A new exploration of mesoscopic structure in the nonlocal macro-meso-scale consistent damage model for quasi-brittle materials

In the present study, a new exploration of the mesoscopic structure is proposed for the nonlocal macro‑meso-scale consistent damage (NMMD) model, and the definition from mesoscopic damage to macroscopic damage in the original NMMD model is expanded. In the proposed model, material points are divided into two types: macroscopic and mesoscopic. For each macroscopic material point, there are mesoscopic material points within its influence domain, and every two different mesoscopic material points form a material point pair. The macroscopic damage at a macroscopic material point is also evaluated as the weighted average of mesoscale damage over material point pairs in the influence domain. However, compared with the original NMMD model, the mesoscale damage of material point pairs is determined by the motion of mesoscopic material points, rather than macroscopic material points. The macroscopic material points in the proposed model only represent the nonlocal effect and the macroscopic damage. Moreover, the shape of the influence domain and the arrangement of material point pairs are arbitrary and not fixed, i.e., the unified mesoscopic structure is abstract. To verify the proposed model, a specific mesoscopic structure is generated for quasi-brittle materials without considering the randomness of material properties. In this mesoscopic structure, the shape of the influence domain is a circle, and the mesoscopic material points are generated by the tangent sphere method. The numerical results indicate that the proposed model can accurately capture the crack patterns of quasi-brittle materials and exhibits excellent numerical robustness. Meanwhile, through a mode-I failure example, it is demonstrated that the computational efficiency of the proposed model is not lower than the original NMMD model. More importantly, the framework of mesoscopic structure modeling provides a new feasible approach for the extension of other models, e.g., virtual internal bond model and peridynamics. The urgent work within the NMMD model framework is to extend the proposed model to anisotropic, composite materials and dynamic crack simulation of large structures in the future.