A fully discrete scaled boundary approach to simulate crack propagation problems on adaptively refined hybrid quadtree meshes

• A quarter-point crack tip element accurately resolves stress singularities. • Near-field crack behavior is captured within the isoparametric framework. • Fracture parameters are computed directly, eliminating stress recovery steps. • Polygonal isoparametric elements enable flexible and robust discretization. • Adaptive remeshing on hybrid quadtree meshes ensures efficiency and accuracy. Fracture mechanics analysis is crucial in component design to predict crack initiation and growth. The resulting crack tip induces a singular stress field, making numerical simulations rather demanding. As a result, accurate crack modeling requires careful consideration of the underlying physical phenomena. Quarter-point elements provide an efficient approach for modelling complex stress fields in the vicinity of crack tips. Additionally, they accurately capture the physical behaviour of cracked structures, since important fracture variables, such as stress intensity factors (SIFs), can directly be determined from their displacement field without any stress recovery procedures. This contribution introduces a quarter-point technique for the crack tip element that adopts the scaling approach from the boundary finite element method (SBFEM). The remaining mesh consists of polygonal elements that are discretized using the isoparametric concept based on a novel set of shape functions which are constructed with SBFEM equations, resulting in higher interpolation orders in radial direction. By using different interpolation functions in scaling and in circumferential directions, the crack tip element can be efficiently coupled to its surrounding linear neighboring edges without the need of cumbersome coupling methods. In contrast to classical SBFEM crack tip elements, the eigenvalue problem does not need to be solved, which improves the computational efficiency. The arbitrariness of polygonal shapes allows for the use of hybrid quadtree meshes without the need of hanging node treatment. In order to increase the resolution of the near-tip mesh sizes, an automatic refinement procedure is adapted, thereby significantly reducing computational durations.