Adaptive phase-field cohesive-zone model for simulation of mixed-mode interfacial and bulk fracture in heterogeneous materials with directional energy decomposition

Interfacial debonding, a critical failure mechanism in heterogeneous materials, is often characterized by mixed-mode fracture. This study develops a numerical framework to simulate bulk and interfacial fractures in composite materials. A phase-field cohesive zone model, incorporating a directional energy decomposition scheme and a modified toughness method, is employed to capture complex fracture behaviors. A level-set method explicitly defines interface positions, while an adaptive mesh refinement strategy enhances computational efficiency. Numerical examples validate the model's accuracy and efficiency in predicting mixed-mode crack propagation and interfacial debonding. This work provides a robust and efficient approach to simulate complex fracture phenomena in heterogeneous materials, especially for the mixed-mode fracture.