Multi-cracking with junction and contact using X-FEM

by D. Colombo, IFPEN

This work has been realized under a collaboration with IFPEN and École Centrale de Nantes

The MODI_MODELE_XFEM command allows to introduce several cracks into an X-FEM model. The keyword JONCTION in the DEFI_FISS_XFEM command allows also to model a specific enrichment to model the kinematics in case of branched cracks (see Intersections and crack branching with X-FEM). It is now possible to use this functionality with contact (see reference). Two application examples are shown.

The first example is a finite plate with multiple cracks for which stress intensity factors are compared to those obtained by a given semi-analytical reference solution on each crack point.
The mesh and cracks are shown in figure 1. Cracks are introduced with X-FEM and the mesh is refined using the macro-command RAFF_XFEM and MACR_ADAP_MAIL.

Figure 1 : Initial mesh with the cracks (left) and adaptive mesh obtained using RAFF_XFEM (right).

A first computation without contact is performed to validate the approach by comparing the results to those given by the reference solution. A second computation with contact shows differences on some points. These differences are explained by the strain obtained in figure 2 where the interpenetrations without contact are corrected when contact is taken into account.

Figure 2 : Strain with an offset of 1000 (right), zoom without and with contact (right).

To quantify the deviations, the propagation velocities with and without contact are computed for each point by using a Paris’s law. Velocities are plotted on figure 3. A difference appear for point B. Indeed it is noticeable that for this point, as seen on the right hand side of figure 2, taking into account contact changes the corresponding crack opening and propagation direction.

Figure 3 : Propagation directions with contact (blue) and without contact (red).

The second example in 3D is a geologic case where contact is modeled for each of the 3 faults of figure 4 in large sliding X-FEM (keyword NB_ITER_GEOM > 1 in the DEFI_CONTACT operator). The F1 fault cuts the whole domain. The F2 fault branches on F1, and the F3 fault branches on F1 and F2. The strain in extension is presented in figure 5.

Figure 4 : Initial mesh of the structure and fault surfaces.

Figure 5 : Strain obtained in extension.

Reference :
M. Siavelis, M. Guiton, P. Massin, N. Moës. Large sliding contact along branched discontinuities with X-FEM, 2012, Comput Mech, DOI 10.1007/s00466-012-0807-6