Adaptive hierarchical refinement of NURBS in cohesive fracture analysis

Adaptive hierarchical refinement in isogeometric analysis is developed to model cohesive crack propagation along a prescribed interface. In the analysis, the crack is introduced by knot insertion in the NURBS basis, which yields C-1 continuous basis functions. To capture the stress state smoothly ahead of the crack tip, the hierarchical refinement of the spline basis functions is used starting from a coarse initial mesh. A multilevel mesh is constructed, with a fine mesh used for quantifying the stresses ahead of the crack tip, knot insertion to insert the crack, and coarsening in the wake of the crack tip, since a lower resolution suffices there. This technique can be interpreted as a moving mesh around the crack tip. To ensure compatibility with existing finite element programs, an element-wise point of view is adopted using Bezier extraction. A detailed description is given how the approach can be implemented in a finite element data structure. The accuracy of the approach to cohesive fracture modelling is demonstrated by several numerical examples, including a double cantilever beam, an L-shaped specimen, and a fibre embedded in an epoxy matrix.