Crack initiation and propagation is an essential aspect in the mechanical behavior of a large variety of materials and structures in all fields of Engineering and, in particular, the prediction of crack trajectories is one of the major challenges of existing numerical methods. Classical procedures to fix crack direction have been based on local criteria such as maximum (tensile) hope stress. However, Fracture Mechanics principles suggest that global criteria should be used instead, such as maximizing structural energy release rates. An emerging trend along this way is based on Configurational Mechanics, which describes a dual version of the mechanical problem in terms of configurational pseudo-stresses, pseudo-forces, etc. all with a physical meaning related to the change in global structural elastic energy caused by changes in the structural geometry (configuration). In the FEM context, these concepts are applied to optimize the total energy of the mesh with respect to reference coordinates using the discrete configurational forces. Configurational stresses given by Eshelby’s energy-momentum tensor may be integrated using standard expressions to give configurational nodal forces. Adequate treatment of these forces in the context of iterative FE calculations, may lead to prediction of crack trajectories in terms of global structural energy.
The paper describes some aspects of the application of XFEM to represent Geomechanical discontinuities, including the choice of additional nodal variables and the appearance and remedies to the oscillations that may take place depending on the mesh layout. An example of application to recover the stresses along a discontinuity line emanating from a tunnel cross-section is presented together with the comparison to an analytical solution. The formulation is developed in terms of the “overhang” displacement variables on the other side of the discontinuity (instead of more traditional displacement jump variables), and the oscillations associated to nodes too close to the discontinuity are solved by moving those nodes onto the discontinuity (instead of moving them away as seems more common in current practice).