New nonlocal multiscale damage model for modelling damage and cracking in quasi-brittle materials

A new method for the simulation of crack initiation and propagation in quasi-brittle materials is proposed that combines the scaled boundary finite element method and a nonlocal multiscale damage model. The scaling centre of the scaled boundary finite element subdomain is taken as the material point. Microscopic damage is defined in terms of the stretch rate of bonds of material points, and macroscale topologic damage is evaluated as the weighted average of microscale damage over bonds in the influence domain. Through the energetic degradation function of phase field analysis, which connects energy-based damage and macroscale topologic damage, the nonlocal multiscale damage model is inserted into the framework of the scaled boundary finite element method. The quadtree discrete mesh technique is used to rapidly obtain a high-quality multilevel mesh by taking full advantage of the hanging nodes that it allows. A detailed arc length method for solving nonlinear equations is also presented in this paper. Four typical ex-amples, one Mode I and three mixed-mode cracking simulations, show that the proposed method can be used to simulate crack initiation and propagation in quasi-brittle materials and correctly describe crack propagation paths and load-deformation curves. Compared with other methods, the nonlocal multiscale damage model presented in this paper can provide a more accurate description of local cracking damage zones, and the results are more reasonable, with higher calculation accuracy and efficiency. The numerical examples also indicate that there is no mesh sensitivity problem when the mesh size of the damage process region is less than 1/5 of the radius of the influence domain.