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Meso-scale calculations of energy localization and initiation in energetic material microstructures must capture the deformation and collapse of pores and high-temperature shear bands, which lead to hotspots. Because chemical reaction rates depend sensitively on temperature, predictive continuum models need to get the pore-collapse dynamics and resulting hotspot temperatures right; this imposes stringent demands on the fidelity of thermophysical model forms and parameters and on the numerical methods employed to perform high-resolution meso-scale calculations. Here, continuum material models for β-HMX are examined in the context of shock-induced pore collapse, treating predictions from all-atom molecular dynamics (MD) simulations as ground truth. Using atomistics-consistent material properties, we show that the currently available strength models for HMX fail to correctly capture pore collapse and hotspot temperatures. Insights from MD are then employed to advance a Modified Johnson–Cook (M-JC) strength model, which is shown to capture key aspects of the physics of shock-induced localization in HMX. The study culminates in a MD-guided strength model for β-HMX that produces continuum pore-collapse results in better alignment on several aspects with those predicted by MD, including pore-collapse mechanism and rate, shear-band formation in the collapse zone, and temperature, strain, and stress fields in the hotspot zone and the surrounding material. The resulting MD-informed/MD-determined M-JC model should improve the fidelity of meso-scale simulations to predict the detonation initiation of HMX-based energetic materials in microstructure-aware multi-scale frameworks. [ABSTRACT FROM AUTHOR]

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]

Material models for single-crystal β-HMX are systematically examined in the context of continuum pore-collapse simulations. Continuum predictions using five different isotropic material models are compared head-to-head with molecular dynamics (MD) predictions for a 50 nm cylindrical pore in β-HMX subject to a range of shock strengths. Shock waves were generated using a reverse-ballistic configuration, propagating along [010] in the MD simulations. The continuum models are improved hierarchically, drawing on temperature- and pressure-dependent MD-derived material parameters. This procedure reveals the sensitivity of the continuum predictions of pore collapse to the underlying thermophysical models. The study culminates in an MD-calibrated isotropic rate- and temperature-dependent strength model, which includes appropriate submodels for the temperature-dependent melting point of β-HMX [M. P. Kroonblawd and R. A. Austin, Mech. Mater. 152, 103644 (2021)], pressure-dependent shear modulus [A. Pereverzev and T. Sewell, Crystals 10, 1123 (2020)], and temperature-dependent specific heat, that produces continuum pore-collapse results similar to those predicted by MD. The resulting MD-informed model should improve the fidelity of simulations to predict the detonation initiation of HMX-based energetic materials containing micrometer-scale pores. [ABSTRACT FROM AUTHOR]

We apply the Green–Kubo (G–K) approach to obtain the thermal conductivity tensor of β‐1,3,5,7‐tetranitro‐1,3,5,7‐tetrazoctane (β‐HMX) as a function of pressure and temperature from equilibrium molecular dynamics (MD) simulations. Direct application of the G–K formula exhibits slow convergence of the integrated thermal conductivity values even for long (120 ns) accumulated simulation times. To partially mitigate this slow convergence, we apply a recently implemented numerical procedure that involves physically justified filtering of the MD‐calculated G–K heat current and fitting the integrated time‐dependent thermal conductivity to a physically motivated double‐exponential function. The thermal conductivity tensor was determined for pressures 0.1 MPa≤P≤ ${\le P\le }$ 30 GPa and temperatures 300 K≤T≤ ${\le T\le }$ 900 K. The thermal conductivity καβT,P ${{\kappa }^{\alpha \beta }\left(T,P\right)}$ increases with increasing pressure, by approximately an order of magnitude over the interval considered, and decreases with increasing temperature. The MD predictions are compared to experimental and other theoretically determined values for the thermal conductivity of β‐HMX. A simple, semi‐empirical fitting form is proposed that captures the behavior of κααT,P ${{\kappa }^{\alpha \alpha }\left(T,P\right)}$ over the pressure and temperature intervals studied. [ABSTRACT FROM AUTHOR]

We present a machine learning framework to train and validate neural networks to predict the anisotropic elastic response of a monoclinic organic molecular crystal known as β$$ \beta $$‐HMX in the geometrical nonlinear regime. A filtered molecular dynamic (MD) simulations database is used to train neural networks with a Sobolev norm that uses the stress measure and a reference configuration to deduce the elastic stored free energy functional. To improve the accuracy of the elasticity tangent predictions originating from the learned stored free energy, a transfer learning technique is used to introduce additional tangential constraints from the data while necessary conditions (e.g., strong ellipticity, crystallographic symmetry) for the correctness of the model are either introduced as additional physical constraints or incorporated in the validation tests. Assessment of the neural networks is based on (1) the accuracy with which they reproduce the bottom‐line constitutive responses predicted by MD, (2) the robustness of the models measured by detailed examination of their stability and uniqueness, and (3) the admissibility of the predicted responses with respect to mechanics principles in the finite‐deformation regime. We compare the training efficiency of the neural networks under different Sobolev constraints and assess the accuracy and robustness of the models against MD benchmarks for β$$ \beta $$‐HMX. [ABSTRACT FROM AUTHOR]

Shock‐induced collapse of an elongated pore in the energetic crystal β‐HMX (β‐1,3,5,7‐tetranitro‐1,3,5,7‐tetrazoctane) is examined using all‐atom molecular dynamics (MD) and continuum mechanics. The continuum simulation employs a recently proposed MD‐guided material model for β‐HMX. Collapse‐induced shear band formation and hotspot‐zone properties are calculated using both MD and continuum mechanics, for nearly identical simulation domains and identical impact conditions. The continuum model predicts shear band patterns and pore collapse behavior in good agreement with MD results; shear localization, plastic heating, and hydrodynamic impact‐generated temperature rise lead to geometrically complicated hotspot zones in the vicinity of the collapse site. This work demonstrates that—for the ≈10 GPa shock pressure studied—isotropic rate‐dependent Johnson‐Cook‐type elastoplastic models for HMX can provide physically consistent pore‐collapse dynamics and hotspot features in comparison to MD, for nontrivial pore shapes. Such physically accurate models are required for reliable predictions of detonation sensitivity and performance for shocked energetic crystals. Opportunities for further model improvement are identified. [ABSTRACT FROM AUTHOR]

Using shock‐induced quasi‐2D pore collapse in β‐HMX as a specific case study, we address three practical questions that arise when designing and interpreting molecular dynamics (MD) simulations of explicit shock wave propagation in crystals. How sensitive are the overall results to sample thickness perpendicular to the (quasi) plane of the problem? For impacts on a given crystal surface, how much does the transverse orientation of the sample matter? And, for a given sample size and orientation, how much run‐to‐run variability exists among results for independent but statistically equivalent realizations of the shock? The first and second questions are interrelated but pertain individually to assessing the roles of finite‐size and crystal anisotropy effects, respectively, on the simulated collapse mechanisms and associated local thermo‐mechanical states in the sample during and after collapse. The third addresses the confidence with which the results of individual simulations can be regarded as representative. All three questions become particularly important if the MD predictions are intended to serve as "ground truth" for validation of continuum mesoscale models. Here, quasi‐2D samples of (010)‐oriented single‐crystal β‐HMX (β‐1,3,5,7‐tetranitro‐1,3,5,7‐tetrazocane) containing a cylindrical pore were subjected to reverse‐ballistic impacts, resulting in explicit, supported shock propagation initially along [010], for impact speeds up =1.0 and 0.5 km s−1. The individual samples differed in either the thickness perpendicular to the sample plane or the transverse crystal orientation normal to [010] in the quasi‐2D cell. Three independent realizations of the shock were performed for a selected case to assess run‐to‐run variability. Comparisons of qualitative features of the collapse, temperature and pressure distributions in the samples, and time scales for pore collapse suggest that there is little sensitivity to sample thickness for the same crystal orientation and moderate sensitivity to transverse crystal orientation for samples of the same thickness. Run‐to‐run variability is evident to the eye in side‐by‐side system observations. However, overall mechanisms of collapse, distributions for temperature and pressure in the samples, and time scales for collapse are in near‐quantitative agreement among the realizations. [ABSTRACT FROM AUTHOR]

All‐atom molecular dynamics (MD) and Eulerian continuum simulations, performed using the LAMMPS and SCIMITAR3D codes, respectively, were used to study thermo‐mechanical aspects of the shock‐induced collapse of an initially cylindrical 50 nm diameter pore in single crystals of 1,3,5‐triamino‐2,4,6‐trinitrobenzene (TATB). Three impact speeds, 0.5 km s−1, 1.0 km s−1 and 2.0 km s−1, were used to generate the shocks. These impact conditions are expected to yield collapse mechanisms ranging from predominantly visco‐plastic to hydrodynamic. For the MD studies, three crystal orientations (relative to shock‐propagation direction) were examined that span the limiting cases with respect to the crystalline anisotropy in TATB. An isotropic constitutive model was used for the continuum simulations, thus crystal anisotropy is absent. The evolution of spatiotemporally resolved quantities during collapse is reported including local pressure, temperature, pore size and shape, and material flow. Multiple models for the melting curve and specific heat were studied. Within the isotropic elastic/perfectly plastic continuum framework and for the range of impact conditions studied, the specific heat and melting curve sub‐models are shown to have modest effects on the continuum hotspot predictions in the present inert calculation. Treating the MD predictions as 'ground truth', albeit with a classical rather than quantum‐like heat capacity, it is clear that – at a minimum – an extension of the constitutive model to account for crystal plasticity and anisotropic strength will be required for a high‐fidelity continuum description. [ABSTRACT FROM AUTHOR]

The melt curve and the liquid-state transport properties shear viscosity, self-diffusion coefficient and thermal conductivity of 1,3,5-triamino-2,4,6-trinitrobenzene (TATB) were predicted using all-atom molecular dynamics simulations. The TATB melt curve was obtained using solid-liquid coexistence simulations and is in good accord with the Simon-Glatzel equation. The temperature dependencies of the shear viscosity and self-diffusion coefficient are predicted to obey Arrhenius behaviour for pressures up to P = 20 kbar. The thermal conductivity has a linear temperature dependence for P < 15 kbar and a linear density (ρ) dependence for ρ > 1200 kg m−3. At similar densities the shear viscosity of liquid TATB is close to the predictions for liquid nitromethane [58] but lower than the predictions for liquid HMX [24] and RDX [59]. The self-diffusion coefficient for TATB is predicted to be higher than predictions for nitromethane, HMX and RDX at similar densities. The conductivity of TATB is ≈20% greater than the conductivity of liquid HMX at a given density. [ABSTRACT FROM AUTHOR]

Abstract: The second‐order elastic stiffness tensor and isotropic moduli of β‐octahydro‐1,3,5,7‐tetranitro‐1,3,5,7‐tetrazocine (β‐HMX, P21/n space group setting) on the 0 K isotherm are presented for hydrostatic pressures between 10−4 GPa and 30 GPa. The results were obtained from molecular statics simulations using a validated all‐atom flexible‐molecule force field. Comparisons to previous experimental and computational determinations are provided. [ABSTRACT FROM AUTHOR]

The cover image is based on the Original Article I Molecular dynamics inferred transfer learning models for finite-strain hyperelasticity of monoclinic crystals: Sobolev training and validations against physical constraints i by Nikolaos Vlassis et al., https://doi.org/10.1002/nme.6992. [Extracted from the article]

The isothermal second-order elastic stiffness tensor and isotropic moduli of β -1,3,5,7- tetranitro-1,3,5,7-tetrazoctane (β -HMX) were calculated, using the P 2 1 /n space group convention, from molecular dynamics for hydrostatic pressures ranging from 10 − 4 to 30 GPa and temperatures ranging from 300 to 1100 K using a validated all-atom flexible-molecule force field. The elastic stiffness tensor components were calculated as derivatives of the Cauchy stress tensor components with respect to linear strain components. These derivatives were evaluated numerically by imposing small, prescribed finite strains on the equilibrated β -HMX crystal at a given pressure and temperature and using the equilibrium stress tensors of the strained cells to obtain the derivatives of stress with respect to strain. For a fixed temperature, the elastic coefficients increase substantially with increasing pressure, whereas, for a fixed pressure, the elastic coefficients decrease as temperature increases, in accordance with physical expectations. Comparisons to previous experimental and computational results are provided where possible. [ABSTRACT FROM AUTHOR]

There are many compelling scientific and technological reasons for understanding the processes leading to burn ignition and detonation initiation in propellants and explosives. Multi-physics continuum simulations have been successfully applied to the crystal scale, accompanied by the development of more sophisticated constitutive models. [Extracted from the article]