Accelerated adaptive phase-field fracture model with an efficient sub-stepping scheme

Abstract

The phase field model emerged as an elegant and powerful computational tool to study fracture behavior and its complex mechanisms in different materials. However, due to the requirement of a fine mesh in areas where fracture occurs, the conventional phase field often demands substantial computational capacity. To overcome this challenge, this work introduces an accelerated adaptive phase-field fracture model that enhances computational efficiency by integrating two key features: (a) adaptive mesh refinement and (b) auto-adaptive sub-stepping algorithms. The adaptive mesh refinement algorithm based on the error indicator derived from the phase-field variable automatically refines the domain where the cracks are likely to propagate. Simultaneously, the auto-sub stepping scheme dynamically adjusts the load increment size during the simulation, which reduces the computational costs while maintaining accuracy and stability. The proposed framework is implemented in FEniCS, an open-source finite element package. The effectiveness and robustness of the proposed implementation are demonstrated through a series of two- and three-dimensional benchmark problems. The results are compared against the standard benchmark problem as well as conventional phase field models that rely on uniform discretization and manual time-step increments.