Sub-grid Numerical Techniques for First Principles Physics Based Tools

Abstract

High strain rate events, such as high velocity impacts and high explosive detonation, require the use of first principles physics based codes to accurately predict the formation of debris during material fracture and fragmentation. However, material fracture behavior is a very complex phenomenon to model due to its stochastic nature and the variability in material properties under dynamic loading conditions (versus static). In addition, physics based codes present challenges in predicting debris pieces that are smaller than the mesh resolution for a large problem domain with a finite number of elements. Yet, these characteristics are important in applications for missile intercepts, satellite collisions and warhead fragmentation, where the debris generated can range in size from large (on the order of meters) to very small (micron-sized). Previous fragmentation models have been implemented in physics based codes, such as the Grady-Kipp energy-based fragmentation model in the CTH Eulerian shock physics package, that produce debris smaller than the numerical grid size. However, recent theories developed by Grady combine the energy-based model with Mott's statistical based theory to more accurately describe the distribution of debris created under fracture. Using Grady's theories, we have developed a methodology that predicts sub- grid debris information from the Lagrangian-based hydro-structural code, Velodyne. This methodology utilizes the strain rate data from the Velodyne simulation to determine further breakup of the finite elements. Although there is limited test data available characterizing debris below 1 gram, we show some comparisons of the debris predictions with explosive filled cylinder experiments.