Unified Approach for Meso-Informed Burn Models in Shocked Energetic Materials

Reactive hydrocode calculations of shock-to-detonation transition in heterogeneous energetic (HE) materials need to be closed with burn models. One requirement of burn models is to supply a macroscale control volume with an energy release rate due to chemical reactions that reflects the subgrid physics of hotspot ignition and growth. Energy localization at hotspots delivers chemical energy at a rate (e)over dot(meso) = Delta H-r/tau(meso), where Delta H-r is the heat of reaction and tmeso is a meso-scale energy localization time scale. This energy deposition rate is much larger than nominal Arrhenius-form chemical energy deposition rates in a homogeneous sample subjected to the same shock loading. To develop meso-informed energy deposition rate models, this paper identifies a meso-scale energy release time scale tau(meso) that is common to burn models based on the hotspot ignition and growth concept. The identification of a common time scale allows for a unified microstructure-aware, physics-based reactive burn model; high-fidelity meso-scale numerical simulations are used to construct a surrogate model for tau(meso). The surrogate model is shown to capture the effects of microstructural parameters on (e)over dot(meso) and can be used for meso-macro coupling in a multiscale model to predict the sensitivity of HE materials.