Adaptation of quadtree meshes in the scaled boundary finite element method for crack propagation modelling

• The SBFEM is combined with quadtree meshes for fracture modelling.
• The quadtree structure leads to rapid mesh generation and stiffness computations.
• The SBFEM accurately models the asymptotic stress field at the crack tip.
• Crack evolution is conveniently modelled by splitting quadtree cells.
• The developed approach is accurate and efficient for crack propagation problems.

A crack propagation modelling technique combining the scaled boundary finite element method and quadtree meshes is developed. This technique automatically satisfies the compatibility requirement between adjacent quadtree cells irrespective of the presence of hanging nodes. The quadtree structure facilitates efficient data storage and rapid computations. Only a single cell is required to accurately model the stress field near crack tips. Crack growth is modelled by splitting the cells in the mesh into two. The resulting polygons are directly modelled by the scaled boundary formulation with minimal changes to the mesh. Four numerical examples demonstrate the salient features of the technique.