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Modeling mesoscale energy localization in shocked HMX, part I: machine-learned surrogate models for the effects of loading and void sizes

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Abstract

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 \( \varSigma_{\text{cr}} = f\left( {P_{\text{s}} ,D_{\text{void}} } \right) \) where \( P_{\text{s}} \) is the imposed shock pressure and \( D_{\text{void}} \) 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.

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References

  1. Molek, C., Welle, E.: Private Communication, Image obtained by Ryan Wixom (LANL)

  2. Mader, C.L.: Numerical Modeling of Explosives and Propellants. CRC Press, Boca Raton (2007)

    Book  Google Scholar 

  3. Field, J.E.: Hot spot ignition mechanisms for explosives. Acc. Chem. Res. 25(11), 489–496 (1992). https://doi.org/10.1021/ar00023a002

    Article  Google Scholar 

  4. Rai, N.K., Schmidt, M.J., Udaykumar, H.S.: Collapse of elongated voids in porous energetic materials: effects of void orientation and aspect ratio on initiation. Phys. Rev. Fluids 2(4), 043201 (2017). https://doi.org/10.1103/PhysRevFluids.2.043201

    Article  Google Scholar 

  5. Levesque, G.A., Vitello, P.: The effect of pore morphology on hot spot temperature. Propellants Explos. Pyrotech. 40(2), 303–308 (2015). https://doi.org/10.1002/prep.201400184

    Article  Google Scholar 

  6. Kapila, A.K., Schwendeman, D.W., Gambino, J.R., Henshaw, W.D.: A numerical study of the dynamics of detonation initiated by cavity collapse. Shock Waves 25, 545–572 (2015). https://doi.org/10.1007/s00193-015-0597-9

    Article  Google Scholar 

  7. Sen, O., Rai, N.K., Diggs, A.S., Hardin, D.B., Udaykumar, H.S.: Multi-scale shock-to-detonation simulation of pressed HMX: A meso-informed ignition and growth model. J. Appl. Phys. 124(8), 085110 (2018). https://doi.org/10.1063/1.5046185

    Article  Google Scholar 

  8. Lee, E.L., Tarver, C.M.: Phenomenological model of shock initiation in heterogeneous explosives. Phys. Fluids 23(12), 2362–2372 (1980). https://doi.org/10.1063/1.862940

    Article  Google Scholar 

  9. Gaul, N.J., Cowles, M.K., Cho, H., Choi, K.K., Lamb, D.: Modified Bayesian Kriging for noisy response problems for reliability analysis. ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers (2015). https://doi.org/10.1115/detc2015-47370

  10. Sen, O., Gaul, N.J., Choi, K.K., Jacobs, G., Udaykumar, H.S.: Evaluation of kriging based surrogate models constructed from mesoscale computations of shock interaction with particles. J. Comput. Phys. 336, 235–260 (2017). https://doi.org/10.1016/j.jcp.2017.01.046

    Article  MathSciNet  Google Scholar 

  11. Sen, O., Davis, S., Jacobs, G., Udaykumar, H.S.: Evaluation of convergence behavior of metamodeling techniques for bridging scales in multi-scale multimaterial simulation. J. Comput. Phys. 294, 585–604 (2015). https://doi.org/10.1016/j.jcp.2015.03.043

    Article  MathSciNet  MATH  Google Scholar 

  12. Sen, O., Gaul, N.J., Choi, K.K., Jacobs, G., Udaykumar, H.S.: Evaluation of multifidelity surrogate modeling techniques to construct closure laws for drag in shock-particle interactions. J. Comput. Phys. 371, 434–451 (2018). https://doi.org/10.1016/j.jcp.2018.05.039

    Article  MathSciNet  Google Scholar 

  13. Sen, O., Gaul, N.J., Davis, S., Choi, K.K., Jacobs, G., Udaykumar, H.S.: Role of pseudo-turbulent stresses in shocked particle clouds and construction of surrogate models for closure. Shock Waves 28, 579–597 (2018). https://doi.org/10.1007/s00193-017-0801-1

    Article  Google Scholar 

  14. Price, D.: Effect of Particle Size on the Shock Sensitivity of Pure Porous HE (High Explosive). Naval Surface Weapons Center, Silver Spring (1986)

    Book  Google Scholar 

  15. Campbell, A.W., Davis, W.C., Ramsay, J.B., Travis, J.R.: Shock initiation of solid explosives. Phys. Fluids 4(4), 511–521 (1961). https://doi.org/10.1063/1.1706354

    Article  Google Scholar 

  16. Dinegar, R., Rochester, R., Millican, M.: The Effect of Specific Surface on the Explosion Times of Shock Initiated PETN. Los Alamos National Laboratory, Los Alamos (1963)

    Book  Google Scholar 

  17. Scott, C.L.: Effect of particle size on shock initiation of PETN, RDX, and Tetryl. 5th International Symposium on Detonation, pp. 259–266. Office of Naval Research (1972)

  18. Howe, P., Frey, R., Taylor, B., Boyle, V.: Shock initiation and the critical energy concept. 6th International Symposium on Detonation, pp. 11–19. Office of Naval Research (1976)

  19. Schwarz, A.C.: Shock initiation sensitivity of hexanitrostilbene (HNS). 7th International Symposium on Detonation, pp. 1024–1028. Office of Naval Research (1981)

  20. Welle, E.J., Molek, C.D., Wixom, R.R., Samuels, P.: Microstructural effects on the ignition behavior of HMX. J. Phys. Conf. Ser. 500, 052049 (2014). https://doi.org/10.1088/1742-6596/500/5/052049

    Article  Google Scholar 

  21. Honodel, C.A., Humphrey, J.R., Weingart, R.C., Lee, R.S., Kramer, P.: Shock initiation of TATB formulations. 7th Symposium (International) on Detonation, pp. 425–434 (1981)

  22. Carroll, M., Holt, A.: Static and dynamic pore-collapse relations for ductile porous materials. J. Appl. Phys. 43(4), 1626–1636 (1972). https://doi.org/10.1063/1.1661372

    Article  Google Scholar 

  23. Frey, R.B.: Cavity Collapse in Energetic Materials. Army Ballistic Research Lab, Aberdeen Proving Ground (1986)

    Google Scholar 

  24. Holt, A., Carroll, M., Butcher, B.: Application of a new theory for the pressure-induced collapse of pores in ductile materials (UCRL-75060). Lawrence Livermore Lab, California University, Livermore (1973)

    Google Scholar 

  25. Moulard, H.: Critical conditions for shock initiation of detonation by small projectile impact. 7th International Symposium on Detonation, pp. 316–324. Office of Naval Research (1981)

  26. Khasainov, B.A., Borisov, A.A., Ermolaev, B.S., Korotkov, A.I.: Two-phase visco-plastic model of shock initiation of detonation in high-density pressed explosives. 7th International Symposium on Detonation, pp. 435–447. Office of Naval Research (1981)

  27. Perry, W.L., Clements, B., Ma, X., Mang, J.T.: Relating microstructure, temperature, and chemistry to explosive ignition and shock sensitivity. Combust. Flame 190, 171–176 (2018). https://doi.org/10.1016/j.combustflame.2017.11.017

    Article  Google Scholar 

  28. Tarver, C.M., Chidester, S.K., Nichols, A.L.: Critical conditions for impact- and shock-induced hot spots in solid explosives. J. Phys. Chem. 100(14), 5794–5799 (1996). https://doi.org/10.1021/jp953123s

    Article  Google Scholar 

  29. Rai, N.K., Schmidt, M.J., Udaykumar, H.S.: High-resolution simulations of cylindrical void collapse in energetic materials: Effect of primary and secondary collapse on initiation thresholds. Phys. Rev. Fluids 2(4), 043202 (2017). https://doi.org/10.1103/PhysRevFluids.2.043202

    Article  Google Scholar 

  30. Rai, N.K., Udaykumar, H.: Three-dimensional simulations of void collapse in energetic materials. Phys. Rev. Fluids 3(3), 033201 (2018). https://doi.org/10.1103/PhysRevFluids.3.033201

    Article  Google Scholar 

  31. Ponthot, J.-P.: Unified stress update algorithms for the numerical simulation of large deformation elasto-plastic and elasto-viscoplastic processes. Int. J. Plast. 18(1), 91–126 (2002). https://doi.org/10.1016/S0749-6419(00)00097-8

    Article  MATH  Google Scholar 

  32. Menikoff, R., Sewell, T.D.: Constituent properties of HMX needed for mesoscale simulations. Combust. Theor. Model. 6(1), 103–125 (2002). https://doi.org/10.1088/1364-7830/6/1/306

    Article  MATH  Google Scholar 

  33. Sambasivan, S., Kapahi, A., Udaykumar, H.S.: Simulation of high speed impact, penetration and fragmentation problems on locally refined Cartesian grids. J. Comput. Phys. 235, 334–370 (2012). https://doi.org/10.1016/j.jcp.2012.10.031

    Article  MathSciNet  Google Scholar 

  34. Kapahi, A., Sambasivan, S., Udaykumar, H.: A three-dimensional sharp interface Cartesian grid method for solving high speed multi-material impact, penetration and fragmentation problems. J. Comput. Phys. 241, 308–332 (2013). https://doi.org/10.1016/j.jcp.2013.01.007

    Article  MathSciNet  MATH  Google Scholar 

  35. Sewell, T.D., Menikoff, R.: Complete equation of state for β-HMX and implications for initiation. AIP Conference Proceedings, vol. 706, p. 157 (2004). https://doi.org/10.1063/1.1780207

  36. Fedkiw, R.P., Aslam, T., Merriman, B., Osher, S.: A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the Ghost Fluid Method). J. Comput. Phys. 152(2), 457–492 (1999). https://doi.org/10.1006/jcph.1999.6236

    Article  MathSciNet  MATH  Google Scholar 

  37. Sethian, J.A.: Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science, vol. 3. Cambridge University Press, Cambridge (1999)

    MATH  Google Scholar 

  38. Rai, N.K., Kapahi, A., Udaykumar, H.S.: Treatment of contact separation in Eulerian high-speed multimaterial dynamic simulations. Int. J. Numer. Meth. Eng. 100(11), 793–813 (2014). https://doi.org/10.1002/nme.4760

    Article  MathSciNet  MATH  Google Scholar 

  39. Rai, N.K., Udaykumar, H.S.: Mesoscale simulation of reactive pressed energetic materials under shock loading. J. Appl. Phys. 118(24), 245905 (2015). https://doi.org/10.1063/1.4938581

    Article  Google Scholar 

  40. Strang, G.: On the construction and comparison of difference schemes. SIAM J. Numer. Anal. 5(3), 506–517 (1968). https://doi.org/10.1137/0705041

    Article  MathSciNet  MATH  Google Scholar 

  41. Fehlberg, E.: Classical Fifth-, Sixth-, Seventh-, and Eighth-Order Runge–Kutta Formulas with Stepsize Control. NASA TR R-287, National Aeronautics and Space Administration (1968)

  42. Taverniers, S., Haut, T.S., Barros, K., Alexander, F.J., Lookman, T.: Physics-based statistical learning approach to mesoscopic model selection. Phys. Rev. E 92(5), 053301 (2015). https://doi.org/10.1103/PhysRevE.92.053301

    Article  Google Scholar 

  43. Haykin, S.: Neural Networks: A Comprehensive Foundation. MacMillon College Division Publishers, New York (2004)

    MATH  Google Scholar 

  44. Springer, H.K., Tarver, C.M., Bastea, S.: Effects of high shock pressures and pore morphology. AIP Conference Proceedings, vol. 1793, p. 080002 (2017). https://doi.org/10.1063/1.4971608

  45. Massoni, J., Saurel, R., Baudin, G., Demol, G.: A mechanistic model for shock initiation of solid explosives. Phys. Fluids 11(3), 710–736 (1999). https://doi.org/10.1063/1.869941

    Article  MathSciNet  MATH  Google Scholar 

  46. Rai, N.K., Udaykumar, H.S.: Void collapse generated meso-scale energy localization in shocked energetic materials: non-dimensional parameters, regimes and criticality of hotspot. Phys. Fluids (under review)

  47. Bourne, N., Milne, A.: The temperature of a shock-collapsed cavity. Proc. R. Soc. Lond. A Math. Phys. Eng. Sci. 459(2036), 1851–1861 (2003). https://doi.org/10.1098/rspa.2002.1101

    Article  MathSciNet  MATH  Google Scholar 

  48. James, H.R.: An extension to the critical energy criterion used to predict shock initiation thresholds. Propellants Explos. Pyrotech. 21(1), 8–13 (1996). https://doi.org/10.1002/prep.19960210103

    Article  Google Scholar 

  49. Bowden, F., Yoffe, A.: Explosion in liquids and solids. Endeavour 21(83–8), 125 (1962)

    Google Scholar 

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Acknowledgements

The authors gratefully acknowledge the financial support from the Air Force Office of Scientific Research (Dynamic Materials Program, program manager: Martin Schmidt) under Grant Number FA9550-15-1-0332 and Eglin AFB, AFRL-RWPC (program manager: Angela Diggs) under the Contract Number FA8651-16-1-0005. The authors are also thankful to K.K. Choi at the University of Iowa and Nicholas J. Gaul at RAMDO LLC, Iowa City, for providing the computational code for the modified Bayesian kriging method.

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  1. Mechanical and Industrial Engineering, The University of Iowa, Iowa City, IA, 52242, USA

    A. Nassar, N. K. Rai, O. Sen & H. S. Udaykumar

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  1. A. Nassar
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Correspondence to H. S. Udaykumar.

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Communicated by A. Higgins.

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Nassar, A., Rai, N.K., Sen, O. et al. Modeling mesoscale energy localization in shocked HMX, part I: machine-learned surrogate models for the effects of loading and void sizes. Shock Waves 29, 537–558 (2019). https://doi.org/10.1007/s00193-018-0874-5

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