstitial Free (IF) steels which have higher ratios of yield strength to elastic modulus, are increasingly used for sheet metal parts in automotive industry to meet the demands. Moreover, the application of sheet metal forming simulations has proven to be beneficial to reduce tool costs in the design stage and to optimize current processes. The Finite Element Method (FEM) is quite successful to simulate metal forming processes but accuracy largely depends on the quality of the material properties provided as input to the material model. Common phenomenological models roughly consist in the fitting of functions on experimental results and do not provide any predictive character for different metals from the same grade. Therefore, the use of accurate plasticity models based on physics would increase predictive capability, reduce parameter identification cost and allow for robust and time-effective finite element simulations. For this purpose, a 3D physically based model at large strain with dislocation density evolution approach was presented in IDDRG2009 by the authors [1]. This model allows the description of work-hardening's behavior for different loading paths (i.e. uni-axial tensile, simple shear and Bauschinger tests) taking into account several data from microstructure (i.e. grain size, texture, etc...). The originality of this model consists in the introduction of microstructure data in a classical phenomenological model in order to achieve work-hardening's predictive character for different metals from the same grade. Indeed, thanks to a microstructure parameter set for an Interstitial Free steel, it is possible to describe work-hardening behavior for different loading paths of other IF steels by only changing the mean grain size and the chemical composition. During sheet metal forming processes local material points may experience multi-axial and multi-path loadings. Before simulating actual industrial parts, automotive manufacturers use validation tools - e.g. the Cross-Die stamping test. Such typical stamping tests enable the evaluation of a complex distribution of strains. The work described is an implementation [2] of a 3D dislocation based model in ABAQUS/Explicit and its validation on a Finite Element (FE) Cross-Die model. In order to assess the performance and relevance of the 3D dislocation based model in the simulation of industrial forming applications, the results of thinning profiles predicted along several directions and the strain distribution were obtained and compared with experimental results for IF steels with grain sizes varying in the 8-22 μm value range.; International audience; With a view to environmental, economic and safety concerns, car manufacturers need to design lighter and safer vehicles in ever shorter development times. In recent years, High Strength Steels (HSS) like Interstitial Free (IF) steels which have higher ratios of yield strength to elastic modulus, are increasingly used for sheet metal parts in automotive industry to meet the demands. Moreover, the application of sheet metal forming simulations has proven to be beneficial to reduce tool costs in the design stage and to optimize current processes. The Finite Element Method (FEM) is quite successful to simulate metal forming processes but accuracy largely depends on the quality of the material properties provided as input to the material model. Common phenomenological models roughly consist in the fitting of functions on experimental results and do not provide any predictive character for different metals from the same grade. Therefore, the use of accurate plasticity models based on physics would increase predictive capability, reduce parameter identification cost and allow for robust and time-effective finite element simulations. For this purpose, a 3D physically based model at large strain with dislocation density evolution approach was presented in IDDRG2009 by the authors [1]. This model allows the description of work-hardening's behavior for different loading paths (i.e. uni-axial tensile, simple shear and Bauschinger tests) taking into account several data from microstructure (i.e. grain size, texture, etc...). The originality of this model consists in the introduction of microstructure data in a classical phenomenological model in order to achieve work-hardening's predictive character for different metals from the same grade. Indeed, thanks to a microstructure parameter set for an Interstitial Free steel, it is possible to describe work-hardening behavior for different loading paths of other IF steels by only changing the mean grain size and the chemical composition. During sheet metal forming processes local material points may experience multi-axial and multi-path loadings. Before simulating actual industrial parts, automotive manufacturers use validation tools - e.g. the Cross-Die stamping test. Such typical stamping tests enable the evaluation of a complex distribution of strains. The work described is an implementation [2] of a 3D dislocation based model in ABAQUS/Explicit and its validation on a Finite Element (FE) Cross-Die model. In order to assess the performance and relevance of the 3D dislocation based model in the simulation of industrial forming applications, the results of thinning profiles predicted along several directions and the strain distribution were obtained and compared with experimental results for IF steels with grain sizes varying in the 8-22 μm value range.

The research work presented in this manuscript is divided into three parts. The first is concerned with the modeling of material instabilities in metallic materials (localization, necking ...). The aim is to develop theoretical and numerical tools for the prediction of these phenomena and to validate them through forming limit diagrams for ferritic and dual-phase steels. Two complementary approaches have been adopted: the first is micromechanical based on crystal plasticity coupled with appropriate scale-transition schemes, while the second is phenomenological using advanced constitutive models, which we have coupled with damage. In particular, Rice's bifurcation criterion, associated with the loss of ellipticity of the governing equations, has been investigated through these two approaches. The effect of both material or microstructure-related parameters and some destabilizing mechanisms on plastic strain localization development has been analyzed. The key role in the prediction of shear band localization of vertex formation on the current yield surface is particularly emphasized. The second part deals with structural/geometric instabilities (buckling, wrinkling ...). In this context, we proposed a new approach based on the stability analysis of the quasi-static evolution. For strain-rate sensitive materials, the absence of both bifurcation and equilibrium states motivates such a problem statement (i.e., stability of quasi-static evolutions). For elasto-plastic materials, this approach is justified by the fact that most often we are dealing with a quasi-static evolution for a given loading path, even though each point of this evolution represents an equilibrium state. The unified stability criterion that we propose requires the positiveness of the second variation of the total energy and is shown to be valid for elasto-plastic, visco-plastic or visco-elastic solids. More recently, we have extended this criterion to higher-order gradient constitutive models. Moreover, its comparison with existing results on plastic buckling allowed revisiting Hill's non-bifurcation criterion in relation to the choice of the adequate plasticity theory. The essential role played by the formation of yield surface vertices in the prediction of plastic buckling is demonstrated once again. The third part of this work deals with the development of solid-shell finite elements. The key idea of this concept is to combine the benefits of both continuum and shell elements to derive new formulations that are particularly suitable for thin-structure modeling. These enhanced formulations have the following advantages over shell elements: the avoidance of complex shell-type kinematics, the use of general three-dimensional constitutive models, direct calculation of thickness (strain) variations, easy treatment of large rotations along with simple updating of configurations, straightforward connection with 3D elements since displacements are the only degrees of freedom, and natural contact conditions on both sides of the structure. In order to improve their computational efficiency and to alleviate some membrane and shear locking phenomena, the reduced integration scheme is used. The spurious zero-energy deformation modes due to this in-plane reduced integration are efficiently controlled by an appropriate stabilization technique.; Les travaux de recherche présentés dans cette HDR sont répartis en trois thématiques complémentaires. La première concerne la modélisation des instabilités locales dans les matériaux métalliques (localisation, striction ...). Il s'agit de développer des outils théoriques et numériques de prédiction de ces phénomènes et leur validation au travers de courbes limites de formage pour des aciers ferritiques ou dual-phase. Deux approches complémentaires ont été adoptées : la première est micromécanique se basant sur la plasticité cristalline couplée à des techniques de transition d'échelles, tandis que la seconde est phénoménologique utilisant des modèles de comportement avancés que nous avons couplé à de l'endommagement. Le critère de bifurcation de Rice, qui est relié à la perte d'ellipticité des équations gouvernant le problème aux limites, a été particulièrement analysé au travers de ces deux approches. L'influence sur l'apparition d'une localisation de plusieurs paramètres matériau ou liés à la microstructure ainsi que l'effet de certains mécanismes déstabilisants ont été analysés. Il est mis en évidence, notamment, le rôle tout à fait essentiel de la formation de points de vertex aux points courants de la surface de plasticité dans la détection d'une localisation de la déformation plastique en bande de cisaillement. Le deuxième axe de recherche est relatif aux instabilités de type structure (flambage, plissement ...). Ces phénomènes se manifestent le plus souvent en présence de structures minces ou relativement élancées. Dans ce cadre, nous proposons une approche basée sur l'étude de stabilité des évolutions quasi statiques. Pour des matériaux sensibles à la vitesse de déformation, l'absence de bifurcation ainsi que d'états d'équilibre nous amènent naturellement à poser le problème comme celui de la stabilité de trajectoires quasi statiques. Pour les matériaux élasto-plastiques, cette approche est justifiée par le fait que bien souvent nous sommes en présence d'une évolution quasi statique, pour un trajet de chargement donné, même si chaque point de cette évolution représente un état d'équilibre. Le critère de stabilité unifié que nous proposons est donné par la positivité de la seconde variation de l'énergie totale et est valable pour des solides visco-élastiques, visco-plastiques ou élasto-plastiques. Plus récemment, nous avons étendu ce critère à des modèles à gradients. Enfin, la comparaison de ce critère avec les résultats existants relatifs au flambage plastique nous a permis de rediscuter le critère de non-bifurcation de Hill en relation avec le choix du modèle de plasticité approprié. Il est mis en évidence, de nouveau, le rôle important joué par le développement de points de vertex sur la surface de plasticité lors de la prédiction du flambage avec la théorie du module tangent élasto-plastique. Le troisième axe de recherche concerne le développement d'éléments finis de type coques volumiques. L'idée de ce nouveau concept est de combiner les avantages des éléments coques et 3D pour formuler des éléments particulièrement adaptés à la simulation des structures minces. Ces nouveaux éléments de coques volumiques ont l'avantage de prendre en compte la flexion suivant une direction choisie tout en conservant la formulation classique des éléments volumiques. Ils permettent ainsi de modéliser des structures comportant des parties minces et des zones épaisses, sans les difficultés habituelles de raccord de maillages contenant des éléments coques et 3D. Leur utilisation en emboutissage est très prometteuse, en particulier pour des problèmes où les effets dans l'épaisseur sont d'importance majeure. Étant sous-intégrés, pour améliorer leurs performances, les modes de hourglass générés sont alors efficacement stabilisés par des techniques récentes. Les modes de verrouillages (membrane et cisaillement transverse) sont éliminés par des techniques de projection pouvant se mettre sous le formalisme " Assumed Strain Method ".

International audience; This work deals with the convergence acceleration of iterative nonlinear methods. Two convergence accelerating techniques are evaluated: the Modified Mininal Polynomial Extrapolation Method (MMPE) and the Padé approximants. The algorithms studied in this work are iterative correctors: Newton’s modified method, a high-order iterative corrector presented in Damil et al. (Commun Numer Methods Eng 15:701–708, 1999) and an original algorithm for vibration of viscoelastic structures. We first describe the iterative algorithms for the considered nonlinear problems. Secondly, the two accelerating techniques are presented. Finally, through several numerical tests from the thin shell theory, Navier–Stokes equations and vibration of viscoelastic shells, the advantages and drawbacks of each accelerating technique is discussed.

International audience; In this work, we propose an iterative linear solver for the linearized equations coming from the Newton-Raphson method. In structural mechanics, the computation of the non-linear solution, with a Newton-Raphson method for example, requires the solution of sparse linear systems of equations: $K^i U^i = F(U^j )$ with $i = 1,...,k$ and $j = 1,...,i − 1$ with $K^i$ designates a $N × N$ symmetric matrix (the tangent matrix), $U^i$ is the unknown displacement vector $(U^i ∈ \mathbb{R}^N)$ and $F(U^j )$ is a load vector which depends on the previous solutions $U^j$ with $j = 1,...,i − 1$.

Automotive industries are more and more subject to restrictive environmental constraints. Weight reduction of structures seems to be an interesting way to satisfy these requirements. This can be achieved either by using new materials, such as high strength steels or by adopting appropriate dimensioning methods to predict the occurrence of strain localization. Forming Limit Diagram (FLD) is a concept widely used to characterize the formability of thin metal sheets. Analytical determination of FLDs is usually based on the use of localization criteria. Some of the existing material instability criteria are for example based on empirical observations, on the maximum load principle [1-3], on the existence of an initial defect in the sheet [4], on a perturbation method [5] or on bifurcation analysis [6]. Although numerous criteria have been developed, they all have advantages but also drawbacks and limitations. Their confrontation on a wide range of materials is still insufficiently developed to compare their respective capability of accurately predicting FLDs for new materials. Adaptations of some criteria to advanced constitutive laws are also made necessary by the use of new high strength materials. The aim of this paper is to give a general formulation of some localization criteria allowing the comparison of the predicted FLDs for a wide range of materials. An implementation of these criteria coupled with different phenomenological constitutive laws is presented and compared for different materials including an aluminium alloy, a brass and a dual phase steel.; International audience; Automotive industries are more and more subject to restrictive environmental constraints. Weight reduction of structures seems to be an interesting way to satisfy these requirements. This can be achieved either by using new materials, such as high strength steels or by adopting appropriate dimensioning methods to predict the occurrence of strain localization. Forming Limit Diagram (FLD) is a concept widely used to characterize the formability of thin metal sheets. Analytical determination of FLDs is usually based on the use of localization criteria. Some of the existing material instability criteria are for example based on empirical observations, on the maximum load principle [1-3], on the existence of an initial defect in the sheet [4], on a perturbation method [5] or on bifurcation analysis [6]. Although numerous criteria have been developed, they all have advantages but also drawbacks and limitations. Their confrontation on a wide range of materials is still insufficiently developed to compare their respective capability of accurately predicting FLDs for new materials. Adaptations of some criteria to advanced constitutive laws are also made necessary by the use of new high strength materials. The aim of this paper is to give a general formulation of some localization criteria allowing the comparison of the predicted FLDs for a wide range of materials. An implementation of these criteria coupled with different phenomenological constitutive laws is presented and compared for different materials including an aluminium alloy, a brass and a dual phase steel.

In this work, an advanced anisotropic elastic-plasticity model is combined with a damage model and a strain localization criterion in the aim to describe accurately the mechanical behavior of sheet metals. Large strain, fully three-dimensional, implicit time integration algorithms are developed for this model and implemented in the finite element code Abaqus. The resulting code is used to predict the strain localization limits as well as the springback after forming of sheet steels. The impact of strain-path dependent hardening models on the limit strains and on the amount of springback is addressed.; International audience; In this work, an advanced anisotropic elastic-plasticity model is combined with a damage model and a strain localization criterion in the aim to describe accurately the mechanical behavior of sheet metals. Large strain, fully three-dimensional, implicit time integration algorithms are developed for this model and implemented in the finite element code Abaqus. The resulting code is used to predict the strain localization limits as well as the springback after forming of sheet steels. The impact of strain-path dependent hardening models on the limit strains and on the amount of springback is addressed.

International audience; A large strain elastic-plastic single crystal constitutive law, based on dislocation annihilation and storage, is implemented in a new self-consistent scheme, leading to a multiscale model which achieves, for each grain, the calculation of plastic slip activity, with help of regularized formulation drawn from visco-plasticity, and dislocation microstructure evolution. This paper focuses on the relationship between the deformation history of a BCC grain and induced microstructure during monotonic and two-stage strain paths.

The aim of this paper is to present a new algorithm based on the Asymptotic Numerical Method for the computation of eigenvalues and eigenvectors of linear problems. It is based on the introduction of an indicator, which is a rational fraction whose roots correspond exactly to eigenvalues of the considered problem., Nous proposons dans ce travail une méthode originale de calcul des pulsations propres d’un problème de vibration de plaque. Cette méthode est basée sur l’introduction d’un indicateur qui est une fraction rationnelle et dont les racines du numérateur sont exactement les pulsations propres recherchées. Le problème est résolu à l’aide d’une méthode de perturbation et des approximants de Padé.

International audience; Sheet metal forming processes often involve complex loading sequences. To improve the prediction of some undesirable phenomena, such as springback, physical behavior models should be considered. This paper investigates springback behavior predicted by advanced elastoplastic hardening models which combine isotropic and kinematic hardening and take strain-path changes into account. A dislocation-based microstructural hardening model formulated from physical observations and the more classical cyclic model of Chaboche have been considered in this work. Numerical implementation was carried out in the ABAQUS software using a return mapping algorithm with a combined backward Euler and semi-analytical integration scheme of the constitutive equations. The capability of each model to reproduce transient hardening phenomena at abrupt strain-path changes has been shown via simulations of sequential theological tests. A springback analysis of strip drawing tests was performed in order to emphasize the impact of several influential parameters, namely: process, numerical and behavior parameters. The effect of the two hardening models with respect to the process parameters has been specifically highlighted.

International audience; The impact of material models on the numerical simulation of springback is investigated. The study is focused on the strain-path sensitivity of two hardening models. While both models predict the Bauschinger effect, their response in the transient zone after a strain-path change is fairly different. Their respective predictions are compared in terms of sequential test response and of strip-drawing springback. For this purpose, an accurate and general time integration algorithm has been developed and implemented in the Abaqus code. The impact of several numerical parameters is also studied in order to assess the overall accuracy of the finite element prediction. For some test geometries, both material and numerical parameters are shown to clearly influence the springback behavior at a large extent. Moreover, a general trend cannot always be extracted, thus justifying the need for the finite element simulation of the stamping process.

The present work deals with a new technique to regularize the elastoplastic constitutive laws in the framework of the asymptotic numerical method., On se propose dans ce travail de présenter une nouvelle technique de régularisation des lois de comportement élasto-plastique dans le cadre de la méthode asymptotique numérique.

This work deals with the convergence acceleration of iterative correctors. Three techniques are evaluated on numerical examples from nonlinear elastic thin shell problems., Ce travail porte sur l'accélération de la convergence de correcteurs itératifs, tels que la méthode de Newton-Raphson modifié ou les correcteurs d'ordre élevé récemment définis. L'objectif est de diminuer le nombre d'itérations de ces correcteurs. Trois techniques d'accélération de la convergence sont étudiées: l'algorithme, une technique d'extrapolation et les approximants de Padé. Les tests numériques sont réalisés sur des exemples de flambage non-linéaire élastique de coques minces.

International audience; In this work, the formulation of the finite element "SHB8PS" is revisited in order to eliminate some persistent membrane or transverse shear locking. Let us recall that the "SHB8PS" is a continuum mechanics shell element obtained from a purely three-dimensional formulation. It therefore possesses eight nodes and five integration points distributed according to the thickness direction. Thus, it can be used to model thin structures while correctly taking into account the various phenomena throughout the thickness. In order to improve its calculation performances and to avoid some blockages, reduced integration was employed. The hourglass modes generated by under-integration are efficiently stabilized and the persistent locking modes are eliminated using a projection technique entering under the "Assumed Strain Method" formalism.; Dans cette étude, la formulation de l'élément « SHB8PS » est revisitée dans le but d'éliminer certains blocages persistants en membrane ou cisaillement transverse. Rappelons que cet élément est de type coque épaisse obtenue à partir d'une formulation purement tridimensionnelle. Il possède donc huit nœuds et cinq points d'intégration répartis selon la direction de l'épaisseur. Ainsi, il peut être utilisé pour modéliser des structures minces tout en prenant correctement en compte les différents phénomènes à travers l'épaisseur. Afin d'améliorer ses performances de calcul et d'éviter certains blocages, l'intégration réduite a été employée. Les modes de hourglass générés par la sous-intégration sont efficacement stabilisés et les modes de blocages persistants sont éliminés par une technique de projection pouvant se mettre sous le formalisme de la « Méthode de Déformation Postulée ».

The aim of this article is to propose and to evaluate analytical models for sandwich structures with three layers (elastic/viscoelastic/elastic). Some models are based on the kinematics of Kirchhoff-Love, Mindlin, Reddy or Touratier, the others on the zigzag principle. The accuracy of these models is studied in the static field (inflection of three points) and the dynamic field (free vibration), for which a Finite-Element-based solution is considered as reference. The parameters of comparisons include vertical deflection, normal strain, transverse shear strain, natural frequencies and loss factors., Le but de cet article est de proposer et d'évaluer les modèles analytiques pour les structures sandwich à trois couches (élastique/viscoélastique/élastique). Certains modèles sont basés sur la cinématique de Kirchhoff-Love, de Mindlin, de Reddy ou de Touratier, les autres selon le principe de zigzag. La validité de ces modèles est étudiée dans le domaine statique (flexion à trois points) et le domaine dynamique (vibration libre), les solutions numériques par éléments finis sont considérées comme solutions de référence pour les comparaisons. Les paramètres de comparaisons incluent le déplacement transversal, la contrainte normale, la contrainte transversale de cisaillement, les fréquences naturelles et les facteurs de perte.

A theoretical model for thin-walled beams with open section is investigated in large torsion. This model is extended to finite element method where beam elements with 14 degrees of freedom are considered. Equilibrium equations are non linear and highly coupled. Iterative methods are used in solution procedure. Some applications are reported. They concern torsion response and post buckling behaviour of columns under compressive loads or beams in lateral-buckling behaviour., RESUME. Un modèle théorique de calcul des poutres à parois minces et à sections ouvertes est développé dans le cas des grandes torsions. Dans le modèle numérique, des éléments poutres 3D à 14 degrés de liberté sont considérés. Au niveau théorique et numérique aucune approximation n'est faite sur l'amplitude de l'angle torsion. Les équations d'équilibre sont non linéaires et toutes couplées en présence de la torsion. Les méthodes itératives sont utilisées dans la solution. Les applications données concernent le comportement non linéaire en torsion et le comportement post-critique sous charges axiales (flambement) ou transversales (déversement).

This thesis concerns the study of metamaterials for water surface waves. The study is based on a laboratory experiment which makes it possible to measure the wave field precisely.In the first part, we demonstrate experimentally and numerically that metamaterials can be used to control the wave propagation and resonance properties of a closed cavity, including the cloaking of its eigenmodes. The anisotropic medium is designed using coordinate transformation theory and the homogenization of a three-dimensional linear water wave problem. This medium consists of a set of vertical plates whose spacing is much lower than the wavelength. This structure imposes an anisotropic bathymetry which influences the propagation of the waves differently according to their direction of propagation. Three different cavities manufactured by a 3D printer are tested and compared to the reference case with bathymetry without structuring. Fourier Transform Profilometry, as well as confocal displacement sensors, are used for measurements of water surface deformation resolved in time and space. Experimental data shows a remarkable ability of the metamaterial to influence the anisotropic propagation of waves on the water surface.The second part concerns the metamaterials submerged between two water layers for which a homogenized model is proposed, and the numerical solution by the modal method is provided. The anisotropic properties of such a structure are investigated experimentally using the same technique. An analysis based on the Bloch-Floquet formalism is performed to verify the dispersion relation of this medium predicted by the homogenization method.The main objective of the third part of this thesis is to experimentally study topologically protected edge states in a waveguide with periodic geometry in both linear and non-linear regimes. One of the representations of topological states, provided by the Su-Schrieffer-Heeger (SSH) model, is applied to describe the observed phenomena. A waveguide with periodic width is compared to the regular case of a rectangular reservoir with constant width. Confocal displacement sensors are used to measure the wave field very precisely. The experimental data is compared with the results of the 2D numerical simulations and the prediction of the SSH model. The results obtained show that this very simple configuration presents all the properties of the SSH model with excellent agreement.; La thèse concerne l'étude des métamatériaux dans le contexte des ondes à la surface de l'eau. Cette étude s'appuie sur une expérience en laboratoire qui permet de mesurer précisément le champ des ondes.Dans la première partie, nous démontrons expérimentalement et numériquement que les métamatériaux peuvent être utilisés pour contrôler la propagation des ondes et les propriétés de résonance d'une cavité fermée, y compris le « cloaking » de ses modes propres. Le milieu anisotrope est conçu à partir de la théorie de la transformation des coordonnées et de l'homogénéisation d'un problème d’onde tridimensionnel. Ce milieu est constitué par un ensemble de plaques verticales dont l’espacement est très inférieur à la longueur d’onde. Cette structure impose une bathymétrie anisotrope qui influe sur la propagation des ondes différemment selon leur direction de propagation par rapport à ce milieu structuré. Trois cavités différentes, fabriquées par une imprimante 3D, sont testées et comparées au cas de référence avec bathymétrie sans structuration. La profilométrie par transformée de Fourier, ainsi que des capteurs de déplacement confocaux, sont utilisés pour les mesures de la déformation de la surface de l'eau résolues en temps et en espace. Les données expérimentales montrent une capacité remarquable du métamatériau à influer sur la propagation anisotrope des ondes à la surface de l'eau.La deuxième partie concerne les métamatériaux immergés entre deux eaux pour lesquels un modèle homogénéisé est proposé et la solution numérique par méthode modale est fournie. Les propriétés anisotropes d'une telle structure sont étudiées expérimentalement en utilisant la même technique. Une analyse basée sur le formalisme de Bloch-Floquet est effectuée pour vérifier la relation de dispersion de ce milieu prédite par la méthode d'homogénéisation.L'objectif principal de la troisième partie de cette thèse est d'étudier expérimentalement les états de bord topologiquement protégés dans un guide d'ondes à géométrie périodique en régime linéaire et non linéaire. Une des représentations des états topologiques, fournie par le modèle Su-Schrieffer-Heeger (SSH), est appliquée pour décrire les phénomènes observés. Un guide d'ondes avec une largeur périodique est comparé au cas régulier d’un réservoir rectangulaire avec une largeur constante. Des capteurs de déplacement confocaux sont utilisés pour mesurer le champ d'onde très précisément. Les données expérimentales sont comparées aux résultats des simulations numériques 2D et à la prédiction du modèle SSH. Les résultats obtenus montrent que cette configuration très simple présente toutes les propriétés du modèle SSH avec un excellent accord.

International audience; This study focuses on the stability of the quasi-static evolution of strain-rate-dependent solids and structures. This approach can deal with the stability of the non-linear problem, and not only with the linearised one. The linearisation method of nonautonomous evolution equations provides a sufficient stability condition. This condition given by the strict positiveness of the second derivative of the total free energy is compared to Hill's non-bifurcation criterion. Finally, some illustrative examples of visco-elasticity and visco-plasticity are presented.

I; This paper presents an identification procedure for the parameters of a thermodynamically based constitutive model for Shape memory Alloys (SMAs). The proposed approach is a gradient-based method and utilizes an analytical computation of the sensitivity matrix. For several loading cases, including superelasticity, that are commonly utilized for the model parameters identification of such a constitutivemodel, a closed-form of the total infinitesimal strain is derived. The partial derivatives of this state variable are developed to find the components of the sensitivity matrix. A LevenbergeMarquardt algorithm is utilized to solve the inverse problem and find the best set of model parameters for specific SMA materials. Moreover, a pre-identification method, based on the second derivative of the total strain components is proposed. This provides a suitable initial set of model parameters, which increases theefficiency of the inverse method. The proposed approach is applied for the simultaneous identification of the non-linear constitutive parameters for two superelastic SMAs. The comparison between experimental and numerical curves obtained for different temperatures shows the capabilities of the developedidentification approach. The robustness and the efficiency of the developed approach are then experimentally validated; International audience; This paper presents an identification procedure for the parameters of a thermodynamically based constitutive model for Shape memory Alloys (SMAs). The proposed approach is a gradient-based method and utilizes an analytical computation of the sensitivity matrix. For several loading cases, including superelasticity, that are commonly utilized for the model parameters identification of such a constitutivemodel, a closed-form of the total infinitesimal strain is derived. The partial derivatives of this state variable are developed to find the components of the sensitivity matrix. A LevenbergeMarquardt algorithm is utilized to solve the inverse problem and find the best set of model parameters for specific SMA materials. Moreover, a pre-identification method, based on the second derivative of the total strain components is proposed. This provides a suitable initial set of model parameters, which increases theefficiency of the inverse method. The proposed approach is applied for the simultaneous identification of the non-linear constitutive parameters for two superelastic SMAs. The comparison between experimental and numerical curves obtained for different temperatures shows the capabilities of the developedidentification approach. The robustness and the efficiency of the developed approach are then experimentally validated

WOS; International audience; Les jonctions tubulaires, fréquemment employées dans l'industrie offshore, sont soumises en service à des contraintes résultant de chargements élémentaires de traction-compression, flexion dans le plan et flexion hors plan. Ce travail porte sur l'analyse des recommandations classiquement utilisées pour le dimensionnement en fatigue des jonctions soudées lors de l'application de sollicitations combinées. Plus particulièrement, il a porté sur l'étude du comportement en fatigue d'une jonction soudée en T soumise à un chargement de type flexion déviée. Tout d'abord, sur le plan numérique, par la réalisation d'un modèle éléments-finis et la mise en œuvre de méthodes telles que celle proposée par l'IIS, puis, sur le plan expérimental, à travers la réalisation d'essais de fatigue sur ce type de jonctions. Les comparaisons essais/calculs ont montré que l'application de ce type de recommandations ne s'avérait pas systématiquement sécuritaire. Aussi, une démarche visant à prendre en compte le caractère multiaxial des contraintes en pied de cordon de soudure a été mise en œuvre afin de compléter les recommandations visant au dimensionnement des jonctions tubulaires soudées.

The goal of this study was to analyze the relation between the behaviour of a clayey material at the macroscopic scale and its microfabric evolution. This may lead to a better understanding of macroscopic strain mechanisms especially the contractancy and dilatancy phenomena. The approach proposed in this paper is based on the study of clay particles orientation by SEM picture analysis after different phases of triaxial loading. In the initial state of the samples (one-dimensional compression), the SEM observations highlight a microstructural anisotropy with a preferential orientation of the particles normal to the loading direction. During isotropic loading, densification of the clayey matrix occurs related to a random orientation of particles indicated by the term ‘depolarization’. In the earlier stages of constant σ3 drained triaxial path on slightly overconsolidated specimens, the microstructural depolarization seems to persist inside a macroscopic domain, in which only the volumetric strains due to the isotropic part of the stress tensor evolve. Then, a rotation mechanism of the particles towards preferred directions seems to be activated. The phenomenon appears directly linked to the evolution of the deviatoric part of the stress tensor. Copyright © 2010 John Wiley & Sons, Ltd.

International audience; Experimental and numerical analysis of the effect of stress-strain heterogeneities (due to elastic anisotropy, grain orientations and interactions) on martensitic transformation are investigated here for a Cu-Based SMA multicrystal. The shape and crystallographic orientation of each grain are measured successively by optical microscopy and Electron Back Scattered Diffraction (EBSD) technique. During a tensile loading at room temperature, the displacement field of the free surface is measured by Digital Image Correlation (DIC) with the software CORRELI-Q4 [Roux, Hild, 2006: Besnard et al., 2006]. The strain field is then derived numerically. A finite element model is designed. The shape of each grain is defined as a subdomain and meshed by three dimensional continuum elements. A behavior law, describing the thermomechanical response of a SMA single crystal, is adopted and implemented into the Abaqus (R) finite element code. It is based on a micromechanical approach and takes into account the various possible active martensitic variants. The study shows that the experimental and numerical results are in good agreement. Moreover, the stress state in grains is disturbed by the neighboring grains and this disturbance has a strong influence on the martensite variant activation. Finally, the study shows that the martensitic transformation mainly occurs in localized bands involving the well crystallographic oriented grains with respect to the loading direction.

The microstructural changes occurring in steels under cyclic loading are responsible for heat dissipation. Therefore, self-heating measurements can be considered as an efficient way to relate fatigue properties to microstructure. However, the dissipative mechanisms are not clearly identified and some questions remain opened. This paper aims to use the experimental estimation of the intrinsic dissipation, in stress amplitude ranges lower than the macroscopic yield strength, to lead to a better understanding of the dissipative mechanisms. First, self-heating measurements enable to evaluate how the free surface affects the spatial distribution of the dissipation sources in the normal direction. Results indicate that, for thin specimens with a high roughness factor, the dissipation sources are mostly activated close to the free surface. Besides, it is experimentally shown that the self-heating curves are not dependent on the mean stress for low stress magnitudes while they are sensitive to the mean stress for higher stress magnitudes. It is deduced that in the loading conditions used to determine the self-heating curves, the dissipative mechanisms imply recoverable strains (anelasticity) for low stress magnitudes and unrecoverable strains (inelasticity) for higher stress magnitudes.

International audience; Dialog between the experiment and the numerical simulation for a shape memory alloy multicrystal. The aim of this study is to make dialog between the numerical simulation and the experiment in the case of the tensile test behavior for a CuAlBe shape memory alloy multicrystal. This dialog allows to compare qualitatively the distributions of martensitic transformation, observed through a long distance microscope, with obtained by Finite element simulation using a thermomechanical behavior law. The last is based on the description of martensitic transformation on a single crystal scale. It is implemented in the Abaqus(R) finite element code. The applied boundary conditions for modeling correspond to the measured ones at the edge of the area by a technique of digital image correlation. Geometrical and crystallographic properties of the various grains of the multicrystal are experimentally determined. The tensile test is carried out at room temperature where the alloy has a superelastic behavior. A good agreement between the experimental observation and numerical results is observed.

An iterative solver is proposed to solve the family of linear equations arising from the numerical computation of non-linear problems. This solver relies on two quantities coming from previous steps of the computations: the preconditioning matrix is a matrix that has been factorized at an earlier step and previously computed vectors yield a reduced basis. The principle is to define an increment in two sub-steps. In the first sub-step, only the projection of the unknown on a reduced subspace is incremented and the projection of the equation on the reduced subspace is satisfied exactly. In the second sub-step, the full equation is solved approximately with the help of the preconditioner. Last, the convergence of the sequences is accelerated by a well-known method, the modified minimal polynomial extrapolation. This algorithm assessed by classical benchmarks coming from shell buckling analysis. Finally, its insertion in path following techniques is discussed. This leads to non-linear solvers with few matrix factorizations and few iterations. Copyright © 2009 John Wiley & Sons, Ltd.

International audience; In this paper an analytical method is proposed for damping analysis of sandwich beams with piezoelectric and viscoelastic layers. Based on the classical zig-zag model and some assumptions about the electric field, this method leads to an analytical expression of the modal loss factor and frequency. Considering two feedback control laws, the obtained hybrid damping of the sandwich beam is characterized. Numerical finite element applications are considered, in order to examine the efficiency and limitations of the presented method.

International audience; Two limestones are studied to compare the fragmentation pattern induced by dy- namic loads. A quasi-static characterization allows one to determine the basic me- chanical properties and to compare the two rocks in terms of Weibull parameters, indicators of microstructural differences. Edge-on impacts are performed and show the important role of the Weibull modulus in the fragmentation pattern. Simula- tions of these experiments are performed and validate the simple model proposed for rocks.

International audience; Many efforts have been done in the modelling of Plinian columns. However, until now, the inverse problem of the reconstruction of a Plinian event from observed data has been only roughly tackled. This paper discusses the efficient variational data assimilation (VDA) that manages the optimization iterate sequence by means of gradient computations. Theoretical developments of VDA are presented for both the Woods equations and a generic system allowing for the modelling of the Navier-Stokes equations. Two- and three-dimensional unsteady Plinian models being based on the latters, VDA could be clearly performed on their differentiable subset of equations. Although no column data are available for the 1982 El Chichon eruptions, identical twin experiments were used to check the abilities of the VDA approach. VDA experiments coupled with a tephra tephra-fall model could be used, to obtain isopach and isopleth maps of past eruptions. Performing VDA experiments with a Plinian model coupled to a tephra-fall model could be an interesting solution to exploit isopach and isopleth maps of the past eruptions of El Chichon. Some of the numerical experiments presented in this paper are downloadable in the PliniAD package which is freely available from the author's webpage.

International audience; Aging of ice single crystals subjected to creep exhibits peculiar behavior. If the sample is unloaded after sufficient strain, a forward jump in creep rate is observed at reloading. Sequences of loading periods alternated with either increasing or decreasing unloading intervals were performed to document this phenomenon. During the tests, acoustic emission was recorded in order to characterize dislocation activity and spatial distribution. Predictions obtained from a field dislocation theory coupling the evolution of statistical and polar dislocation densities compare fairly well with experimental results. Polar dislocation density reflects lattice incompatibility and long-range internal stresses. The associated back-stress and its relaxation during aging are seen as the origin of the acceleration effect. The interplay between dislocation velocity enhancement and polar dislocation annihilation during aging controls the phenomenon, whereas statistical dislocations only play a minor role. The reverse relaxation deformation observed during unloading periods is reproduced well by the model.

International audience; The thermal wrinkling behavior of thin membranes is investigated in this paper. Wrinkles often occur at multiple length scales where induced compressive stresses are located during thermal loading. In the present study, the method of double scale Fourier series is used to deduce the macroscopic membrane wrinkling equations. The obtained equations account for the global and local wrinkling modes. Numerical examples are conducted to assess the validity of the approach developed. The present membrane's model needs only few degrees of freedom to recover more accurately the post-buckling equilibrium curves and the wrinkling shapes. Different parameters such as membrane's aspect ratio, wave number, and pre-stressed membranes are discussed from a numerical point of view and the properties of the wrinkles (critical load, wavelength, size, and location) are presented.

National audience; Cet article présente un modèle micromécanique visco-endommageable pour les composites à matrice thermoplastique renforcée par des fibres de verre courtes et soumis à un chargement en fatigue. L'approche multi-échelles développée est fondée sur la méthode de Mori-Tanaka, modifiée afin d'inclure des inclusions enrobées et l'évolution des mécanismes d'endommagement à l'échelle microscopique. Le modèle développé intègre les cinétiques d'endommagement tout en tenant compte de la viscoélasticité matricielle et de la microstucture. La prise en compte de ces derniers se base sur des travaux précédemment menés par les auteurs sur le PA66/GF30 moulé par injection [3-5]. Des scénarios d'endommagement ont été proposés et regroupent trois mécanismes : la décohésion interfaciale fibre­ matrice, la fissuration matricielle et les ruptures de fibres. Chaque mécanisme d'endommagement est associé à une loi d'évolution dépendant des champs de contraintes à l'échelle microscopique. La loi constitutive du volume élémentaire représentatif est implémentée dans Abaqus en tant qu'User MATerial subroutine. L'identification du modèle se fait par méthodes inverses, bénéficiant ainsi des résultats multi-échelles précédemment obtenus à l'aide de tests in-situ au MEB ou à partir de l'analyse quantitative et qualitative de données issus de la microtomographie. La validation expérimentale est réalisée par des tests en fatigue contrôlés en déformation.

International audience; This paper revisits the modeling of compressive failure of long fiber composite materials by considering a multiscale finite element approach. It is well known that this failure follows from a fiber microbuckling phenomenon. Fiber microbuckling is governed by both material and geometrical quantities: the elastoplastic shear behavior of the matrix and the fiber misalignment. Although all these parameters are easily accounted by a finite element analysis at the local level, the failure is also influenced by macrostructural quantities. That is why a multilevel finite element model (FE²) is relevant to describe the compressive failure of composite. Furthermore, fiber local buckling leads to a loss of ellipticity of the macroscopic model, which can be a criterion of failure.

This PhD thesis is composed essentially of two main parts, of unequal sizes, which are summarized as follows: Part I: It is concerned with stability and bifurcation issues relating to strain-rate-independent solids and structures (i.e., elastic or elasto-plastic). A thorough and comprehensive review of the various investigations in this field allowed us to propose an original and compact presentation of the theory of stability and bifurcation. An illustration of this theory is then shown through an industrial collaboration with SNECMA. More specifically, numerical simulations of blade forming (for new aircraft engines) are carried out along with the analysis of the associated critical buckling states. These investigations reveal clearly that the material rate sensitivity needs to be taken into account, which motivates the second part of this work. Part II: This part contains the main contributions of the thesis. It deals with stability issues of strain-rate-dependent solids and structures (e.g., visco-elastic or elasto-viscoplastic). The objective of this study is twofold: First, theoretical modeling of the stability of viscous solids is proposed. In this approach, the stability issue of the quasi-static evolution of the structure under consideration is addressed. Indeed, the absence of equilibrium states for such viscous solids naturally suggests considering the stability of their quasi-static evolutions. The strain-rate dependency of these quasi-static evolutions is another source of difficulty in such an analysis. This new approach of stability, which considers the non-stationary response, generalizes the more classical concept of equilibrium stability. On the other hand, stability criteria for these quasi-static evolutions are investigated in close relation with the mathematical results related to non-autonomous differential equations. Note that the non-autonomous nature of the governing equations represents here the main difficulty. Sufficient conditions of stability are then derived using two main methods. In the first approach, the linearization technique is used or a Lyapunov functional, appropriate to the physics of the problem, is constructed. The second approach is more elaborate, but it can be applied to both elasto-plastic and elasto-viscoplastic solids and structures. Finally, to illustrate this methodology and to demonstrate the range of applicability of the resulting criteria, the proposed approach is applied to structural problems (beams, columns ...), corresponding to various elasto-plastic, elasto-viscoplastic or visco-elastic behavior models.; Ces travaux de thèse sont composés principalement de deux grandes parties de volumes inégaux dont voici le résumé des contenus : Partie I : Elle concerne les problèmes de stabilité et de bifurcation rencontrés dans les matériaux indépendants du temps physique (i.e., élastiques ou élasto-plastiques). Une analyse approfondie et détaillée des différentes études dans ce domaine nous permet de faire une présentation originale et synthétique de la théorie de la stabilité et de la bifurcation. Une illustration de cette théorie est ensuite donnée à travers une collaboration industrielle avec la SNECMA. On y effectue des simulations numériques du formage des aubes de réacteurs d'avions accompagnées d'analyses des états critiques de flambage. Les conclusions de ces simulations montrent clairement la nécessité de tenir compte du comportement visqueux du matériau et motivent ainsi la seconde partie de la thèse. Partie II : La deuxième partie des travaux de thèse est la plus importante quant au volume et au fond. Elle concerne les problèmes de stabilité des matériaux dépendant du temps physique (i.e., visco-élastiques ou visco-plastiques). L'objectif de cette étude est double : D'une part, une modélisation théorique du problème de stabilité des solides visqueux est proposée. Cette modélisation a pour but de poser le problème étudié comme un problème de stabilité de l'évolution quasi statique du solide visqueux considéré. En effet, l'absence d'équilibres pour de telles structures visqueuses nous amène naturellement à étudier la stabilité de leurs évolutions quasi statiques. Ces dernières dépendent bien entendu de la vitesse du chargement, ce qui constitue une source de difficultés dans une telle analyse. Cette façon de poser le problème en termes de stabilité de trajectoires est, à notre connaissance, originale et généralise la notion plus classique de la stabilité d'un équilibre. Elle consiste, en quelque sorte, à mesurer la sensibilité des mouvements aux perturbations extérieures. D'autre part, la recherche de critères assurant la stabilité de l'évolution visqueuse est menée en étroite liaison avec les résultats mathématiques relatifs aux équations différentielles non autonomes. Il est mis en évidence, notamment, que la principale difficulté dans cette analyse vient du caractère non autonome des équations différentielles régissant l'évolution quasi statique visqueuse. Les conditions suffisantes de stabilité auxquelles on aboutit sont obtenues principalement par deux méthodes. La première consiste à construire des fonctionnelles de Lyapunov adéquates à la physique du problème ou à utiliser la méthode de linéarisation autour de la réponse quasi statique. L'autre démarche est plus directe et permet d'établir le critère de stabilité de l'évolution par des considérations de continuité de la réponse par rapport aux données initiales. Cette deuxième démarche a l'avantage de s'appliquer aussi bien aux évolutions visco-plastiques qu'aux évolutions élasto-plastiques. Enfin, l'application de ces différents résultats aux modèles de tiges de Shanley et pour le cas des poutres permet d'illustrer notre méthodologie sur des exemples concrets et de comprendre la portée des critères de stabilité ainsi obtenus.

International audience; This work deals with the vibrations of sandwich visco-elastic structures. The central visco-elastic layer included between two metallic layers leads to solve a problem of complex and non-linear eigenvalues. Indeed the core material depends on the frequency. Several methods exist to solve this type of problem. But the dimension of matrices to be manipulated can become very large and generate substantial computational times. A reduction technique is proposed herein. It is applied and compared to the high order Newton method.

Stress analyses by X-ray diffraction are performed on a cast duplex (32% ferrite) stainless steel elbow and a bainitic (95% ferrite) pressure vessel steel. During an in situ tensile test, micrographic observations are made (visible glides and microcracks) and related to the stress state determined in the individual ferritic grains (aged duplex) and the ferritic phase (bainite loaded at low temperatures). Several material parameters have been identified at different scales, as for example, the critical resolved shear stress of 245 MPa for the aged ferritic grain (duplex) or 275 MPa for bainite (–60 ◦C), a crystallographic cleavage propagation criterion of 465 MPa (stress normal to {100} planes), and a fracture stress of approximately 700 MPa in the ferritic phase. Even though the two steels are different in many respects, the macroscopic fracture strains and stresses are well predicted by the polycrystalline model developed for bainite, whatever the temperatures tested (considering 7% of the grains reaching the local criterion).; International audience; Stress analyses by X-ray diffraction are performed on a cast duplex (32% ferrite) stainless steel elbow and a bainitic (95% ferrite) pressure vessel steel. During an in situ tensile test, micrographic observations are made (visible glides and microcracks) and related to the stress state determined in the individual ferritic grains (aged duplex) and the ferritic phase (bainite loaded at low temperatures). Several material parameters have been identified at different scales, as for example, the critical resolved shear stress of 245 MPa for the aged ferritic grain (duplex) or 275 MPa for bainite (–60 ◦C), a crystallographic cleavage propagation criterion of 465 MPa (stress normal to {100} planes), and a fracture stress of approximately 700 MPa in the ferritic phase. Even though the two steels are different in many respects, the macroscopic fracture strains and stresses are well predicted by the polycrystalline model developed for bainite, whatever the temperatures tested (considering 7% of the grains reaching the local criterion).

Ferroelasticity and ferroelectricity are the non linear behaviours exhibited by piezoceramics, especially in the case of high electric field or stress. Many studies have focused on the role of ferroelastic and ferroelectric switching in fracture of actuators. However, engineering reliability analyses are carried out with tools like finite element software that do not take into account these non linear phenomena. To overcome such a problem, a simplified phenomenological constitutive law has been developed and describe the hysteresis effect of piezoceramics. It is time-independent and relies on the introduction of remnant polarization and remnant strain as internal variables. Two loading surfaces, similar to the ones used in plasticity, provide the evolution laws for the internal variables. Besides, polarization-induced anisotropy in the piezoelectric tensor is taken into account. That constitutive law has been implemented in the commercial software ABAQUS. It has been necessary to develop a finite element with electrical and mechanical degrees of freedom: it is an eight node hexahedron. The stiffness matrix integrates the constitutive law from the four tangent operators given by the constitutive law. The non linear problem is solved by the Newtons method. This finite element tool is used to study the effects of applied voltage on the electroelastic field concentrations ahead of electrodes in a multilayer piezoelectric actuator. The study lies on the experimental observations made by Shindo et al. [1]. Electroelastic analysis on piezoceramics with surface electrode showed that high values of stress and electric displacement arose in the neighbourhood of the electrode tip. Thus, the strain, stress and electric displacement concentrations were calculated and the numerical results showed that ferroelectric switching arose in the area of the electrode tip, causing a change in remnant polarization and remnant strain.

International audience; The purpose of the present paper is to study interaction phenomena between an abradable material (M601) and a titanium alloy (TA6V). This interaction which can occur in an aircraft engine when the rotating blade tips rub on the compressor casing, is analyzed on an experimental laboratory set-up. Only orthogonal cutting conditions are considered in this preliminary study to monitor the load evolution with velocity. The experimental results obtained for a range of velocities $10 < V < 10^7$ m/s and for a range interaction depth $0.05 < t_1 < 0.5$ mm are presented. After analysis of measurements, the mean interaction force increases proportionally to the interaction depth increment. The effects of the contact geometry on the loads, especially the radius of the edge, are investigated. The increase of the radius value for a given interaction depth increases the load value.This work provides new basic data for behaviour laws introduced in numerical models simulating the interaction between the blade tip and the compressor casing in turbine engine applications. Original high-speed photographs recorded in real time during the process illustrate the chip separation by brittle manner. A temperature field in the abradable material will be able to be obtained for only a low speed of 5 m/s.

WOS; International audience; In offshore tubular structures, a typical tubular joint may be subjected to three different types of basic loadings: axial, in-plane bending and out-of-plane bending, through its brace members. Each type will cause a different stress distribution at the joint intersection of structures. Moreover, the actual load condition of a tubular joint can be any combination of the above three basic load cases, for this reason, a combined loading was investigated in addition to these three basic loadings. This load is composed of an axial loading combined with a continuation of rotational bending loading obtained while rotate center of the brace around a circle. Different types of planar joints such as T, Y, X, K, DT, DY, DX, TY, TK, DTX, DTDY, and DTDK, with braces subjected to combined loading, were numerically analyzed to study the effect of those different cases of loading and different types of joints, on the stress concentration zone and values.

International audience; This two-part paper reviews the latest developments in the modeling of shape memory alloys (SMAs) constitutive behavior. The basic properties of SMAs are presented in Part I, including the shape memory effect, pseudoelasticity, as well as other properties such as the acquired and two-way shape memory effect, damping capacity and fatigue life. Part I focuses on the modeling at the single crystal level, dealing with the kinematics of the phase transformation and addressing different approaches for the development of the free energy and dissipation in order to derive constitutive equations. Some of the commonly used SMAs are reviewed by chemical composition and thermomechanical properties. The effects that different processing techniques have on their properties are also discussed. The kinematics associated with the martensitic phase transformation in a single crystal is described for a cubic to tetragonal and cubic to monoclinic transformation, and the lattice invariant strain by plastic slip is discussed. The transformation strain in a representative volume element (RVE) and its evolution are then defined. The free energy and dissipative potentials are derived together with the interaction energy for single variant and multivariant formulations in single crystals. A discussion on scale transitions to polycrystalline SMAs is finally presented. Part II deals with the polycrystalline modeling, considering both micromechanical approaches and phenomenological ones. It also includes considerations about the numerical implementation of SMA constitutive models and their integration into finite element codes.

Shape Memory Alloys; International audience; In this study, a phenomenological model describing superelasticity, shape memory effect under constant stress and the reorientation process in the martensitic phase is proposed. This model is based on a thermodynamical description of the phase transformation which involves two internal variables: the overall martensite volume fraction and the mean transformation strain. An explicit Gibbs free energy expression is deduced from micromechanical considerations. The evolution laws of the internal variables are derived from this potential, assuming a symmetry of the behaviour between tension and compression and considering only proportional loadings. The behaviour of a representative volume element (RVE) of SMA is deduced and the model is implemented in the ABAQUS finite elements software. Results for uniaxial tensile loadings and a three-point bending test are analysed.

International audience; In this paper, a modal approach is realized to define the damping properties of piezoelectric/elastic/piezoelectric beams. This method is based on the classical laminated beam theory and some simple assumptions about the electric fields. This leads to an electromechanical beam constitutive law. The piezoelectric layers play the role of sensor and actuator and two feedback control laws are considered. The equivalent stiffness, eigenfrequencies and loss factors of the whole system beam/control device are obtained.

International audience; The nonlinear Eshelby problem is considered for an elastic viscoplastic inclusion. An approximate solution has been proposed by [Molinari et al., 1997. On the self-consistent modelling of elastic–plastic behavior of polycrystals. Mech. Mater. 26, 43–62] who have postulated a simplified interaction law. With this interaction law, the average strain rate in the inclusion can be related to the far field loading prescribed in the matrix. In the present work, the matrix and the inclusion have elastic-viscoplastic behavior described by a nonlinear Maxwell law. Comparisons between predictions derived from the interaction law and finite element results are performed. It is observed that the approximate solution is in good agreement with numerical results as far as average strain rates and stresses are considered in the inclusion. Various inclusion shapes, material parameters and loading conditions are taken into account.

The focus of this paper is to investigate the nonlinear behavior exhibited by ferroelectric and ferroelastic ceramics under high electromechanical loading. External loads, such as electric field and stress, can induce a remanent strain or polarization due to domain switching. Two internal variables are introduced in order to capture the history dependance and dissipation that characterize ferroelectricity and ferroelasticity. Two loading surfaces are introduced so that associated flow rules provide the evolution laws of the internal variables. In addition, these variables must verify kinematical constraints that may depend on the stress state since experiments indicate that tensile and compressive states have to be considered in this order. Then, dielectric, butterfly, and ferroelastic hysteresis are represented. Mechanical depolarization is also captured. All the tangent operators are expressed so that a resolution with a finite element method can be achieved.

International audience; The object of this study was to understand and characterize dilatancy in clay in relation to the overconsolidation ratio. This phenomenon was investigated along a large range of loading paths, with strong emphasis placed on constant mean stress paths given that it was possible to measure the volumetric strain created by the sole deviatoric stress. Triaxial tests performed on remolded clay (Kaolinite P300) allowed us to determine three different types of behaviour for specimen submitted to a deviatoric stress: no volume change, dilatancy and contraction. In the (p', q) plane these domains are limited by the maximum strength envelope zeta, which coincides with the perfect plasticity line M for OCRs < 2. The experimental results were then compared to plastic flow theories used in the Cam Clay model and in Rowe's dilatancy theory. Finally, by measuring the plastic strain increment vectors along different stress paths in the (p', q) plane, we demonstrated that the uniqueness hypothesis of the plastic potential is not valid. The results could be explained by using two plastic strain mechanisms: a deviatoric one and an isotropic one.