Time homogenization: An acceleration scheme for phase-field modeling of fatigue

This study proposes a novel time homogenization scheme designed for phase-field formulations in fatigue fracture analysis. Inspired by the methodologies for evaluating the long-term behavior of asphalt pavements, this study builds upon a phase-field formulation that accounts for material degradation due to fatigue and the Representative Crack Element formulation as an energy split. The novelty of this approach lies in its application of a methodology based on computational homogenization to fracture mechanics. The time homogenization accelerates the simulation by upscaling micro-scale behaviors over extended macro-time periods. Through comparisons between high-fidelity simulations and those employing the homogenization scheme, the study evaluates the potential and accuracy of the approach. Numerical examples demonstrate the model’s effectiveness in capturing crack growth under diverse loading conditions. While the homogenized model approximates damage progression observed in detailed simulations, it exhibits a delay in response during advanced stages of crack propagation, suggesting areas for further refinement. Overall, this research validates time homogenization within phase-field formulations as a tool for fracture analysis. Further model potential is discussed and necessary development for the time homogenization method is concluded, setting the stage for future development and optimization efforts. • Time homogenization is used to accelerate phase-field fatigue. • Realistic crack kinematics is derived from Representative Crack Element. • Method performance is evaluated through comparison to high-fidelity simulations. • Necessary improvements for the time-homogenisation scheme are identified.