A cohesive–frictional phase-field model for hybrid fracture in quasi-brittle materials incorporating strength criteria

Fracture nucleation with phase-field models has recently gained significant attention as classical phase-field models often fall short in capturing the onset of fracture in the bulk material with small cracks under multi-axial loading conditions. In this study, we propose a micromechanics-based cohesive phase-field approach with a stress-dependent characteristic length for accurately modeling fracture nucleation in quasi-brittle materials subjected to multi-axial loading. Our analytical solutions reveal that the fracture nucleation criterion is independent of the phase-field length scale parameter and aligns with the material’s strength surface. Compared with available experimental data under biaxial and triaxial loading, we demonstrate that the proposed model is capable of predicting the strength surfaces that transition from extension to compression, while the existing models fail to represent these failure surfaces. Our three-dimensional numerical simulation shows that the proposed model reproduces the transition of fracture pattern from extension to compression.