A novel hybrid approach for level set characterization and tracking of non-planar 3D cracks in the extended finite element method

Abstract

In this paper, the limitations associated with implicit and explicit representations of cracks in the extended finite element method (XFEM) is recapitulated via numerical explorations followed by the development of a novel hybrid approach for the characterization of non-planar 3D cracks along with its capability demonstration. In the XFEM, the crack geometry is independent of the structural mesh, and is often described implicitly by means of two level set functions. The implicit representation is very convenient for purposes of computing the crack front velocity and for handling situations where the crack front is concave and the velocity vectors may cross. The main difficulty of this implicit description is the formulation of an efficient and robust update scheme for the level set values after a propagation step. On the other hand, the crack geometry can be described by an explicit triangulated mesh which can be easily updated after a propagation step. The explicit representation has its own shortcomings, e.g., difficulties in handling crack overlaps and extraction of crack local coordinates. Given the difficulties associated with the use of either implicit or explicit method for the geometric description of complex crack geometry, a novel hybrid method is developed by a combination of an implicit level set representation of the crack and an explicit triangulated mesh representation. In the hybrid approach, the implicit representation is updated after each propagation step and disconnected crack surfaces are removed using a paint-fill algorithm based on the current explicit representation of the crack. Then, an updated explicit representation is constructed based on the updated implicit representation using the marching cubes algorithm. Finally, the implicit representation is rebuilt from the explicit representation. The use of the explicit representation ensures that the data in the level set representation is generated from a consistent crack description. The effectiveness of the developed hybrid approach is demonstrated by analyzing several 3D crack propagation problems including a quarter-circular crack in a complex helicopter component, a U-shaped crack and an inclined elliptical crack in cuboids, and an inclined edge crack in a three-point bending beam.