Les outillages de mise en forme en acier martensitique de type AISI H11 sont des pièces critiques dont le comportement en service est étroitement lié à leurs structures internes et à leur évolution. Les conditions des sollicitations lors de la mise en oeuvre du procédé est souvent à l'origine de modifications microstructurales en surface, à savoir la morphologie des lattes de martensite, les orientations cristallographiques, l'état d'écrouissage interne ou encore le profil de surface. Ces aspects peuvent éventuellement altérer les performances mécaniques de l'acier AISI H11. Afin d'appréhender et d'optimiser le comportement mécanique de celui-ci, une approche multi-échelle est mise en oeuvre dans ce travail. Celle-ci s'articule autour d'une investigation expérimentale et d'un traitement numérique. L'étude expérimentale s'attache à reproduire, à l'échelle du laboratoire, des surfaces équivalentes à celles issues lors des procédés de mise en oeuvre des outillages. Des techniques de caractérisation spécifiques, à savoir le MEB, l'EBSD, la nanoindentation ou encore l'altimétrie permettent de mettre en évidence un gradient de la stéréologie du matériau en surface et sous-surface. Les hétérogénéités locales induites concernent la morphologie des lattes de martensite, les orientations cristallographiques, l'état d'écrouissage interne mais également le profil de surface. Des essais mécaniques in-situ associés à la technique de corrélation d'images numériques sont réalisés pour des chargements monotones quasi-statiques et cycliques de type traction-traction. Une investigation des champs mécaniques locaux en surface est ainsi effectuée, elle permet d'analyser les schémas de localisations des déformations non linéaires liés aux artéfacts stéréologiques. Le traitement numérique s'intéresse à une modélisation multi-échelle, et plus particulièrement à des calculs par la méthode des éléments finis sur des microstructures virtuelles générées par tesselations de Voronoï. Celles-ci sont effectuées de manière à reproduire les structures martensitiques et considèrent des relations d'orientations spécifiques (de type Kurdjumov-Sachs) à l'issue du traitement thermique entre les lattes de martensite et le grain austénitique parent. Les équations constitutives du modèle de plasticité cristalline (élasto-viscoplastique) de Méric-Cailletaud sont implantées dans le code de calcul par éléments finis Abaqus dans le cadre de l'hypothèse des petites perturbations (HPP) et de la théorie des transformations finies. La formulation du modèle dans le contexte de la théorie des transformations finies est effectuée dans le cadre d'une description spatiale où la notion de dérivée objective est considérée. Celle-ci consiste en celle d'Oldroyd ou de Truesdell de manière à ce qu'une telle formulation soit équivalente à une description lagrangienne. Le traitement numérique a permis de reproduire de manière qualitative les schémas de localisation en surface mise en évidence lors de l'investigation expérimentale. L'influence des divers paramètres stéréologiques, évoqués ci-dessus, sur les champs mécaniques locaux a été analysée. De par cette approche, il a été possible de mettre en évidence certains mécanismes élémentaires, notamment les effets d'interaction et de surface. Enfin, il a été constaté que la prise en compte des rotations des réseaux cristallins par la théorie des transformations finies permet de relâcher certaines zones de localisation des champs mécaniques autour d'artéfacts stéréologiques. / AISI H11 martensitic tool steels are critical mechanical components that behaviour during service is drastically linked to their internal structures and their possible evolution. Their manufacture processes are often at the origin of microstructural changes at the surface, namely the morphology of martensitic laths, the crystallographic orientations, the internal hardening state and the surface profile These aspects can potentially alter the mechanical performance of AISI H11 martensitic steel. In order to get better insight into and optimize its mechanical behaviour, a multi-scale approach involving an experimental investigation and a numerical treatment is taken in this work.The experimental investigation focuses to reproduce, at the laboratory scale, equivalent surfaces to those resulting from tool steels manufacture processes. Specific characterization techniques, namely SEM, EBSD, nanoindentation and altimetry enable to highlight a stereology gradient of the material in surface and sub-surface. The induced local heterogeneities consist in morphology of martensitic laths and crystallographic orientations, internal hardening state and surface profile. In-situ mechanical tests with digital image correlation technique (DIC) are carried out for monotonous quasi-static and tension-tension cyclic loads. An investigation of the local mechanical fields at the surface is thus performed and allows to analyze the localizations schemes of nonlinear strains which are related to stereological artifacts.The numerical treatment is focused on a multi-scale modelling, and more particularly on finite element calculations on virtual microstructures which are generated by Voronoi tesselations. The latters are carried out such that to reproduce martensitic structures and consider a specific orientation relationship between martensitic laths and parent austenitic grains (i.e. Kurdjumov-Sachs) after the heat treatment. The constitutive equations of the (elasto-viscoplastic) crystal plasticity of Méric-Cailletaud are implemented in the finite element code Abaqus in the context of the small strain assumption and the finite strain theory. The formulation of the model in the context of finite strain theory is is given a spatial description where the notion of objective derivative, namely the so called one of Oldroyd or Truesdell, is used in such a way that such formulation is equivalent to a Lagrangian description.The numerical treatment has allowed to qualitatively reproduce the localization patterns at the surface which have been highlighted in the experimental investigation. The influence of the different stereological parameters mentioned above on the local mechanical fields was analyzed. By this approach, it was possible to highlight some elementary mechanisms including interaction and surface effects. Finally, it was found that the inclusion of lattice rotations via the theory of finite strain allows to release certain areas of mechanical fields localization that are related to stereological artifacts.

Les simulations en mécanique du solide présentent des difficultés comme le traitement de l'incompressibilité ou les non-linéarités dues aux grandes déformations, aux lois de comportement et de contact. L'objectif principal de ce travail est de proposer des méthodes éléments finis capables de gérer l'incompressibilité en grandes déformations en utilisant des éléments de faible ordre. Parmi les approches de la littérature, les formulations mixtes offrent un cadre théorique intéressant. Dans ce travail, une formulation mixte à trois champs (déplacements, pression, gonflement) est introduite. Dans certains cas, cette formulation peut être condensée en formulation à deux champs. Cependant, il est connu que le problème discret obtenu par une approche éléments finis de type Galerkin n'hérite pas automatiquement de la condition de stabilité “inf-sup” du problème continu : les éléments finis utilisés, et notamment les ordres d'interpolation doivent être choisis de sorte à vérifier cette condition de stabilité. Cependant, il est possible de s'affranchir de cette contrainte en ajoutant des termes de stabilisation à la formulation EF Galerkin. Cette approche permet entre autres d'utiliser des ordres d'interpolation égaux. Dans ce travail, des éléments finis stables de type P2/P1 sont utilisés comme référence, et comparés à une formulation P1/P1, stabilisée soit avec une fonction bulle, soit avec une méthode VMS (Variational Multi-Scale) basée sur un espace sous-grille orthogonal à l'espace EF. Combinées à un modèle grandes déformations basé sur des déformations logarithmiques, ces approches sont d'abord validées sur des cas académiques puis sur des cas industriels. / Simulations in solid mechanics exhibit difficulties as dealing with incompressibility or nonlinearities due to finite strains, constitutive laws and contact. The basic motivation of our work is to propose efficient finite element methods capable of dealing with incompressibility in finite strain context, and using low order elements. Among the approaches in the literature, mixed formulations offer an interesting theoretical framework. In this work, a three-field mixed formulation (displacement, pressure, volumetric strain) is investigated. In some cases, this formulation can be condensed in a two-field formulation. However, it is well-known that the discrete problem given by the Galerkin finite element technique, does not inherit the “inf-sup” stability condition from the continuous problem: the finite elements used, and in particular the interpolation orders must be chosen so as to satisfy this stability condition. However, it is possible to circumvent it, by adding terms stabilizing the FE Galerkin formulation. The latter approach allows the use of equal order interpolation. In this work, stable finite elements of type P2/P1 are used as reference, and compared to a P1/P1 formulation, stabilized with a bubble function, or with a VMS method (Variational Multi-Scale) based on a sub-grid-space orthogonal to the FE space. Combined to a finite strain model based on logarithmic strain, these approaches are first validated on academic cases and then on industrial cases.

The aim of this work is to develop and validate a continuum model for the simulation of the thermomechanical response of a shape memory polymer (SMP). Rather than integral type viscoelastic model, the approach here is based on the idea of two inter-penetrating networks, one which is permanent and the other which is transient together with rate equations for the time evolution of the transient network. We find that the activation stress for network breakage and formation of the material controls the gross features of the response of the model, and exhibits a "thermal Bauschinger effect". The model developed here is similar to a thermoviscoelastic model, and is developed with an eye towards ease of numerical solutions to boundary value problems. The primary hypothesis of this model is that the hysteresis of temperature dependent activation-stress plays a lead role in controlling its main response features. Validation of this hypothesis is carried out for the uniaxial response from the experimental data available in the literature for two different SMP samples: shape memory polyurethane and Veriflex, to show the control of the evolution of the temperature sensitive activation stress on the response. We extend the validated 1D model to a three dimensional small strain continuum SMP model and carry out a systematic parameter optimization method for the identification of the activation stress coefficients, with different weights given to different features of the response to match the parameters with experimental data. A comprehensive parametric study is carried out, that varies each of the model material and loading parameters, and observes their effect on design-relevant response characteristics of the model undergoing a thermomechanical cycle. We develop "response charts" for the response characteristics: shape fixity, shape recovery and maximum stress rise during cooling, to give the designer an idea of how the simultaneous variation of two of the most influential material parameters changes a specific response parameter. To exemplify the efficacy of the model in practical applications, a thermoviscoelastic extension of a beam theory model will be developed. This SMP beam theory will account for activation stress governed inelastic response of a SMP beam. An example of a three point bend test is simulated using the beam theory model. The numerical solution is implemented by using an operator split technique that utilizes an elastic predictor and dissipative corrector. This algorithm is validated by using a three-point bending experiment for three different material cases: elastic, plastic and thermoplastic response. Time step convergence and mesh density convergence studies are carried out for the thermoviscoelastic FEM model. We implement and study this model for a SMP beam undergoing three-point bending strain recovery, stress recovery and cyclic thermomechanical loading. Finally we develop a thermodynamically consistent finite continuum model to simulate the thermomechanical response of SMPs. The SMP is modeled as an isotropic viscoplastic material where thermal changes govern the evolution of the activation stress of the material. The response of the SMP in a thermomechanical cycle is modeled as a combination of a rubbery and a glassy element in series. Using these assumptions, we propose a specific form for the Helmholtz potential and the rate of dissipation. We use the technique of upper triangular decomposition for developing the constitutive equations of the finite strain SMP model. The resulting model is implemented in an ODE solver in MATLAB, and solved for a simple shear problem. We study the response of the SMP model for shear deformation as well as cyclic shear deformation at different initial temperatures. Finally, we implement the thermomechanical cycle under shear deformations and study the behavior of the model.

Ce travail s’inscrit dans le cadre d’un partenariat international Airbus Safran Launchers ", " Ecole Centrale de Lyon " et " Ecole Nationale d’Ingénieurs de Tunis ". Les composés élastomériques sont largement utilisés dans l’industrie pour leurs déformabilité et leurs capacités d’amortissement. Soumis aux combinaisons complexes de fabrication et de charges de service, les élastomères montrent la capacité de subir des conditions de chargement sévères et le cas de pré-déformation statique superposée par une excitation dynamique de petite amplitude est couramment utilisé pour des applications industrielles, par exemple des pneus, des amortisseurs, applications aérospatiales ... Pour concevoir efficacement ces composés industriels, il est primordial de prédire la réponse des produits à travers des processus de modélisation simples qui ont multiplié les méthodes d’analyse: expérimentale, théorique et numérique. Dans ce contexte, le présent travail se concentre sur la conception et l’analyse des propriétés dynamiques d’un dispositif élastomère autour d’une configuration préformée. À cette fin, trois mélanges de caoutchouc ont été expérimentés: Caoutchouc naturel (NR), Bromobutyl (BIIR) et un mélange des deux (NR / BIIR). Une discussion est faite avec préoccupation pour la mise en place expérimentale ainsi que les procédures utilisées pour des essais expérimentaux efficaces. Avec ces conclusions, nous avons fait un jugement sur les capacités de prévision, dans les domaines temporels et fréquentiels, de certains modèles hyper-visco-élastique à base d’intégrale unique sous l’hypothèse de séparabilité des effets temps-déformation. Les modèles considérés sont largement utilisés pour les applications d’ingénierie. Ce travail est suivi d’une application sur un composant industriel. Dans le cadre de cette thèse, le code de calcul d’éléments finis ABAQUS 6.14 a été utilisé pour étudier les propriétés dynamiques de cette structure. Une méthodologie d’analyse a été présentée pour identifier soigneusement l’ensemble des paramètres dans le but de satisfaire certaines exigences industrielles, principalement des capacités de masse, de rigidité et d’amortissement. / This work is conducted as international collaboration with " Airbus Safran Launchers ", " Ecole Centrale de Lyon " and " National Engineering School of Tunis ". Elastomeric compounds are widely used in industry for their high deformability and damping capabilities. Subjected to complex combinations of manufacturing and service loadings, elastomers show the fact to undergo severe loading conditions and the load case of large static predeformation superimposed by small amplitude dynamic excitation is commonly encountred for industrial applications e.g tires, shock-absorbing bushes, construction industry, aerospace applications... To design such industrial compounds efficiently, it is of major importance to predict the response of the products through simple modeling processes which have multiplied analysis methods: experimental, theoretical and numerical. Within this context, the present work focuses on design and analysis of dynamic properties of an elastomeric device at a predeformed configuration. To this end, three rubber mixtures have been experimentally investigated: Natural Rubber (NR), Bromobutyl (BIIR) and a mixture of both (NR/BIIR). A discussion is made with concern to experimental set-up as well as the used procedures for an efficient specimens testings. Within these findings, we made judgement on the predictive capabilities, in time and frequency domains, of some single integral based hyper-visco-elastic models under time-strain seperability assumption. The considered models are widely used for engineering applications and focus have been made on the Simo model implemented in finite element commercial software Abaqus. This work is followed by an application on an industrial component. In the framework of this thesis, the finite element calculation code ABAQUS 6.14 was used to investigate the dynamic properties of such structure. An analysis methodology have been presented to carefully identify the set of parameters with the objective of satisfaction of some industrial requirements mainly mass, stiffness and damping capabilities.

In this thesis a theory for large deformation of plates is presented. Herein aspects of the common 3D-theory for large deformation with the Kirchhoff hypothesis for reducing the dimension from 3D to 2D is combined. Even though the Kirchhoff assumption was developed for small strain and linear material laws, the deformation of thin plates made of isotropic non-linear material was investigated in a numerical experiment. Finally a heavily deformed shell without any change in thickness arises. This way of modeling leads to a two-dimensional strain tensor essentially depending on the first two fundamental forms of the deformed mid surface. Minimizing the resulting deformation energy one ends up with a nonlinear equation system defining the unknown displacement vector U. The aim of this thesis was to apply the incremental Newton technique with a conformal, C^1-continuous finite element discretization. For this the computation of the second derivative of the energy functional is the key difficulty and the most time consuming part of the algorithm. The practicability and fast convergence are demonstrated by different numerical experiments.:1 Introduction 2 The deformation problem in the three-dimensional space 2.1 General differential geometry of deformation in the three-dimensional space 2.2 Equilibrium of forces 2.3 Material laws 2.4 The weak formulation 3 Newton’s method 3.1 The modified Newton algorithm 3.2 Second linearization of the energy functional 4 Differential geometry of shells 4.1 The initial mid surface 4.2 The initial shell 4.3 The plate as an exception of a shell 4.4 Kirchhoff assumption and the deformed shell 4.4.1 Differential geometry of the deformed shell 4.4.2 The Lagrangian strain tensor of the deformed plate 5 Shell energy and boundary conditions 5.1 The resulting Kirchhoff deformation energy 5.2 Boundary conditions 5.3 The resulting weak formulation 6 Newton’s method and implementation 6.1 Newton algorithm 6.2 Finite Element Method (FEM) 6.2.1 Bogner-Fox-Schmidt (BFS) elements 6.2.2 Hsiegh-Clough-Tocher (HCT) elements 6.3 Efficient solution of the linear systems of equation 6.4 Implementation 6.5 Newton’s method and mesh refinement 7 Numerical examples 7.1 Plate deflection 7.1.1 Approximation with FEM using BFS-elements 7.1.2 Approximation with FEM using reduced HCT-elements 7.2 Bending-dominated deformation 7.2.1 Approximation with FEM using BFS-elements 7.2.1.1 1st example: Cylinder 7.2.1.2 2nd example: Cylinder with further rotated edge normals 7.2.1.3 3rd example: Möbiusstrip 7.2.1.4 4th example: Plate with twisted edge 7.2.2 Approximation with FEM using reduced HCT-elements 7.2.2.1 1st example: Partly divided annular octagonal plate 7.2.2.2 2nd example: Divided annulus with rotated edge normals 8 Outlook and open questions Bibliography Notation Theses List of Figures List of Tables

<p dir="ltr">The brain is a dynamic tissue that is passively driven by a combination of the cardiac cycle, respiration, and slow wave oscillations. The function of the brain relies on its ability to maintain a normal homeostatic balance between its mechanical environment and metabolic demands, which can be greatly altered in the cases of neurodegeneration or traumatic brain injury. It has been a challenge in the field to quantify the dynamics of the tissue and cerebrospinal fluid flow in human subjects on a patient-specific basis over the many spatial and temporal scales that it relies upon. Non-invasive imaging tools like structural, functional, and dynamic MRI sequences provide modern researchers with an unprecedented view into the human brain. Our work leverages these sequences by developing novel, open-source pipelines to 1) quantify the biomechanical environment of the brain tissue over 133 functional brain regions, and 2) estimate real-time cerebrospinal fluid velocity from flow artifacts on functional MRI by employing breathing regimens to enhance fluid motion. These pipelines provide a comprehensive view of the macroscale tissue and fluid motion in a given patient. Additionally, we sought to understand how the transmission of macroscale forces, in the context of traumatic brain injury, contribute to neuronal damage by 3) developing a digital twin to simulate 30-200 g-force loading of 2D neuronal cultures and observing the morphological and electrophysiological consequences of these impacts in vitro by our collaborators. Taken together, we believe these works are a steppingstone that will enable future researchers to deeply understand the mechanical contributions that underly clinical neurological outcomes and perhaps lead to the development of earlier diagnostics, which is of dire need in the case of neurodegenerative diseases.</p>

The effective behavior of composite materials is of great interest in materials science. The properties of such a material at the macroscale can be directly coupled to the properties of the material at the microscale. The random distribution of microscopic phases can be simulated using models of stochastic geometry. Random, two-dimensional, two-phase microstructures were constructed by stochastic simulation using the planar Boolean model. An extensive study was conducted to relate the effective hyperelastic material behavior to the stochastic parameters of the Boolean model and the physical parameters of the microstructure. Well-known approaches to determine the size of the representative volume element were adapted for this context and their results were compared.

Optimal control problems for finite-strain elasticity are considered. An inner pressure or an inner fiber tension is acting as a driving force. Such internal forces are typical, for instance, for the motion of heliotropic plants, and for muscle tissue. Non-standard objective functions relevant for elasticity problems are introduced. Optimality conditions are derived on a formal basis, and a limited-memory quasi-Newton algorithm for their solution is formulated in function space. Numerical experiments confirm the expected mesh-independent performance.

Optimal control problems for finite-strain elasticity are considered. An inner pressure or an inner fiber tension is acting as a driving force. Such internal forces are typical, for instance, for the motion of heliotropic plants, and for muscle tissue. Non-standard objective functions relevant for elasticity problems are introduced. Optimality conditions are derived on a formal basis, and a limited-memory quasi-Newton algorithm for their solution is formulated in function space. Numerical experiments confirm the expected mesh-independent performance.

Der Vortrag beschreibt die Grundlagen der Elasto-Plastizität sowie die softwaretechnische Anwendung mit dem FEM-Programm Creo Simulate bzw. Pro/MECHANICA von PTC. Der erste Teil des Vortrages beschreibt die Charakteristika plastischen Verhaltens, unterschiedliche plastische Materialgesetze, Fließkriterien bei mehrachsiger Beanspruchung und unterschiedliche Verfestigungsmodelle. Im zweiten Vortragsteil werden Möglichkeiten und Grenzen der Berechnung elasto-plastischer Probleme mit der Software dargestellt sowie Anwendungstipps gegeben. Im dritten Vortragsteil schließlich werden verschiedene Beispiele vorgestellt, davon besonders ausführlich das Verhalten einer einachsigen elasto-plastischen Zugprobe vor und nach dem Eintreten der Einschnürdehnung. / This presentation describes the basics of elasto-plasticity and its application with the finite element software Creo Simulate (formerly Pro/MECHANICA) from PTC. The first part describes the characteristics of plastic behavior, different plastic material laws, yield criteria for multiaxial stress states and different hardening models. In the second part, the opportunities and limitations of analyzing elasto-plastic problems with the FEM-code are described and user information is provided. The last part finally presents different examples. Deeply treated is the behavior of a uniaxial tensile test specimen before and after elongation with necking appears.