Phase-field modelling of quasi-static and dynamic brittle fracture: a FreeFEM++ implementation

This work presents a robust phase-field formulation for brittle fracture, combining a quasi-monolithic solution strategy with a frozen history field, Houbolt time integration for dynamic/transient regimes, and adaptive remeshing in FreeFEM++. This approach enhances numerical robustness, simplifies parameter calibration, and facilitates extensions to multi-physics fracture problems. Despite widespread interest, building on this framework, a key contribution is the first open serial implementation of this framework in FreeFEM++, offering advantages in mesh adaptivity, solver flexibility, and concise variational syntax. The mesh adaptivity feature concentrates resolution near evolving crack tips to efficiently capture fracture evolution. The implementation is validated on standard benchmarks, showing close agreement with reference crack paths, load-displacement, and dissipated energy responses. By releasing a concise, well-documented FreeFEM++ code, this work bridges a reproducibility gap and establishes a methodological foundation for future developments.