  Phase-field models of fatigue are capable of reproducing the main
phenomenology of fatigue behavior. However, phase-field computations in the
high-cycle fatigue regime are prohibitively expensive, due to the need to
resolve spatially the small length scale inherent to phase-field models and
temporally the loading history for several millions of cycles. As a remedy, we
propose a fully adaptive acceleration scheme based on the cycle jump technique,
where the cycle-by-cycle resolution of an appropriately determined number of
cycles is skipped while predicting the local system evolution during the jump.
The novelty of our approach is a cycle-jump criterion to determine the
appropriate cycle-jump size based on a target increment of a global variable
which monitors the advancement of fatigue. We propose the definition and
meaning of this variable for three general stages of the fatigue life. In
comparison to existing acceleration techniques, our approach needs no
parameters and bounds for the cycle-jump size, and it works independently of
the material, specimen or loading conditions. Since one of the monitoring
variables is the fatigue crack length, we introduce an accurate, flexible and
efficient method for its computation, which overcomes the issues of
conventional crack tip tracking algorithms and enables the consideration of
several cracks evolving at the same time. The performance of the proposed
acceleration scheme is demonstrated with representative numerical examples,
which show a speedup reaching four orders of magnitude in the high-cycle
fatigue regime with consistently high accuracy.
