Crack propagation with the extended finite element method and a hybrid explicit–implicit crack description

Abstract

SUMMARYA method for two-dimensional and three-dimensional crack propagation that combines the advantages of explicit and implicit crack descriptions is presented. An implicit description in the frame of the level set method is advantageous for the simulation within the extended finite element method (XFEM). The XFEM has proven its potential in fracture mechanics as it provides accurate solutions without any remeshing during the crack simulation. On the other hand, an explicit representation of the crack, for example, by means of a polyhedron, enables a simple update of the crack during the propagation. A key aspect in the proposed method is the introduction of three level set functions that are computed exactly from the explicit representation. These functions imply a coordinate system at the crack front and serve as a basis for the enrichment. Furthermore, a simple model for the crack propagation is presented. One of the biggest achievements of the proposed method is that two-dimensional and three-dimensional crack simulations are treated in a consistent manner. That is, the extension from two to three dimensions is truly straightforward.

Isogeometric boundary element methods for three dimensional static fracture and fatigue crack growth

“…Chopp and Sukumar [91] proposed the fast marching method to update the crack front, thus facilitating the process of updating the crack surface [29]. Fries and Baydoun [92] proposed an implicit-explicit method, in which the level set represented crack is explicitly discretized by triangular facets. Analogous idea is the vector level set method [35].…”

Poro-elasto-plastic modeling of complex hydraulic fracture propagation: simultaneous multi-fracturing and producing well interference

“…The displacement vector u can be approximated with the partition of unity enrichment [33]: (9) where ( ) are the usual nodal shape functions, which have a value of 1 at the node whose number it bears and zero at all other nodes.…”

3D Ductile crack propagation with the XFEM

“…A Detailed description of this method can be found in reference [5]. The algorithm for tracking the crack during it's evolution follows a concept similar to [6]. Since our model is defined in an inelastic finite deformation framework the classical criterion of crack propagation can't be applied here.…”

“…A remedy for this is the modeling of cracks with the eXtended Finite Element Method (XFEM) nearly independent of the mesh. Here the three dimensional extension of the corrected XFEM [5] is used in combination with the crack propagation algorithm proposed in [6] and [7]. In consequence of the aforementioned reason we use the non-local damage model to predict the nucleation an growth of voids and use a discrete crack representation with damage based propagation criterion for evolving fracture.…”