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：相场疲劳模型能够再现疲劳行为的主要现象学特征。然而，在高周疲劳区域进行相场计算的计算成本极高，这源于两方面需求：在空间上需要解析相场模型固有的微小长度尺度，在时间上需要解析数百万次循环的加载历程。为解决此问题，我们提出了一种基于循环跳跃技术的全自适应加速方案。该方案通过预测跳跃期间局部系统的演化，跳过适当数量循环的逐周期解析。本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一般阶段，提出了该变量的定义及其物理意义。与现有加速技术相比，我们的方法无需设置循环跳跃步长的参数和边界，且独立于材料、试样或载荷条件运行。由于监测变量之一是疲劳裂纹长度，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局限，并能同时考虑多条扩展裂纹。通过代表性数值算例验证了所提加速方案的性能，结果表明在高周疲劳区域可实现高达四个数量级的加速，同时保持一贯的高精度。