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High-fidelity constitutive models are critical for accurate meso-scale continuum modeling and prediction of shock initiation of crystalline energetic materials (EMs). While empirically calibrated or atomistic-guided anisotropic elastoplastic models of EM such as cyclotetramethylene-tetranitramine (HMX) and cyclotrimethylene-trinitramine (RDX) capture important micromechanical phenomena (such as dislocation evolution, slip-resistance, and anisotropic elasticity), the computational cost of using anisotropic single-crystal plasticity models can become prohibitive for meso-scale computations of void-collapse and hotspot formation in microstructures. Thermo-mechanically representative, isotropic, pressure, temperature, and rate-dependent material constitutive models are practical alternatives for meso-scale simulations of the shock response of microstructures. To this end, this work constructs physically consistent isotropic plasticity from anisotropic single-crystal plasticity models for HMX and RDX. State-of-the-art crystal plasticity models for HMX and RDX are used to compute the stress states in single crystals oriented in three different directions relative to shocks generated by impact at velocities ranging from 100 to 1000 m/s. Post-shock von Mises stress fields for the three orientations are then used to calibrate the strain-rate hardening coefficient and the reference strain rate for a rate-dependent Johnson–Cook (JC) yield surface model. We compare the pressures and the post-shock von Mises stresses between the JC and the anisotropic models to show that the isotropic computations closely approximate the averaged deformation response of the three different crystal orientations. We then model the interaction of a shock generated by a 500 m/s impact with a 0.5 μm void and show that the pressures and the deviatoric stresses obtained using the isotropic model closely match those computed from anisotropic models for both HMX and RDX. The resulting isotropic J2 plastic flow model for HMX and RDX can be employed to perform meso-scale simulations for energy localization due to shear bands and void collapse in the two materials. [ABSTRACT FROM AUTHOR]

This paper demonstrates a novel Eulerian computational framework for modeling anisotropic elastoplastic deformations of organic crystalline energetic materials (EM) under shocks. While Eulerian formulations are advantageous for handling large deformations, constitutive laws in such formulations have been limited to isotropic elastoplastic models, which may not fully capture the shock response of crystalline EM. The present Eulerian framework for high-strain rates, large deformation material dynamics of EM incorporates anisotropic isochoric elasticity via a hypo-elastic constitutive law and visco-plastic single-crystal models. The calculations are validated against atomistic calculations and experimental data and benchmarked against Lagrangian (finite element) crystal plasticity computations for shock-propagation in a monoclinic organic crystal, octahydro-1,3,5,7-tetranitro-1,3,5,7 tetrazocine (β-HMX). The Cauchy stress components and the resolved shear stresses calculated using the present Eulerian approach are shown to be in good agreement with the Lagrangian computations for different crystal orientations. The Eulerian framework is then used for computations of shock-induced inert void collapse in β-HMX to study the effects of crystal orientations on hotspot formation under different loading intensities. The computations show that the hotspot temperature distributions and the collapse profiles are sensitive to the crystal orientations at lower impact velocities (viz., 500 m/s); when the impact velocity is increased to 1000 m/s, the collapse is predominantly hydrodynamic and the role of anisotropy is modest. The present methodology will be useful to simulate energy localization in shocked porous energetic material microstructures and other situations where large deformations of single and polycrystals govern the thermomechanical response. [ABSTRACT FROM AUTHOR]

In this article, we trained a machine learning (ML) model to connect microstructural details of an energetic material formulation to its performance for the purpose of guiding the discovery of new explosive formulations. Our hypothesis was that the algorithm would robustly learn the training data and produce an accurate surrogate model. Specifically, the algorithm learned the relationship between details of the void size distribution (VSD), initiating shock pressure, and the energetic material performance. We used realistic constraints on the VSD and a range of cases were ingested by a physically informed reactive flow model working within a hydrodynamic solver running on high-performance computing resources. The ML algorithm produced a surrogate model that accurately predicted known test points around the parameter space. In addition to the utility of the model and the process used for its development, we noted interesting comparisons between what we, the authors—subject matter experts, would heuristically conclude from the training data and the surrogate model predictions. We detected nuanced details that were missed by the surrogate model; however, these details are not important to an energetic material formulator. We concluded that the algorithm did indeed robustly learn the training data and produce an accurate surrogate model. We further concluded that the surrogate model is a powerful tool to guide the formulator in the absence of subject matter experts and limited-access computing resources. [ABSTRACT FROM AUTHOR]

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, f v − v . Previously, MES-IG was applied to predict the sensitivity and reactive response of EM, where f v − v was assumed to be a function of the overall sample porosity alone. This paper performs a deeper analysis to model the strong dependency of f v − v 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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The sensitivity of an energetic material is strongly influenced by its microstructure. This work distinguishes the roles played by the microstructure (i.e., the meso-scale) in the macro-scale shock sensitivity of two different materials: TATB and HMX. To quantify sensitivity, we develop a meso-informed energy deposition model for a porous TATB material, following procedures from the previous work on HMX. Simulations of reactive void collapse in TATB are employed to calculate the rate of initiation and growth of hotspots. These rates are expressed as surrogate models, expressing meso-scale (hotspot) quantities of interest as functions of shock strength P s and void size D v o i d . The hotspot ignition and growth rate surrogates for TATB are compared with those for HMX, providing insights into meso-scale physics underlying shock sensitivity of these two energetic materials. The surrogate models are then used in a meso-informed ignition and growth (MES-IG) model to close macro-scale simulations of the shock response of porous TATB. We also obtain the run-to-detonation distances and generate Pop-plots to quantify macro-scale sensitivity. It is shown that Pop-plots for HMX-based energetic materials accord with behavior observed in experimental studies; however, there is a significant discrepancy between MES-IG predictions and experiments for TATB; the causes for this difference between HMX and TATB are discussed, pointing to areas for future work. [ABSTRACT FROM AUTHOR]

Artificial intelligence (AI) is rapidly emerging as a enabling tool for solving complex materials design problems. This paper aims to review recent advances in AI‐driven materials‐by‐design and their applications to energetic materials (EM). Trained with data from numerical simulations and/or physical experiments, AI models can assimilate trends and patterns within the design parameter space, identify optimal material designs (micro‐morphologies, combinations of materials in composites, etc.), and point to designs with superior/targeted property and performance metrics. We review approaches focusing on such capabilities with respect to the three main stages of materials‐by‐design, namely representation learning of microstructure morphology (i. e., shape descriptors), structure‐property‐performance (S−P−P) linkage estimation, and optimization/design exploration. We leave out "process" as much work remains to be done to establish the connectivity between process and structure. We provide a perspective view of these methods in terms of their potential, practicality, and efficacy towards the realization of materials‐by‐design. Specifically, methods in the literature are evaluated in terms of their capacity to learn from a small/limited number of data, computational complexity, generalizability/scalability to other material species and operating conditions, interpretability of the model predictions, and the burden of supervision/data annotation. Finally, we suggest a few promising future research directions for EM materials‐by‐design, such as meta‐learning, active learning, Bayesian learning, and semi‐/weakly‐supervised learning, to bridge the gap between machine learning research and EM research. [ABSTRACT FROM AUTHOR]

Artificial intelligence (AI) is rapidly emerging as a enabling tool for solving complex materials design problems. This paper aims to review recent advances in AI‐driven materials‐by‐design and their applications to energetic materials (EM). Trained with data from numerical simulations and/or physical experiments, AI models can assimilate trends and patterns within the design parameter space, identify optimal material designs (micro‐morphologies, combinations of materials in composites, etc.), and point to designs with superior/targeted property and performance metrics. We review approaches focusing on such capabilities with respect to the three main stages of materials‐by‐design, namely representation learning of microstructure morphology (i. e., shape descriptors), structure‐property‐performance (S−P−P) linkage estimation, and optimization/design exploration. We leave out "process" as much work remains to be done to establish the connectivity between process and structure. We provide a perspective view of these methods in terms of their potential, practicality, and efficacy towards the realization of materials‐by‐design. Specifically, methods in the literature are evaluated in terms of their capacity to learn from a small/limited number of data, computational complexity, generalizability/scalability to other material species and operating conditions, interpretability of the model predictions, and the burden of supervision/data annotation. Finally, we suggest a few promising future research directions for EM materials‐by‐design, such as meta‐learning, active learning, Bayesian learning, and semi‐/weakly‐supervised learning, to bridge the gap between machine learning research and EM research. [ABSTRACT FROM AUTHOR]

Predictive simulations of shock-to-detonation transitions (SDTs) of energetic materials must contend with uncertainties in the material properties, reactive models, and the microstructures of the material. In this work, we analyze the effects of uncertainties in the run-to-detonation distance h of a pressed energetic (HMX) material due to variabilities in the thermomechanical properties of HMX. The run distances are computed using a recently developed machine-learning based multiscale modeling framework, viz., the Meso-informed Ignition and Growth (MES-IG) model. The input uncertainties are first used in the MES-IG model to quantify the variabilities in the hotspot dynamics at the mesoscale. A Kriging-based Monte Carlo method is used to construct probability density functions (pdfs) for the mesoscale reaction-product formation rates; these are used to propagate the mesoscale uncertainties to the macroscale reaction-progress variables to construct pdfs for the run-to-detonation distance h. We evaluate uncertainties in h due to variabilities in six material properties, viz., specific heat, Grüneisen parameter, bulk modulus, yield strength, thermal expansion coefficient, and the thermal conductivity of the material. Among these six properties, h is found to be most sensitive to the variabilities in the specific heat of the material; the uncertainties in the specific heat amplify exponentially across scales and result in logarithmic pdfs for h. Thus, the paper not only quantifies and propagates uncertainties in material properties across scales in a multiscale model of SDT, but also ranks the properties with respect to the sensitivity of the SDT response of heterogeneous energetic materials on each property. [ABSTRACT FROM AUTHOR]

A Cartesian grid-based sharp interface method is presented for viscous simulations of shocked particle-laden flows. The moving solid–fluid interfaces are represented using level sets. A moving least-squares reconstruction is developed to apply the no-slip boundary condition at solid–fluid interfaces and to supply viscous stresses to the fluid. The algorithms developed in this paper are benchmarked against similarity solutions for the boundary layer over a fixed flat plate and against numerical solutions for moving interface problems such as shock-induced lift-off of a cylinder in a channel. The framework is extended to 3D and applied to calculate low Reynolds number steady supersonic flow over a sphere. Viscous simulation of the interaction of a particle cloud with an incident planar shock is demonstrated; the average drag on the particles and the vorticity field in the cloud are compared to the inviscid case to elucidate the effects of viscosity on momentum transfer between the particle and fluid phases. The methods developed will be useful for obtaining accurate momentum and heat transfer closure models for macro-scale shocked particulate flow applications such as blast waves and dust explosions. [ABSTRACT FROM PUBLISHER]

A Lagrangian particle cloud model is proposed that accounts for the effects of Reynolds-averaged particle and turbulent stresses and the averaged carrier-phase velocity of the subparticle cloud scale on the averaged motion and velocity of the cloud. The SPARSE (subgrid particle averaged Reynolds stress equivalent) model is based on a combination of a truncated Taylor expansion of a drag correction function and Reynolds averaging. It reduces the required number of computational parcels to trace a cloud of particles in Eulerian-Lagrangian methods for the simulation of particle-laden flow. Closure is performed in an a priori manner using a reference simulation where all particles in the cloud are traced individually with a point-particle model. Comparison of a first-order model and SPARSE with the reference simulation in one dimension shows that both the stress and the averaging of the carrier-phase velocity on the cloud subscale affect the averaged motion of the particle. A three-dimensional isotropic turbulence computation shows that only one computational parcel is sufficient to accurately trace a cloud of tens of thousands of particles. [ABSTRACT FROM AUTHOR]