A Self-Correcting Adaptive Remeshing Strategy for Three-Dimensional Phase-Field Fracture Simulation

Abstract

Three-dimensional phase-field fracture simulations are computationally demanding, as the geometric complexity and topological evolution of crack surfaces in 3D space require a vast number of degrees of freedom to achieve sufficient accuracy. Yet, most existing spatial adaptive schemes rely on rigid refinement patterns and empirical control parameters, which hinder local flexibility and effective adaptive mesh control. To address these limitations, a self-correcting global–local adaptive meshing method (SC-GL-AMM) is developed. A normalized nodal density field is first defined to provide a quantitative indicator of local resolution demand and guide adaptive refinement, enabling efficient and targeted mesh control. Subsequently, global crack sampling is conducted through filtering and clustering to capture 3D fracture features and perform Voronoi partitioning. Within each subdomain, a hexagonal close-packed node seeding algorithm is applied, supporting parallel processing and adaptively adjusting the distribution of mesh nodes according to the local nodal density field. Constrained Delaunay tetrahedralization is then employed to construct the adaptive mesh, ensuring geometric conformity and maintaining topological consistency across refined regions. Furthermore, a self-correcting framework is introduced, which is utilized to dynamically update the adaptive criterion based on the evolving solution-dependent indicators, enhancing robustness for complex 3D fracture scenarios. Comparative and ablation studies are conducted to assess the roles and effects of key algorithmic components. Numerical examples further demonstrate that the proposed method generates high-quality meshes with flexible adaptation, achieving up to a sixfold speed-up compared with the conventional tetrahedral subdivision strategy. This strategy thus constitutes a significant enhancement in adaptive mesh control, providing an efficient tool for large-scale three-dimensional phase-field fracture simulations.