Accurate simulation of mixed-mode cohesive crack propagation in quasi-brittle structures using exact asymptotic fields in XFEM: an overview

The extended finite element (XFEM) enriches the standard local FE approximations with known information about the problem, with the use of the partition of unity. This allows the use of meshes that do not conform to a discontinuity and avoids adaptive re-meshing as the discontinuity grows as required with the conventional FEM. When the crack tip asymptotic field is available and used as the enrichment function, XFEM is more accurate than FEM allowing the use of a much coarser mesh around the crack tip. Such asymptotic fields have been known for a long time for traction-free cracks (the Williams expansions) but have only recently been derived for cohesive cracks (Karihaloo–Xiao expansions). In this paper an overview of latter expansions is given for a range of cohesive laws and their usefulness in the simulation of cohesive crack propagation is demonstrated on two examples of concrete and fibre-reinforced concrete flexural members.