Generalities
===========


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    During an X- FEM calculation, since the information concerning the crack is not contained in the mesh, it is necessary to store it in a specific data structure (SD). Then, the enrichment of the elements leads to new finite elements, some of which characteristics will be stored in the model. Then, if the contact is defined on the lips of the crack, a contact charge is then created, which contains information specific to X- FEM. During the resolution of the contact problem a specific SD is created and then destroyed during the execution of STAT_NON_LINE. Thus, the objects relating to the X- FEM method are divided into 4 different SDs: sd_fiss_xfem, model, load, and SD created during the resolution of the touch-friction problem. The SD defining the contact load, produced by DEFI_CONTACT, is fully described in [:ref:`D4.06.14 <D4.06.14>`]. The objects of this SD specific to the formulation X- FEM are described in [:external:ref:`D4.06.14, §8 <D4.06.14, §8>`]. The three other SDs are the subject of the three main parts of this document.


    An object of type sd_fiss_xfemdescribes a crack contained in a 2D or 3D mesh, without this mesh necessarily conforming to the geometry of the crack. The sd_fiss_xfem data structure contains the description of the crack through level sets, the associated local databases, data related to the enrichment of finite elements around the crack, topological information concerning the sub-distribution of enriched finite elements, and data related to the contact between the lips of the crack. In addition, this structure is enriched by the addition of data necessary for the propagation of the crack.


    The enriched model makes it possible to globalize local information at each crack in the global mesh. It also contains information about cracks in the model. This document only describes model objects that are specific to X- FEM (for the description of the sd_model, see [:ref:`D4.06.02 <D4.06.02>`]).


    If contact is defined on the lips, the contact SD contains information specific to X- FEM, in particular concerning the algorithm for constructing Lagrange multipliers to satisfy condition LBB: lists of relationships to be imposed,... This document only describes contact objects specific to X- FEM and stored in the sd_model or in the SD created during contact resolution (for the description of SDs related to contact friction, see [:ref:`D4.06.14 <D4.06.14>`]).