Multi-scale modeling of shock wave propagation in energetic solid-state composites

Abstract

We present a novel structural dynamics code for modeling shock and detonation waves in Polymer-Bonded Explosives (PBXs), which are crucial for conventional munitions and propulsion components. Our code uses a stable and efficient solution strategy based on a Taylor–Galerkin finite element (FE) discretization to accurately predict PBX behavior under extreme shock loading. To model the PBXs, we implement equations of state for the solid unreacted material and gaseous reaction products using a pressure mixture rule governed by pressure-based reaction rates. We verify the FE model using analytical solutions for SOD shock and ZND detonation models. In addition to the continuum model, we also introduce a first-order multi-scale model that uses a Taylor approach to compute macro-scale fluxes and properties from the underlying microstructural sub-problems using averaging schemes. Our numerical results demonstrate the effectiveness of our multi-scale model in accurately predicting pressure profiles and detonation velocities for microstructures with varying mass fractions. These findings have significant implications for microstructure design and highlight the importance of considering microstructural variability in PBX behavior. Overall, our structural dynamics code represents a significant step towards improving the understanding and design of PBXs under extreme shock loading conditions.