Nonlocal dynamic damage modelling of quasi-brittle composites using the scaled boundary finite element method

Abstract

In this contribution, a nonlocal approach is proposed to model the dynamic damage of quasi-brittle composites within the framework of the scaled boundary finite element method (SBFEM). The image-based quadtree decomposition is used to automatically achieve multi-level mesh of a domain with geometric as well as material discontinuities. By enforcing a 2:1 balanced condition, only limited types of S-domains are used. Owning to the salient capability of the SBFEM in constructing polygons with arbitrary edges and nodes, there is no extra burden on dealing with hanging nodes between neighbouring S-domains in different sizes. Furthermore, the strain modes and the original stiffness matrix of each S-domain and the weighting matrix for nonlocal formulation are all pre-computed initially and extracted in subsequent time steps. Consequently, the computational efficiency of the proposed approach is considerably accelerated. The mesh dependence is well eliminated by using an integral-type nonlocal model. Several benchmarks are simulated to demonstrate the efficiency, robustness and variability of the proposed approach for macroscale and mesoscale problems. It is found that the proposed method can model multiple crack propagation and crack branching as well. Compared with the case under static load, the failure mode of quasi-brittle materials under dynamic load depends not only on the strength of each component but also on the propagation of stress wave.