Simulation of the dynamic cracking of brittle materials using a nonlocal damage model with an effective strain rate effect

In this study, a nonlocal multiscale damage model that considers the effect of a strain rate is presented. Moreover, this model is combined with the scaled boundary finite element method (SBFEM) and quadtree mesh for dynamic crack propagation in quasi-brittle materials. The scaling centre of each SBFEM subdomain was selected as the material point, and the bond connecting two material points was referred to as the material bond. Microscopic damage was quantified based on the stretch rate of the material bond, and macroscale topological damage was calculated by taking the weighted average of the microscopic damage over the bonds within the influence domain. The bell distribution function is utilised as the weight function in the calculation of the nonlocal weight function. To account for the impact of the strain rate during dynamic loading, an effective rate R is introduced to enhance multiscale damage by modifying the damage threshold and bond softening coefficient throughout the analysis process. By analysing the energetic degradation function of the phase field, which establishes a connection between the macroscale topological damage and energybased damage, a nonlocal multiscale damage model was incorporated into the framework of the SBFEM. Quadtree mesh discretization was employed to achieve rapid and high-quality multilevel mesh generation by effectively utilising the hanging nodes. Three typical dynamic cracking examples were simulated using the proposed model, and the results were compared with the relevant experimental results and references. The results show that the method is suitable for accurate dynamic cracking simulation in quasi-brittle materials. Moreover, the results indicate that the proposed method can spontaneously simulate dynamic crack bifurcation without introducing additional crack bifurcation criteria. For a compact tensile test of concrete under different loading rates, the method proposed in this study can accurately simulate the corresponding failure modes. The results also show that without considering the effect of the strain rate, the damage develops rapidly in an unconstrained state, which is inconsistent with the actual case.