Physically evocative meso-informed sub-grid source term for energy localization in shocked heterogeneous energetic materials

Reactive burn models for heterogeneous energetic materials (EMs) must account for chemistry as well as microstructure to predict shock-to-detonation transition (SDT). Upon shock loading, the collapse of individual voids leads to ignition of hotspots, which then grow and interact to consume the surrounding material. The sub-grid dynamics of shock-void interactions and hotspot development are transmitted to macro-scale SDT calculations in the form of a global reactive "burn model." This paper presents a physically evocative model, called meso-informed sub-grid source terms for energy localization (MISSEL), to close the macro-scale governing equations for calculating SDT. The model parameters are explicitly related to four measurable physical quantities: two depending on the microstructure (the porosity phi and average pore size D(void)), one depending on shock-microstructure interaction (the fraction of critical voids xi(cr)), and the other depending on the chemistry (the burn front velocity V-hs). These quantities are individually quantifiable using a small number of rather inexpensive meso-scale simulations. As constructed, the model overcomes the following problems that hinder the development of meso-informed burn models: (1) the opacity of more sophisticated surrogate/machine-learning approaches for bridging meso- and macro-scales, (2) the rather large number of high-resolution mesoscale simulations necessary to train machine-learning algorithms, and (3) the need for calibration of many free parameters that appear in phenomenological burn models. The model is tested against experimental data on James curves for a specific class of pressed 1,3,5,7-tetranitro-1,3,5,7-tetrazoctane materials. The simple, evocative, and fast-to-construct MISSEL model suggests a route to develop frameworks for physics-informed, simulation-derived meso-informed burn models.