The resolution of many nonlinear solid mechanical problems with the Finite Elements Method requires remeshing when very large deformations occur. The remeshing operation is divided into two parts: the generation of the new mesh and the data transfer from the old to the new mesh. In dynamic plasticity problems, two kinds of fields have to be transferred: the first is defined thanks to the nodal values and the second one is defined at the integration points. These two kinds of fields are transferred thanks to an original computation of the Data Transfer Method based on the Finite Volume Elements. This method is compared to another one using Mortar Elements to solve metal forming problems.

Le contact mécanique est le problème de mécanique des solides qui présente les non-linéarités les plus difficiles à prendre en compte. La bonne résolution numérique de ce problème est fortement perturbée par la non-linéarité et la non-différentiabilité des équations régissant le contact mécanique frottant (collement-décollement et amorce du glissement). Encore aujourd'hui, il n'existe pas de méthode permettant de résoudre le problème de contact frottant de manière universelle. Ce travail porte donc sur l'élaboration de méthodes permettant de résoudre le plus grand nombre de types de problème de contact frottant. II peut être décomposé en deux parties. La première partie porte sur la formation du système d'équations et l'algorithme de résolution. Les méthodes les plus utilisées sont celles de pénalisation et du lagrangien augmenté. Bien que très simples, ces méthodes sont assez difficiles à utiliser en raison de la difficulté d'identification des valeurs des coefficients de pénalisation (normale et tangentielle). Afin de pallier les carences de ces méthodes, une nouvelle approche est proposée, celle dite du « lagrangien augmenté adapté ». Cette nouvelle méthode est basée sur celle du lagrangien augmenté jumelée à une adaptation de la pénalité. Elle présente l'avantage de ne plus obliger l'utilisateur à choisir des coefficients de pénalisation. De plus, elle cumule la rapidité de l'adaptation de la pénalité et la fiabilité de la méthode du lagrangien augmenté. La deuxième partie porte sur la prise en compte du contact sous une discrétisation spatiale. La méthode la plus utilisée est la méthode « point-surface ». Le contact est calculé pour chacun des points d'une des surfaces avec l'autre surface. Cette méthode présente de nombreuses limites, notamment au niveau de la représentativité et de la régularité de la solution lorsque les deux surfaces sont déformables et irrégulières. Une autre méthode fait l'objet d'intense recherche, la méthode « surface-surface »basée sur les éléments joints. Le contact est calculé pour chaque noeud d'une des surface en fonction des deux surfaces ce qui rend la solution plus régulière et plus représentative. Cependant, les complications induites par cette méthode ne permettent pas de résoudre les problèmes en trois dimensions. Une variante de cette méthode est donc présentée afin de pouvoir être utilisée pour les problèmes en deux ou trois dimensions. Toutes ces méthodes sont testées sur des problèmes académiques simples et également sur des problèmes industriels multiphysiques.

This work deals with the numerical simulation and material flow visualization of Friction Stir Welding (FSW) processes. The fourth order Runge- Kutta (RK4) integration method is used for the computation of particle trajectories. The particle tracing method is used to study the effect of input process parameters and pin shapes on the weld quality. The results show that the proposed method is suitable for the optimization of the FSW process.

In many cases, the numerical computation of mechanical problem with Finite Element Method has to transfer some information between two different meshes. For example, if a remeshing is needed or if several meshes are used (e.g. one for a thermal problem and another one for a mechanical problem). In spite of the research on the Transfer Methods, none of them has been so far clearly established as the best. Each method has advantages and disadvantages. Many problems can happen during the field transfer, like the minimization of the numerical diffusion, the value of the field on the boundaries, etc. This paper compares on the one hand the performances of the Field Transfer Method by classical interpolation with on the other hand one using Mortar Elements. The comparison of the two methods is based on two indicators: the numerical diffusion and the evaluation of the field on the boundaries. In this paper, only the continuous fields are considered.

The aim of this work is to propose a new numerical method for solving the mechanical frictional contact problem in the general case of multi-bodies in a three dimensional space. This method is called adapted augmented Lagrangian method (AALM) and can be used in a multi-physical context (like thermo-electro-mechanical fields problems). This paper presents this new method and its advantages over other classical methods such as penalty method (PM), adapted penalty method (APM) and, augmented Lagrangian method (ALM). In addition, the efficiency and the reliability of the AALM are proved with some academic problems and an industrial thermo-electromechanical problem.

In this contribution, one proposes a new strategy to model forming processes involving non-linear phenomena. The contact between the tool and the structure is enforced using a penalty approach. To free the user from the strict conforming between the structure and the mesh boundaries, one uses the level set and the extended finite element method for material/void interfaces. However, even if the finite element mesh does not need to conform with the boundaries, it still deforms with the structure. Then, an Arbitrary Lagrangian Eulerian formulation is introduced to relocate the mesh in its initial configuration and avoid distortions. From a user point of view, the whole calculation is then performed on a fixed Eulerian mesh.

Cet article présente une nouvelle méthode de résolution du problème de contact mécanique frottant, celle du lagrangien augmenté adapté. Contrairement aux méthodes les plus utilisées (pénalisation et lagrangien augmenté), l’utilisateur ne doit pas déterminer les valeurs des coefficients de pénalisation. Cette méthode est performante aussi bien avec des matériaux élastiques qu’élasto-plastiques. Le problème de Hertz est présenté. Cette méthode est au si utilisée dans le contexte multi-physique.

In nonlinear solid Mechanics, the Arbitrary Lagrangian Eulerian (ALE) formalism is a common way to avoid mesh distortion when very large deformations occur in the modelled process. Usually, the ALE resolution procedure is based on an “operator split”, the second part of which is a Data Transfer between two meshes sharing the same topology (same number of nodes and same number of element neighbours for each of them). Thanks to this interesting property, classical ALE transfer algorithms can bemuchmore optimised in terms of CPU time than the ones that are used in the frame of a complete remeshing. However, the resulting CPU-efficient transfer schemes suffer from two main drawbacks. The first one is a spurious crosswind diffusion coming from the corner fluxes that have been neglected. The second issue is the number of explicit transfer steps which may become very large when the element size decreases. In this paper, these classical ALE Data Transfer methods are compared to more general algorithms which do not make any assumption on the topology of both meshes.

Friction stir welding (FSW) process is a solid‐state joining process during which materials to be joined are not melted. As a consequence, the heat‐affected zone is smaller and the quality of the weld is better with respect to more classical welding processes. Because of extremely high strains in the neighborhood of the tool, classical numerical simulation techniques have to be extended in order to track the correct material deformations. The Arbitrary Lagrangian–Eulerian (ALE) formulation is used to preserve a good mesh quality throughout the computation. With this formulation, the mesh displacement is independent from the material displacement. Moreover, some advanced numerical techniques such as remeshing or a special computation of transition interface is needed to take into account non‐cylindrical tools. During the FSW process, the behavior of the material in the neighborhood of the tool is at the interface between solid mechanics and fluid mechanics. Consequently, a numerical model of the FSW process based on a solid formulation is compared to another one based on a fluid formulation. It is shown that these two formulations essentially deliver the same results in terms of pressures and temperatures.

Many problems solved with the finite element method require more than one mesh (i.e. one specific mesh for each Physic or a remeshing is needed). The Data Transfer Method used, has a great importance in the capacity to solve the problem and in the reliability of the solution. In general, the data is composed of two kinds of fields (defined thanks to the nodal values or at the integration points). In this paper, the more used Data Transfer Method is compared with the Data Transfer Methods based on a Weak Form (using Mortar Element or Finite Volume).

This paper deals with data transfer between two meshes as it happens in a finite element context when a remeshing has to be performed. We propose a finite-volume-based data transfer method for an efficient remeshing of three-dimensional solid mechanics problems. The originality of this transfer method stems from a linear reconstruction of the fields to be transferred on an auxiliary finite volume mesh, a fast computation of the transfer operator and the application to the complete remeshing of 3D problems. This procedure is applicable to both nodal values and discrete fields defined at quadrature points. In addition, a data transfer method using mortar elements is presented. The main improvement made to this second method comes from a fast computation of mortar elements. These two data transfer methods are compared with the simplest transfer method, which consists of a classical interpolation. After some academic examples, we present 2D forging and 3D friction stir welding applications.

Friction Stir Welding (FSW) process is a solid-state joining process during which materials to be joined are not melted. As a consequence, the heat-affected zone is smaller and the quality of the weld is better with respect to more classical welding processes. Because of extremely high strains in the neighbourhood of the tool, classical numerical simulation techniques have to be extended in order to track the correct material deformations. The Arbitrary Lagrangian Eulerian (ALE) formulation is used to preserve a good mesh quality throughout the computation. With this formulation the mesh displacement is independent from the material displacement. Moreover, some advanced numerical techniques such as remeshing or a special computation of transition interface is needed to take into account non-cylindrical tools. During the FSW process, the behaviour of the material in the neighbourhood of the tool is at the interface between solid mechanics and fluid mechanics. Consequently, a numerical model of the FSW process based on a solid formulation is compared to another one based on a fluid formulation. It is shown that these two formulations essentially deliver the same results in terms of pressures and temperatures.

One of the most widely used cutting techniques in sheet metal forming processes for mass production is the blanking process. In this process, a metallic sheet is placed between a die and a blankholder, and is then cut by the action of a punch which moves downward. The quality of the final product is directly linked to the resulting shape of the cut edge. Due to the complexity of the separation step, the set-up of the blanking process in practice is often driven by empirical knowledge. Thus, an accurate numerical tool is extremely desirable to optimize the setting parameters of this technique and will lead to a better understanding of the entire process. The numerical approach must be able to deal with three main issues involved in blanking: large and localized deformation, friction and contact, and ductile fracture. Furthermore, due to requirements of mass production the punch velocity is normally high and the effects of the strain rate must also be considered. Several approaches have been developed in order to model this cutting process but its accuracy still presents some numerical challenges.