Dynamic fracture simulations using the scaled boundary finite element method on hybrid polygon–quadtree meshes

• Develop a framework based on the scaled boundary finite element method for hybrid polygon–quadtree discretisations.
• Incompatibility between adjacent cells due to hanging nodes is eliminated by treating the cell as polygon and hence no special integration rule required.
• Crack tip singularity is modelled semi-analytically.
• Propose a simple remeshing algorithm that combines the quadtree decomposition with Boolean operations.
• Dynamic stress intensity factors can be directly extracted from their definition.

In this paper, we present an efficient computational procedure to model dynamic fracture within the framework of the scaled boundary finite element method (SBFEM). A quadtree data structure is used to discretise the domain, and 2:1 ratio between the cells is maintained. This limits the number of patterns in the quadtree decomposition and allows for efficient computation of the system matrices. The regions close to the boundary are discretised with arbitrary sided polygons so as to facilitate accurate modelling of the curved boundaries. The stiffness and the mass matrix over all the cells are computed by the SBFEM. Moreover, the semi-analytical nature of the SBFEM enables accurate modelling of the asymptotic stress fields in the vicinity of the crack tip. An efficient remeshing algorithm that combines the quadtree decomposition with simple Boolean operations is proposed to model the crack propagation. The remeshing is restricted only to a small region in the vicinity of the crack tip. The efficiency and the convergence properties of the proposed framework are demonstrated with a few benchmark problems.