非均质炸药冲击起爆数值模拟研究现状综述

姚天子; 王硕; 田占东; 陈荣

doi:10.11858/gywlxb.20240948

非均质炸药冲击起爆数值模拟研究现状综述

doi: 10.11858/gywlxb.20240948

国防科技大学理学院, 湖南长沙　410073

基金项目: 国家自然科学基金（12072369）

详细信息

作者简介:
姚天子（2000－），男，博士研究生，主要从事非均质炸药冲击起爆数值模拟研究. E-mail：yaotianzi18@nudt.edu.cn

通讯作者:
陈　荣（1981－），男，博士，教授，主要从事装药安全性研究. E-mail：r_chen@nudt.edu.cn

中图分类号: TJ55; O521.9
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- 文章访问数: 243
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出版历程
- 收稿日期: 2024-11-26
- 修回日期: 2025-01-16
- 刊出日期: 2025-08-05

Review of Numerical Simulation on Shock Initiation of Heterogeneous Explosives

College of Science, National University of Defense Technology, Changsha 410073, Hunan, China

摘要

摘要: 综述了非均质炸药冲击起爆的微/细观数值模拟和宏观数值模拟的研究现状，分析了非均质炸药冲击起爆数值模拟的未来发展趋势，旨在对数值模拟方法以及冲击起爆机理有更深入的理解。现有用于冲击起爆的细观数值模拟手段都具有各自的局限性，需要发展一种能够兼顾边界识别、大变形计算和高计算效率的全新计算框架，捕捉冲击起爆过程中的各种机制。目前已发现的热点机制包括结构缺陷引起的热点机制和无损伤热点机制，2类热点在冲击下都会产生能量局域化效应。冲击下不同类型热点之间的耦合机制尚不明确，需要深入研究各种类型和各个尺度热点之间的耦合作用，以全面揭示热点在冲击起爆中的作用机理，从而为冲击起爆各个阶段的数值模拟提供支撑。现有冲击起爆宏观反应速率模型考虑的物理机制不足且普适性不强，需要进一步发展能够考虑多热点耦合作用和热点统计分布的反应速率模型，从而提高反应速率模型的通用性和预测能力。在模拟冲击起爆全过程时使用宏观模拟会忽略较多细节，使用微/细观数值模拟则计算量巨大，因此，需要结合2种方法的优势发展跨尺度计算方法，从而在宏观模拟中减小计算量并引入小尺度信息。
- 非均质炸药 /
- 冲击起爆 /
- 细观模拟 /
- 热点 /
- 宏观模拟
Abstract: This paper reviews the state of art on microscopic/mesoscopic numerical simulation and macroscopic numerical simulation for the shock initiation process of heterogeneous explosives, summarizes the development trends of numerical simulation of shock initiation in heterogeneous explosives, and enables readers to have a deeper understanding of numerical simulation methods and the mechanism of shock initiation. Both the microscopic and mesoscopic methods have their own limitations, therefore, it is necessary to develop a new computational framework that can capture various mechanisms in the shock initiation process while considering boundary identification, large deformation calculation, and computational efficiency. Hot spots in heterogeneous explosives can be classified into defect-induced and defect-free hot spots based on the presence of structural defects, and both types of hotspots exhibit energy localization effects under shock. The coupling mechanisms between different types of hotspots under shock are not yet clear, and it is necessary to conduct research on the coupling interactions among various types and scales of hotspots to comprehensively reveal the mechanism of hotspots in shock initiation, thereby providing support for numerical simulations of various stages of shock initiation. The physical mechanisms considered in the existing macroscopic reaction rate models for shock initiation are not comprehensive and have weak universality. It is necessary to develop models that account for the coupled effects of multiple hotspots and their statistical distributions which will enhance the universality and predictive capability of macroscope simulation. In the simulation of the entire shock initiation process, macro simulation may overlook many details, while micro/meso numerical simulation requires huge computational complexity. Consequently, it is essential to combine the advantages of both methods to develop multiscale simulation methods to reduce computational consumption and introduce some necessary microscopic information in macro simulation.
- heterogeneous explosives /
- shock initiation /
- mesoscopic simulation /
- hot spot /
- macroscopic simulation

HTML全文

图 1 冲击起爆各尺度数值模拟的特点

Figure 1. Characteristics of multi-scale numerical simulations for shock initiation

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图 2 单个和多个孔隙的坍缩过程

Figure 2. Collapse processes of single pore and multi pores

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图 3 非均质炸药中裂纹在冲击作用下的温度场^[51]

Figure 3. Temperature field of cracks in heterogeneous explosives under shock load^[51]

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图 4 冲击起爆过程中形成的剪切网络示意图

Figure 4. Schematic diagram of the shear network formed during shock initiation

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图 5 含铝炸药的计算模型(a)以及炸药中各组分在冲击起爆不同阶段的反应程度(b)^[9]

Figure 5. Computational model of aluminium-containing explosives (a) and degree of reaction of the explosive components at different stages of shock initiation (b)^[9]

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图 6 非均质炸药的三维细观数值模拟^[10]

Figure 6. Three-dimensional mesoscopic numerical simulation of heterogeneous explosives^[10]

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图 7 不同能量密度（E）和功率密度（Π）加载下HMX 炸药发生点火的概率（P）分布^[13]

Figure 7. Probability (P) distribution of ignition of HMX explosives loaded with different energy fluence （E） and power flux（Π）^[13]

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图 8 4种孔隙分布对爆轰概率的影响^[7]

Figure 8. Effect of four kinds of pore distributions on the probability of detonation^[7]

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图 9 单球壳模型（左）和双球壳模型（右）示意图

Figure 9. Schematic diagrams of single-sphere shell model (left) and double-sphere shell model (right)

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图 10 PBX炸药细观结构示意图^[87]

Figure 10. Schematic diagrams of the mesoscopic structure of PBX explosives^[87]

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图 11 反应速率模型对比

Figure 11. Comparison of reaction rate models

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图 12 细观孔隙坍缩模型示意图^[136]

Figure 12. Schematic diagram of the mesoscale pore collapse model^[136]

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图 13 统一热点模型示意图^[65–66]

Figure 13. Schematic diagram of the unified hotspot model^[65–66]

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图 14 Akiki等^[56]进行的冲击起爆细观数值模拟

Figure 14. Mesoscopic numerical simulation of shock initiation by Akiki, et al.^[56]

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参考文献(136)

[1]	段卓平, 白志玲, 黄风雷. 非均质固体炸药冲击起爆与爆轰研究进展 [J]. 火炸药学报, 2020, 43(3): 237–253. doi: 10.14077/j.issn.1007-7812.202006017 DUAN Z P, BAI Z L, HUANG F L. Advances in shock initiation and detonation of heterogeneous solid explosives [J]. Chinese Journal of Explosives & Propellants, 2020, 43(3): 237–253. doi: 10.14077/j.issn.1007-7812.202006017
[2]	裴红波, 李淑睿, 郭文灿, 等. 基于反向撞击法的RDX基含铝炸药冲击起爆实验研究 [J]. 含能材料, 2023, 31(5): 425–430. doi: 10.11943/CJEM2021285 PEI H B, LI S R, GUO W C, et al. Shock initiation measurement of RDX-based aluminized explosives with reverse-impact method [J]. Chinese Journal of Energetic Materials, 2023, 31(5): 425–430. doi: 10.11943/CJEM2021285
[3]	白志玲, 段卓平, 黄风雷. 高聚物黏结炸药冲击起爆统计热点反应速率模型 [J]. 兵工学报, 2021, 42(11): 2379–2387. doi: 10.3969/j.issn.1000-1093.2021.11.011 BAI Z L, DUAN Z P, HUANG F L. A statistical hot spot reaction rate model for shock initiation of PBX [J]. Acta Armamentarii, 2021, 42(11): 2379–2387. doi: 10.3969/j.issn.1000-1093.2021.11.011
[4]	于继东, 王文强, 刘仓理, 等. 炸药冲击响应的二维细观离散元模拟 [J]. 爆炸与冲击, 2008, 28(6): 488–493. doi: 10.3321/j.issn:1001-1455.2008.06.002 YU J D, WANG W Q, LIU C L, et al. Two-dimensional mesoscale discrete element simulation of shock response of explosives [J]. Explosion and Shock Waves, 2008, 28(6): 488–493. doi: 10.3321/j.issn:1001-1455.2008.06.002
[5]	王晨, 陈朗, 刘群, 等. 多组分PBX炸药细观结构冲击点火数值模拟 [J]. 爆炸与冲击, 2014, 34(2): 167–173. doi: 10.11883/1001-1455(2014)02-0167-07 WANG C, CHEN L, LIU Q, et al. Numerical simulation for analyzing shock to ignition of PBXs with different compositions in meso-structural level [J]. Explosion and Shock Waves, 2014, 34(2): 167–173. doi: 10.11883/1001-1455(2014)02-0167-07
[6]	WEI Y C, RANJAN R, ROY U, et al. Integrated Lagrangian and Eulerian 3D microstructure-explicit simulations for predicting macroscopic probabilistic SDT thresholds of energetic materials [J]. Computational Mechanics, 2019, 64(2): 547–561. doi: 10.1007/s00466-019-01729-9
[7]	COFFELT C, OLSEN D, MILLER C, et al. Effect of void positioning on the detonation sensitivity of a heterogeneous energetic material [J]. Journal of Applied Physics, 2022, 131(6): 065101. doi: 10.1063/5.0081188
[8]	YARRINGTON C D, WIXOM R R, DAMM D L. Shock interactions with heterogeneous energetic materials [J]. Journal of Applied Physics, 2018, 123(10): 105901. doi: 10.1063/1.5022042
[9]	CHOI S, KIM B, HAN S, et al. Multiscale modeling of transients in the shock-induced detonation of heterogeneous energetic solid fuels [J]. Combustion and Flame, 2020, 221: 401–415. doi: 10.1016/j.combustflame.2020.08.012
[10]	MILLER C, OLSEN D, WEI Y C, et al. Three-dimensional microstructure-explicit and void-explicit mesoscale simulations of detonation of HMX at millimeter sample size scale [J]. Journal of Applied Physics, 2020, 127(12): 125105. doi: 10.1063/1.5136234
[11]	OLSEN D, ZHOU M. Shock-to-detonation transition behavior of functionally graded energetic materials [J]. Journal of Applied Physics, 2023, 134(11): 115901. doi: 10.1063/5.0160553
[12]	BARUA A, KIM S, HORIE Y, et al. Prediction of probabilistic ignition behavior of polymer-bonded explosives from microstructural stochasticity [J]. Journal of Applied Physics, 2013, 113(18): 184907. doi: 10.1063/1.4804251
[13]	KIM S, WEI Y C, HORIE Y, et al. Prediction of shock initiation thresholds and ignition probability of polymer-bonded explosives using mesoscale simulations [J]. Journal of the Mechanics and Physics of Solids, 2018, 114: 97–116. doi: 10.1016/j.jmps.2018.02.010
[14]	AKIKI M, GALLAGHER T P, MENON S. Mechanistic approach for simulating hot-spot formations and detonation in polymer-bonded explosives [J]. AIAA Journal, 2017, 55(2): 585–598. doi: 10.2514/1.J054898
[15]	LI D Y, ELALEM K, ANDERSON M J, et al. A microscale dynamical model for wear simulation [J]. Wear, 1999, 225(Pt 1): 380−386.
[16]	JACKSON T L, ZHANG J. Density-based kinetics for mesoscale simulations of detonation initiation in energetic materials [J]. Combustion Theory and Modelling, 2017, 21(4): 749–769. doi: 10.1080/13647830.2017.1296975
[17]	JACKSON T L, JOST A M D, ZHANG J, et al. Multi-dimensional mesoscale simulations of detonation initiation in energetic materials with density-based kinetics [J]. Combustion Theory and Modelling, 2018, 22(2): 291–315. doi: 10.1080/13647830.2017.1401121
[18]	MCGLAUN J M, THOMPSON S L, ELRICK M G. CTH: a three-dimensional shock wave physics code [J]. International Journal of Impact Engineering, 1990, 10(1/2/3/4): 351–360. doi: 10.1016/0734-743X(90)90071-3
[19]	AUSTIN R A, BARTON N R, HOWARD W M, et al. Modeling pore collapse and chemical reactions in shock loaded HMX crystals [J]. Journal of Physics: Conference Series, 2014, 500: 052002. doi: 10.1088/1742-6596/500/5/052002
[20]	NAJJAR F M, HOWARD W M, FRIED L E, et al. Computational study of 3-D hot-spot initiation in shocked insensitive high-explosive [J]. AIP Conference Proceedings, 2012, 1426(1): 255–258. doi: 10.1063/1.3686267
[21]	LEVESQUE G, VITELLO P, HOWARD W M. Hot-spot contributions in shocked high explosives from mesoscale ignition models [J]. Journal of Applied Physics, 2013, 113(23): 233513. doi: 10.1063/1.4811233
[22]	于继东. 炸药冲击响应的二维细观离散元模拟 [D]. 绵阳: 中国工程物理研究院, 2007. YU J D. Two-dimensional mesoscale discrete element simulation of shock response of explosives [D]. Miangyang: China Academy of Engineering Physics, 2007.
[23]	尚海林. 非均质炸药冲击载荷作用下热点形成的离散元模拟研究 [D]. 绵阳: 中国工程物理研究院, 2009. SHANG H L. Discrete element simulation of hot spot formation under shock loading of heterogeneous explosives [D]. Miangyang: China Academy of Engineering Physics, 2009.
[24]	刘超, 石艺娜, 梁仙红. 冲击作用下非均质炸药热点形成的离散元方法 [J]. 计算物理, 2014, 31(5): 523–530. doi: 10.3969/j.issn.1001-246X.2014.05.003 LIU C, SHI Y N, LIANG X H. DEM study on hot spots formation of heterogeneous explosives under shock loading [J]. Chinese Journal of Computational Physics, 2014, 31(5): 523–530. doi: 10.3969/j.issn.1001-246X.2014.05.003
[25]	KROONBLAWD M P, FRIED L E. High explosive ignition through chemically activated nanoscale shear bands [R]. Livermore, United States: Lawrence Livermore National Laboratory, 2020.
[26]	JARAMILLO E, SEWELL T D, STRACHAN A. Atomic-level view of inelastic deformation in a shock loaded molecular crystal [J]. Physical Review B, 2007, 76(6): 064112. doi: 10.1103/PhysRevB.76.064112
[27]	CAWKWELL M J, SEWELL T D, ZHENG L Q, et al. Shock-induced shear bands in an energetic molecular crystal: application of shock-front absorbing boundary conditions to molecular dynamics simulations [J]. Physical Review B, 2008, 78(1): 014107. doi: 10.1103/PhysRevB.78.014107
[28]	HAMILTON B W, GERMANN T C. Influence of pore surface structure and contents on shock-induced collapse and energy localization [J]. The Journal of Physical Chemistry C, 2023, 127(20): 9887–9895. doi: 10.1021/acs.jpcc.3c01556
[29]	LIU R Q, WU Y Q, WANG X J, et al. Shock-induced energy localization and reaction growth considering chemical-inclusions effects for crystalline explosives [J]. Defence Technology, 2024, 33: 278–294. doi: 10.1016/j.dt.2023.02.011
[30]	KROONBLAWD M P, FRIED L E. High explosive ignition through chemically activated nanoscale shear bands [J]. Physical Review Letters, 2020, 124(20): 206002. doi: 10.1103/PhysRevLett.124.206002
[31]	IZVEKOV S, RICE B M. Bottom-up coarse-grain modeling of plasticity and nanoscale shear bands in α-RDX [J]. The Journal of Chemical Physics, 2021, 155(6): 064503. doi: 10.1063/5.0057223
[32]	IZVEKOV S, RICE B M. Microscopic mechanism of nanoscale shear bands in an energetic molecular crystal (α-RDX): a first-order structural phase transition [J]. Physical Review B, 2022, 106(10): 104109. doi: 10.1103/PhysRevB.106.104109
[33]	DING K, WANG X J, HUANG F L. Shock-induced nanoscale pore collapse and hotspot in cyclotetramethylene tetranitramine (HMX) [J]. International Journal of Mechanical Sciences, 2024, 281: 109644. doi: 10.1016/j.ijmecsci.2024.109644
[34]	LEE PERRY W, CLEMENTS B, MA X, et al. Relating microstructure, temperature, and chemistry to explosive ignition and shock sensitivity [J]. Combustion and Flame, 2018, 190: 171–176. doi: 10.1016/j.combustflame.2017.11.017
[35]	KHASAINOV B A, ERMOLAEV B S, PRESLES H N, et al. On the effect of grain size on shock sensitivity of heterogeneous high explosives [J]. Shock Waves, 1997, 7(2): 89–105. doi: 10.1007/s001930050066
[36]	WEN L J, DUAN Z P, ZHANG L S, et al. Effects of HMX particle size on the shock initiation of PBXC03 explosive [J]. International Journal of Nonlinear Sciences and Numerical Simulation, 2012, 13(2): 189–194. doi: 10.1515/ijnsns-2011-129
[37]	AUSTIN R A, BARTON N R, REAUGH J E, et al. Direct numerical simulation of shear localization and decomposition reactions in shock-loaded HMX crystal [J]. Journal of Applied Physics, 2015, 117(18): 185902. doi: 10.1063/1.4918538
[38]	EASON R M, SEWELL T D. Molecular dynamics simulations of the collapse of a cylindrical pore in the energetic material α-RDX [J]. Journal of Dynamic Behavior of Materials, 2015, 1(4): 423–438. doi: 10.1007/s40870-015-0037-z
[39]	KAPAHI A, UDAYKUMAR H S. Dynamics of void collapse in shocked energetic materials: physics of void-void interactions [J]. Shock Waves, 2013, 23(6): 537–558. doi: 10.1007/s00193-013-0439-6
[40]	KAPAHI A, UDAYKUMAR H S. Three-dimensional simulations of dynamics of void collapse in energetic materials [J]. Shock Waves, 2015, 25(2): 177–187. doi: 10.1007/s00193-015-0548-5
[41]	FRIED L E, HOWARD W M. An accurate equation of state for the exponential-6 fluid applied to dense supercritical nitrogen [J]. The Journal of Chemical Physics, 1998, 109(17): 7338–7348. doi: 10.1063/1.476520
[42]	傅华, 赵峰, 谭多望, 等. 冲击作用下HMX晶体孔洞塌缩热点生成机制的细观数值模拟 [J]. 高压物理学报, 2011, 25(1): 8–14. doi: 10.11858/gywlxb.2011.01.002 FU H, ZHAO F, TAN D W, et al. Mesoscale simulation of cavity collapse hot spot mechanism in HMX under shock loading [J]. Chinese Journal of High Pressure Physics, 2011, 25(1): 8–14. doi: 10.11858/gywlxb.2011.01.002
[43]	SPRINGER H K, BASTEA S, NICHOLS III A L, et al. Modeling the effects of shock pressure and pore morphology on hot spot mechanisms in HMX [J]. Propellants, Explosives, Pyrotechnics, 2018, 43(8): 805–817. doi: 10.1002/prep.201800082
[44]	TRAN L, UDAYKUMAR H S. Simulation of void collapse in an energetic material, part 1: inert case [J]. Journal of Propulsion and Power, 2006, 22(5): 947–958. doi: 10.2514/1.13146
[45]	LEVESQUE G A, VITELLO P. The effect of pore morphology on hot spot temperature [J]. Propellants, Explosives, Pyrotechnics, 2015, 40(2): 303–308. doi: 10.1002/prep.201400184
[46]	LIU C, OU Z C, DUAN Z P, et al. Influence of void configurations on hot spot temperature in PBXs under impact loading [J]. Propellants, Explosives, Pyrotechnics, 2021, 46(6): 912–925. doi: 10.1002/prep.202000268
[47]	LI C Y, STRACHAN A. Shock-induced collapse of porosity, mapping pore size and geometry, collapse mechanism, and hotspot temperature [J]. Journal of Applied Physics, 2022, 132(6): 065901. doi: 10.1063/5.0098808
[48]	BARUA A, HORIE Y, ZHOU M. Energy localization in HMX-estane polymer-bonded explosives during impact loading [J]. Journal of Applied Physics, 2012, 111(5): 054902. doi: 10.1063/1.3688350
[49]	WEI Y C, KIM S, HORIE Y, et al. Quantification of probabilistic ignition thresholds of polymer-bonded explosives with microstructure defects [J]. Journal of Applied Physics, 2018, 124(16): 165110. doi: 10.1063/1.5031845
[50]	TANG L, WANG H F, LU G C, et al. Mesoscale study on the shock response and initiation behavior of Al-PTFE granular composites [J]. Materials & Design, 2021, 200: 109446. doi: 10.1016/j.matdes.2020.109446
[51]	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 [J]. Physical Review Fluids, 2017, 2(4): 043201. doi: 10.1103/PhysRevFluids.2.043201
[52]	LI C Y, HAMILTON B W, STRACHAN A. Hotspot formation due to shock-induced pore collapse in 1, 3, 5, 7-tetranitro-1, 3, 5, 7-tetrazoctane (HMX): role of pore shape and shock strength in collapse mechanism and temperature [J]. Journal of Applied Physics, 2020, 127(17): 175902. doi: 10.1063/5.0005872
[53]	KHAN M, PICU C R. Shear localization in molecular crystal cyclotetramethylene-tetranitramine (β-HMX): constitutive behavior of the shear band [J]. Journal of Applied Physics, 2020, 128(10): 105902. doi: 10.1063/5.0020561
[54]	LI J H, ZHANG C G, WANG Y, et al. The formation mechanism of twin type shear bands in β-HMX: molecular rotation and translation [J]. Journal of Molecular Modeling, 2024, 30(2): 30. doi: 10.1007/s00894-023-05825-9
[55]	HAMILTON B W, GERMANN T C. High pressure suppression of plasticity due to an overabundance of shear embryo formation [J]. NPJ Computational Materials, 2024, 10: 147. doi: 10.1038/s41524-024-01348-w
[56]	BAER M R, KIPP M E, SWOL F V. Micromechanical modeling of heterogeneous energetic materials [R]. Albuquerque, United States: Sandia National Laboratories, 1998.
[57]	KIM S, MILLER C, HORIE Y, et al. Computational prediction of probabilistic ignition threshold of pressed granular octahydro-1, 3, 5, 7-tetranitro-1, 3, 5, 7-tetrazocine (HMX) under shock loading [J]. Journal of Applied Physics, 2016, 120(11): 115902. doi: 10.1063/1.4962211
[58]	AKIKI M, MENON S. A model for hot spot formation in shocked energetic materials [J]. Combustion and Flame, 2015, 162(5): 1759–1771. doi: 10.1016/j.combustflame.2014.11.037
[59]	MILLER C, KITTELL D, YARRINGTON C, et al. Prediction of probabilistic detonation threshold via millimeter-scale microstructure-explicit and void-explicit simulations [J]. Propellants, Explosives, Pyrotechnics, 2020, 45(2): 254–269. doi: 10.1002/prep.201900214
[60]	GRESSHOFF M, HROUSIS C A. Probabilistic shock threshold criterion [C]//Proceedings of the 14th International Detonation Symposium. Coeur d’Alene, USA: Lawrence Livermore National Laboratory, 2010.
[61]	JAMES H R. An Extension to the critical energy criterion used to predict shock initiation thresholds [J]. Propellants, Explosives, Pyrotechnics, 1996, 21(1): 8–13. doi: 10.1002/prep.19960210103
[62]	WALKER E J, WASLEY R J. Critical energy for shock initiation of heterogeneous explosives [J]. Explosivstoffe, 1969, 17(1): 9–13.
[63]	MILLER C M, SPRINGER H K. Probabilistic effects of porosity and chemical kinetics on the shock initiation of an octahydro-1, 3, 5, 7-tetranitro-1, 3, 5, 7-tetrazocine (HMX) based explosive [J]. Journal of Applied Physics, 2021, 129(21): 215104. doi: 10.1063/5.0049122
[64]	温丽晶, 段卓平, 张震宇, 等. 不同加载压力下炸药冲击起爆过程实验和数值模拟研究 [J]. 兵工学报, 2013, 34(3): 283–288. doi: 10.3969/j.issn.1000-1093.2013.03.005 WEN L J, DUAN Z P, ZHANG Z Y, et al. Experimental and numerical study on the shock initiation of PBXC03 explosive under the different loading pressure [J]. Acta Armamentarii, 2013, 34(3): 283–288. doi: 10.3969/j.issn.1000-1093.2013.03.005
[65]	YANO K, HORIE Y, GREENING D. Mechanistic model of hot-spot: a unifying framework [J]. AIP Conference Proceedings, 2002, 620(1): 983–986. doi: 10.1063/1.1483702
[66]	HAMATE Y, HORIE Y. Ignition and detonation of solid explosives: a micromechanical burn model [J]. Shock Waves, 2006, 16(2): 125–147. doi: 10.1007/s00193-006-0038-x
[67]	MADER C L, FOREST C A. Two-dimensional homogeneous and heterogeneous detonation wave propagation [R]. New Mexico, United States: Los Alamos National Laboratory, 1976.
[68]	LEE E L, TARVER C M. Phenomenological model of shock initiation in heterogeneous explosives [J]. The Physics of Fluids, 1980, 23(12): 2362–2372. doi: 10.1063/1.862940
[69]	JOHNSON J N, TANG P K, FOREST C A. Shock-wave initiation of heterogeneous reactive solids [J]. Journal of Applied Physics, 1985, 57(9): 4323–4334. doi: 10.1063/1.334591
[70]	STARKENBERG J, DORSEY T M. An assessment of the performance of the history variable reactive burn explosive initiation model in the CTH code [C]//Proceeding of the 11th Symposium (International) on Detonation, Colorado: Snowmass Conference Center, 1998: 621−631.
[71]	WESCOTT B L, STEWART D S, DAVIS W C. Equation of state and reaction rate for condensed-phase explosives [J]. Journal of Applied Physics, 2005, 98(5): 053514. doi: 10.1063/1.2035310
[72]	YANG Y, DUAN Z P, LI S R, et al. A new ignition-growth reaction rate model for shock initiation [J]. Defence Technology, 2023, 23: 126–136. doi: 10.1016/j.dt.2022.01.009
[73]	DUAN Z P, WEN L J, LIU Y, et al. A pore collapse model for hot-spot ignition in shocked multi-component explosives [J]. International Journal of Nonlinear Sciences and Numerical Simulation, 2010, 11(Suppl 1): 19–23. doi: 10.1515/IJNSNS.2010.11.S1.19
[74]	DESBIENS N, MATIGNON C, SORIN R. Temperature-based model for condensed-phase explosive detonation [J]. Journal of Physics: Conference Series, 2014, 500(15): 152004. doi: 10.1088/1742-6596/500/15/152004
[75]	ASLAM T D. Shock temperature dependent rate law for plastic bonded explosives [J]. Journal of Applied Physics, 2018, 123(14): 145901. doi: 10.1063/1.5020172
[76]	HANDLEY C A. The CREST reactive burn model [J]. AIP Conference Proceedings, 2007, 955: 373–376. doi: 10.1063/1.2833061
[77]	MENIKOFF R, SHAW M S. Reactive burn models and ignition and growth concept [C]//Proceedings of the European Physical Journal Web of Conferences: EPJ Science, 2010.
[78]	COOK M D, HASKINS P J, STENNETT C. Development and implementation of an ignition and growth model for homogeneous and heterogeneous explosives [R]. Arlinton: Office of Naval Research, 1998: 589−598.
[79]	KIM K, SOHN C H. Modeling of reaction buildup processes in shocked porous explosives [C]//Proceedings of the 8th Symposium International on Detonation. Albuquerque: Office of Naval Research, 1985: 926−933.
[80]	KIM K. Development of a model of reaction rates in shocked multicomponent explosives [C]//Proceedings of the 9th Symposium International on Detonation. Sandiego: Office of Naval Research, 1989: 593−603.
[81]	田占东, 张震宇. PBX-9404炸药冲击起爆细观反应速率模型 [J]. 含能材料, 2007, 15(5): 464–467. doi: 10.3969/j.issn.1006-9941.2007.05.006 TIAN Z D, ZHANG Z Y. A mesomechanic model of shock initiation in PBX-9404 explosive [J]. Chinese Journal of Energetic Materials, 2007, 15(5): 464–467. doi: 10.3969/j.issn.1006-9941.2007.05.006
[82]	温丽晶, 段卓平, 张震宇, 等. 弹黏塑性双球壳塌缩热点反应模型 [J]. 高压物理学报, 2011, 25(6): 493–500. doi: 10.11858/gywlxb.2011.06.003 WEN L J, DUAN Z P, ZHANG Z Y, et al. An elastic/viscoplastic pore collapse model of double-layered hollow sphere for hot-spot ignition in shocked explosives [J]. Chinese Journal of High Pressure Physics, 2011, 25(6): 493–500. doi: 10.11858/gywlxb.2011.06.003
[83]	温丽晶, 段卓平, 张震宇, 等. 刚塑性黏结剂的双球壳塌缩热点反应模型 [J]. 北京理工大学学报, 2011, 31(8): 883–887. doi: 10.15918/j.tbit1001-0645.2011.08.003 WEN L J, DUAN Z P, ZHANG Z Y, et al. Pore-collapse model of double hollow sphere with rigid-plastic binders for hot-spot ignition in shock explosives [J]. Transactions of Beijing Institute of Technology, 2011, 31(8): 883–887. doi: 10.15918/j.tbit1001-0645.2011.08.003
[84]	LI S R, DUAN Z P, GAO T Y, et al. Size effect of explosive particle on shock initiation of aluminized 2, 4-dinitroanisole (DNAN)-based melt-cast explosive [J]. Journal of Applied Physics, 2020, 128(12): 125903. doi: 10.1063/5.0016310
[85]	LI S R, DUAN Z P, ZHANG L S, et al. A melt-cast Duan-Zhang-Kim mesoscopic reaction rate model and experiment for shock initiation of melt-cast explosives [J]. Defence Technology, 2021, 17(5): 1753–1763. doi: 10.1016/j.dt.2020.09.019
[86]	段卓平, 刘益儒, 欧卓成, 等. 多元混合PBX炸药孔隙塌缩热点模型 [J]. 北京理工大学学报, 2013, 33(8): 771–775. doi: 10.3969/j.issn.1001-0645.2013.08.001 DUAN Z P, LIU Y R, OU Z C, et al. A pore collapse hot-spot ignition model for shocked multi-component PBX explosives [J]. Transactions of Beijing Institute of Technology, 2013, 33(8): 771–775. doi: 10.3969/j.issn.1001-0645.2013.08.001
[87]	LIU Y R, DUAN Z P, ZHANG Z Y, et al. A mesoscopic reaction rate model for shock initiation of multi-component PBX explosives [J]. Journal of Hazardous Materials, 2016, 317: 44–51. doi: 10.1016/j.jhazmat.2016.05.052
[88]	刘益儒. 多元混合PBX炸药冲击起爆细观反应流模型研究 [D]. 北京: 北京理工大学, 2015. LIU Y R. Research on mesoscopic reactive flow model of shock initiation of multi-component PBX [D]. Beijing: Beijing Institute of Technology, 2015.
[89]	白志玲, 段卓平, 温丽晶, 等. PBX炸药冲击起爆的改进细观反应速率模型 [J]. 含能材料, 2019, 27(8): 629–635. doi: 10.11943/CJEM2018354 BAI Z L, DUAN Z P, WEN L J, et al. A modified mesoscopic reaction rate model for shock initiation of PBXs [J]. Chinese Journal of Energetic Materials, 2019, 27(8): 629–635. doi: 10.11943/CJEM2018354
[90]	白志玲. PBX炸药冲击起爆机理及其系列反应速率模型研究 [D]. 北京: 北京理工大学, 2019. BAI Z L. Physical mechanism and series of chemical reaction rate models for detonation initiation in PBX explosives [D]. Beijing: Beijing Institute of Technology, 2019.
[91]	BAI Z L, DUAN Z P, WEN L J, et al. Comparative analysis of detonation growth characteristics between HMX- and TATB-based PBXs [J]. Propellants, Explosives, Pyrotechnics, 2019, 44(7): 858–869. doi: 10.1002/prep.201800390
[92]	BAI Z L, DUAN Z P, WEN L J, et al. Shock initiation of multi-component insensitive PBX explosives: experiments and MC-DZK mesoscopic reaction rate model [J]. Journal of Hazardous Materials, 2019, 369: 62–69. doi: 10.1016/j.jhazmat.2019.02.028
[93]	SEN O, RAI N K, DIGGS A S, et al. Multi-scale shock-to-detonation simulation of pressed energetic material: a meso-informed ignition and growth model [J]. Journal of Applied Physics, 2018, 124(8): 085110. doi: 10.1063/1.5046185
[94]	NICHOLS III A L, TARVER C M. A statistical hot spot reactive flow model for shock initiation and detonation of solid high explosives [C]//Proceedings of the 12th International Detonation Symposium. San Diego: Office of Naval Research, 2002.
[95]	NICHOLS III A L. Statistical hot spot model for explosive detonation [J]. AIP Conference Proceedings, 2006, 845: 465–470. doi: 10.1063/1.2263361
[96]	HILL L G. The shock-triggered statistical hot spot model [J]. AIP Conference Proceedings, 2012, 1426(1): 307–310. doi: 10.1063/1.3686280
[97]	DESBIENS N. Modeling of the jack rabbit series of experiments with a temperature based reactive burn model [J]. AIP Conference Proceedings, 2017, 1793(1): 040034. doi: 10.1063/1.4971528
[98]	REYNAUD M, SORIN R, DUBOIS V, et al. WGT: a mesoscale-informed reactive burn model [J]. Journal of Applied Physics, 2020, 127(6): 065901. doi: 10.1063/1.5135362
[99]	COCHRAN S G. Statistical treatment of heterogeneous chemical reaction in shock-initiated explosives [R]. Livermore: University of California, 1980.
[100]	HAMATE Y, HORIE Y. A statistical approach on mechanistic modeling of high-explosive ignition [J]. AIP Conference Proceedings, 2004, 706(1): 335–338. doi: 10.1063/1.1780247
[101]	LIU C, OU Z C, DUAN Z P, et al. Ubiquitiform hotspot ignition model of PBX for shock initiation [J]. Propellants, Explosives, Pyrotechnics, 2021, 46(10): 1561–1571. doi: 10.1002/prep.202100089
[102]	SHOW M S, MENIKOFF R. A reactive burn model for shock initiation in a PBX: scaling and separability based on the hot spot concept [C]//Proceedings of the 14th International Detonation Symposium. Coeur: Los Alamos National Laboratory, 2010.
[103]	BAI Z L, DUAN Z P, WANG X J, et al. A statistical hot spot reaction rate model for shock initiation of polymer-bonded explosives [J]. Propellants, Explosives, Pyrotechnics, 2021, 46(11): 1723–1732. doi: 10.1002/prep.202100106
[104]	陈朗, 冯长根, 黄毅民. 含铝炸药圆筒试验及爆轰产物JWL状态方程研究 [J]. 火炸药学报, 2001, 24(3): 13–15. doi: 10.3969/j.issn.1007-7812.2001.03.005 CHEN L, FENG C G, HUANG Y M. The cylinder test and JWL equation of state detontion product of aluminized explosives [J]. Chinese Journal of Explosives & Propellants, 2001, 24(3): 13–15. doi: 10.3969/j.issn.1007-7812.2001.03.005
[105]	KURY J W, HORNIG H C, LEE E L. Metal acceleration by chemical explosive [C]//Proceedings of the 4th Symposium on Detonation. Berlin: Springer, 1965: 3−13.
[106]	FICKETT W, WOOD W W, SALSBURG Z W. Investigations of the detonation properties of condensed explosives with equations of state based on intermolecular potentials. Ⅰ. RDX with fixed product composition [J]. The Journal of Chemical Physics, 1957, 27(6): 1324–1329. doi: 10.1063/1.1744001
[107]	MIAO F C, YAO J P, LI D D. Comparative study on the equation of state of detonation products [J]. AIP Advances, 2024, 14(4): 045305. doi: 10.1063/5.0204013
[108]	TANAKA K. Detonation properties of high explosives calculated by revised Kihara-Hikita equation of state [C]//Proceedings of the 8th Symposium International on Detonation. Albuquerque: Naval Surface Weapons Center, 1985: 548–558.
[109]	MADER C L. Numerical modeling of explosives and propellants [M]. 3rd ed. Boca Raton: CRC Press, 2007.
[110]	吴雄. VLW爆轰产物状态方程的发展及应用 [J]. 火炸药学报, 2021, 44(1): 1–7. doi: 10.14077/j.issn.1007-7812.202008015 WU X. Development and application of VLW equation of state for detonation products [J]. Chinese Journal of Explosives & Propellants, 2021, 44(1): 1–7. doi: 10.14077/j.issn.1007-7812.202008015
[111]	BAKER E L, STUNZENAS G M, STIEL L I, et al. High explosive thermodynamic equations of state for combined fragmentation and blast loading [M]//SCHLEYE G, BREBBIA B A. Structures Under Shock and Impact Ⅻ. Southampton: WIT Press, 2012: 135–144.
[112]	MILLER P J. A reactive flow model with coupled reaction kinetics for detonation and combustion in non-ideal explosives [J]. MRS Online Proceedings Library, 1995, 418(1): 413–420. doi: 10.1557/PROC-418-413
[113]	田少康, 李席, 刘波, 等. 一种RDX基温压炸药的JWL-Miller状态方程研究 [J]. 含能材料, 2017, 25(3): 226–231. doi: 10.11943/j.issn.1006-9941.2017.03.009 TIAN S K, LI X, LIU B, et al. Study on JWL-Miller equation of state of RDX-based thermobaric explosive [J]. Chinese Journal of Energetic Materials, 2017, 25(3): 226–231. doi: 10.11943/j.issn.1006-9941.2017.03.009
[114]	薛再清, 徐更光, 王廷增, 等. 用KHT状态方程计算炸药爆轰参数 [J]. 爆炸与冲击, 1998, 18(2): 172–176. doi: 10.11883/1001-1455(1998)02-0172-5 XUE Z Q, XU G G, WANG T Z, et al. By use of KHT equation of state to calculate detonation parameters of explosives [J]. Explosion and Shock Waves, 1998, 18(2): 172–176. doi: 10.11883/1001-1455(1998)02-0172-5
[115]	韩勇, 龙新平, 郭向利. 一种简化维里型状态方程预测高温甲烷PVT关系 [J]. 物理学报, 2014, 63(15): 150505. doi: 10.7498/aps.63.150505 HAN Y, LONG X P, GUO X L. Prediction of methane PVT relations at high temperatures by a simplified virial equation of state [J]. Acta Physica Sinica, 2014, 63(15): 150505. doi: 10.7498/aps.63.150505
[116]	韩勇, 郭向利, 龙新平. 高温高压CO₂状态方程研究 [J]. 含能材料, 2016, 24(5): 462–468. doi: 10.11943/j.issn.1006-9941.2016.05.007 HAN Y, GUO X L, LONG X P. High temperature and high pressure equation of state of carbon dioxide [J]. Chinese Journal of Energetic Materials, 2016, 24(5): 462–468. doi: 10.11943/j.issn.1006-9941.2016.05.007
[117]	PENG Y, LONG X P, JIANG X H, et al. A new high order virial equation of state and its application in the Chapman-Jouguet parameters calculation of explosives [J]. Propellants, Explosives, Pyrotechnics, 2023, 48(1): e202100371. doi: 10.1002/prep.202100371
[118]	彭钺, 张蕾, 谢明伟, 等. 一种新爆轰产物状态方程及其在炸药爆轰性能预测上的应用 [J]. 含能材料, 2024, 32(9): 942–951. doi: 10.11943/CJEM2024021 PENG Y, ZHANG L, XIE M W, et al. A novel equation of state for detonation products and its application in predicting the detonation performance of explosives [J]. Chinese Journal of Energetic Materials, 2024, 32(9): 942–951. doi: 10.11943/CJEM2024021
[119]	苗飞超, 郭子如, 李丹丹. 一种基于Virial理论的爆轰产物状态方程 [J]. 工程爆破, 2024, 30(1): 18–25, 43. doi: 10.19931/j.EB.20220413 MIAO F C, GUO Z R, LI D D. A Virial-based equation of state for detonation products [J]. Engineering Blasting, 2024, 30(1): 18–25, 43. doi: 10.19931/j.EB.20220413
[120]	COWPERTHWAITE M, ZWISLER W H. The JCZ equations of state for detonation products and their incorporation in the TIGER code [C]//Proceedings of the Sixth Symposium (International) on Detonation. Coronado, CA: Naval Surface Weapons Center. 1976: 162–172.
[121]	CHIRAT R, PITTION-ROSSILLON G. A new equation of state for detonation products [J]. The Journal of Chemical Physics, 1981, 74(8): 4634–4642. doi: 10.1063/1.441653
[122]	赵波, 崔季平, 樊菁. 高温高压气体状态方程研究及钱学森方程改进 [J]. 力学学报, 2010, 42(2): 151–158. doi: 10.6052/0459-1879-2010-2-2009-029 ZHAO B, CUI J P, FAN J. An improvement of Tsien’s equation of state in high-temperature and high-pressure gases [J]. Chinese Journal of Theoretical and Applied Mechanics, 2010, 42(2): 151–158. doi: 10.6052/0459-1879-2010-2-2009-029
[123]	张震宇, 田占东, 陈军, 等. 爆轰物理 [M]. 长沙: 国防科技大学出版社, 2016: 78−79. ZHANG Z Y, TIAN Z D, CHEN J, et al. Detonation physics [M]. Changsha: National University of Defense Technology Press, 2016: 78−79.
[124]	薛再清, 徐更光, 王廷增, 等. 用修正的KHT状态方程预报炸药爆轰性能 [J]. 北京理工大学学报, 1998, 18(3): 269–273. XUE Z Q, XU G G, WANG T Z, et al. Using revised KHT equation of state to predict explosives detonation property [J]. Journal of Beijing Institute of Technology, 1998, 18(3): 269–273.
[125]	张志江, 徐更光. 高能炸药水中爆炸能量输出特性数值分析 [J]. 含能材料, 2008, 16(2): 171–174. doi: 10.3969/j.issn.1006-9941.2008.02.014 ZHANG Z J, XU G G. Numerical analysis on energy output of underwater explosion for high energetic explosives [J]. Chinese Journal of Energetic Materials, 2008, 16(2): 171–174. doi: 10.3969/j.issn.1006-9941.2008.02.014
[126]	项大林, 荣吉利, 李健, 等. 基于KHT程序的RDX基含铝炸药JWL状态方程参数预测研究 [J]. 北京理工大学学报, 2013, 33(3): 239–243. doi: 10.3969/j.issn.1001-0645.2013.03.005 XIANG D L, RONG J L, LI J, et al. JWL equation of state parameters prediction of RDX-based aluminized explosive based on KHT code [J]. Transactions of Beijing Institute of Technology, 2013, 33(3): 239–243. doi: 10.3969/j.issn.1001-0645.2013.03.005
[127]	陈朗, 龙新平, 冯长根, 等. 含铝炸药爆轰 [M]. 北京: 国防工业出版社, 2004. CHEN L, LONG X P, FENG C G, et al. Aluminized explosive detonation [M]. Beijing: National Defense Industry Press, 2004.
[128]	赵铮, 陶钢, 杜长星. 爆轰产物JWL状态方程应用研究 [J]. 高压物理学报, 2009, 23(4): 277–282. doi: 10.11858/gywlxb.2009.04.007 ZHAO Z, TAO G, DU C X. Application research on JWL equation of state of detonation products [J]. Chinese Journal of High Pressure Physics, 2009, 23(4): 277–282. doi: 10.11858/gywlxb.2009.04.007
[129]	温丽晶, 段卓平, 张震宇, 等. 采用遗传算法确定炸药爆轰产物JWL状态方程参数 [J]. 爆炸与冲击, 2013, 33(Suppl 1): 130–134. WEN L J, DUAN Z P, ZHANG Z Y, et al. Determination of JWL-EOS parameters for explosive detonation products using genetic algorithm [J]. Explosion and Shock Waves, 2013, 33(Suppl 1): 130–134.
[130]	王成, 徐文龙, 郭宇飞. 基于基因遗传算法和γ律状态方程的JWL状态方程参数计算 [J]. 兵工学报, 2017, 38(Suppl 1): 167–173. WANG C, XU W L, GUO Y F. Calculation of JWL equation of state parameters based on genetic algorithm and γ equation of state [J]. Acta Armamentarii, 2017, 38(Suppl 1): 167–173.
[131]	崔浩, 郭锐, 宋浦, 等. 基于遗传算法辨识炸药JWL状态方程参数的研究 [J]. 振动与冲击, 2022, 41(9): 174–180. doi: 10.13465/j.cnki.Jvs.2022.09.023 CUI H, GUO R, SONG P, et al. Identification of parameters of explosive JWL state equation based on genetic algorithm [J]. Journal of Vibration and Shock, 2022, 41(9): 174–180. doi: 10.13465/j.cnki.Jvs.2022.09.023
[132]	何伟平, 黄菊, 陈厚和, 等. 基于BKW状态方程的爆轰产物及参数的改进算法 [J]. 火炸药学报, 2017, 40(3): 53–59. doi: 10.14077/j.issn.1007-7812.2017.03.009 HE W P, HUANG J, CHEN H H, et al. Improved algorithm of detonation products and parameters based on the BKW equation of state [J]. Chinese Journal of Explosives & Propellants, 2017, 40(3): 53–59. doi: 10.14077/j.issn.1007-7812.2017.03.009
[133]	崔浩, 郭锐, 顾晓辉, 等. BP神经网络和圆筒能量模型标定炸药的JWL参数 [J]. 火炸药学报, 2021, 44(5): 665–673. doi: 10.14077/j.issn.1007-7812.202104016 CUI H, GUO R, GU X H, et al. Calibration of JWL parameters of explosive by BP neural network and cylinder energy model [J]. Chinese Journal of Explosives & Propellants, 2021, 44(5): 665–673. doi: 10.14077/j.issn.1007-7812.202104016
[134]	KHASAINOV B A, BORISOV A A, ERMOLAEV B, et al. Two-phase viscoplastic model of shock initiation of detonation in high density pressed explosives [C]//Proceeding of the 7th Symposium (International) on Detonation. Annapolis: Office of Naval Research, 1981.
[135]	KANG J, BUTLER P B, BAER M R. A thermomechanical analysis of hot spot formation in condensed-phase, energetic materials [J]. Combustion and Flame, 1992, 89(2): 117–139. doi: 10.1016/0010-2180(92)90023-I
[136]	MASSONI J, SAUREL R, BAUDIN G, et al. A mechanistic model for shock initiation of solid explosives [J]. Physics of Fluids, 1999, 11(3): 710–736. doi: 10.1063/1.869941