by S. Géniaut, EDF R&D/ AMA
In collaboration with IFPEN and École Centrale de Nantes, the PHD theses of M. Siavelis focused on the development of crack intersections and crack branching with X-FEM.
Conventionally, each crack is represented by a pair of "level sets" functions. A graph of intersection is then defined in order to determine for each intersection a "master" crack and a "slave" crack. The finite elements which are cut by several cracks (i.e. several discontinuities) are enriched with a Heaviside function associated with each crack. A further enrichment, of Junction type, must also be defined.
This feature can be also coupled to crack propagation (see Propagation de fissures avec la méthode X-FEM and 3D crack propagation : X-FEM and mesh adaptation). In the illustration below, we consider a plate with two cracks. Tensile loading is applied on the left face and the right face. Here is the simulation of the propagation of the two cracks due to fatigue with constant amplitude. The vertical crack propagates in a straight line and just plug into the horizontal crack, which did not really propagate, because the more weakly charged. After intersection, the horizontal crack is then subjected to Mode I+II, which causes the bifurcation, until the complete failure of the structure.