Three-dimensional damage analysis by the scaled boundary finite element method

A novel and effective approach within the framework of the scaled boundary finite element method (SBFEM) is proposed for the damage analysis of structures in three dimensions. The integral-type nonlocal model is extended to SBFEM to eliminate the mesh sensitivity concerning the strain localization. In order to reduce the number of degrees of freedoms (DOFs), an automatic mesh generation algorithm using octree decomposition is employed to refine the localized damage process zone (DPZ), but no extra effort is required to deal with hanging nodes existing between adjacent subdomains with different sizes. A double-notched tension beam is simulated with two different meshes to illustrate the mesh-independence. Three benchmarks are modelled to further verify the effectiveness and robustness of the proposed approach. It is shown that the proposed computational approach is capable of accurately capturing the damage evolution under complicated boundary conditions, and the results agree well with the experimental observations and prior numerical simulations reported in the literatures.