SUMMARYThe extended finite element method (X-FEM) has been developed to minimize requirements on the mesh design in a problem with a displacement discontinuity. This advantage, however, still remains limited to the small deformation hypothesis when considering sliding discontinuities. The approach presented in this paper proposes to couple X-FEM with a Lagrangian large sliding frictionless contact algorithm. A new hybrid X-FEM contact element was developed with a contact search algorithm allowing for an update of contacting surfaces pairing. The stability of the contact formulation is ensured by an algorithm for fulfilling Ladyzhenskaya-Babuska-Brezzi (LBB) condition. Several 2D simple examples are presented in this paper in order to prove its efficiency and stability.

This paper presents a 3D non-locking contact approach, within the eXtended Finite Element Method (X-FEM) framework. X-FEM allows one to introduce interface independently of the mesh. The contact problem on the interface leads to an Augmented Lagrangian formulation derived from the discretization of its continuous formulation. It is shown that a simple choice of the Lagrange multiplier space is not suitable and leads to contact pressure oscillations. An algorithm for the restriction of the Lagrange multiplier approximation space is proposed to stabilize the formulation. The stability of the mixed displacement-contact pressure formulation is discussed in terms of convergence of the energy error. Numerical examples performed with the Finite Element software Code_Aster illustrate this approach while solving three-dimensional problems with contact. RÉSUMÉ. Cet article présente une formulation stabilisée pour les problèmes de contact en 3D, dans le cadre de la méthode des éléments finis étendue (X-FEM), méthode qui autorise des interfaces indépendantes du maillage. Pour la formulation du problème de contact sur l'interface, nous utilisons un Lagrangien Augmenté, qui dérive de la discrétisation du problème de contact écrit sous sa forme continue. Nous montrons qu'un choix simple de l'espace des multiplicateurs de Lagrange n'est pas satisfaisant car cela conduit à des oscillations des pressions de contact. Un algorithme de restriction de l'espace d'approximation des multiplicateurs de Lagrange est proposé afin de stabiliser la formulation. La stabilité de la formulation mixte (déplacement-pression de contact) est démontrée à l'aide des taux de convergence des erreurs. Des exemples numériques réalisés avec le logiciel éléments finis Code_Aster illustrent cette approche pour la résolution de problèmes tridimensionnels avec contact.

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Companies exploiting industrial installations are currently submitted to various constraints in the context of maintenance and lifecycle problem analysis: time and cost of production stops, efficiency of maintenance solutions, production safety criteria, etc. Hence, the reduction of the time of projects may lead to important research perspectives in terms of fast numerical prototyping and solution assessment methods. In this paper, we present a typical industrial problem of fast assessment of mechanical state of a production installation. We focused on the study of a cracked component of a reheater as well as we proposed a new design for this component to improve its mechanical behavior under an exceptional overload. In order to reduce the operational study time, the Extended Finite Element Method (X-FEM) has been used to model non-linear crack phenomenon without any human modification of a complex 3D model on the level of geometric model and mesh. An alternative design of a damageable element has been proposed to avoid all risk of possible cracking. This design task requires a mechanical analysis of locally modified structure under a cyclic loading. We also present a new prototyping method based on direct modification of meshes and allowing reducing the time of numerical study.