An Adaptive Dynamic Mode Decomposition Strategy for Efficient Fatigue Crack Growth Simulation
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Fatigue failure is one of the most critical degradation mechanisms in engineering structures. Phase-field methods based on variational principles have recently emerged as robust tools for simulating fatigue crack initiation and growth. However, the high computational cost of high-fidelity simulations—due to fine spatial resolution and cyclic loading—limits their practical applicability. To overcome this challenge, an adaptive dynamic mode decomposition (DMD) framework is proposed to accelerate fatigue phase-field simulations. The method leverages DMD’s capability to extract dominant modes from high-fidelity (HF) data and efficiently extrapolate system dynamics, thereby significantly reducing the overall computational effort. To ensure accuracy, a strategy to keep the accuracy of the solution is introduced to automatically monitor prediction quality and prevent the accumulation of errors. When the prediction accuracy deteriorates, the simulation reverts to the most recent reliable anchor point, where new HF data are generated. Benchmark studies in one- and two-dimensional settings confirm that the proposed approach maintains predictive accuracy while achieving substantial reductions in computational time. These results highlight the potential of DMD-based strategies as efficient accelerators for large-scale fatigue phase-field simulations.
