This thesis is a summary of my research works at the MSM department of the University of Liège since 1989. These research works are devoted to the numerical simulation of the three-dimensional sheet metal forming processes by the finite element method. Several research areas, including the finite element modelling, the time-integration technique of material constitutive laws and the 3D contact treatments are covered. The theoretical methodologies, the numerical implementation and industrial applications will be presented. The thesis begins with a brief overview made in chapter 1. In chapter 2, a 8-node mixed brick element based on the HU-WASHIZU variational principle is developed (JET3D element). Special attention is paid to avoid hourglass modes as well as locking phenomena, including "shear locking" and "volumetric locking" in nonlinear analysis. Numerical examples are used at the end of this chapter to assess the performance and applicability of this element. In chapter 3, a 3D four-node shallow element, which was originally developed by Ph. JETTEUR and then has been improved by him and his co-workers, is recalled (COQJ4 element). Special care is taken to the finite rotation problems and a new formulation for the finite rotation is developed. An example is used at the end of the chapter to show the performance of the proposed formulation for the finite rotation problems. A special contact element is developed for the shell element in chapter 4. In this chapter, some basics aspects of numerical tretments of contact problem are discussed and some attentions are paid to the contact searching algorithms, which has proved to be very important in 3D cases. In chapter 5, the appropriate constitutive equations are examined together with the techniques of time-integration and the evaluation of the tangent stiffness matrix. Much attention is paid to the implicit integration methods, which have proved to be very efficient for large increments of deformation. Finally, in chapter 6, two benchmark tests are used as validation of the code. Special attention is paid to the possibility of using dynamic explicit procedure in the numerical simulation of sheet metal forming, although it is often characterised as a quasi-static process. All the developments made in the thesis have been implemented into the finite element code LAGAMINE developed since 1982 at the MSM department of the University of Liège.

This study aims at the description, modelling and numerical prediction of ductile fracture in inelastic solids undergoing thermomechanical static or dynamic loading. Several research areas of contemporary interest in computer analysis of solids and structures are covered. The theoretical methodologies, computer implementations and practical applications will be treated. This thesis summarizes my recent research works since 1989 at the MSM Department of the University of Liège. However, it should also be useful to those who are interested in the most recent developments in finite element methods and in applying these techniques to the analysis of real industrial problems. Numerous references to original sources are included. For the convenience of the reader, each chapter of the thesis is designed to be self-contained, starts with a summary of the topic addressed, and finishes with an outline of the main results presented. Numerical examples are organized at the end of chapter 2 to 8 to assess the performance and applicability of the proposed mechanical and finite element models developed in each of them. Hereafter, a brief overview of the thesis is given. After a brief introduction in chapter 1, the numerical tools that are necessary to perform large strain thermomechanical static or dynamic analysis of solids are presented. In chapter 2, a general strategy for nonlinear dynamic finite element formulation is presented, including explicit and implicit time integration schemes. A special emphasis is placed on the application of high-speed metalforming and frictional contact-impact problems. Chapter 3 describes a strategy for solving problems involving transient thermal and thermomechanical analysis. A class of unified and mixed solid, thermal and coupled thermomechanical finite elements by assumed strain method is developed in chapter 4. Special care is taken to hourglass ans locking control. Once these developments are validated and their efficiency tested, it is then possible to tackle the problem of ductile fracture prediction and propagation. In chapter 5, a bibliographic research on the "local approach of ductile fracture" is presented. The implementation of six fracture criteria into various constitutive laws for predicting fracture initiation sites is also shown. A fully coupled elasto(-visco)-plastic damage model for isotropic material is developed in chapter 6. This model is based on irreversible thermodynamics theory and on the energy equivalence hypothesis. Chapter 7 presents the theoretical and experimental comparison for isotropic ductile material at fracture. Finally in chapter 8, the isotropic damage model of chapter 6 is extended to the case of anisotropic solids in which the damage growth itself is also anisotropic. The above developments have been implemented to an existing finite element code LAGAMINE developed since 1982 at the MSM Department of the University of Liège and are applied to many real engineering problems such as high speed rolling, magnetoforming, impact upsetting, dynamic forging, deep drawing of axisymmetric ans square cups, hot upsetting, warm folding of 3D sheet, non-isothermal hemispherical punch stretching, and other contact-impact examples.

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Les objectifs principaux de la géomodélisation sont la représentation et la compréhension du sous-sol. Les structures géologiques ont un rôle important pour comprendre et prédire son comportement physique. Nous avons défini un modèle géologique comme étant composé d'un ensemble de structures et de leurs connexions. Les maillages sont des supports numériques servant à résoudre les équations modélisant la physique du sous-sol. Il est donc important de construire un maillage représentant un modèle géologique afin de prendre en compte l'impact de ces structures dans les phénomènes du sous-sol. L'objectif de cette thèse est de développer des méthodes de maillage volumique pour les modèles géologiques. Nous proposons une méthode de génération de maillages non structurés volumiques permettant de construire deux types de maillages : un maillage tétraédrique et un maillage hex-dominant (c'est-à-dire composé de tétraèdres, prismes à base triangulaire, pyramides à base quadrilatérale et hexaèdres). Cette méthode génère dans un premier temps un maillage tétraédrique qui peut respecter différents types de données : (1) un modèle géologique défini par frontières afin de capturer les structures dans le maillage volumique, (2) des trajectoires de puits représentées par un ensemble de segments, (3) une propriété de taille d'éléments afin de contrôler la longueur des arêtes des éléments et (4) un champ de directions pour contrôler des alignements de sommets/éléments dans le maillage afin de favoriser certaines caractéristiques comme des éléments possédant des angles droits. Dans un deuxième temps, ce maillage tétraédrique peut être transformé en un maillage multi-éléments. La méthode reconnaît des relations combinatoires entre tétraèdres permettant l'identification de nouveaux éléments comme les prismes, les pyramides et les hexaèdres. Cette méthode est ensuite utilisée pour générer des maillages aux caractéristiques spécifiques correspondant à une application donnée afin de limiter les erreurs lors du calcul numérique. Plusieurs domaines d'applications sont considérés tels que les simulations géomécaniques, d'écoulements et de propagation d'ondes sismiques. / The geomodeling main goals are to represent and understand the subsurface. The geological structures have an important role for understanding and predicting its physical behavior. We defined a geological model as a set of structures and their connections. The meshes are numerical supports to solve the equations modeling the subsurface physics. So it is important to build a mesh representing a geological model to take into account the impact of these structures on the subsurface phenomena. The objective of this thesis is to develop volumetric meshing methods for geological models. We propose a volumetric unstructured meshing method to build two mesh types: an adaptive tetrahedral mesh and an hex-dominant mesh (i.e. made of tetrahedra, triangular prisms, quadrilateral pyramids and hexahedra). This method generates first a tetrahedral mesh that can respect different types of data: (1) a geological model defined by its boundaries to capture the structures in the volumetric mesh, (2) well paths represented as a set of segments, (3) a mesh size property to control the mesh element edge length and (4) a direction field to control vertex/element alignments inside the mesh to increase some features such as elements with right angles. Then, this tetrahedral mesh can be transformed in a mixed-element mesh. The method recognizes combinatorial relationships between tetrahedra to identify new elements such as prisms, pyramids and hexahedra. This method is then used to generate meshes whose features correspond to a given application in order to reduce errors during numerical computation. Several application domains are considered such as geomechanical, ow and wave propagation simulations.