Abstract Summary
In explicit dynamic simulations, an estimation of the critical time step size is necessary to ensure a stable computation. A direct computation of the critical time step by solving the corresponding eigenvalue problem is too time-consuming and requires the stiffness matrix, which is usually not calculated in explicit dynamics. There are several approaches to estimate the critical time step. Eigenvalue estimates such as Gershgorin’s theorem can be used to find an upper bound for the highest eigenfrequency and heuristic formulas based on geometric considerations exist. They are used to estimate a characteristic length of the element, which is then divided by the wave speed to obtain the critical time step. An example is the estimation of the characteristic length by the element area divided by the longest diagonal for 2d solid elements. The latter approach has the disadvantage that the resulting estimation is not necessarily conservative, which leads to the introduction of a so-called safety factor. In this contribution, we present a data-driven approach to time step estimation. We explain how a representative data set can be generated. Based on this data, we analyze the performance of the estimates mentioned above and propose several improvements. We present a data-driven method to make an existing estimate conservative and develop new time step estimates, which achieve significantly better results than state-of-the-art estimates with only little extra cost.
