Phase-field modeling of fracture via homogenization

This study presents a novel phase-field modeling approach for brittle fracture that incorporates computational homogenization techniques to characterize the microstructural degradation of the material. Traditional phase-field models often implement degradation and dissipation functions in terms of the phase-field variable that, despite offering satisfactory results, their physical interpretation and their extension to anisotropic fracture behavior is not always clear. To address this challenge, we develop a framework inspired by the nucleation, growth, and coalescence of microstructural voids to model macroscopic fracture. The proposed approach employs homogenization techniques to calculate the effective material properties when introducing voids of varying sizes and shapes. By solving the homogenization problem for different void geometries, we obtain degradation functions that relate the size of microstructural voids to the homogenized constitutive tensor. These degradation functions provide a direct link between microscale damage mechanisms and macroscale fracture behavior. Comparative analyses with conventional AT1 and AT2 models reveal strong correlations between their response and those obtained via homogenization techniques. This relationship highlights the ability of homogenized models to not only replicate established results but also provide a new understanding of the phase-field variable.