A new nonlocal macro-meso-scale consistent damage model for crack modeling of quasi-brittle materials

Crack initiation and propagation simulation is crucial for the safety and integrity assessment of structures. Though to this problem great efforts have been devoted and great advances have been made in both theory and numerical implementation, challenges still exist. To this end, inspired by the peridynamics and the unified phase-field method, in the present paper a novel nonlocal macro-meso-scale consistent damage model is proposed to simulate fracture process without prescribed initial crack and potential crack path. In this method, a meso-scale damage is firstly defined in terms of the stretch rate of bonds of material points. Then the macro-scale topologic damage is evaluated as the weighted averaging of meso-scale damage over bonds in the influence domain. Through the energetic degradation function, which connects the energy-based damage and the macro-scale topologic damage, the above damage model is inserted into the framework of irreversible thermodynamics consistent continuum damage mechanics. Numerical algorithms by the finite element discretization are elaborated. Three examples, including the Mode I and Mixed-Mode cracking simulation, are studied. It is shown that the proposed method can capture not only the crack pattern but also the load-deformation curves quantitatively. Moreover, there is no mesh sensitivity. Computationally, the proposed method belongs to the smeared crack modeling. The proposed method is presently limited to quasi-static crack modeling of isotropic quasi-brittle materials. The extension to anisotropic materials and dynamic crack modeling is possible and shall be studied in the future.