Data-Based Time Step Estimation in Explicit Dynamics: Efficient, Accurate, and Conservative Estimators

  • Schilling, Maximilian (University of Stuttgart - IBB)
  • Reinken, Lisa-Marie (University of Stuttgart - IBB)
  • Bischoff, Manfred (University of Stuttgart - IBB)

Please login to view abstract download link

In the context of computational structural dynamics, the stability of dynamic finite element simulations with explicit time integration is determined by the critical time step of the system Currently, this system's critical time step is typically estimated element-wise using a variety of heuristic formulas that rely on element geometric parameters. However, these heuristics are inherently limited in accuracy. Such heuristics often yield overly conservative or non-conservative estimates, particularly for irregular element geometries, necessitating the use of safety factors to mitigate instability risks. To date, evaluations of these estimators have been limited to select, idealized element configurations (Askes et al. (2015)), leaving their performance across the full spectrum of possible configurations largely unassessed. By leveraging a discrete representation of all possible quadrilateral element configurations, recent work by Willmann et al. (2022, 2025) enabled the first comprehensive comparison of different estimators. This analysis revealed substantial inaccuracies in state-of-the-art heuristic estimators, with one example from a widely used commercial software exhibiting an average error of 11% and a maximum error of 65% when taking into account all element configurations. Addressing these limitations, Willmann et al. (2022, 2025) developed more accurate data-based time step estimators, achieving unprecedented accuracy at the element level. Building on this, this contribution shifts the focus to the practical integration of these data-based time step estimators into relevant engineering simulations. We showcase more efficient and highly accurate data-based time step estimators to achieve an acceleration of structural dynamics simulations. Lastly, we explore the potential of a neighborhood-aware estimation, where information from adjacent elements is incorporated to improve the prediction of the system's critical time step. This approach is particularly promising for tetrahedral solid elements, where a conventional element-wise estimation of the critical time step is excessively conservative. We gratefully acknowledge the support for this research from the German Research Foundation (DFG), Research Grant BI 722/15-1.