Crack Propagation Modeling with Scaled Boundary Polygons

Abstract

Crack propagation is modelled using scaled boundary polygons. The polygons discretise the computational domain and can be of any number of sides, leading to more flexible mesh generation. The scaled boundary finite element method is used to construct shape functions of the polygon elements. These shape functions form a partition of unity and are linearly complete. They can accurately model any kind of stress singularity without local mesh refinement or asymptotic enrichment functions. The scaled boundary shape functions enable the method to be further developed to model the response of heterogeneous and nonlinear materials. As the polygons can be of any number of sides, simple re-meshing algorithms can be devised to model crack propagation. Two numerical benchmarks are modeled to illustrate the salient features of the scaled boundary polygons.