Efficient phase-field fracture simulations for fracture analysis in heterogeneous materials

Abstract Fracture in heterogeneous materials with complex microstructures poses significant challenges due to the intricate interactions between material heterogeneities and crack propagation. The phase-field method for brittle fracture has emerged as a particularly suitable and powerful simulation technique for addressing these challenges, offering a robust framework for capturing complex crack paths, branching, and coalescence of multiple cracks. The method, however, has notable drawbacks that can hinder its application to real-world simulations. Key limitations include its computationally intensive nature, driven by the need for fine spatial discretizations to resolve the smeared crack phase-field, small time step sizes for accurate crack detection, and slow convergence of staggered solution schemes during critical load steps. These challenges are addressed by proposing a combination of three complementary techniques to enhance both the performance and robustness of the phase-field fracture simulations: adaptive spatial refinement to focus computational effort near fractures, physically motivated convergence criterion to improve solver efficiency, and adaptive temporal refinement and coarsening to optimize time step sizes dynamically. The goal is to achieve efficient simulations without compromising physical accuracy, enabling reliable fracture modeling in heterogeneous microstructures. This study investigates the elastic and fracture responses of materials with varying microscopic properties, such as filler volume fraction and inclusion sizes.