A multiscale phase field model for anisotropic brittle and ductile fracture in geomaterials with randomly distributed microcracks

The fracture behavior of geomaterials is largely governed by their internal microcrack structures, and establishing a link between microcrack evolution and macroscopic fracture remains a key challenge. In this work, a multiscale anisotropic phase field model is proposed to simulate the complex fracture processes of geomaterials with randomly distributed microcracks. Within the framework of asymptotic homogenization, the system energy under brittle fracture during microcrack opening and ductile fracture induced by frictional sliding during microcrack closure is characterized. By statistically describing the distribution of microcracks, the microstructural features are incorporated into the homogenized stiffness, plastic yield criterion, and phase field structure tensor, enabling the model to naturally capture the anisotropy of stiffness, plasticity, and fracture toughness arising from the preferential orientation of microcracks. Under the principle of energy conservation and the stability condition, the variationally consistent governing equations of the proposed model are derived. Numerical examples demonstrate that the model can accurately reproduce the brittle or ductile fracture behavior of geomaterials under tensile, compressive, and mixed-mode loading conditions, and can reasonably predict fracture anisotropy induced by the preferential orientation of microcracks.