Accurate simulations of the shock response of heterogeneous energetic (HE) materials require closure models, which account for energy localization in the micro-structure. In a multi-scale framework, closure is provided by reaction rate models that account for ignition and growth of hotspots, allowing for prediction of the overall macro-scale sensitivity of a HE material. In the present meso-informed ignition and growth (MES-IG) model, the reaction rate is expressed as a function of shock pressure and morphology of the void field in a pressed energetic material. In MES-IG, the void morphology is quantified in terms of a limited number of parameters: viz., overall porosity, void size, and shape (aspect ratio and orientation). In this paper, we quantify the effects of arbitrary variations in void shapes on meso-scale energy deposition rates. A collection of voids of arbitrary shapes is extracted from scanning electron microscope (SEM) images of real, pressed HMX (octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine) samples and classified into groups based on their similarity in shapes. Direct numerical simulations (DNS) are performed on the highly contorted “real” void shapes, and the calculated hotspot ignition and growth rates are compared with values predicted by the MES-IG. It is found that while the parameterization of complex void morphologies in terms of orientation and aspect ratio gives fairly good agreement between DNS and MES-IG reaction rates, the intricate details of highly complex void shapes impact hotspot characteristics to a significant extent. This work suggests possible improvements for the prediction of reaction rate in the energetic microstructure by adopting a more detailed description of shapes.
The thermo-mechanical response of shock-initiated energetic materials (EMs) is highly influenced by their microstructures, presenting an opportunity to engineer EM microstructures in a “materials-by-design” framework. However, the current design practice is limited, as a large ensemble of simulations is required to construct the complex EM structure-property-performance linkages. We present the physics-aware recurrent convolutional (PARC) neural network, a deep learning algorithm capable of learning the mesoscale thermo-mechanics of EM from a modest number of high-resolution direct numerical simulations (DNS). Validation results demonstrated that PARC could predict the themo-mechanical response of shocked EMs with comparable accuracy to DNS but with notably less computation time. The physics-awareness of PARC enhances its modeling capabilities and generalizability, especially when challenged in unseen prediction scenarios. We also demonstrate that visualizing the artificial neurons at PARC can shed light on important aspects of EM thermos-mechanics and provide an additional lens for conceptualizing EM.
Meso-scale simulations of pressed energetic materials are performed using synthetic microstructures generated using deep feature representation, a deep convolutional neural network-based approach. Synthetic microstructures are shown to mimic real microstructures in the statistical representation of global and local features of micro-morphology for three different classes of pressed HMX with distinctive micro-structural characteristics. Direct numerical simulations of shock-loaded synthetic microstructures are performed to calculate the meso-scale reaction rates. For all three classes, the synthetic microstructures capture the effect of morphological uncertainties of real microstructures on the response to shock loading. The calculated reaction rates for different classes also compare well with those of the corresponding real microstructures. Thus, the article demonstrates that machine-generated ensembles of synthetic microstructures can be employed to derive structure–property–performance linkages of a wide class of real pressed energetic materials. The ability to manipulate the synthetic microstructures using deep learning-based approaches then provides an opportunity for material designers to develop and manufacture pressed energetic materials that can yield targeted performance.
Heterogeneous energetic materials (EMs) contain microstructural defects such as voids, cracks, interfaces, and delaminated zones. Under shock loading, these defects offer potential sites for energy localization, i.e., hotspot formation. In a porous EM, the collapse of one void can generate propagating blast waves and hotspots that can influence the hotspot phenomena at neighboring voids. Such void–void interactions must be accounted for in predictive multi-scale models for the reactive response of a porous EM. To infuse such meso-scale phenomena into a multi-scale framework, a meso-informed ignition and growth model (MES-IG) has been developed, where the influence of void–void interactions is incorporated into the overall reaction rate through a function, [Formula: see text]. Previously, MES-IG was applied to predict the sensitivity and reactive response of EM, where [Formula: see text] was assumed to be a function of the overall sample porosity alone. This paper performs a deeper analysis to model the strong dependency of [Formula: see text] on other factors, such as void size and shock strength. The improved model for void–void interactions produces good agreement with direct numerical simulations of the HE microstructures and, thus, advances the predictive capability of multi-scale models of the shock response and sensitivity of EM.
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