In this work, we present a computational approach to high cycle fatigue life prediction with an efficient solver employing time-discontinuous Galerkin (TDG) based space-time finite element method and its enriched version [1, 2] in three dimensions. While the robustness of TDG based space-time FEM has been extensively demonstrated, a critical barrier for the extensive application is the large computational effort due to the additional temporal dimension and enrichment that are introduced. By formulating a new preconditioner and utilizing the properties of Kronecker product, we developed a generic iterative algorithm for solving the fully-coupled block-structured matrix equations formulated by space-time FEM. This approach reduces the computational cost to the same order of solving the corresponding static FE problems. The established numerical framework is further integrated with a multiscale damage model for the purpose of capturing failure initiation and propagation. The efficiency and robustness of the proposed method are illustrated in numerical examples, in which we show much better performance over direct solution of the original TDG matrix equations using either sparse direct or iterative solvers.

References

[1]        S. Bhamare, T. Eason, S. Spottswood, S. Mannava, V. Vasudevan, and D. Qian, "A multi-temporal scale approach to high cycle fatigue simulation," Computational Mechanics, pp. 1-14, 2013/08/29 2013.

[2]        Y. Yang, S. Chirputkar, D. N. Alpert, T. Eason, S. Spottswood, and D. Qian, "Enriched space-time finite element method: a new paradigm for multiscaling from elastodynamics to molecular dynamics," International Journal For Numerical Methods In Engineering, vol. 92, pp. 115-140, Oct 12 2012.