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.

翻译：疲劳相场模型能够重现疲劳行为的主要现象学特征。然而，在高周疲劳范围内进行相场计算成本极高，因为需要在空间上解析相场模型固有的小尺度特征，同时在时间上解析数百万次循环的加载历史。为此，我们提出了一种基于循环跳跃技术的完全自适应加速方案，该方案跳过适当确定数量的逐循环解析过程，同时预测跳跃期间局部系统的演化。本文方法的新颖之处在于提出了一种循环跳跃准则，该准则基于监测疲劳进展的全局变量的目标增量来确定合适的循环跳跃步长。我们针对疲劳寿命的三个典型阶段提出了该变量的定义及其意义。与现有加速技术相比，我们的方法无需为循环跳跃步长设定参数和边界，且独立于材料、试件或加载条件。由于监测变量之一为疲劳裂纹长度，我们引入了一种精确、灵活且高效的计算方法，克服了传统裂纹尖端追踪算法的缺陷，并可同时考虑多条裂纹的演化。通过代表性数值算例展示了所提加速方案的性能，结果表明在高周疲劳范围内可实现高达四个数量级的加速比，且始终保持高精度。