Toward a Predictive Hierarchical Multiscale Modeling Approach for Energetic Materials

This chapter describes efforts to enable multiscale modeling of energetic material response to insult through a concurrent hierarchical multiscale framework. As a demonstration, a quantum-derived, particle-based coarse-grain model of an energetic material is used to provide part of the constitutive response in a finite element multiphysics simulation. Bottom-up coarse-grain models of hexahydro-1,3,5-trinitro-s-triazine (RDX) and the methods used to perform reactive simulations at the microscale will be described. Simulations demonstrating microstructure-dependent initiation are also presented. Research opportunities addressing the remaining challenges related to detonation are discussed.

[1]  G. Ji,et al.  Initial decomposition of the condensed-phase β-HMX under shock waves: molecular dynamics simulations. , 2012, The journal of physical chemistry. B.

[2]  Pep Español,et al.  Markovian approximation in a coarse-grained description of atomic systems. , 2006, The Journal of chemical physics.

[3]  J. Koelman,et al.  Dynamic simulations of hard-sphere suspensions under steady shear , 1993 .

[4]  Kaushik L Joshi,et al.  Reactive simulation of the chemistry behind the condensed-phase ignition of RDX from hot spots. , 2015, Physical chemistry chemical physics : PCCP.

[5]  B. Rice.  A perspective on modeling the multiscale response of energetic materials , 2015 .

[6]  Gregory A Voth,et al.  Efficient, Regularized, and Scalable Algorithms for Multiscale Coarse-Graining. , 2010, Journal of chemical theory and computation.

[7]  E. Dougherty,et al.  Big data need big theory too , 2016, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[8]  Fpt Frank Baaijens,et al.  An approach to micro-macro modeling of heterogeneous materials , 2001 .

[9]  L. Fried.  The Reactivity of Energetic Materials At Extreme Conditions , 2006 .

[10]  Florian Müller-Plathe,et al.  Classical reactive molecular dynamics implementations: state of the art. , 2012, Chemphyschem : a European journal of chemical physics and physical chemistry.

[11]  M. Couty,et al.  Conservative and dissipative force field for simulation of coarse-grained alkane molecules: a bottom-up approach. , 2014, The Journal of chemical physics.

[12]  Julia Ling,et al.  Machine learning strategies for systems with invariance properties , 2016, J. Comput. Phys..

[13]  Leo Breiman,et al.  Statistical Modeling: The Two Cultures (with comments and a rejoinder by the author) , 2001 .

[14]  Julien Roussel,et al.  New parallelizable schemes for integrating the Dissipative Particle Dynamics with Energy conservation. , 2016, The Journal of chemical physics.

[15]  Ying Li,et al.  Multistage reaction pathways in detonating high explosives , 2014 .

[16]  N. Barton,et al.  Defect evolution and pore collapse in crystalline energetic materials , 2009 .

[17]  S. Izvekov.  Mori-Zwanzig theory for dissipative forces in coarse-grained dynamics in the Markov limit. , 2017, Physical review. E.

[18]  W G Noid,et al.  Perspective: Coarse-grained models for biomolecular systems. , 2013, The Journal of chemical physics.

[19]  I. Pagonabarraga,et al.  Dissipative particle dynamics for interacting systems , 2001, cond-mat/0105075.

[20]  D. Scott Stewart,et al.  The Dynamics of Detonation in Explosive Systems , 2007 .

[21]  E. Reed,et al.  Simulations of shocked methane including self-consistent semiclassical quantum nuclear effects. , 2012, The journal of physical chemistry. A.

[22]  W. Goddard,et al.  Elucidation of the Dynamics for Hot-Spot Initiation at Nonuniform Interfaces of Highly Shocked Materials , 2011 .

[23]  Martin Ostoja-Starzewski,et al.  Stochastic finite elements as a bridge between random material microstructure and global response , 1999 .

[24]  Somnath Ghosh.  Foundational aspects of a multi-scale modeling framework for composite materials , 2015, Integrating Materials and Manufacturing Innovation.

[25]  Sergei Izvekov,et al.  The multiscale coarse-graining method: assessing its accuracy and introducing density dependent coarse-grain potentials. , 2010, The Journal of chemical physics.

[26]  B. Rice,et al.  On the importance of shear dissipative forces in coarse-grained dynamics of molecular liquids. , 2015, Physical chemistry chemical physics : PCCP.

[27]  Wing Kam Liu,et al.  Nonlinear Finite Elements for Continua and Structures , 2000 .

[28]  W. Goddard,et al.  Initial Steps of Thermal Decomposition of Dihydroxylammonium 5,5′-bistetrazole-1,1′-diolate Crystals from Quantum Mechanics , 2014 .

[29]  E. Reed.  Electron-Ion Coupling in Shocked Energetic Materials , 2012 .

[30]  M. Cawkwell,et al.  Equations of state for the α and γ polymorphs of cyclotrimethylene trinitramine , 2016 .

[31]  Bernard Haasdonk,et al.  Surrogate modeling of multiscale models using kernel methods , 2015 .

[32]  H. S. Udaykumar,et al.  Evaluation of convergence behavior of metamodeling techniques for bridging scales in multi-scale multimaterial simulation , 2015, J. Comput. Phys..

[33]  Heming Xiao,et al.  Initial chemical events in shocked octahydro-1,3,5,7-tetranitro-1,3,5,7- tetrazocine: a new initiation decomposition mechanism. , 2012, The Journal of chemical physics.

[34]  A. Strachan,et al.  Thermal conduction in molecular materials using coarse grain dynamics: role of mass diffusion and quantum corrections for molecular dynamics simulations. , 2009, The Journal of chemical physics.

[35]  S. Menon,et al.  A model for hot spot formation in shocked energetic materials , 2015 .

[36]  E. Reed,et al.  Explosive chemistry: Simulating the chemistry of energetic materials at extreme conditions , 2003 .

[37]  Jinshan Li,et al.  Influence of Dislocations on the Shock Sensitivity of RDX: Molecular Dynamics Simulations by Reactive Force Field , 2015 .

[38]  X. Long,et al.  Cluster evolution during the early stages of heating explosives and its relationship to sensitivity: a comparative study of TATB, β-HMX and PETN by molecular reactive force field simulations. , 2015, Physical chemistry chemical physics : PCCP.

[39]  D. Scott Stewart,et al.  Equation of state and reaction rate for condensed-phase explosives , 2005 .

[40]  M Scott Shell,et al.  The relative entropy is fundamental to multiscale and inverse thermodynamic problems. , 2008, The Journal of chemical physics.

[41]  M. Baer.  Mesoscale Modeling of Shocks in Heterogeneous Reactive Materials , 2007 .

[42]  P. G. Hall.  Thermal decomposition and phase transitions in solid nitramines , 1971 .

[43]  A. V. van Duin,et al.  Development of a ReaxFF reactive force field for ammonium nitrate and application to shock compression and thermal decomposition. , 2014, The journal of physical chemistry. A.

[44]  L. Soulard,et al.  A reduced model for shock and detonation waves. II. The reactive case , 2007, cond-mat/0701496.

[45]  Blaine W. Asay,et al.  IGNITION CHEMISTRY IN HMX FROM THERMAL EXPLOSION TO DETONATION , 2001 .

[46]  Ioannis G. Kevrekidis,et al.  Good coupling for the multiscale patch scheme on systems with microscale heterogeneity , 2017, J. Comput. Phys..

[47]  J. Ávalos,et al.  Dissipative particle dynamics with energy conservation: Modelling of heat flow , 1999 .

[48]  Yushi Wen,et al.  Early Decay Mechanism of Shocked ε-CL-20: A Molecular Dynamics Simulation Study , 2016 .

[49]  E Weinan,et al.  The heterogeneous multiscale method* , 2012, Acta Numerica.

[50]  S. Haussühl.  Elastic and thermoelastic properties of selected organic crystals: acenaphthene, trans-azobenzene, benzophenone, tolane, trans-stilbene, dibenzyl, diphenyl sulfone, 2,2´-biphenol, urea, melamine, hexogen, succinimide, pentaerythritol, urotropine, malonic acid, dimethyl malonic acid, maleic acid, hip , 2001 .

[51]  Christoph Dellago,et al.  Neural networks for local structure detection in polymorphic systems. , 2013, The Journal of chemical physics.

[52]  Ignacio Pagonabarraga,et al.  Self-consistent dissipative particle dynamics algorithm , 1998 .

[53]  Shi-aki Hyodo,et al.  Equation of motion for coarse-grained simulation based on microscopic description. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[54]  P. A. Urtiew,et al.  Nonequilibrium Zeldovich-von Neumann-Doring theory and reactive flow modeling of detonation , 2007 .

[55]  R. C. Picu,et al.  Molecular conformational stability in cyclotrimethylene trinitramine crystals. , 2011, The Journal of chemical physics.

[56]  M. Baer,et al.  Probabilistic models for reactive behaviour in heterogeneous condensed phase media , 2010 .

[57]  Zhen Li,et al.  Multiscale Universal Interface: A concurrent framework for coupling heterogeneous solvers , 2014, J. Comput. Phys..

[58]  M. Shell,et al.  COARSE‐GRAINING WITH THE RELATIVE ENTROPY , 2016 .

[59]  Ellad B. Tadmor,et al.  A unified framework and performance benchmark of fourteen multiscale atomistic/continuum coupling methods , 2009 .

[60]  R. Yetter,et al.  Development of Gas-Phase Reaction Mechanisms for Nitramine Combustion , 1995 .

[61]  Florian Müller-Plathe,et al.  Coarse-graining in polymer simulation: from the atomistic to the mesoscopic scale and back. , 2002, Chemphyschem : a European journal of chemical physics and physical chemistry.

[62]  J. Behler.  Perspective: Machine learning potentials for atomistic simulations. , 2016, The Journal of chemical physics.

[63]  W. Goddard,et al.  ReaxFF reactive molecular dynamics on silicon pentaerythritol tetranitrate crystal validates the mechanism for the colossal sensitivity. , 2014, Physical chemistry chemical physics : PCCP.

[64]  Sudhir B. Kylasa,et al.  The ReaxFF reactive force-field: development, applications and future directions , 2016 .

[65]  John K. Brennan,et al.  CECAM Workshop: ‘Dissipative particle dynamics: addressing deficiencies and establishing new frontiers’ (16–18 July 2008, Lausanne, Switzerland) , 2009 .

[66]  Jörg F. Unger,et al.  Multiscale Modeling of Concrete , 2011 .

[67]  Jaroslaw Knap,et al.  A computational framework for scale‐bridging in multi‐scale simulations , 2016 .

[68]  W. Goddard,et al.  Compressive Shear Reactive Molecular Dynamics Studies Indicating That Cocrystals of TNT/CL-20 Decrease Sensitivity , 2014 .

[69]  C. Eckhardt,et al.  The elastic constants and related properties of the energetic material cyclotrimethylene trinitramine (RDX) determined by Brillouin scattering. , 2006, The Journal of chemical physics.

[70]  W. Goddard,et al.  Prediction of the Chapman-Jouguet chemical equilibrium state in a detonation wave from first principles based reactive molecular dynamics. , 2016, Physical chemistry chemical physics : PCCP.

[71]  L. Fried,et al.  The Reactivity of Energetic Materials Under High Pressure and Temperature , 2014 .

[72]  Li‐Min Liu,et al.  Dynamic Responses and Initial Decomposition under Shock Loading: A DFTB Calculation Combined with MSST Method for β-HMX with Molecular Vacancy. , 2015, The journal of physical chemistry. B.

[73]  Zhenwei Li,et al.  Molecular dynamics with on-the-fly machine learning of quantum-mechanical forces. , 2015, Physical review letters.

[74]  L. Fried,et al.  Decomposition of HMX at extreme conditions: A molecular dynamics simulation , 2002 .

[75]  W. Goddard,et al.  Inhibition of Hotspot Formation in Polymer Bonded Explosives Using an Interface Matching Low Density Polymer Coating at the Polymer–Explosive Interface , 2014 .

[76]  L. Lucy.  A numerical approach to the testing of the fission hypothesis. , 1977 .

[77]  Gregory A Voth,et al.  The multiscale coarse-graining method. II. Numerical implementation for coarse-grained molecular models. , 2008, The Journal of chemical physics.

[78]  E Weinan,et al.  Heterogeneous multiscale methods: A review , 2007 .

[79]  William D. Mattson,et al.  Parallel implementation of isothermal and isoenergetic Dissipative Particle Dynamics using Shardlow-like splitting algorithms , 2014, Comput. Phys. Commun..

[80]  Avisek Das,et al.  The multiscale coarse-graining method. III. A test of pairwise additivity of the coarse-grained potential and of new basis functions for the variational calculation. , 2009, The Journal of chemical physics.

[81]  Kurt Kremer,et al.  Multiscale simulation of soft matter systems – from the atomistic to the coarse-grained level and back , 2009 .

[82]  Ilias Bilionis,et al.  Gaussian processes with built-in dimensionality reduction: Applications in high-dimensional uncertainty propagation , 2016, 1602.04550.

[83]  R. Kosloff,et al.  Atomistic-scale simulations of the initial chemical events in the thermal initiation of triacetonetriperoxide. , 2005, Journal of the American Chemical Society.

[84]  T. Sewell,et al.  Characteristics of energy exchange between inter- and intramolecular degrees of freedom in crystalline 1,3,5-triamino-2,4,6-trinitrobenzene (TATB) with implications for coarse-grained simulations of shock waves in polyatomic molecular crystals. , 2016, The Journal of chemical physics.

[85]  D. McDowell.  A perspective on trends in multiscale plasticity , 2010 .

[86]  Valentina Tozzini,et al.  Coarse-grained models for proteins. , 2005, Current opinion in structural biology.

[87]  Thomas L. Jackson,et al.  Modeling the Microstructure of Energetic Materials with Realistic Constituent Morphology , 2011 .

[88]  Anuj Chaudhri,et al.  Velocity and stress autocorrelation decay in isothermal dissipative particle dynamics. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[89]  Heming Xiao,et al.  Coupling of temperature with pressure induced initial decomposition mechanisms of two molecular crystals: An ab initio molecular dynamics study , 2016, Journal of Chemical Sciences.

[90]  Jack J. Dongarra,et al.  Exascale computing and big data , 2015, Commun. ACM.

[91]  Matthias Rupp,et al.  Big Data Meets Quantum Chemistry Approximations: The Δ-Machine Learning Approach. , 2015, Journal of chemical theory and computation.

[92]  J. Koelman,et al.  Simulating microscopic hydrodynamic phenomena with dissipative particle dynamics , 1992 .

[93]  C. M. Tarver,et al.  Phenomenological model of shock initiation in heterogeneous explosives , 1980 .

[94]  S. Klippenstein.  From theoretical reaction dynamics to chemical modeling of combustion , 2017 .

[95]  Sergei Izvekov,et al.  Multi-scale coarse-graining of non-conservative interactions in molecular liquids. , 2014, The Journal of chemical physics.

[96]  Al Geist,et al.  A survey of high-performance computing scaling challenges , 2017, Int. J. High Perform. Comput. Appl..

[97]  G. Ji,et al.  Pressure-induced metallization of condensed phase β-HMX under shock loadings via molecular dynamics simulations in conjunction with multi-scale shock technique , 2014, Journal of Molecular Modeling.

[98]  Gregory A Voth,et al.  The multiscale coarse-graining method. X. Improved algorithms for constructing coarse-grained potentials for molecular systems. , 2012, The Journal of chemical physics.

[99]  T. Sewell,et al.  Monte Carlo calculations of the elastic moduli and pressure-volume-temperature equation of state for hexahydro-1,3,5-trinitro-1,3,5-triazine , 2000 .

[100]  Nirmal Kumar Rai,et al.  Mesoscale simulation of reactive pressed energetic materials under shock loading , 2015 .

[101]  M. Lísal,et al.  Free-energy calculations using classical molecular simulation: application to the determination of the melting point and chemical potential of a flexible RDX model. , 2016, Physical chemistry chemical physics : PCCP.

[102]  Gregory A Voth,et al.  The multiscale coarse-graining method. IV. Transferring coarse-grained potentials between temperatures. , 2009, The Journal of chemical physics.

[103]  Eric Darve,et al.  Computing generalized Langevin equations and generalized Fokker–Planck equations , 2009, Proceedings of the National Academy of Sciences.

[104]  Jim Pfaendtner,et al.  Lexicography of kinetic modeling of complex reaction networks , 2005 .

[105]  W. Brekelmans,et al.  FE2 computational homogenization for the thermo-mechanical analysis of heterogeneous solids , 2008 .

[106]  Crystal structure prediction for cyclotrimethylene trinitramine (RDX) from first principles. , 2009, Physical chemistry chemical physics : PCCP.

[107]  Gregory A Voth,et al.  Multiscale coarse graining of liquid-state systems. , 2005, The Journal of chemical physics.

[108]  Ilpo Vattulainen,et al.  Integration schemes for dissipative particle dynamics simulations: From softly interacting systems towards hybrid models , 2002, cond-mat/0211332.

[109]  W. Goddard,et al.  The co-crystal of TNT/CL-20 leads to decreased sensitivity toward thermal decomposition from first principles based reactive molecular dynamics , 2015 .

[110]  B. Rice,et al.  Theoretical Study of Shocked Formic Acid: Born-Oppenheimer MD Calculations of the Shock Hugoniot and Early-Stage Chemistry. , 2016, The journal of physical chemistry. B.

[111]  Roger A. Sauer,et al.  A CONTINUUM MECHANICAL SURROGATE MODEL FOR ATOMIC BEAM STRUCTURES , 2015 .

[112]  Karel Matous,et al.  A nonlinear manifold-based reduced order model for multiscale analysis of heterogeneous hyperelastic materials , 2016, J. Comput. Phys..

[113]  E. Reed,et al.  Nitrogen-rich heterocycles as reactivity retardants in shocked insensitive explosives. , 2009, Journal of the American Chemical Society.

[114]  S. Kalidindi,et al.  Estimating the response of polycrystalline materials using sets of weighted statistical volume elements , 2012 .

[115]  Berend Smit,et al.  Mesoscopic models of biological membranes , 2006 .

[116]  Particle Based Multi-Scale Modeling of the Dynamic Response of RDX , 2011 .

[117]  M. Ostoja-Starzewski.  Material spatial randomness: From statistical to representative volume element☆ , 2006 .

[118]  R. D. Groot,et al.  Mesoscopic model for colloidal particles, powders, and granular solids. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[119]  Decarlos Taylor.  Pressure dependent elastic constants of alpha and gamma cyclotrimethylene trinitramine: A quantum mechanical study , 2014 .

[120]  Maj Thijs Michels,et al.  Thermodynamic consistency in dissipative particle dynamics simulations of strongly nonideal liquids and liquid mixtures , 2002 .

[121]  V. Kouznetsova,et al.  Multi‐scale constitutive modelling of heterogeneous materials with a gradient‐enhanced computational homogenization scheme , 2002 .

[122]  Avisek Das,et al.  The multiscale coarse-graining method. VIII. Multiresolution hierarchical basis functions and basis function selection in the construction of coarse-grained force fields. , 2012, The Journal of chemical physics.

[123]  Introduction to Detonation Physics , 1998 .

[124]  B. Rice,et al.  Quantum-Informed Multiscale M&S for Energetic Materials , 2014 .

[125]  Kipton Barros,et al.  Spatial adaptive sampling in multiscale simulation , 2014, Comput. Phys. Commun..

[126]  Jaroslaw Knap,et al.  A call to arms for task parallelism in multi‐scale materials modeling , 2011 .

[127]  M. R. Baer,et al.  Modeling heterogeneous energetic materials at the mesoscale , 2002 .

[128]  B. Holian,et al.  Energy exchange between mesoparticles and their internal degrees of freedom. , 2005, Physical review letters.

[129]  James P. Larentzos,et al.  Transferable Reactive Force Fields: Extensions of ReaxFF-lg to Nitromethane. , 2017, The journal of physical chemistry. A.

[130]  Tony Shardlow,et al.  Splitting for Dissipative Particle Dynamics , 2002, SIAM J. Sci. Comput..

[131]  Leo Breiman,et al.  Statistical Modeling: The Two Cultures (with comments and a rejoinder by the author) , 2001, Statistical Science.

[132]  A. Strachan,et al.  Nonequilibrium Reaction Kinetics in Molecular Solids , 2016 .

[133]  Julien Yvonnet,et al.  Multiscale modeling of microstructure–property relations , 2016 .

[134]  Gregory A Voth,et al.  The multiscale coarse-graining method. VII. Free energy decomposition of coarse-grained effective potentials. , 2011, The Journal of chemical physics.

[135]  F. Huang,et al.  Anisotropic shock sensitivity in a single crystal δ-cyclotetramethylene tetranitramine: a reactive molecular dynamics study. , 2015, Physical chemistry chemical physics : PCCP.

[136]  Avisek Das,et al.  The multiscale coarse-graining method. IX. A general method for construction of three body coarse-grained force fields. , 2012, The Journal of chemical physics.

[137]  Gregory A Voth,et al.  A multiscale coarse-graining method for biomolecular systems. , 2005, The journal of physical chemistry. B.

[138]  Surya R. Kalidindi,et al.  Materials Data Science: Current Status and Future Outlook , 2015 .

[139]  P. Español,et al.  Dissipative particle dynamics with energy conservation , 1997 .

[140]  J. Elliott.  Novel approaches to multiscale modelling in materials science , 2011 .

[141]  Gregory A Voth,et al.  The multiscale coarse-graining method. VI. Implementation of three-body coarse-grained potentials. , 2010, The Journal of chemical physics.

[142]  A. V. Duin,et al.  ReaxFF: A Reactive Force Field for Hydrocarbons , 2001 .

[143]  D. Stewart,et al.  Mirrored continuum and molecular scale simulations of the ignition of high-pressure phases of RDX. , 2016, The Journal of chemical physics.

[144]  A. Niklasson,et al.  Extended Lagrangian Born-Oppenheimer molecular dynamics simulations of the shock-induced chemistry of phenylacetylene. , 2015, The Journal of chemical physics.

[145]  Dirk Reith,et al.  Deriving effective mesoscale potentials from atomistic simulations , 2002, J. Comput. Chem..

[146]  Matej Praprotnik,et al.  Transport properties controlled by a thermostat: An extended dissipative particle dynamics thermostat. , 2007, Soft matter.

[147]  X. Long,et al.  Cluster Evolution at Early Stages of 1,3,5-Triamino-2,4,6-trinitrobenzene under Various Heating Conditions: A Molecular Reactive Force Field Study. , 2016, The journal of physical chemistry. A.

[148]  A. Louis.  Beware of density dependent pair potentials , 2002, cond-mat/0205110.

[149]  F. Huang,et al.  Hot spot formation and chemical reaction initiation in shocked HMX crystals with nanovoids: a large-scale reactive molecular dynamics study. , 2016, Physical chemistry chemical physics : PCCP.

[150]  Gabriel Stoltz.  Stable schemes for dissipative particle dynamics with conserved energy , 2017, J. Comput. Phys..

[151]  R. Kosloff,et al.  Effects of Nanoscale Heterogeneities on the Reactivity of Shocked Erythritol Tetranitrate , 2016 .

[152]  Gregory A. Voth,et al.  The multiscale coarse-graining method. I. A rigorous bridge between atomistic and coarse-grained models. , 2008, The Journal of chemical physics.

[153]  Harold S. Park,et al.  The bridging scale for two-dimensional atomistic/continuum coupling , 2005 .

[154]  Giovanni Samaey,et al.  Equation-free multiscale computation: algorithms and applications. , 2009, Annual review of physical chemistry.

[155]  E. Reed,et al.  A transient semimetallic layer in detonating nitromethane , 2008 .

[156]  S. N. Todd,et al.  Modeling Damage Induced Initiation of Explosives , 2012 .

[157]  C. Tarver.  Detonation Reaction Zones in Condensed Explosives , 2005 .

[158]  R. Buckingham,et al.  The Classical Equation of State of Gaseous Helium, Neon and Argon , 1938 .

[159]  E. Prince,et al.  The crystal structure of cyclotrimethylenetrinitramine , 1972 .

[160]  Richard D. Hornung,et al.  Adaptive sampling in hierarchical simulation , 2007 .

[161]  Qiang Wu,et al.  Special catalytic effects of intermediate-water for rapid shock initiation of β-HMX , 2016 .

[162]  B. Rice,et al.  Particle-based multiscale coarse graining with density-dependent potentials: application to molecular crystals (hexahydro-1,3,5-trinitro-s-triazine). , 2011, The Journal of chemical physics.

[163]  Naresh Chennamsetty,et al.  An introduction to coarse-graining approaches: linking atomistic and mesoscales , 2011 .

[164]  Arindrajit Chowdhury,et al.  Analysis of RDX-TAGzT pseudo-propellant combustion with detailed chemical kinetics , 2011 .

[165]  Michael L. Klein,et al.  Coarse grain models and the computer simulation of soft materials , 2004 .

[166]  E. Reed,et al.  Quantum mechanical corrections to simulated shock Hugoniot temperatures. , 2009, The Journal of chemical physics.

[167]  E. Bourasseau,et al.  Ab initio simulations of thermodynamic and chemical properties of detonation product mixtures. , 2009, The Journal of chemical physics.

[168]  A. V. van Duin,et al.  ReaxFF reactive force field for molecular dynamics simulations of hydrocarbon oxidation. , 2008, The journal of physical chemistry. A.

[169]  James P. Larentzos,et al.  Coarse-Grain Model Simulations of Nonequilibrium Dynamics in Heterogeneous Materials. , 2014, The journal of physical chemistry letters.

[170]  F. Zhang.  Shock Waves Science and Technology Library, Vol. 6 , 2012 .

[171]  Janna K. Maranas,et al.  Why are coarse-grained force fields too fast? A look at dynamics of four coarse-grained polymers. , 2011, The Journal of chemical physics.

[172]  E. Vanden-Eijnden,et al.  Mori-Zwanzig formalism as a practical computational tool. , 2010, Faraday discussions.

[173]  A. Nichols,et al.  Application of the Peng–Robinson Equation of State to Energetic Materials RDX and TNT: Pure Components, Liquid Mixtures, and Solid Mixtures , 2016 .

[174]  James Theiler,et al.  Adaptive Strategies for Materials Design using Uncertainties , 2016, Scientific Reports.

[175]  Avisek Das,et al.  The multiscale coarse-graining method. V. Isothermal-isobaric ensemble. , 2010, The Journal of chemical physics.

[176]  S. Solares,et al.  Simulations of high-pressure phases in RDX. , 2011, The journal of physical chemistry. B.

[177]  Jaroslaw Knap,et al.  LAMMPS integrated materials engine (LIME) for efficient automation of particle-based simulations: application to equation of state generation , 2017 .

[178]  H. S. Fogler,et al.  Elements of Chemical Reaction Engineering , 1986 .

[179]  M. Ortiz,et al.  Shock-induced subgrain microstructures as possible homogenous sources of hot spots and initiation sites in energetic polycrystals , 2010 .

[180]  Nir Goldman,et al.  Catalytic behaviour of dense hot water. , 2009, Nature chemistry.

[181]  William J. Rider,et al.  Sensitivity analysis techniques applied to a system of hyperbolic conservation laws , 2012, Reliab. Eng. Syst. Saf..

[182]  L. Fried,et al.  Direct numerical simulation of shear localization and decomposition reactions in shock-loaded HMX crystal , 2015 .

[183]  H. Cady.  Coefficient of thermal expansion of pentaerythritol tetranitrate and hexahydro-1,3,5-trinitro-s-triazine (RDX) , 1972 .

[184]  E. Reed,et al.  A method for tractable dynamical studies of single and double shock compression. , 2003 .

[185]  ERRATUM: A reduced model for shock and detonation waves. I. The inert case , 2006, cond-mat/0610038.

[186]  F. Huang,et al.  Shock initiated thermal and chemical responses of HMX crystal from ReaxFF molecular dynamics simulation. , 2014, Physical chemistry chemical physics : PCCP.

[187]  Martin Lísal,et al.  Dissipative particle dynamics at isothermal, isobaric, isoenergetic, and isoenthalpic conditions using Shardlow-like splitting algorithms. , 2011, The Journal of chemical physics.

[188]  Chris Oostenbrink,et al.  Are Automated Molecular Dynamics Simulations and Binding Free Energy Calculations Realistic Tools in Lead Optimization? An Evaluation of the Linear Interaction Energy (LIE) Method , 2006, J. Chem. Inf. Model..

[189]  Heming Xiao,et al.  Decomposition of a 1,3,5-Triamino-2,4,6-trinitrobenzene Crystal at Decomposition Temperature Coupled with Different Pressures: An ab Initio Molecular Dynamics Study , 2015 .

[190]  Heming Xiao,et al.  Cooperative effects of different temperatures and pressures on the initial and subsequent decomposition reactions of the nitrogen-rich energetic crystal 3,3'-dinitroamino-4,4'-azoxyfurazan. , 2016, Physical chemistry chemical physics : PCCP.

[191]  Wei Chen,et al.  Statistical volume element method for predicting microstructure–constitutive property relations , 2008 .

[192]  James E. Gubernatis,et al.  Multi-fidelity machine learning models for accurate bandgap predictions of solids , 2017 .

[193]  P. B. Warren.  Vapor-liquid coexistence in many-body dissipative particle dynamics. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[194]  E. Kober,et al.  Ultrafast Chemistry under Nonequilibrium Conditions and the Shock to Deflagration Transition at the Nanoscale , 2015 .

[195]  Grant D. Smith,et al.  Quantum chemistry based force field for simulations of HMX , 1999 .

[196]  Donald W. Brenner,et al.  A second-generation reactive empirical bond order (REBO) potential energy expression for hydrocarbons , 2002 .

[197]  G. Ji,et al.  Anisotropic responses and initial decomposition of condensed-phase β-HMX under shock loadings via molecular dynamics simulations in conjunction with multiscale shock technique. , 2014, The journal of physical chemistry. B.

[198]  Xiaoxing Zhang,et al.  Molecular dynamics simulations for 5,5′-bistetrazole-1,1′-diolate (TKX-50) and its PBXs , 2016 .

[199]  John Shalf,et al.  The International Exascale Software Project roadmap , 2011, Int. J. High Perform. Comput. Appl..

[200]  G. Stoltz,et al.  Mesoscopic simulations of shock-to-detonation transition in reactive liquid high explosive , 2011 .

[201]  J. Monaghan.  Smoothed particle hydrodynamics , 2005 .

[202]  Steve Plimpton,et al.  Fast parallel algorithms for short-range molecular dynamics , 1993 .

[203]  Kipton Barros,et al.  Distributed Database Kriging for Adaptive Sampling (D2KAS) , 2015, Comput. Phys. Commun..

[204]  W. Schommers.  A pair potential for liquid rubidium from the pair correlation function , 1973 .

[205]  I. Vattulainen,et al.  How would you integrate the equations of motion in dissipative particle dynamics simulations , 2003 .

[206]  Heming Xiao,et al.  How does low temperature coupled with different pressures affect initiation mechanisms and subsequent decompositions in nitramine explosive HMX? , 2015, Physical chemistry chemical physics : PCCP.

[207]  W. Goddard,et al.  Initial decomposition reaction of di-tetrazine-tetroxide (DTTO) from quantum molecular dynamics: implications for a promising energetic material , 2015 .

[208]  O. Sharia,et al.  Molecular Theory of Detonation Initiation: Insight from First Principles Modeling of the Decomposition Mechanisms of Organic Nitro Energetic Materials , 2016, Molecules.

[209]  Hieu Chi Dam,et al.  Novel mixture model for the representation of potential energy surfaces. , 2016, The Journal of chemical physics.

[210]  J. Ávalos,et al.  Dissipative particle dynamics with energy conservation , 1997, cond-mat/9706217.

[211]  W. Goddard,et al.  Reaction mechanism from quantum molecular dynamics for the initial thermal decomposition of 2,4,6-triamino-1,3,5-triazine-1,3,5-trioxide (MTO) and 2,4,6-trinitro-1,3,5-triazine-1,3,5-trioxide (MTO3N), promising green energetic materials , 2015 .

[212]  A. Strachan,et al.  Coarse grain modeling of spall failure in molecular crystals: role of intra-molecular degrees of freedom , 2008 .

[213]  V. G. Kouznetsova,et al.  Multi-scale computational homogenization: Trends and challenges , 2010, J. Comput. Appl. Math..

[214]  Marc G. D. Geers,et al.  A review of predictive nonlinear theories for multiscale modeling of heterogeneous materials , 2017, J. Comput. Phys..

[215]  J. N. Johnson,et al.  Shock‐wave initiation of heterogeneous reactive solids , 1985 .

[216]  Sidney Yip,et al.  Multiscale materials modelling at the mesoscale. , 2013, Nature materials.

[217]  J. Reaugh.  HERMES: A Model to Describe Deformation, Burning, Explosion, and Detonation , 2011 .

[218]  Brian C. Barnes,et al.  A coarse-grain force field for RDX: Density dependent and energy conserving. , 2016, The Journal of chemical physics.

[219]  E. Reed,et al.  A multi-scale approach to molecular dynamics simulations of shock waves , 2004 .

[220]  M. Manaa,et al.  Ultrafast detonation of hydrazoic acid (HN3). , 2012, Physical review letters.

[221]  Sándor Suhai,et al.  Self-consistent-charge density-functional tight-binding method for simulations of complex materials properties , 1998 .