Extending the XFEM approach for fast transient three-dimensional crack propagation in ductile materials

This PhD thesis presents numerical methods is dedicated to three-dimensional crack propagation in the framework of fast explicit structural dynamics using EUROPLEXUS software (currently abbreviated EPX, co-owned by CEA and EC/JRC). An approach based on the well-known XFEM method is proposed, representing the crack through level set functions. Special care is given to the update of the level set functions from the propagation velocity expressed on the crack edge, since the most widely used method based on the solution of Hamilton-Jacobi equations lacks robustness for fast transient crack propagations, even when level-sets are computed on an auxiliary regular finite difference grid. It is therefore chosen instead to implement a 3D approximated geometric method to update both level-sets. As far as failure mechanics is concerned, a local stress criterion on the edge of the crack, first developed by Haboussa et al., gives characteristic parameters of the material fracture. Mechanical equivalent quantities (strain, deformation) around the crack front are weighted by a Gaussian function, which gives more importance to Gauss integration points located near the crack tip. The maximum of the equivalent stress tensor near the crack tip gives the direction of the crack, and the Kanninen equation gives the crack velocity. Besides, because of the discontinuous displacement field, the numerical integration for elements cut by the crack yields performance issues. Increasing the number of quadrature points is CPU time consuming and quite hard to handle if it is chosen to change the number of points only for elements in the vicinity of the crack. Another approach tested here consists in keeping constant the number and position of quadrature points and modifying their weights in cut elements to obtain an accurate integration of several reference discontinuous fields. The proposed methods are tested and validated on significant examples, both two-dimensional, to ensure the backward compatibility with the existing 2D-restricted formalism in EPX, and three-dimensional, to illustrate the new capabilities of the program. (author)