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During compaction of large ensembles of metallic particles, the deformation and redistribution of the particles are strongly influenced by the bulk and interfacial properties of the interacting materials. Using a sharp-interface Eulerian approach, this paper studies the physics of shock compaction of clusters of particles by accurately capturing the interfacial dynamics of particle-particle interactions. The effect of disparity in bulk material properties such as impedance and yield strength and interfacial phenomena such as friction are quantified using interfacial area evolution as a measure of mixing of the materials. The results show that friction between the particles increases the mixing of the materials only for lower initial theoretical mean densities but does not significantly affect the overall dynamics of the compaction. The deformation and contact between the particles are most strongly influenced by the impedance mismatch of the materials. The difference in yield stress plays a minor role due to the predominance of pressure over deviatoric stresses. The results provide insights into the individual effects of impedance and yield stress mismatch between material pairs and also into the combined influence of mismatches in both properties. It is shown that apart from property mismatch, the average impedance of the mixture also plays a key role in mixing of the materials. [ABSTRACT FROM AUTHOR]

This paper studies the physics of shock compaction of metallic powder mixtures by focusing on two particles interacting under conditions of high compressive strain rates. Particle-particle interactions are simulated using a sharp interface Eulerian approach. Specifically, the present work seeks to understand how the disparity in bulk material properties such as yield strength and impedance leads to differences in spreading, heating, and contact area of the materials. In addition, the effects of interfacial phenomena such as friction and interfacial melting are examined using the sharp interface framework. The results show that the extent of interfacial contact between the materials is affected by material deformation and jetting. Of the material properties studied, the impedance mismatch exerts the highest influence on the heating of materials. Material yield strength also plays a significant role; the melting of materials is shown to play a minor role in the spreading and evolution of contact of the materials for the shock strengths tested. By focusing on two particles, this work provides insights elucidating the physics of shock compaction of powder mixtures, specifically the influence of bulk and interfacial properties on the extent of interfacial contact between dissimilar materials. [ABSTRACT FROM AUTHOR]

Crystals of energetic materials, such as 1,3,5,7-Tetranitro-1,3,5,7-tetrazocane (HMX), embedded in plastic binders are the building blocks of plastic-bonded explosives (PBX). Such heterogeneous energetic materials contain microstructural features such as sharp corners, interfaces between crystal and binder, intra- and extra-granular voids, and other defects. Energy localization or "hotspots" arise during shock interaction with the microstructural heterogeneities, leading to initiation of PBXs. In this paper, high-resolution numerical simulations are performed to elucidate the mechanistic details of shock-induced initiation in a PBX; we examine four different mechanisms: (1) shock-focusing at sharp corners or edges and its dependency on the shape of the crystal and the strength of the applied shock; (2) debonding between crystal and binder interfaces; (3) collapse of voids in the binder located near an HMX crystal; and (4) the collapse of voids within HMX crystals. Insights are obtained into the relative contributions of these mechanisms to the ignition and growth of hotspots. Understanding these mechanisms of energy localization and their relative importance for hotspot formation and initiation sensitivity of PBXs will aid in the design of energetic material-driven systems with controlled sensitivity, to prevent accidental initiation and ensure reliable performance. [ABSTRACT FROM AUTHOR]

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 ϕ and average pore size D ¯ v o i d ), one depending on shock–microstructure interaction (the fraction of critical voids ξ c r ), and the other depending on the chemistry (the burn front velocity V h s ). 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. [ABSTRACT FROM AUTHOR]

Sensitivity in polymer-bonded explosives (PBXs) relies on the presence of defects, such as cracks and voids, which create localized thermal energy, commonly known as hotspots, and initiate reactions through various localization phenomena. Our prior research has explored the use of internal gas pressure induced by thermite ignition to generate localized defects for PBX sensitization. However, further research is required to gain a more comprehensive understanding of the defect generation process resulting from internal gas pressure. This study investigates the process of defect generation in PBXs in response to internally induced gas pressure by applying controlled compressed gas to a fabricated cavity within the materials, simulating the gas pressure emitting from thermite. X-ray micro-computed tomography was employed to visualize the microstructure of the sample before and after gas injection. The experiments reveal the significance of gas pressure, cavity shape, temperature, and specimen compaction pressure in the defect generation. Numerical simulations using Abaqus/Standard were conducted to assess the defect generation in mock PBXs under varying gas pressures, cohesive properties, and binder thicknesses. The simulation results demonstrate the substantial influence of these properties on the ability to generate defects in mock PBXs. This study contributes to a better understanding of the factors influencing defect generation in mock PBXs. This knowledge is crucial for achieving precise control over defect generation, leading to improved ignition and detonation characteristics in PBXs. [ABSTRACT FROM AUTHOR]

Shock load analysis of two different samples of pressed HMX energetic material is performed using the Eulerian compressible multimaterial code SCIMITAR3D. The numerical framework uses an image to computation approach to perform shock analysis on real microstructures of the energetic samples. Image processing algorithms are applied on SEM images of both samples to implicitly represent the microstructures using level set functions. The chemical decomposition of HMX is modeled using the Henson-Smilowitz multi-step kinetic mechanism. It is observed that microstructural characteristics play a crucial role in determining the ignition behavior of the energetic materials. For the applied shock loads and for the particular samples investigated, class III sample leads to initiation of chemical reaction and the class V sample does not ignite. It is also shown that the orientation of elongated voids with respect to incident shock load is an important factor contributing to the initiation of chemical reactions in the class III sample. This is explained by performing numerical experiments of elongated void oriented at different angles with respect to the shock load. Results show the importance of microstructural details, such as void size, distribution, and orientation for initiation. [ABSTRACT FROM AUTHOR]

The formation of hotspots due to collapse of voids leads to enhanced sensitivity of heterogeneous energetic (HE) materials. Several mechanisms of void collapse have been identified, but the regimes in which these mechanisms dominate have not been clearly delineated using scaling arguments and dimensionless parameters. This paper examines void collapse in cyclotetramethylene-tetranitramine (HMX) to demarcate regimes where plastic collapse and hydrodynamic jetting play dominant roles in influencing hotspot related sensitivity. Using scaling arguments, a criticality envelope for HMX is derived in the form Σ c r = ∑ ( P s , D v o i d ) , i.e., as a function of shock pressure Ps and void size Dvoid, which are controllable design parameters. Once a critical hotspot forms, its subsequent growth displays a complex relationship to Ps and Dvoid. These complexities are explained with scaling arguments that clarify the physical mechanisms that predominate in various regimes of hotspot formation. The insights and scaling laws obtained can be useful in the design of HE materials. [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]

Multi-scale predictive models for the shock sensitivity of energetic materials connect energy localization ("hotspots") in the microstructure to macro-scale detonation phenomena. Calculations of hotspot ignition and growth rely on models for chemical reaction rates expressed in Arrhenius forms; these chemical kinetic models, therefore, are foundational to the construction of physics-based, simulation-derived meso-informed closure (reactive burn) models. However, even for commonly used energetic materials (e.g., HMX in this paper) there are a wide variety of reaction rate models available. These available reaction rate models produce reaction time scales that vary by several orders of magnitude. From a multi-scale modeling standpoint, it is important to determine which model best represents the reactive response of the material. In this paper, we examine three global Arrhenius-form rate models that span the range of reaction time scales, namely, the Tarver 3-equation, the Henson 1-equation, and the Menikoff 1-equation models. They are employed in a meso-informed ignition and growth model which allows for connecting meso-scale hotspot dynamics to macro-scale shock-to-detonation transition. The ability of the three reaction models to reproduce experimentally observed sensitivity is assessed by comparing the predicted criticality envelope (Walker–Wasley curve) with experimental data for pressed HMX Class V microstructures. The results provide a guideline for model developers on the plausible range of time-to-ignition that are produced by physically correct Arrhenius rate models for HMX. [ABSTRACT FROM AUTHOR]

A Cartesian grid solver is developed that is capable of simulating the convection-dominated melting processes in a latent-heat thermal storage device (TSD). The Navier-Stokes equations are solved using a dynamically refined mesh. The phase boundary is tracked using the enthalpy method. Conjugate heat transfer is calculated with a strongly coupled implicit scheme. The approach does not require the creation of a geometry-specific grid, and so allows for efficient prototyping of different complex geometric designs. Systematic benchmarking of the results against other numerical approaches is conducted, followed by tests of two basic prototypes for the design of a TSD. [ABSTRACT FROM PUBLISHER]

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]

The interaction of shocks with multimaterial interfaces can occur in several applications, including high-speed flows with droplets, bubbles, and particles and hypervelocity impact and penetration. To simulate such complicated interracial dynamics problems, a fixed Cartesian grid approach in conjunction with level-set interface tracking is attractive. In this regard, the ghost fluid method has been widely used to capture the interface dynamics. However, ghost fluid method experiences difficulties, particularly when strong shocks impinge on the interface. It has been shown that an accurate representation and decomposition of the wave systems (by solving a Riemann problem at the interface) significantly alleviates the shortcomings confronted by the ghost fluid method. Variants of the ghost fluid method proposed in the past differed in the way in which this Riemann problem was invoked at the interface. In this work, a simple, robust, and multidimensional procedure to construct the Riemann problem at the interface is presented. The work focuses primarily on resolving interface dynamics due in strong shocks interacting with embedded fluid-fluid interfaces (gas--gas and gas--liquid interfaces) in compressible flows. Several one- and two-dimensional problems involving moderate-to-very-large deformation of the embedded interface have been computed. The numerical examples demonstrate the flexibility, stability, and versatility of the approach in successfully resolving the embedded material interface. [ABSTRACT FROM AUTHOR]

Numerical simulation of shock waves interacting with multimaterial interface is immensely challenging, particularly when the embedded interface is retained as a sharp entity. The challenge lies in accurately capturing and representing the interface dynamics and the wave patterns at the interface. In this regard, the ghost fluid method has been successfully used to capture the interlace conditions for both fluid-fluid and solid-fluid interfaces. However, the ghost fluid method results in over/underheating errors when shocks impact interfaces, and hence must he supplemented with numerical corrective measures to mitigate these errors. Such corrections typically fail for strong shock applications. Variants and extensions of the ghost fluid method have been purposed in remedy its shortcomings with mixed success. In this paper, the performance of approaches based on the ghost fluid method, in the case of strong shocks impinging on immersed solid boundaries in compressible flows, is evaluated. It is found that (from the viewpoint of simplicity, robustness, and accuracy) a reflective boundary condition used in curt junction with a local Riemann solver at the interface proves to be a good choice. The method is found to be stable, accurate, and robust for wide range problems involving strong shocks interacting with embedded solid objects. [ABSTRACT FROM AUTHOR]

The flow dynamics through the peripheral and hinge regions of a bi-leaflet mechanical heart valve are complex and result in abnormally high shear stresses particularly during the closing phase of the valve function. It has been observed that the late stages of closure are more significant in the dynamics of platelet activation; therefore, the later stages of closure are simulated by solving the two-dimensional Navier–Stokes equations using an Eulerian Levelset-based sharp interface Cartesian grid method. Using a fixed Cartesian mesh incorporating local mesh refinement for solution accuracy and efficiency, the flow-through within a recessed hinge design and an open pivot hinge design is compared. Platelets are modeled as point particles by Lagrangian particle tracking algorithm with one way coupling. A dilute particle flow is assumed and particle–particle interactions are neglected. It was observed that the hinge region of the open pivot valve indicated a lower potential for activation of platelets compared to that in valves with a recessed hinge design. [ABSTRACT FROM AUTHOR]

Sharp interface Cartesian grid methods are capable of simulating complex moving boundary problems on fixed meshes while treating embedded interfaces accurately. This article further enhances the effectiveness of the sharp interface method by devising techniques for adaptive mesh resolution combined with parallel processing. These extensions enable dealing with problems involving disparate length scales encountered in many applications. A tree-based adaptive local mesh refinement scheme is developed to complement the sharp interface Cartesian grid method for efficient and optimised calculations. Detailed timing and accuracy data are presented for a variety of benchmark problems involving moving boundaries. Guidelines for selecting mesh refinement criteria for moving boundary calculations are developed. Issues associated with parallelisation of the overall framework are tackled. The capabilities of the method are demonstrated in a number of moving boundary problems, which require adequate resolution of a wide range of length scales and three-dimensional flows. [ABSTRACT FROM AUTHOR]

We present and validate a numerical technique for computing dendritic growth of crystals from pure melts. The solidification process is computed in the diffusion-driven limit. The governing equations are solved on a fixed Cartesian mesh and a mixed Eulerian-Lagrangian framework is used to treat the immersed phase boundary as a sharp solid-fluid interface. A conservative finite-volume discretization is employed which allows the boundary conditions to be applied exactly at the moving surface. The results from our calculations are compared with two-dimensional microscopic solvability theory. It is shown that the method predicts dendrite tip characteristics in good agreement with the theory. The sharp interface treatment allows discontinuous material property variation at the solid-liquid interface. Calculations with such discontinuities are also shown to produce results in agreement with solvability and with other sharp interface simulations. [ABSTRACT FROM AUTHOR]

We present a numerical technique for computing flowfields around moving solid boundaries immersed in fixed meshes. The mixed Eulerian–Lagrangian framework treats the immersed boundaries as sharp solid–fluid interfaces and a conservative finite volume formulation allows boundary conditions at the moving surfaces to be exactly applied. A semi-implicit second-order accurate spatial and temporal discretization is employed with a fractional-step scheme for solving the flow equations. A multigrid accelerator for the pressure Poisson equations has been developed to apply in the presence of multiple embedded solid regions on the mesh. We present applications of the method to two types of problems: (a) solidification in the presence of flows and particles, (b) fluid–structure interactions in flow control. In both these problems, the sharp interface method presents advantages by being able to track arbitrary interface motions, while capturing the full viscous, unsteady dynamics. Copyright © 2001 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

For many materials processing techniques, the meniscus of liquid bridging the crystal to the melt is critical in determining the properties of the solidified crystal. It is standard practice for existing theoretical models to use equilibrium meniscus shapes with specified contact angle to represent the behavior of the meniscus. It is shown here that with such boundary conditions, multiple solutions exist to the axisymmetric form of the Laplace–Young equation. Furthermore, these possible meniscus profiles may, depending on the interaction of Bond number, pressurization, aspect ratio and contact angle, correspond to minima, maxima or nonextrema points, as far as energy is concerned. The implications of this observation on meniscus stability are explored. The effect of direction of pulling in relation to gravity is also investigated. It appears that for tall menisci, commonly adopted equilibrium shapes may be unstable and the consequent dynamic behavior must be considered. Quasiequilibrium dynamics of the meniscus is simulated using a simplified hysteresis model for the contact angle at the top of the meniscus. A variety of behavior is found to arise, which is not fully captured by relations governing meniscus behavior used hitherto in many theoretical simulations. [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]

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]

Head-to-head comparisons of multiple experimental observations and numerical simulations on a deconstructed plastic-bonded explosive consisting of an octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine crystal embedded in a polymeric binder with a 4 ns duration 20 GPa input shock are presented. Hot spots observed in high-resolution direct numerical simulations are compared with micro-scale shock-induced reactions visualized using nanosecond microscope imaging and optical pyrometry. Despite the challenges and limitations of both the experimental and simulation techniques, an agreement is obtained on many of the observed features of hot spot evolution, e.g., (1) the magnitude and time variation of temperatures in the hot spots, (2) the time to fully consume the crystals (∼100 ns) of size (100–300 μm) employed in this study, and (3) the locations of hot spot initiation and growth. Three different mechanisms of hot spot formation are indicated by simulations: (1) high-temperature hot spots formed by pore collapse, (2) lower temperature hot spots initiated at the polymer–crystal interface near corners and asperities, and (3) high-temperature reaction waves leading to fast consumption of the energetic crystal. This first attempt at a head-to-head comparison between experiments and simulations not only provides new insight but also highlights efforts needed to bring models and experiments into closer alignment, in particular, highlighting the importance of distinctly three-dimensional and multiple mechanisms of the hot spot ignition and growth. [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]

The response of a wide class of heterogeneous energetic materials (HEs) to loads is determined by dynamics at the meso-scale, i.e., by physicochemical processes in their underlying microstructure. Structure–property–performance (S–P–P) linkages for such materials can be developed in a multi-scale framework, connecting the physics and thermophysical properties at the meso-scale to response at the macro-scale. Due to the inherent stochasticity of the microstructure, ensembles of microstructures are required to conduct meso-scale simulations to establish S–P–P linkages. Here, a deep neural network-based method called deep feature representation is applied to generate a range of material microstructures from heterogeneous energetic materials to metal foams and metallic mixtures. The method allows for the generation of stochastic microstructures using a single real microstructure as the input and is not limited to low packing density or topological complexity of solids. In its application to pressed energetic materials, we show that qualitative and quantitative features of real (i.e., imaged) microstructures are captured in the synthetic microstructures. Therefore, a stochastic ensemble of synthetic microstructures can be created for use in reactive meso-scale simulations to relate the microstructures of HEs to their performance. While the focus is on pressed HE microstructures, we also show that the method is general and useful for generating microstructures for in silico experiments for a wide range of composite/multiphase materials, which can be used to establish S–P–P linkages. [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]

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]

The hinge region of a mechanical bileaflet valve is implicated in blood damage and initiation of thrombus formation. Detailed fluid dynamic analysis in the complex geometry of the hinge region during the closing phase of the bileaflet valve is the focus of this study to understand the effect of fluid-induced stresses on the activation of platelets. A fixed-grid Cartesian mesh flow solver is used to simulate the blood flow through a two-dimensional geometry of the hinge region of a bileaflet mechanical valve. Use of local mesh refinement algorithm provides mesh adaptation based on the gradients of flow in the constricted geometry of the hinge. Leaflet motion is specified from the fluid-structure interaction analysis of the leaflet dynamics during the closing phase from a previous study, which focused on the fluid mechanics at the gap between the leaflet edges and the valve housing. A Lagrangian particle tracking method is used to model and track the platelets and to compute the magnitude of the shear stress on the platelets as they pass through the hinge region. Results show that there is a boundary layer separation in the gaps between the leaflet ear and the constricted hinge geometry. Separated shear layers roll up into vortical structures that lead to high residence times combined with exposure to high-shear stresses for particles in the hinge region. Particles are preferentially entrained into this recirculation zone, presenting the possibility of platelet activation, aggregation, and initiation of thrombi. [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]

This work presents a multiscale modeling framework for predictive simulations of shock-to-detonation transition (SDT) in pressed energetic (HMX) materials. The macro-scale computations of SDT are performed using an ignition and growth (IG) model. However, unlike in the traditional semi-empirical ignition-and-growth model, which relies on empirical fits, in this work meso-scale void collapse simulations are used to supply the ignition and growth rates. This results in a macro-scale model which is sensitive to the meso-structure of the energetic material. Energy localization at the meso-scale due to hotspot ignition and growth is reflected in the shock response of the energetic material via surrogate models for ignition and growth rates. Ensembles of meso-scale reactive void collapse simulations are used to train the surrogate model using a Bayesian Kriging approach. This meso-informed Ignition and Growth (MES-IG) model is applied to perform SDT simulations of pressed HMXs with different porosity and void diameters. The computations are successfully validated against experimental pop-plots. Additionally, the critical energy for SDT is computed and the experimentally observed P s 2 τ s = constant relations are recovered using the MES-IG model. While the multiscale framework in this paper is applied in the context of an ignition-and-growth model, the overall surrogate model-based multiscale approach can be adapted to any macro-scale model for predicting SDT in heterogeneous energetic materials. [ABSTRACT FROM AUTHOR]

Climate change mitigation demands rapid decarbonization; in cold regions such as the US Midwest, building thermal control (BTC) presents a potential for significant cuts in emissions by combining renewable energy with heat pumps. Trends in natural gas and electricity pricing over the period 2007–2020 have significantly upended economic feasibility of this decarbonization approach. Heat pump‐based BTC has moved from being cost advantageous in operations but higher GHG emitting (in 2007), to the exact opposite—higher cost but lower emitting (in 2020). Due to energy price fluctuations, the coefficient of performance required of a heat pump to breakeven on operational cost with high efficiency natural gas heating has doubled, changing from 2.25 to 4.5 over the period 2007–2019. The value of 4.5 is infeasible for all available cold‐climate heat pump systems. Thus, while electrification via both air‐source and ground‐source heat pumps is a commonly identified component of decarbonization plans in the region, actual implementation has declined. Improvements in heat pump performance, overcoming adoption barriers, and adopting policies that buffer long‐term climate solutions against short‐term price fluctuations are all needed. In part due to continuing decreases in carbon intensity of electricity, heat pump climate benefits can be substantial over project life cycles; however, there is no current policy mechanism to enable this benefit to be considered relative to short‐run economic considerations. [ABSTRACT FROM AUTHOR]

For material modeling and discovery, synthetic microstructures play a critical role as digital twins. They provide stochastic samples upon which direct numerical simulations can be conducted to populate material databases. A large ensemble of simulation data on synthetic microstructures may provide supplemental data to inform and refine macroscopic material models, which might not be feasible from physical experiments alone. However, synthesizing realistic microstructures with realistic microstructural attributes is highly challenging. Thus, it is often oversimplified via rough approximations that may yield an inaccurate representation of the physical world. Here, we propose a novel deep learning method that can synthesize realistic three-dimensional microstructures with controlled structural properties using the combination of generative adversarial networks (GAN) and actor-critic (AC) reinforcement learning. The GAN-AC combination enables the generation of microstructures that not only resemble the appearances of real specimens but also yield user-defined physical quantities of interest (QoI). Our validation experiments confirm that the properties of synthetic microstructures generated by the GAN-AC framework are within a 5% error margin with respect to the target values. The scientific contribution of this paper resides in the novel design of the GAN-AC microstructure generator and the mathematical and algorithmic foundations therein. The proposed method will have a broad and substantive impact on the materials community by providing lenses for analyzing structure-property-performance linkages and for implementing the notion of 'materials-by-design'. [ABSTRACT FROM AUTHOR]

The sensitivity of heterogeneous energetic (HE) materials (propellants, explosives, and pyrotechnics) is critically dependent on their microstructure. Initiation of chemical reactions occurs at hot spots due to energy localization at sites of porosities and other defects. Emerging multi-scale predictive models of HE response to loads account for the physics at the meso-scale, i.e. at the scale of statistically representative clusters of particles and other features in the microstructure. Meso-scale physics is infused in machine-learned closure models informed by resolved meso-scale simulations. Since microstructures are stochastic, ensembles of meso-scale simulations are required to quantify hot spot ignition and growth and to develop models for microstructure-dependent energy deposition rates. We propose utilizing generative adversarial networks (GAN) to spawn ensembles of synthetic heterogeneous energetic material microstructures. The method generates qualitatively and quantitatively realistic microstructures by learning from images of HE microstructures. We show that the proposed GAN method also permits the generation of new morphologies, where the porosity distribution can be controlled and spatially manipulated. Such control paves the way for the design of novel microstructures to engineer HE materials for targeted performance in a materials-by-design framework. [ABSTRACT FROM AUTHOR]

Morphology and dynamics at the mesoscale play crucial roles in the overall macro- or system-scale flow of heterogeneous materials. In a multi-scale framework, closure models upscale unresolved sub-grid (mesoscale) physics and therefore encapsulate structure–property (S–P) linkages to predict performance at the macroscale. This work establishes a route to S–P linkage, proceeding all the way from imaged microstructures to flow computations in one unified level-set-based framework. Level sets are used to: (1) define embedded geometries via image segmentation; (2) simulate the interaction of sharp immersed boundaries with the flow field; and (3) calculate morphological metrics to quantify structure. Mesoscale dynamics is computed to calculate sub-grid properties, i.e., closure models for momentum and energy equations. The S–P linkage is demonstrated for two types of multi-material flows: interaction of shocks with a cloud of particles and reactive meso-mechanics of pressed energetic materials. We also present an approach to connect local morphological characteristics in a microstructure containing topologically complex features with the shock response of imaged samples of such materials. This paves the way for using geometric machine learning techniques to associate imaged morphologies with their properties. [ABSTRACT FROM AUTHOR]

Surrogate models for hotspot ignition and growth rates were presented in Part I (Nassar et al., Shock Waves 29(4):537–558, 2018), where the hotspots were formed by the collapse of single cylindrical voids. Such isolated cylindrical voids are idealizations of the void morphology in real meso-structures. This paper therefore investigates the effect of non-cylindrical void shapes and void–void interactions on hotspot ignition and growth. Surrogate models capturing these effects are constructed using a Bayesian Kriging approach. The training data for machine learning the surrogates are derived from reactive void collapse simulations spanning the parameter space of void aspect ratio, void orientation (θ) , and void fraction (ϕ) . The resulting surrogate models portray strong dependence of the ignition and growth rates on void aspect ratio and orientation, particularly when they are oriented at acute angles with respect to the imposed shock. The surrogate models for void interaction effects show significant changes in hotspot ignition and growth rates as the void fraction increases. The paper elucidates the physics of hotspot evolution in void fields due to the creation and interaction of multiple hotspots. The results from this work will be useful not only for constructing meso-informed macroscale models of HMX, but also for understanding the physics of void–void interactions and sensitivity due to void shape and orientation. [ABSTRACT FROM AUTHOR]

This work presents the procedure for constructing a machine-learned surrogate model for hot-spot ignition and growth rates in pressed HMX materials. A Bayesian kriging algorithm is used to assimilate input data obtained from high-resolution mesoscale simulations. The surrogates are built by generating a sparse set of training data using reactive mesoscale simulations of void collapse by varying loading conditions and void sizes. Insights into the physics of void collapse and ignition and growth of hot spots are obtained. The criticality envelope for hot spots is obtained as the function Σ cr = f P s , D void where P s is the imposed shock pressure and D void is the void size. Criticality of hot spots is classified into the plastic collapse and hydrodynamic jetting regimes. The information obtained from the surrogate models for hot-spot ignition and growth rates and the criticality envelope can be utilized in meso-informed ignition and growth models to perform multi-scale simulations of pressed HMX materials. [ABSTRACT FROM AUTHOR]

Macroscale computations of shocked particle-laden flows rely on closure laws to model the heat transfer between the fluid and particle phases. Typically, closure models are semiempirical and obtained for a limited range of parameters because experiments can be difficult and expensive to perform. This paper describes an approach to obtain closures for heat and momentum exchanges from ensembles of high-fidelity mesoscale computations of shock-cylinder interactions. The simulations are performed for flow over a single cylinder for a wide range of Reynolds ReD and Mach numbers Ms. The results are used to construct a metamodel for the drag coefficient CD and the Nusselt number Nu correlation using a modified Bayesian kriging method. To study the effects of the particle volume fraction ϕ, mesoscale computations are performed for cylinder clusters and the Nu and CD are calculated. The metamodel shows that, although the Nusselt number Nu is primarily a function of the ReD, the Ms and ϕ also significantly affect the interphase heat transfer. In particular, the Nusselt number Nu first decreases until Ms~1.5-1.8 and increases for values of Ms>1.8. The results show that compressibility and viscous effects must be taken into account to provide accurate closure laws for interphase heat transfer in shocked particle-laden flows. [ABSTRACT FROM AUTHOR]

Macroscale models of shock-particle interactions require closure terms for unresolved solid-fluid momentum and energy transfer. These comprise the effects of mean as well as fluctuating fluid-phase velocity fields in the particle cloud. Mean drag and Reynolds stress equivalent terms (also known as pseudo-turbulent terms) appear in the macroscale equations. Closure laws for the pseudo-turbulent terms are constructed in this work from ensembles of high-fidelity mesoscale simulations. The computations are performed over a wide range of Mach numbers (M) and particle volume fractions (ϕ) and are used to explicitly compute the pseudo-turbulent stresses from the Favre average of the velocity fluctuations in the flow field. The computed stresses are then used as inputs to a Modified Bayesian Kriging method to generate surrogate models. The surrogates can be used as closure models for the pseudo-turbulent terms in macroscale computations of shock-particle interactions. It is found that the kinetic energy associated with the velocity fluctuations is comparable to that of the mean flow—especially for increasing M and ϕ. This work is a first attempt to quantify and evaluate the effect of velocity fluctuations for problems of shock-particle interactions. [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]