Simulation of Fatigue Fracture Processes with the eXtended Phase-Field Method
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During the last years, the phase-field method for fracture has gained a lot of attention. Its biggest advantage is the fact that it can capture crack propagation, branching, coalescence and initiation without the evaluation of additional criteria in a post-processing step. Another advantage compared to the very efficient XFEM/GFEM technique is that additional crack tracking algorithms and implicit or explicit representations of the crack geometry are not required. However, the main disadvantage of the classical phase-field method is the necessity of very fine meshes in the vicinity of an existing crack and its front and thus a very high computational effort amplified by the highly nonlinear behaviour even for the simulation of linear elastic fracture mechanics processes. For fatigue simulations [1] high-performance compute clusters are mandatory. Recently, an enriched/extended phase-field approach to fracture (XPFM) has been proposed [2], which combines the advantages of the XFEM/GFEM and those of the classical phase-field method. Within the XPFM, for the phase-field a transformed ansatz is used which resembles the analytical solution for a 1D phase-field problem. The displacement field is enriched based on the phase-field solution. The XPFM allows for significantly coarser meshes and a much lower number of degrees of freedom compared to the classical phase-field method. The technique has been extended to fatigue fracture problems [3] taking into account the same model assumption as presented in [1]. In this presentation, the latest developments concerning the XPFM for fatigue fracture problems are shown and properties are discussed. REFERENCES [1] P. Carrara, M. Ambati, R. Alessi and L. de Lorenzis: A novel framework to model the fatigue behavior of brittle materials based on a variational phase-field approach. Computer Methods in Applied Mechanics and Engineering, Vol. 361, 112731, 2020 [2] S. Loehnert, C. Krüger, V. Klempt and L. Munk: An enriched phase-field method for the efficient simulation of fracture processes. Computational Mechanics, Vol. 71(5), pp. 1015-1039, 2023. [3] C. Krüger, V. Curos , u and S. Loehnert: An Extended Phase-Field Approach for the Efficient Simulation of Fatigue Fracture Processes. International Journal for Numerical Methods in Engineering DOI: https://doi.org/10.1002/nme.7422 , 2024