A novel two-scale microcrack band damage model for quasi-brittle materials

Phase-field fracture models generally encounter the challenge of missing fracture propcess zones caused by the regularization of sharp crack topology and lack efficient calibration methods for the energetic degradation process. To address the limitations, this work develops a two-scale microcrack band damage model that integrates the phase-field model and micromechanical damage model. The macroscale crack surface is explicitly defined by the equivalent transformation of microcrack distribution, rather than the regularization of sharp crack topology. Within the thermodynamic framework, an energy minimization damage evolution law with the microcrack density parameter as the internal variable is established. In the model, the geometric distribution process fully represents the damage distribution within the fracture process zone, and its width depends on the allowable microcrack density parameter of the material. The correlation between macroscopic elastic stiffness and microcrack density parameter is achieved using a homogenization method, which calibrates the energetic degradation process. And, the energetic degradation process remains basically consistent across various length scale values. The geometric distribution function and energetic degradation function collectively dictate the global mechanical response of materials, which remains unaffected by length scale. The irreversible damage of the model is validated, and the asymmetry of tensile and compressive stresses is also effectively addressed. Several representative benchmark examples have substantiated the capability of the proposed model to predict complex cracking behavior, confirming its negligible sensitivity to length scale and mesh size. Endowed with powerful crack prediction capabilities and a solid physical underpinnings, this model is highly promising in the realm of solid mechanics fracture.