An adaptive acceleration scheme for phase-field fatigue J. Heinzmann1,∗, P. Carrara1, A. M. Mirzaei2, L. De Lorenzis1 1 ETH Zürich, IMES, Computational Mechanics Group, Tannenstrasse 3, 8092 Zürich, Switzerland 2 Politecnico di Torino, Department of Structural, Geotechnical and Building Engineering Corso Duca degli Abruzzi 24, 10129 Torino, Italy ∗ jheinzmann@ethz.ch Keywords: phase-field fatigue, acceleration scheme, crack tip tracking Phase-field models for fatigue fracture, e.g. [1,2], represent a versatile approach capable of reproducing the main characteristics of fatigue behavior. However, the associated computational effort makes the cycle-by-cycle analysis of components in the high cycle fatigue (HCF) regime with cycle counts n >104...105 practically unfeasible. To overcome this, a cycle-jump acceleration scheme can be adopted, where the explicit cycle-by-cycle resolution of a certain number of cycles ∆n is skipped by instead extrapolating selected state variables based on their evolution during only some explicitly computed cycles in between the cycle jumps. To exploit the full potential of this strategy, an adaptive cycle-jump algorithm is proposed in [3] for the model presented in [1] which degrades the fracture toughness of the material as a representative fatigue history variable accumulates above a certain threshold. In the proposed scheme, the core idea lies in deciding when and how many cycles can be skipped based on the cycle-wise rate of a scalar variable Λ which is representative of the fatigue lifetime advancement. For this, the fatigue life of a component is divided into three stages: (1) an initial stage before fatigue effects are triggered, (2) the crack nucleation stage, and (3) crack propagation (including the Paris regime) ending with failure of the component. During the first stage, the system behaves linearly, which can be exploited to calculate how many cycles are needed such that the fatigue history variable hits the threshold to trigger the fatigue effects and thus directly jump to that point. Within the second stage, ∆n is computed such to elicit a target increment of the maximum of the phase field variable within the domain. Analogously, in the third stage, the number of cycles to skip is determined such to provoke a certain crack growth which is related to the phase-field regularization length. For this final stage, where the crack growth rate determines the cycle jump size, a novel, numerically efficient and precise crack tip tracking algorithm is presented which overcomes issues of conventional approaches [3]. The behavior and reliability of the proposed cycle-jump scheme is first demonstrated by comparing cycle-by-cycle with accelerated results. Then, the adaptive cycle-jump scheme is used to analyze the fatigue life of various virtual specimens. Finally, the obtained accuracy and speedup are compared with those from other available cycle-jump approaches. References [1] Carrara, P., Ambati, M., Alessi, R. and De Lorenzis, L. (2020). A framework to model the 112
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