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 math formula 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 multi-level mesh is constructed, with a fine mesh used for quantifying the stresses ahead of the crack tip, and 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 Bézier 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. This article is protected by copyright. All rights reserved.