Nonlocal damage modelling by the scaled boundary finite element method

The progressive damage of structures is fruitfully simulated by using the semi-analytical scaled boundary finite element method (SBFEM). The integral-type nonlocal model combined with the isotropic damage model is extended to eliminate the mesh sensitivity concerning the strain localization. An automatic and efficient quadtree mesh generation algorithm is employed to refine the localized damage process zone (DPZ) and reduce the number of degrees of freedom (DOFs). Owing to the salient advantage of the SBFEM in using arbitrary polygonal subdomains, side-effects associated with hanging nodes can be eliminated. Furthermore, the computational effort of strain/stress field and damage variables can be considerably saved in the framework of the SBFEM. Four numerical benchmarks with regular-shaped domain and a porous plate with irregular holes are simulated to demonstrate the effectiveness and robustness of the proposed approach.