Phase-Field Modeling of Pressurized Fracture Propagation in Mixed Failure Mode

ABSTRACT: The phase field method (PFM) has emerged as a powerful tool for simulating fracture propagation in complex systems, due to its ability to model fracture propagation without explicitly tracking fracture surfaces. Based on energy minimization prin-ciples, the PFM characterizes fractures by using a continuous damage field (phase field), smoothly transitioning from intact to damaged (fractured) states. The PFM thus allows modeling complex fracture mechanics problems, e.g., fracture coalescence and branching, with high accuracy and stability. This work offers a rigorous yet accessible explanation of the PFM framework for fracture mechanics, grounded in energy considerations and micro-scale mechanisms. An energy decomposition model expressed in terms of volumetric and deviatoric strain components is modified to account for the distinct strain energy consumption mechanisms involved in mode I (tensile) and mode II (shear) fracture failures. The modified phase-field model approach is then applied to simulate the propagation of pressurized fractures in both homogeneous and layered media, with a particular focus on energetic analysis for different failure modes. This study not only advances the theoretical understanding of PFM but also provides fundamental insights into fracture propagation under single and mixed failure modes.