Determining reaction rate parameters for an energetic material through inverse multi-scale analysis of shock-to-detonation transition

In multi-scale predictive models of shock-to-detonation transition (SDT), microstructure-aware burn models are employed to connect meso-scale dynamics with macro-scale energy release. Meso-scale calculations of hotspot ignition and growth rely on chemical reaction rates expressed in Arrhenius forms. However, even for well-studied energetic materials such as HMX, the reaction time scales and pathways provided by available reaction kinetic schemes vary widely. Uncertainties in reaction rate parameters can amplify to produce large uncertainties in predicted initiation envelopes (James curves or Pop-plots). To better pin down reaction rate parameters for HMX, we perform an inverse analysis to extract the rate constants in an Arrhenius model (assuming a single reaction global kinetics model) that best predicts an experimentally obtained criticality envelope. Interestingly, the estimated global kinetic scheme is shown to conform to the well-known Henson 1-equation model. To establish the validity of the inverse analysis, we further carry out a forward analysis using the determined rate law and demonstrate good predictions of SDT for a different class of pressed HMX material. While the inverse analysis has been applied herein to HMX, the paper presents a general route to arrive at global kinetics models that can be applied to a wide class of EM species.