Integrated Lagrangian and Eulerian 3D microstructure-explicit simulations for predicting macroscopic probabilistic SDT thresholds of energetic materials

Computational predictions of measures for macroscopic material attributes from the microstructure scale is a fundamental challenge in materials science. Data transfer across scales and physics-based models plays a central role in this highly material-specific process. Here, we present an approach for computationally establishing the probabilistic shock-to-detonation transition (SDT) threshold or “pop plot” (PP, the relation between run-to-detonation distance and applied pressure) of polymer-bonded explosives (PBXs) from three-dimensional (3D) simulations. The approach takes respective advantages of multiphysics Lagrangian and Eulerian modeling frameworks. The combined Lagrangian and Eulerian simulations provide an explicit account of 3D heterogeneous material microstructure at sizes up to tens of mm, mechanisms for the development of hotspots, and the coupled mechanical-thermal-chemical-transport processes which underlie the behaviors being predicted. Data transfers in the form of hotspot intensity fields from the Lagrangian simulations to the Eulerian simulations link the two frameworks. To capture the fundamental nature of the multiphysics processes, the source, and the propagation of the stochastic variations in material behavior, a 3D statistically equivalent microstructure sample set (SEMSS) is designed and used. The approach facilitates an efficient quantification of the probabilistic macroscopic detonation thresholds, leading to an analytical expression for the PP that accounts for both the microstructure effects and uncertainties. The material system modeled tracks the properties of PBX 9501 and the loading conditions studied involve shock pressure Ps in the range of 11–15 GPa. The results are in good agreement with available experimental data.