预测不同冲击载荷下弹药响应特性的HOTM方法

廖祜明; 杨燕红; 郭至荣; 王浩; 黄致达; 杨宏涛; 马千里; 贾宪振; 黎波

doi:10.11883/bzycj-2025-0178

预测不同冲击载荷下弹药响应特性的HOTM方法

doi: 10.11883/bzycj-2025-0178

廖祜明^{1, 2,},
杨燕红^{1, 2},
郭至荣^{1, 2},
王浩^{1, 2},
黄致达^{1, 2},
杨宏涛³,
马千里³,
贾宪振⁴,
黎波^3, ,

1.
云翼（嘉兴）软件科技有限公司，浙江嘉兴 314500
2.
云翼超算（北京）软件科技有限公司，北京 100028
3.
北京大学力学与工程科学学院，北京 100871
4.
西安近代化学研究所，陕西西安 710065

详细信息

作者简介:
廖祜明（1987－　），男，博士，liao@escaas.com.cn

通讯作者:
黎　波（1979－　），男，博士，长聘副教授，bo.li@pku.edu.cn

中图分类号: O381; TJ410.1
计量
- 文章访问数: 243
- HTML全文浏览量: 40
- PDF下载量: 41
- 被引次数: 0
出版历程
- 收稿日期: 2025-06-16
- 修回日期: 2025-11-03
- 网络出版日期: 2025-11-04
- 刊出日期: 2026-03-05

The HOTM method for predicting ammunition response characteristics under different impact load conditions

LIAO Huming^{1, 2
,},
YANG Yanhong^{1, 2},
GUO Zhirong^{1, 2},
WANG Hao^{1, 2},
HUANG Zhida^{1, 2},
YANG Hongtao³,
MA Qianli³,
JIA Xianzhen⁴,
LI Bo^{3
, ,}

1.
ESCAAS Co., Ltd., Jiaxing 314500, Zhejiang, China
2.
ESCAAS (Beijing) Co., Ltd., Beijing 100028, China
3.
School of Mechanics and Engineering Science, Peking University, Beijing 100871, China
4.
Xi’an Modern Chemistry Research Institute, Xi’an 710065, Shaanxi, China

摘要

摘要: 基于热最优输运无网格（hot optimal transportation meshfree, HOTM）方法，提出了能够准确预测弹药在冲击载荷下响应特性的无网格数值仿真方法，建立了炸药在冲击载荷下的高精度热-力-化学耦合模型，综合考虑了炸药起爆过程中的温度效应和压力效应，将炸药起爆的Arrhenius热-化学反应耦合模型和局部高压引发的Lee-Tarver压力三项式点火模型有机耦合，实现了对不同冲击速度下炸药不同起爆机制的准确模拟，从而预测弹药在遭受冲击载荷过程中的高速接触、金属外壳大塑性变形、材料断裂、热传导、炸药起爆、化学反应产物膨胀做功等复杂的物理现象。以子弹撞击弹药（850 m/s）和破片撞击弹药（1850 m/s）2种不同冲击速度的典型冲击场景数值模拟为例，分析了冲击速度对炸药起爆机制和弹药整体响应的影响规律，并与相关试验结果进行了对比。结果表明，本方法可有效刻画冲击作用下的材料大变形、摩擦生热、热点形成及化学反应传播等耦合机制，可为弹药抗冲击设计优化和安全性评估提供可靠的技术支撑。
- 子弹/破片撞击 /
- 弹药安全性 /
- HOTM方法 /
- 热-力-化学耦合
Abstract: With the development of modern weapon systems, the requirements for the survivability of ammunition in various complex environments have been continuously increasing. During the processes of storage, flight, and combat, ammunition may be subjected to extreme impact loads such as high-speed impacts, shock waves, bullet and fragment impacts. The external impacts can induce plastic deformation and fracture of the ammunition casing, and even detonate the internal explosives. These responses involve complex phenomena including impact loading, thermo-mechanical coupling of materials, chemical reactions of explosives, and blast effects, representing a typical dynamic response problem of reactive materials under extreme thermo-mechanical coupling conditions. Accurately predicting the responses of ammunition under impact loading is critical for its design optimization and safety assessment. Based on the Hot Optimal Transportation Meshfree (HOTM) method, a meshfree numerical approach was proposed to accurately predict the ammunition responses under different impact loadings. Meanwhile, a thermo-mechanical-chemical coupling constitutive model of explosives was established, which took the effects of temperature and pressure on the explosive’s chemical reaction and detonation into account. The Arrhenius thermal-chemical reaction coupling model for explosive initiation and the Lee-Tarver three-term pressure ignition model induced by local high pressure were integrated to accurately simulate the different initiation mechanisms of explosives under varying impact velocities, thereby predict complex physical phenomena during the impact loading of ammunition. These phenomena include high-speed contact, large plastic deformation of the metal casing, material fracture, heat conduction, explosive initiation, and the expansion work performed by chemical reaction products. Taking the numerical simulations of two typical impact scenarios—bullet impact on ammunition at 850 m/s and fragment impact at 1850 m/s—as examples, the influence of impact velocity on the initiation mechanisms of explosives and the overall response of ammunition was analyzed, with comparisons made against relevant experimental results. The proposed approach and findings provide reliable technical support for the optimization of impact-resistant design and safety assessment of ammunition.
- bullet/fragment impact /
- ammunition safety /
- HOTM method /
- thermal-mechanical-chemical coupling

HTML全文

图 1 热-力-化学强耦合求解框架

Figure 1. Thermal-mechanical-chemical coupling solution framework

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图 2 钢材杨氏模量和屈服强度与温度的关系

Figure 2. Relationship of Youngʼs modulus and yield strength of steel with temperature

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图 3 空间离散示意图^[34]

Figure 3. Spatial discrete schematic diagram^[34]

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图 4 本征侵蚀裂纹扩展算法等效能量释放率计算示意图^[45]

Figure 4. Schematic of the equivalent energy release rate calculation of the eigen erosion crack propagation algorithm^[45]

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图 5 1/4对称子弹撞击计算模型（单位：mm）

Figure 5. Calculation model with quarter-symmetry for bullet impact (unit: mm)

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图 6 子弹高速撞击弹药引发炸药燃烧过程

Figure 6. Simulation of the deflagration process in explosives induced by high-speed bullet impact on ammunition

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图 7 267 μs时刻炸药沿中轴线反应分布

Figure 7. Reaction distribution along the central axis of the explosive at 267 μs

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图 8 仿真和试验结果对比

Figure 8. Comparison between simulation and experimental results

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图 9 1/4对称破片撞击计算模型（单位：mm）

Figure 9. Calculation model with quarter-symmetry for fragment impact (unit: mm)

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图 10 破片高速撞击弹药引发炸药爆轰过程仿真

Figure 10. Simulation of high-speed fragment impact on ammunition initiating explosive detonation process

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图 11 45 μs时刻炸药沿中轴线反应分布

Figure 11. Reaction distribution along the central axis of the explosive at 45 μs

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表 1 材料物性参数^[50]

Table 1. Property parameters for materials^[50]

材料	ρ/(kg∙m⁻³)	E/GPa	υ	δ_cr/(kJ∙m⁻²)
4340钢	7850	200	0.3	200
45钢	7800	200	0.3	200
PBX-3	1820	2.62	0.21
高强钢	7850	200	0.29	1000

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表 2 材料本构模型参数^[50-51]

Table 2. Parameters of constitutive models for materials^[50-51]

材料	σ₀/MPa	ε_pl,0	$ {\dot{\varepsilon }}_{\mathrm{p}\text{l},0} $/s⁻¹	n	m	l	T_m/K
4340钢^[51]	580	0.001	1.0	0.15	0.013	0.8856	1795
45钢^[51]	500	0.05	1.0	0.22	0.135	0.8856	1795
PBX-3^[50]	5.4	0.00006	0.00164	0.05	0.15	0.5	550
高强钢^[51]	1000	0.001	1.0	0.083	0.00294	1.17	1777

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参考文献(51)

[1]	马晗晔, 王雨时, 王光宇. 国外不敏感炸药综述 [J]. 兵器装备工程学报, 2020, 41(5): 166–174. DOI: 10.11809/bqzbgcxb2020.05.032. MA H H, WANG Y S, WANG G Y. Summary of foreign insensitive explosives [J]. Journal of Ordnance Equipment Engineering, 2020, 41(5): 166–174. DOI: 10.11809/bqzbgcxb2020.05.032.
[2]	NATO. Bullet attack test for munitions: NATO-STANAG 4241 [S]. NATO, 1991.
[3]	United States Department of Defense. Hazard assessment tests for non-nuclear munitions: MIL-STD-2105C—2003 [S]. Department of Defense, 2003.
[4]	NATO. Policy for introduction and assessment of insensitive munitions: STANAG 4439: 2010 [S]. NATO Standardization Office, 2010.
[5]	NATO. Guidance on the assessment and development of insensitive munitions (IM): AOP-39 [S]. NATO Standardization Agency, North Atlantic Treaty Organization (NATO), 2010.
[6]	国防科学技术工业委员会. 炸药试验方法: GJB 772A—1997 [S]. 北京: 国防科学技术工业委员会, 1997. Explosive test method: GJB 772A—1997 [S]. Beijing: Commission of Science, Technology and Industry for National Defense of the PRC, 1997.
[7]	KIMURA E, OYUMI Y. Sensitivities of azide polymer propellants in fast cook-off, card gap and bullet impact tests [J]. Journal of Energetic Materials, 1997, 15(2/3): 163–178. DOI: 10.1080/07370659708216080.
[8]	DAGLEY I J, HO S Y, NANUT V. Effects of the polymer matrix density on the shock, bullet impact and high strain-rate ignition sensitivity of polymer bonded explosives [J]. Propellants, Explosives, Pyrotechnics, 1997, 22(5): 296–300. DOI: 10.1002/prep.19970220509.
[9]	魏祥庚, 刘佩进, 何国强, 等. HTPB和NEPE固体推进剂枪击低易损性实验研究 [J]. 弹箭与制导学报, 2005, 25(4): 714–716. DOI: 10.3969/j.issn.1673-9728.2005.04.233. WEI X G, LIU P J, HE G Q, et al. Experimental research on the low vulnerability of HTPB and NEPE solid propellant [J]. Journal of Projectiles, Rockets, Missiles and Guidance, 2005, 25(4): 714–716. DOI: 10.3969/j.issn.1673-9728.2005.04.233.
[10]	李小柱, 裴养卫. 固体火箭发动机枪击低易损性试验研究 [J]. 弹箭与制导学报, 2000(2): 39–42. DOI: 10.3969/j.issn.1673-9728.2000.02.008. LI X Z, PEI Y W. Low vulnerability experimental study of solid rocket engine under popping condition [J]. Journal of Projectiles, Rockets, Missiles and Guidance, 2000(2): 39–42. DOI: 10.3969/j.issn.1673-9728.2000.02.008.
[11]	齐任超. 破片冲击作用下战斗部装药失效响应研究 [D]. 北京: 北京理工大学, 2015. QI R C. Research on the low vulnerability method of warhead case under the impact of fragment [D]. Beijing: Beijing Institute of Technology, 2015.
[12]	胡杰, 杜剑英, 陈桦, 等. 破片撞击不敏感弹药研究进展 [J]. 兵器装备工程学报, 2022, 43(8): 36–43. DOI: 10.11809/bqzbgcxb2022.08.006. HU J, DU J Y, CHEN H, et al. Research progress of fragment impact insensitive ammunition [J]. Journal of Ordnance Equipment Engineering, 2022, 43(8): 36–43. DOI: 10.11809/bqzbgcxb2022.08.006.
[13]	JONES D A, KEMISTER G, BORG R A J. Numerical simulation of detonation in condensed phase explosives: DSTO-TR-0705, AR-010-605 [R]. 1998.
[14]	代晓淦, 申春迎, 吕子剑, 等. 枪击试验中不同尺寸PBX-2炸药响应规律研究 [J]. 含能材料, 2008, 16(4): 432–435. DOI: 10.3969/j.issn.1006-9941.2008.04.017. DAI X G, SHEN C Y, LÜ Z J, et al. Reaction properties for different size PBX-2 explosives in bullet impact test [J]. Chinese Journal of Energetic Materials, 2008, 16(4): 432–435. DOI: 10.3969/j.issn.1006-9941.2008.04.017.
[15]	庄建华, 毛佳, 张为华, 等. 固体火箭发动机枪击过程数值模拟 [J]. 固体火箭技术, 2009, 32(4): 422–426. DOI: 10.3969/j.issn.1006-2793.2009.04.016. ZHUANG J H, MAO J, ZHANG W H, et al. Numerical simulation of the gunshot process of solid rocket motor [J]. Journal of Solid Rocket Technology, 2009, 32(4): 422–426. DOI: 10.3969/j.issn.1006-2793.2009.04.016.
[16]	HAMAIDE S, QUIDOT M, BRUNET J. Tactical solid rocket motors response to bullet impact [J]. Propellants, Explosives, Pyrotechnics, 1992, 17(3): 120–125. DOI: 10.1002/prep.19920170306.
[17]	濮赞泉. 破片撞击起爆战斗部影响因素及判据研究 [D]. 南京: 南京理工大学, 2016. PU Z Q. Study on influencing factors and criterion of fragment impact initiation warhead [D]. Nanjing: Nanjing University of Science and Technology, 2016.
[18]	刘沫言. 带壳装药的破片撞击和冲击波感度研究 [D]. 沈阳: 沈阳理工大学, 2020. LIU M Y. Study on fragment impingement and shock wave sensitivity with shell charge [D]. Shenyang: Shenyang Ligong University, 2020.
[19]	GINGOLD R A, MONAGHAN J J. Smoothed particle hydrodynamics: theory and application to non-spherical stars [J]. Monthly Notices of the Royal Astronomical Society, 1977, 181(3): 375–389. DOI: 10.1093/mnras/181.3.375.
[20]	LIU W K, JUN S, ZHANG Y F. Reproducing kernel particle methods [J]. International Journal for Numerical Methods in Fluids, 1995, 20(8/9): 1081–1106. DOI: 10.1002/fld.1650200824.
[21]	ZHANG X, CHEN Z, LIU Y. The material point method [M]. Oxford: Academic Press, 2017: 37–101.
[22]	LIU M B, LIU G R, LAM K Y, et al. Computer simulation of shaped charge detonation using meshless particle method [J]. Fragblast, 2003, 7(3): 181–202. DOI: 10.1076/frag.7.3.181.16789.
[23]	LIU M B, ZHANG Z L, FENG D L. A density-adaptive SPH method with kernel gradient correction for modeling explosive welding [J]. Computational Mechanics, 2017, 60(3): 513–529. DOI: 10.1007/s00466-017-1420-5.
[24]	YANG G, HAN X, HU D A. Simulation of explosively driven metallic tubes by the cylindrical smoothed particle hydrodynamics method [J]. Shock Waves, 2015, 25(6): 573–587. DOI: 10.1007/s00193-015-0588-x.
[25]	YANG G, LIU R Q, HU D, et al. Simulation of one dimension shock initiation of condensed explosive by SPH method [J]. Engineering Computations, 2016, 33(2): 528–542. DOI: 10.1108/EC-03-2015-0076.
[26]	刘赛, 张伟贵, 吕振华. 穿甲燃烧弹侵彻陶瓷复合装甲和玻璃复合装甲的FEM-SPH耦合计算模型 [J]. 爆炸与冲击, 2021, 41(1): 014201. DOI: 10.11883/bzycj-2020-0069. LIU S, ZHANG W G, LYU Z H. An FEM-SPH coupled model for simulating penetration of armor-piercing bullets into ceramic composite armors and glass composite armors [J]. Explosion and Shock Waves, 2021, 41(1): 014201. DOI: 10.11883/bzycj-2020-0069.
[27]	ZHOU G H. A reproducing kernel particle method framework for modeling failure of structures subjected to blast loadings [M]. San Diego: University of California, 2016.
[28]	BAEK J, CHEN J S, ZHOU G H, et al. A semi-Lagrangian reproducing kernel particle method with particle-based shock algorithm for explosive welding simulation [J]. Computational Mechanics, 2021, 67(6): 1601–1627. DOI: 10.1007/s00466-021-02008-2.
[29]	MA S, ZHANG X, LIAN Y P, et al. Simulation of high explosive explosion using adaptive material point method [J]. Computer Modeling in Engineering and Sciences, 2009, 39(2): 101–124. DOI: 10.3970/cmes.2009.039.101.
[30]	LIAN Y P, ZHANG X, ZHOU X, et al. Numerical simulation of explosively driven metal by material point method [J]. International Journal of Impact Engineering, 2011, 38(4): 238–246. DOI: 10.1016/j.ijimpeng.2010.10.031.
[31]	CUI X X, ZHANG X, SZE K Y, et al. An alternating finite difference material point method for numerical simulation of high explosive explosion problems [J]. Computer Modeling in Engineering and Sciences, 2013, 92(5): 507–538. DOI: 10.3970/cmes.2013.092.507.
[32]	LI B, HABBAL F, ORTIZ M. Optimal transportation meshfree approximation schemes for fluid and plastic flows [J]. International Journal for Numerical Methods in Engineering, 2010, 83(12): 1541–1579. DOI: 10.1002/nme.2869.
[33]	WANG H, LIAO H M, FAN Z Y, et al. The hot optimal transportation meshfree (HOTM) method for materials under extreme dynamic thermomechanical conditions [J]. Computer Methods in Applied Mechanics and Engineering, 2020, 364: 112958. DOI: 10.1016/j.cma.2020.112958.
[34]	廖祜明, 黎波, 樊江, 等. 超高速撞击下碎片云的OTM分析 [J]. 爆炸与冲击, 2022, 42(10): 103301. DOI: 10.11883/bzycj-2021-0275. LIAO H M, LI B, FAN J, et al. OTM analysis of debris cloud under hypervelocity impact [J]. Explosion and Shock Waves, 2022, 42(10): 103301. DOI: 10.11883/bzycj-2021-0275.
[35]	JIANG H, SCOTT V, LI B. Modeling and simulations of high and hypervelocity impact of small ice particles [J]. International Journal of Impact Engineering, 2021, 155: 103906. DOI: 10.1016/j.ijimpeng.2021.103906.
[36]	WANG H, LI X B, PHIPPS M, et al. Numerical and experimental study of hot pressing technique for resin-based friction composites [J]. Composites Part A: Applied Science and Manufacturing, 2022, 153: 106737. DOI: 10.1016/j.compositesa.2021.106737.
[37]	JIANG H, WANG H, SCOTT V, et al. Numerical analysis of oblique hypervelocity impact damage to space structural materials by ice particles in cryogenic environment [J]. Acta Astronautica, 2022, 195: 392–404. DOI: 10.1016/j.actaastro.2022.02.029.
[38]	马天宝, 粟鑫, 郝莉. 基于OTM方法的超高速碰撞问题数值模拟 [J]. 北京理工大学学报, 2020, 40(6): 617–622. DOI: 10.15918/j.tbit1001-0645.2019.120. MA T B, SU X, HAO L. Numerical simulation of hypervelocity impact based on the optimal transportation meshfree method [J]. Transactions of Beijing Institute of Technology, 2020, 40(6): 617–622. DOI: 10.15918/j.tbit1001-0645.2019.120.
[39]	王浩, 廖祜明, 王淼辉, 等. 带相变热流固耦合问题的数值方法及金属增材制造仿真 [J]. 中国科学: 物理学力学天文学, 2022, 52(10): 104713. DOI: 10.1360/SSPMA-2022-0222. WANG H, LIAO H M, WANG M H, et al. Numerical approach for a strongly coupled thermomechanical process with multi-phase transition and applications in additive manufacturing [J]. Scientia Sinica: Physica, Mechanica, and Astronomica, 2022, 52(10): 104713. DOI: 10.1360/SSPMA-2022-0222.
[40]	YANG Q, STAINIER L, ORTIZ M. A variational formulation of the coupled thermo-mechanical boundary-value problem for general dissipative solids [J]. Journal of the Mechanics and Physics of Solids, 2006, 54(2): 401–424. DOI: 10.1016/j.jmps.2005.08.010.
[41]	CEN. Stainless steels. Part 1: list of stainless steels: BS EN 10088-1: 2023 [S]. Standards Policy and Strategy Committee, 2024.
[42]	GARDNER L, INSAUSTI A, NG K T, et al. Elevated temperature material properties of stainless steel alloys [J]. Journal of Constructional Steel Research, 2010, 66(5): 634–647. DOI: 10.1016/j.jcsr.2009.12.016.
[43]	LEE E L, TARVER C M. Phenomenological model of shock initiation in heterogeneous explosives [J]. Physics of Fluids, 1980, 23(12): 2362–2372. DOI: 10.1063/1.862940.
[44]	LEE E, FINGER M, COLLINS W. JWL equation of state coefficients for high explosives: UCID-16189 [R]. Livermore: University of California, 1973. DOI: 10.2172/4479737.
[45]	ARROYO M, ORTIZ M. Local maximum-entropy approximation schemes: a seamless bridge between finite elements and meshfree methods [J]. International Journal for Numerical Methods in Engineering, 2006, 65(13): 2167–2202. DOI: 10.1002/nme.1534.
[46]	FAN J, LIAO H M, WANG H, et al. Local maximum-entropy based surrogate model and its application to structural reliability analysis [J]. Structural and Multidisciplinary Optimization, 2018, 57(1): 373–392. DOI: 10.1007/s00158-017-1760-y.
[47]	SCHMIDT B, FRATERNALI F, ORTIZ M. Eigenfracture: an eigendeformation approach to variational fracture [J]. Multiscale Modeling and Simulation, 2009, 7(3): 1237–1266. DOI: 10.1137/080712568.
[48]	PANDOLFI A, ORTIZ M. An eigenerosion approach to brittle fracture [J]. International Journal for Numerical Methods in Engineering, 2012, 92(8): 694–714. DOI: 10.1002/nme.4352.
[49]	FAN Z Y, LIAO H M, JIANG H, et al. A dynamic adaptive eigenfracture method for failure in brittle materials [J]. Engineering Fracture Mechanics, 2021, 244: 107540. DOI: 10.1016/j.engfracmech.2021.107540.
[50]	贾宪振, 南海, 王晓峰, 等. 有氧化剂(AP)含铝炸药水中爆炸数值模拟 [J]. 科学技术与工程, 2015, 15(6): 1–4, 11. DOI: 10.3969/j.issn.1671-1815.2015.06.001. JIA X Z, NAN H, WANG X F, et al. Numerical simulation of underwater explosion of aluminized explosive containingoxidizer (AP) [J]. Science Technology and Engineering, 2015, 15(6): 1–4, 11. DOI: 10.3969/j.issn.1671-1815.2015.06.001.
[51]	STEINBERG D J. Equation of state and strength properties of selected materials [M]. Livermore: Lawrence Livermore National Laboratories, 1996.