长杆高速侵彻问题研究进展

焦文俊; 陈小伟

doi:10.6052/1000-0992-17-021

长杆高速侵彻问题研究进展

doi: 10.6052/1000-0992-17-021

焦文俊^1,2,
陈小伟^3,4,, ,

¹ 中国科学技术大学近代力学系, 合肥 230027
² 中国工程物理研究院总体工程研究所, 四川绵阳 621999
³ 北京理工大学爆炸科学与技术国家重点实验室, 北京 100081
⁴ 北京理工大学前沿交叉科学研究院, 北京 100081

基金项目: 国家杰出青年基金(11225213)和国家自然科学基金(11872118)资助项目

详细信息

作者简介:
通讯作者: †E-mail: chenxiaoweintu@bit.edu.cn

作者简介：陈小伟, 教授, 博导.2017年1月入职北京理工大学前沿交叉科学研究院.国家杰出青年科学基金获得者(2012), 国家首批中青年科技创新领军人才(2013), “万人计划”首批科技创新领军人才(2014). 北京大学理学学士(1989), 香港科技大学理学硕士(1999), 新加坡南洋理工大学工学博士(2003). 曾获中国工程物理研究院首批杰出专家(2012),中物院第12届邓稼先青年科技奖(2010)和第8届于敏数理科学奖(2010),中国科协“求是”杰出青年实用工程奖(2012), 四川省学术技术带头人(2014).1989.12—2017.01在中物院总体工程研究所工作,长期从事复杂结构力学、结构冲击动力学、穿甲动力学和常规武器战斗部设计的研究,在穿甲/侵彻力学领域已开展有国际影响的独创性系统研究,工作涵盖深侵彻、金属靶穿甲、弹体响应与失效破坏和战斗部结构分析等,其成果已在国内外同领域产生了较大影响. 已取得9项部委级科技进步奖(其中二等奖5项), 发表论文130余篇 (其中SCI收录近60篇),国内外大会报告和院校邀请报告60余次.担任工程材料与结构冲击与振动四川省重点实验室主任, 担任International Journal of ProtectiveStructures,《爆炸与冲击》《振动与冲击》《兵工学报》《应用数学和力学》《含能材料》《防护工程》《解放军理工大学学报(自然科学版)》编委, 担任西南科技大学讲座教授,中物院研究生院、北京大学工学院、解放军陆军工程大学冲击爆炸防灾减灾国家重点实验室、北京理工大学安全与防护协同创新中心和中国科技大学兼职教授/兼职博导.

通讯作者:
陈小伟

中图分类号: O385;
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出版历程
- 收稿日期: 2017-11-25
- 刊出日期: 2019-02-08

Review on long-rod penetration at hypervelocity

JIAO Wenjun^1,2,
CHEN Xiaowei^{3,4,
, ,}

¹ Department of Modern Mechanics, Universityof Science and Technology of China, Hefei 230027, China
² Institute of Systems Engineering, China Academy of Engineering Physics, Sichuan, Mianyang 621999, China
³ The State Key Lab of Explosion Science and Technology,Beijing Institute of Technology, Beijing 100081, China
⁴ Advanced Research Institute for Multidisciplinary Science,Beijing Institute of Technology, Beijing 100081, China

More Information

Author Bio:
corresponding Author: †E-mail: chenxiaoweintu@bit.edu.cn

Corresponding author: CHEN Xiaowei

摘要

摘要: 由高密度金属制成的长杆弹在1.5$\sim$3.0km/s的下具有很强的侵彻和贯穿能力,长杆高速侵彻问题现已成为穿甲侵彻领域的研究热点.本文综述了长杆高速侵彻问题的最新研究进展,首先介绍了长杆高速侵彻的基本概念、研究方法和理论模型;其次重点论述了研究中关注的突出问题与应用, 包括弹靶材料性质、长杆弹头部形状、长径比效应与分段杆设计、陶瓷靶抵抗长杆侵彻与界面击溃和非理想长杆侵彻;最后对未来的研究工作提出一些建议.
- 长杆弹 /
- 高速 /
- 侵彻 /
- 理论模型 /
- 穿甲力学
Abstract: Made by high-density metals, long-rod penetrators have excellent performances on penetration and perforation when launched at hypervelocities around 1.5$\sim $3.0km/s. Due to their important background in the military application, long-rod penetration at hypervelocity has become an active research focus. The present paper reviews research advance up-to-date on long-rod penetration at hypervelocity. Firstly, basic concepts, research methods, and theoretical models are introduced. Secondly, highlighted issues which are focused in past studies and their applications, including rod and target materials, nose shape, $L/D$ effect and segmented rods, ceramic targets and interface defeat, as well as non-ideal long-rod penetration, etc. Finally, some future research proposals are suggested.
- long-rod penetrator /
- hypervelocity /
- penetration /
- theoretical models /
- penetration mechanics

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参考文献(244)

[1]	陈小伟. 2009. 穿甲/侵彻问题的若干工程研究进展. 力学进展, 39: 316-351 (Chen X W.2009. Advances in the penetration/perforation of rigid projectiles. Advances in Mechanics, 39: 316-351).
[2]	陈小伟, 陈裕泽. 2006. 脆性陶瓷靶高速侵彻/穿甲动力学的研究进展. 力学进展, 36: 85-102 (Chen X W, Chen Y Z.2006. Review on the penetration/perforation of ceramics targets. Advances in Mechanics, 36: 85-102).
[3]	陈小伟, 李继承, 张方举, 陈刚. 2012. 钨纤维增强金属玻璃复合材料弹穿甲钢靶的实验研究. 爆炸与冲击, 32: 346-354 (Chen X W, Li J C, Zhang F J, Chen G.2012. Experimental research on the penetration of tungsten-fiber/metallic glass-matrix composite material penetrator into steel target. Explosion and Shock Waves, 32: 346-354).
[4]	程兴旺, 王富耻, 李树奎, 王鲁. 2007. 不同头部形状长杆弹侵彻过程的数值模拟. 兵工学报, 28: 930-933 (Cheng X W, Wang F Z, Li S K, Wang L.2007. Numerical simulation on the penetrations of long-rod projectiles with different nose shapes. Acta Armamentarii, 28: 930-933).
[5]	高光发, 李永池, 黄瑞源, 李平. 2012. 杆弹头部形状对侵彻行为的影响及其机制. 弹箭与制导学报, 32: 51-54 (Gao G F, Li Y C, Huang R Y, Li P.2012. Effect of nose shape on the penetration performance of long-rod penetrator and its mechanism. Journal of Projectiles, Rockets Missiles and Guidance, 32: 51-54).
[6]	蒋东, 李永池, 于少娟, 邓世春. 2010. 钨合金长杆弹侵彻约束AD95陶瓷复合靶. 爆炸与冲击, 30: 91-95 (Jiang D, Li Y C, Yu S J, Deng S C.2010. Penetation of confined AD95 ceramic composite targets by tungsten long rods. Explosion and Shock Waves, 30: 91-95).
[7]	孔祥振, 方秦, 吴昊, 龚自明. 2017. 长杆弹超高速侵彻半无限靶理论模型的对比分析与讨论. 振动与冲击, 36: 7 (X Kong, Q Fang, H Wu, Z Gong.2017. Compaision of long rod high velocity penetration models for semi-infinite targets. Journal of Vibration and Shock, 36: 7).
[8]	兰彬. 2008. 长杆弹侵彻半无限靶的数值模拟和理论研究. [博士论文]. 合肥: 中国科学技术大学 (Lan B.2008. A combined numerical and theoretical study of long rod penetration into semi-infinite targets. [PhD Thesis]. Hefei: University of Science and Technology of China).
[9]	兰彬, 文鹤鸣. 2008. 钨合金长杆弹侵彻半无限钢靶的数值模拟及分析. 高压物理学报, 22: 245-252 (Lan B, Wen H M.2008. Numerical simulation and analysis of the penetration of tungsten-alloy long rod into semi-infinite armor steel targets. Chinese Journal of High Pressure Physics, 22: 245-252).
[10]	兰彬, 文鹤鸣. 2009. 半球形弹头钢长杆弹侵彻半无限铝合金靶的数值模拟. 工程力学, 26: 183-190 (Lan B, Wen H M.2009. A numerical simulation of the penetration of a spherical-nosed 4340 steel long-rod into semi-infinite 6061-T6511 aluminum targets. Engineering Mechanics, 26: 183-190).
[11]	郎林, 陈小伟, 雷劲松. 2011. 长杆和分段杆侵彻的数值模拟. 爆炸与冲击, 30: 127-134 (Lang L, Chen X W, Lei J S.2011. Numerical simulation on long rod and segmented rods penetration into steel targets. Explosion and Shock Waves, 30: 127-134).
[12]	李继承, 陈小伟. 2011a. 尖锥头长杆弹侵彻的界面击溃分析. 力学学报, 43: 63-70 (Li J C, Chen X W.2011a. Theoratical analysis on the interface defeat of a conical-nosed projectile penetration. Chinese Journal of Theoretical and Applied Mechanics, 43: 63-70).
[13]	李继承, 陈小伟. 2011b. 柱形长杆弹侵彻的界面击溃分析. 爆炸与冲击, 30: 141-147 (Li J C, Chen X W.2011b. Theoretical analysis on the interface deafeat of a long rod penetration. Explosion and Shock Waves, 30: 141-147).
[14]	李继承, 陈小伟. 2011c. 块体金属玻璃及其复合材料的压缩剪切特性和侵彻/穿甲“自锐”行为. 力学进展, 41: 480-518 (Li J C, Chen X W.2011c. Compressive-shear behavior and self-sharpening of bulk metallic glass and their composite materials. Advances in Mechanics, 41: 480-518).
[15]	李金柱, 黄风雷, 张连生. 2014. 陶瓷材料抗长杆弹侵彻阻抗研究. 北京理工大学学报, 34 : 1-4 (Li J Z, Huang F L, Zhang L S.2014. Penetration resistance of ceramic materials subjected to projectile's impact. Transactions of Beijing Institute of Technology, 34: 1-4).
[16]	李志康, 黄风雷. 2010. 高速长杆弹侵彻半无限混凝土靶的理论分析. 北京理工大学学报, 30: 10-13 (Li Z K, Huang F L.2010. High velocity long rod projectile's penetration into semi-infinite concrete targets. Transactions of Beijing Institute of Technology, 30: 10-13).
[17]	楼建锋. 2012. 侵彻半无限厚靶的理论模型与数值模拟研究. [博士论文]. 绵阳: 中国工程物理研究院 (Lou J F.2012. Theoretical model and numerical study on penetration into semi-infinite targets. [PhD Thesis]. Mianyang: China Academy of Engineering Physics).
[18]	钱伟长. 1984. 穿甲力学. 北京: 国防工业出版社 (Qian W C.1984.Penetration Mechanics. Beijing: National Defense Industry Press).
[19]	谈梦婷, 张先锋, 包阔, 伍杨, 吴雪. 2019. 装甲陶瓷的界面击溃效应. 力学进展, 49: doi: 10.6052/1000-0992-17-015 (Tan M T, Zhang F X, Bao K, Wu Y, Wu X.2019. Interface defeat of ceramic armor. Advances in Mechanics , 49: doi: 10.6052/1000-0992-17-015).
[20]	谈梦婷, 张先锋, 葛贤坤, 刘闯, 熊玮. 2017. 长杆弹撞击装甲陶瓷界面击溃/侵彻转变速度理论模型. 爆炸与冲击, 37: 1093-1100 (Tan M T, Zhang F X, Ge X K, Liu C, Xiong W.2017. Theoretical model of interface defeat/penetration transition velocity of ceramic armor impacted by long-rod projectile. Explosion and Shock Waves, 37: 1093-1100).
[21]	谈梦婷, 张先锋, 何勇, 刘闯, 于溪, 郭磊. 2016. 长杆弹撞击装甲陶瓷的界面击溃效应数值模拟. 兵工学报, 37: 627-634 (Tan M T, Zhang X F, He Y, Liu C, Yu X, Guo L.2016. Numerical simulation on interface defeat of ceramic armor impacted by long-rod projectile. Acta Armamentarii, 37: 627-634).
[22]	王杰, 陈小伟, 韦利明, 雷劲松. 2014. 80%钨纤维增强锆(Zr)基块体金属玻璃复合材料长杆弹侵彻钢靶实验研究. 实验力学, 29: 279-285 (Wang J, Chen X W, Wei L M, Lei J S.2014. Experimental research on steel target penetration of long rod projectile made of 80% W-fiber/Zr-based BMG. Experimental Mechanics, 29: 279-285).
[23]	魏雪英, 俞茂宏. 2002. 钨杆弹高速侵彻陶瓷靶的理论分析. 兵工学报, 23: 167-170 (Wei X Y, Yu M H.2002. Analysis of tungsten rods on penetrating ceramic targets at high velocity. Acta Armamentarii, 23: 167-170).
[24]	徐晨阳, 张先锋, 刘闯, 邓佳杰, 郑应民. 2018. 大着速范围长杆弹侵彻深度变化及其影响因素的数值模拟. 高压物理学报, 32: 1-9 (Xu C Y, Zhang X F, Liu C, Deng J J, Zheng Y M.2018. Depth of penetration and its influence factors of long rod projectile impacting on semiInfinite target with elevated velocity. Chinese Journal of High Pressure Physics, 32: 1-9).
[25]	翟阳修, 吴昊, 方秦. 2017. 基于A-T模型的长杆弹超高速侵彻陶瓷靶体强度分析. 振动与冲击, 36: 183-188 (Zhai Y X, Wu H, Fang Q.2017. Strength analysis of ceramic targets against hypervelocity penetration of long-rod projectiles based on A-T model. Journal of Vibration and Shock, 36: 183-188).
[26]	张连生, 黄风雷. 2005. 抗弹陶瓷材料抗弹性能的理论表征. 北京理工大学学报, 25: 651-654 (Zhang L S, Huang F L.2005. Theoretical characterization of ballistic performance of armor ceramics. Transactions of Beijing Institute of Technology, 25: 651-654).
[27]	Alekseevskii V P.1966. Penetration of a rod into a target at high velocity. Combustion, Explosion, and Shock Waves, 2: 63-66.
[28]	Allen W A, Rogers J W.1961. Penetration of a rod into a semi-infinite target. Journal of the Franklin Institute, 272: 275-284.
[29]	Aly S Y, Li Q M.2008. Numerical investigation of penetration performance of non-ideal segmented-rod projectiles. Transactions of Tianjin University, 14: 391-395.
[30]	Anderson Jr. C E.1987. An overview of the theory of hydrocodes. International Journal of Impact Engineering, 5: 33-59.
[31]	Anderson Jr C E.2003. From fire to ballistics: A historical retrospective. International Journal of Impact Engineering, 29: 13-67.
[32]	Anderson Jr. C E.2017. Analytical models for penetration mechanics: A review. International Journal of Impact Engineering, 108: 3-26.
[33]	Anderson Jr. C E, Behner T, Orphal D L, Nicholls A E, Holmquist T J, Wickert M.2008. Long-rod penetration into intact and pre-damaged SiC ceramic. Southwest Research Institute, San Antonio, TX, USA.
[34]	Anderson Jr. C E, Behner T, Holmquist T J, King N L, Orphal D L.2011a. Interface defeat of long rods impacting oblique silicon carbide. Southwest Research Institute, San Antonio, TX, USA.
[35]	Anderson Jr. C E, Chocron S, Bigger R P.2011b. Time-resolved penetration into glass: Experiments and computations. International Journal of Impact Engineering, 38: 723-731.
[36]	Anderson Jr. C E, Hohler V, Walker J D, Stilp A J.1999a. The influence of projectile hardness on ballistic performance. International Journal of Impact Engineering, 22: 619-632.
[37]	Anderson Jr. C E, Holmquist T J.2013. Application of a computational glass model to compute propagation of failure from ballistic impact of borosilicate glass targets. International Journal of Impact Engineering, 56: 2-11.
[38]	Anderson Jr. C E, Morris B L.1992. The ballistic performance of confined Al$_{2}$O$_{3}$ ceramic tiles. International Journal of Impact Engineering, 12: 167-187.
[39]	Anderson Jr. C E, Morris B L, Littlefield D L.1992a. A penetration mechanics database. Final Report Southwest Research Inst.
[40]	Anderson Jr. C E, Littlefield D L, Walker J D.1993. Long-rod penetration, target resistance, and hypervelocity impact. International Journal of Impact Engineering, 14: 1-12.
[41]	Anderson Jr. C E, Orphal D L.2003. Analysis of the terminal phase of penetration. International Journal of Impact Engineering, 29: 69-80.
[42]	Anderson Jr. C E, Orphal D L.2008. An examination of deviations from hydrodynamic penetration theory. International Journal of Impact Engineering, 35: 1386-1392.
[43]	Anderson Jr. C E, Orphal D L, Behner T, Hohler V, Templeton D W.2006. Re-examination of the evidence for a failure wave in SiC penetration experiments. International Journal of Impact Engineering, 33: 24-34.
[44]	Anderson Jr. C E, Orphal D L, Behner T, Templeton D W.2009. Failure and penetration response of borosilicate glass during short-rod impact. International Journal of Impact Engineering, 36: 789-798.
[45]	Anderson Jr. C E, Orphal D L, Franzen R R, Walker J D.1999b. On the hydrodynamic approximation for long-rod penetration. International Journal of Impact Engineering, 22: 23-43.
[46]	Anderson Jr. C E, Riegel Iii J J P.2015. A penetration model for metallic targets based on experimental data. International Journal of Impact Engineering, 80: 24-35.
[47]	Anderson Jr. C E, Royal-Timmons S A.1997. Ballistic performance of confined 99.5%-Al$_{2}$O$_{3}$ ceramic tiles. International Journal of Impact Engineering, 19: 703-713.
[48]	Anderson Jr. C E, Walker J D.1991. An examination of long-rod penetration. International Journal of Impact Engineering, 11: 481-501.
[49]	Anderson Jr. C E, Walker J D.2005. An analytical model for dwell and interface defeat. International Journal of Impact Engineering, 31: 1119-1132.
[50]	Anderson Jr. C E, Walker J D, Bless S J, Partom Y.1996. On the L/D effect for long-rod penetrators. International Journal of Impact Engineering, 18: 247-264.
[51]	Anderson Jr. C E, Walker J D, Bless S J, Sharron T R.1995. On the velocity dependence of the $L/D$ effect for long-rod penetrators. International Journal of Impact Engineering, 17: 13-24.
[52]	Anderson Jr. C E, Walker J D, Hauver G E.1992b. Target resistance for long-rod penetration into semi-infinite targets. Nuclear Engineering & Design, 138: 93-104.
[53]	Andersson O, Lundberg P, Renstr?m R.2007. Influence of confinement on the transition velocity of silicon carbide//Proceedings of the 23rd international symposium on ballistics, Tarragona, Spain: 16-20.
[54]	Aydelotte B, Schuster B.2015. Impact and penetration of SiC: The role of rod strength in the transition from dwell to penetration. Procedia Engineering, 103: 19-26.
[55]	Behner T, Anderson Jr. C E, Holmquist T J, Wickert M, Templeton D W.2008. Interface defeat for unconfined SiC ceramics//Proceedings of the 24th international symposium on ballistics, New Orleans: 35-42.
[56]	Behner T, Anderson Jr. C E, Holmquist T J, Orphal D L, Wickert M, Templeton D W.2011. Penetration dynamics and interface defeat capability of silicon carbide against long Rod impact. International Journal of Impact Engineering, 38: 419-425.
[57]	Behner T, Anderson Jr. C E, Orphal D L, Hohler V, Moll M, Templeton D W.2008. Penetration and failure of lead and borosilicate glass against rod impact. International Journal of Impact Engineering, 35: 447-456.
[58]	Behner T, Heine A, Wickert M.2013. Protective properties of finite-extension ceramic targets against steel and copper projectiles//Proceedings of the 27th International Symposium on Ballistics, Freiburg, Germany.
[59]	Behner T, Heine A, Wickert M.2016. Dwell and penetration of tungsten heavy alloy long-rod penetrators impacting unconfined finite-thickness silicon carbide ceramic targets. International Journal of Impact Engineering, 95: 54-60.
[60]	Behner T, Orphal D L, Hohler V, Anderson Jr. C E, Mason R L, Templeton D W.2006. Hypervelocity penetration of gold rods into SiC-N for impact velocities from 2.0 to 6.2km/s. International Journal of Impact Engineering, 33: 68-79.
[61]	Belyakov L V, Vitman F F, Zlatin N A.1963. Collision of deformable bodies and its modeling. Soviet Physics-Technical Physics, 8: 736-739.
[62]	Birkhoff G, Macdougall D P, Pugh E M, Taylor S G.1948. Explosives with Lined Cavities. Journal of Applied Physics, 19: 563-582.
[63]	Bjerke T W, Silsby G F, Scheffler D R, Mudd R M.1992. Yawed long-rod armor penetration. International Journal of Impact Engineering, 12: 281-292.
[64]	Bless S J, Barber J P, Bertke R S, Swift H F.1978. Penetration mechanics of yawed rods. International Journal of Engineering Science, 16: 829-834.
[65]	Bless S J, Rosenberg Z, Yoon B.1987. Hypervelocity penetration of ceramics. International Journal of Impact Engineering, 5: 165-171.
[66]	Bukharev Y I, Zhukov V I.1995. Model of the penetration of a metal barrier by a rod projectile with an angle of attack. Combustion, Explosion, and Shock Waves, 31: 362-367.
[67]	Burkins M S, Paige J I, Hansen J S.1996. A ballistic evaluation of Ti-6Al-4v vs. long rod penetrators. Army Research Laboratory Report ARL-TR-1146.
[68]	Charters A C, Menna T L, Piekutowski A J.1990. Penetration dynamics of rods from direct ballistic tests of advanced armor components at 2-3km/s. International Journal of Impact Engineering, 10: 93-106.
[69]	Chen X W, Li Q M.2002. Deep penetration of a non-deformable projectile with different geometrical characteristics. International Journal of Impact Engineering, 27: 619-637.
[70]	Chen X W, Li Q M.2004. Transition from Nondeformable Projectile Penetration to Semihydrodynamic Penetration. Journal of Engineering Mechanics, 130: 123-127.
[71]	Chen X W, Li X L, Huang F L, Wu H J, Chen Y Z.2008. Damping function in the penetration/perforation struck by rigid projectiles. International Journal of Impact Engineering, 35: 1314-1325.
[72]	Chen X W, Wei L M, Li J C.2015. Experimental research on the long rod penetration of tungsten-fiber/Zr-based metallic glass matrix composite into Q235 steel target. International Journal of Impact Engineering, 79: 102-116.
[73]	Chocron S, Anderson Jr. C E, Walker J D, Ravid M.2003. A unified model for long-rod penetration in multiple metallic plates. International Journal of Impact Engineering, 28: 391-411.
[74]	Christman D R, Gehring J W.1966. Analysis of High-Velocity Projectile Penetration Mechanics. Journal of Applied Physics, 37: 1579-1587.
[75]	Cuadros J H.1990. Monolithic and segmented projectile penetration experiments in the 2 to 4 kilometers per second impact velocity regime. International Journal of Impact Engineering, 10: 147-157.
[76]	Deshpande V S, Evans A G.2008. Inelastic deformation and energy dissipation in ceramics: A mechanism-based constitutive model. Journal of the Mechanics and Physics of Solids, 56: 3077-3100.
[77]	Eichelberger R J.1956. Experimental test of the theory of penetration by metallic jets. Journal of Applied Physics, 27: 63-68.
[78]	Eichelberger R J, Gehring J W.1962. Effects of meteoroid impacts on space vehicles. ARS Journal, 32: 1583-1591.
[79]	Forrestal M J, Altman B S, Cargile J D, Hanchak S J.1994. An empirical equation for penetration depth of ogive-nose projectiles into concrete targets. International Journal of Impact Engineering, 15: 395-405.
[80]	Forrestal M J, Frew D J, Hanchak S J, Brar N S.1996. Penetration of grout and concrete targets with ogive-nose steel projectiles. International Journal of Impact Engineering, 18: 465-476.
[81]	Forrestal M J, J. Piekutowski A.2000. Penetration experiments with 6061-T6511 aluminum targets and spherical-nose steel projectiles at striking velocities between 0.5 and 3.0km/s. International Journal of Impact Engineering, 24: 57-67.
[82]	Forrestal M J, Longcope D B.1990. Target strength of ceramic materials for high-velocity penetration. Journal of Applied Physics, 67: 3669-3672.
[83]	Forrestal M J, Piekutowski A J, Luk V K.1988. Long-rod penetration into simulated geological targets at an impact velocity of 3.0km/s. Military Technology Weaponry & National Defense.
[84]	Franzen R R, Orphal D L, Anderson Jr. C E.1997. The influence of experimental design on depth-of-penetration (DOP) test results and derived ballistic efficiencies. International Journal of Impact Engineering, 19: 727-737.
[85]	Franzen R R, Walker J D, Orphal D L, Anderson Jr C E.1994. An upper limit for the penetration performance of segmented rods with segment-$L/D leq 1$. International Journal of Impact Engineering, 15: 661-668.
[86]	Galanov B A, Kartuzov V V, Ivanov S M.2008. New analytical model of expansion of spherical cavity in brittle material based on the concepts of mechanics of compressible porous and powder materials. International Journal of Impact Engineering, 35: 1522-1528.
[87]	Gold V M, Vradis G C, Pearson J C.1996. Concrete penetration by eroding projectiles: Experiments and analysis. Journal of Engineering Mechanics, 122: 145-152.
[88]	Goldsmith W.1999. Non-ideal projectile impact on targets. International Journal of Impact Engineering, 22: 95-395.
[89]	Grabarek C L.1971. Penetration of Armor by Steel and High Density Penetrators (U). Ballistic Research Laboratories.
[90]	Hauver G, Gooch W, Netherwood P, Benck R, Perciballi W, Burkins M.1992. Variation of target resistance during long-rod penetration into ceramics//Proceedings of the 13th International Symposium on Ballistics, Sundyberg, Sweden: 257-264.
[91]	He Y, Wen H M.2013. Predicting the penetration of long rods into semi-infinite metallic targets. Science China (Technological Sciences), 56: 2814-2820.
[92]	Herrmann W, Wilbeck J S.1987. Review of hypervelocity penetration theories. International Journal of Impact Engineering, 5: 307-322.
[93]	Hetherington J G, Lemieux P F.1994. The effect of obliquity on the ballistic performance of two component composite armours. International Journal of Impact Engineering, 15: 131-137.
[94]	Hirt C W, Amsden A A, Cook J L.1974. An arbitrary Lagrangian-Eulerian computing method for all flow speeds. Journal of computational physics, 14: 227-253.
[95]	Hohler V, Behner T.1999. Influence of the yaw angle on the performance reduction of long rod projectiles//Proceedings of the 18th international symposium on ballistics, Antonio, TX: 931-938.
[96]	Hohler V, Rothenhausler H, Schneider E, Senf H, Stilp A J, Tham R.Untersuchung der Shockwirkung auf Panzerfahrzeuge. Ernst Mach Institute Report, 1978.
[97]	Hohler V, Stilp A J.1977. Penetration of steel and high density rods in semi-infinite steel targets//Proceedings of the 3rd international symposium on ballistics.
[98]	Hohler V, Stilp A J.1987. Hypervelocity impact of rod projectiles with L/D from 1 to 32. International Journal of Impact Engineering, 5: 323-331.
[99]	Hohler V, Stilp A J, Walker J D, Anderson C E.1993. Penetration of long rods into steel and glass targets: Experiments and computations. Annals of Clinical Psychiatry, 29: 211-217.
[100]	Hohler V, Stilp A J, Weber K.1995. Hypervelocity penetration of tungsten sinter-alloy rods into aluminum. International Journal of Impact Engineering, 17: 409-418.
[101]	Hohler V, Stilp A.2002. Penetration performance of segmented rods at different spacing-comparison with homogeneous rods at 2.5-3.5km/s. Journal of Neuroscience the Official Journal of the Society for Neuroscience, 22: 2541-2549.
[102]	Hohler V, Weber K, Tham R, James B, Barker A, Pickup I.2001. Comparative analysis of oblique impact on ceramic composite systems. International Journal of Impact Engineering, 26: 333-344.
[103]	Holmquist T J, Anderson C E, Behner T, Orphal D L.2010. Mechanics of dwell and post-dwell penetration. Advances in Applied Ceramics, 109: 467-479.
[104]	Holmquist T J, Johnson G R.2003. Modeling projectile impact onto prestressed ceramic targets. Journal De Physique IV, 110: 597-602.
[105]	Holmquist T J, Johnson G R.2005. Modeling prestressed ceramic and its effect on ballistic performance. International Journal of Impact Engineering, 31: 113-127.
[106]	Holmquist T J, Johnson G R.2011. A Computational Constitutive Model for Glass Subjected to Large Strains, High Strain Rates and High Pressures. Journal of Applied Mechanics, 78: 51003.
[107]	Holmquist T J, Johnson G R, Cook W H.1993.A computational constitutive model for concrete subjected to large strains, high strain rates and high pressures//Proceedings of 14th international symposium on Ballistics, Quebec, Canada.
[108]	Islam M J, Swaddiwudhipong S, Liu Z S.2013. Penetration of concrete targets using a modified Holmquist-Johnson-Cook material model. International Journal of Computational Methods, 9: 185-197.
[109]	Jiao W J, Chen X W.2018. Approximate solutions of the Alekseevskii--Tate model of long-rod penetration. Acta Mechanica Sinica, 34: 334-348.
[110]	Johnson G R, Cook W H.1983. A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures//Proceedings of the 7th International Symposium on Ballistics: 541-547.
[111]	Johnson G R, Holmquist T J.1994. An improved computational constitutive model for brittle materials. High Pressure Science and Technology, 309: 981-984.
[112]	Johnson G R, Holmquist T J, Beissel S R.2003. Response of aluminum nitride (including a phase change) to large strains, high strain rates, and high pressures. Journal of Applied Physics, 94: 1639-1646.
[113]	Johnson G R, Stryk R A.2003. Conversion of 3D distorted elements into meshless particles during dynamic deformation. International Journal of Impact Engineering, 28: 947-966.
[114]	Johnson G R, Stryk R A, Beissel S R, Holmquist T J.2002. An algorithm to automatically convert distorted finite elements into meshless particles during dynamic deformation. International Journal of Impact Engineering, 27: 997-1013.
[115]	Kong X Z, Fang Q, Li Q M, Wu H, Crawford J E.2017a. Modified K & C model for cratering and scabbing of concrete slabs under projectile impact. International Journal of Impact Engineering, 108: 217-228.
[116]	Kong X Z, Fang Q, Wu H, Peng Y.2016a. Numerical predictions of cratering and scabbing in concrete slabs subjected to projectile impact using a modified version of HJC material model. International Journal of Impact Engineering, 95: 61-71.
[117]	Kong X, Li Q M, Fang Q.2016b. Critical Impact Yaw for Long-Rod Penetrators. Journal of Applied Mechanics, 83: 121008.
[118]	Kong X Z, Wu H, Fang Q, Peng Y.2017b. Rigid and eroding projectile penetration into concrete targets based on an extended dynamic cavity expansion model. International Journal of Impact Engineering, 100: 13-22.
[119]	Kong X Z, Wu H, Fang Q, Zhang W, Xiao Y K.2017c. Projectile penetration into mortar targets with a broad range of striking velocities: Test and analyses. International Journal of Impact Engineering, 106: 18-29.
[120]	Lambert J P.1978. A residual velocity predictive model for long rod penetrators. Aberdeen Proving Ground, BRL, Report No. ARBRL-MR-02828.
[121]	Lan B, Wen H M.2010. Alekseevskii-Tate revisited: An extension to the modified hydrodynamic theory of long rod penetration. Science China Technological Sciences, 53: 1364-1373.
[122]	Lee M.2000. An engineering impact model for yawed projectiles. International Journal of Impact Engineering, 24: 797-807.
[123]	Lee M.2003. Hypervelocity impact into oblique ceramic/metal composite systems. International Journal of Impact Engineering, 29: 417-424.
[124]	Lee M, Bless S J.1998. Cavity models for solid and hollow projectiles. International Journal of Impact Engineering, 21: 881-894.
[125]	Lee M, Bless S.1996. Cavity dynamics for long rod penetration. The Univercity of Texas at Austin Institute for Advanced Technology.
[126]	Lee W, Lee H, Shin H.2002. Ricochet of a tungsten heavy alloy long-rod projectile from deformable steel plates. Journal of Physics D: Applied Physics, 35: 2676.
[127]	Li J C, Chen X W.2017. Theoretical analysis of projectile-target interface defeat and transition to penetration by long rods due to oblique impacts of ceramic targets. International Journal of Impact Engineering, 106: 53-63.
[128]	Li J C, Chen X W, Huang F L.2015a. FEM analysis on the “self-sharpening” behavior of tungsten fiber/metallic glass matrix composite long rod. International Journal of Impact Engineering, 86: 67-83.
[129]	Li J C, Chen X W, Ning F.2014. Comparative analysis on the interface defeat between the cylindrical and conical-nosed long rods. International Journal of Protective Structures, 5: 21-46.
[130]	Li J C, Chen X W, Ning F, Li X L.2015b. On the transition from interface defeat to penetration in the impact of long rod onto ceramic targets. International Journal of Impact Engineering, 83: 37-46.
[131]	Li J Z, Zhang L S, Huang F L.2017. Experiments and simulations of tungsten alloy rods penetrating into alumina ceramic/603 armor steel composite targets. International Journal of Impact Engineering, 101: 1-8.
[132]	Li Q M, Chen X W.2003. Dimensionless formulae for penetration depth of concrete target impacted by a non-deformable projectile. International Journal of Impact Engineering, 28: 93-116.
[133]	Littlefield D L, Anderson Jr C E, Partom Y, Bless S J.1997. The penetration of steel targets finite in radial extent. International Journal of Impact Engineering, 19: 49-62.
[134]	Liu J C, Pi A G, Huang F L.2015. Penetration performance of double-ogive-nose projectiles. International Journal of Impact Engineering, 84: 13-23.
[135]	Liu Y, Ma A, Huang F L.2009. Numerical simulations of oblique-angle penetration by deformable projectiles into concrete targets. International Journal of Impact Engineering, 36: 438-446.
[136]	Lu Z C, Wen H M.2018. On the penetration of high strength steel rods into semi-infinite aluminium alloy targets. International Journal of Impact Engineering, 111: 1-10.
[137]	Lundberg P, Renstr?m R, Andersson O.2013. Influence of length scale on the transition from interface defeat to penetration in unconfined ceramic targets. Journal of Applied Mechanics, 80: 979-985.
[138]	Lundberg P, Lundberg B.2005. Transition between interface defeat and penetration for tungsten projectiles and four silicon carbide materials. International Journal of Impact Engineering, 31: 781-792.
[139]	Lundberg P, Renstr?m R, Lundberg B.2000. Impact of metallic projectiles on ceramic targets: Transition between interface defeat and penetration. International Journal of Impact Engineering, 24: 259-275.
[140]	Lundberg P, Renstr?m R, Lundberg B.2006. Impact of conical tungsten projectiles on flat silicon carbide targets: Transition from interface defeat to penetration. International Journal of Impact Engineering, 32: 1842-1856.
[141]	Lundberg P, Westerling L, Lundberg B.1996. Influence of scale on the penetration of tungsten rods into steel-backed alumina targets. International Journal of Impact Engineering, 18: 403-416.
[142]	Madhu V, Ramanjaneyulu K, Balakrishna Bhat T, Gupta N K.2005. An experimental study of penetration resistance of ceramic armour subjected to projectile impact. International Journal of Impact Engineering, 32: 337-350.
[143]	Magness L S, Frarand T G.1990. Deformation behavior and its relationship to the penetration performance of high-velocity KE penetrator material//Proceedings of the 1990 Army Science conference, Durham: 465-479.
[144]	Malvar L J, Crawford J E, Wesevich J W, Simons D.1997. A plasticity concrete material model for DYNA3D. International Journal of Impact Engineering, 19: 847-873.
[145]	Mcglaun J M, Thompson S L, Elrick M G.1990. CTH: A three-dimensional shock wave physics code. International Journal of Impact Engineering, 10: 351-360.
[146]	Mellgrad I, Holmberg L, Olsson G L.1989. An experimental method to compare the ballistic efficiencies of different ceramics against long rod projectiles//Proceedings of the 11th International Symposium on Ballistics, Bruseels, Belgium: 323-331.
[147]	Nia A, Zolfaghari M, Khodarahmi H, Nili M, Gorbankhani A.2014. High velocity penetration of concrete targets with eroding long- rod projectiles: An experiment and analysis. International Journal of Protective Structures, 5: 47-64.
[148]	Orphal D L.1997. Phase three penetration. International Journal of Impact Engineering, 20: 601-616.
[149]	Orphal D L.2006. Explosions and impacts. International Journal of Impact Engineering, 33: 496-545.
[150]	Orphal D L, Anderson Jr. C E.1999. Streamline reversal in hypervelocity penetration. International Journal of Impact Engineering, 23: 699-710.
[151]	Orphal D L, Anderson Jr. C E.2006. The dependence of penetration velocity on impact velocity. International Journal of Impact Engineering, 33: 546-554.
[152]	Orphal D L, Anderson Jr. C E, Behner T, Templeton D W.2009. Failure and penetration response of borosilicate glass during multiple short-rod impact. International Journal of Impact Engineering, 36: 1173-1181.
[153]	Orphal D L, Anderson Jr. C E, Franzen R R, Babcock S M.1995. Variation of crater geometry with projectile $L/D$ for $L/D leq 1$. International Journal of Impact Engineering, 17: 595-604.
[154]	Orphal D L, Anderson Jr. C E, Franzen R R, Walker J D, Schneidewind P N, Majerus M E.1993. Impact and penetration by $L/Dleq 1$ projectiles. International Journal of Impact Engineering, 14: 551-560.
[155]	Orphal D L, Franzen R R.1990. Penetration mechanics and performance of segmented rods against metal targets. International Journal of Impact Engineering, 10: 427-438.
[156]	Orphal D L, Franzen R R.1997. Penetration of confined silicon carbide targets by tungsten long rods at impact velocities from 1.5 to 4.6km/s. International Journal of Impact Engineering, 19: 1-13.
[157]	Orphal D L, Franzen R R, Charters A C, Menna T L, Piekutowski A J.1997. Penetration of confined boron carbide targets by tungsten long rods at impact velocities from 1.5 to 5.0km/s. International Journal of Impact Engineering, 19: 15-29.
[158]	Orphal D L, Franzen R R, Piekutowski A J, Forrestal M J.1996. Penetration of confined aluminum nitride targets by tungsten long rods at 1.5-4.5km/s. International Journal of Impact Engineering, 18: 355-368.
[159]	Orphal D L, Miller C W.1991. Penetration performance of nonideal segmented rods. International Journal of Impact Engineering, 11: 457-461.
[160]	Ortiz M.1996. Computational micromechanics. Computational Mechanics, 18: 321-338.
[161]	Partom Y, Littlefield D L.1995. Validation and calibration of a lateral confinement model for long-rod penetration at ordnance and high velocities. International Journal of Impact Engineering, 17: 615-626.
[162]	Piekutowski A J.1996. Formation and description of debris clouds produced by hypervelocity impact. National Aeronautics and Space Administration, Marshall Space Flight Center.
[163]	Piekutowski A J, Forrestal M J, Poormon K L, Warren T L.1999. Penetration of 6061-T6511 aluminum targets by ogive-nose steel projectiles with striking velocities between 0.5 and 3.0km/s. International Journal of Impact Engineering, 23: 723-734.
[164]	Polanco-Loria M, Hopperstad O S, B?rvik T, Berstad T.2008. Numerical predictions of ballistic limits for concrete slabs using a modified version of the HJC concrete model. International Journal of Impact Engineering, 35: 290-303.
[165]	Rajendran A M.1994. Modeling the impact behavior of AD85 ceramic under multiaxial loading. International Journal of Impact Engineering, 15: 749-768.
[166]	Rajendran A M, Grove D J.1996. Determination of Rajendran-Grove Ceramic Constitutive Model Constants//AIP: 539-542.
[167]	Reaugh J E, Holt A C, Welkins M L, Cunningham B J, Hord B L, Kusubov A S.1999. Impact studies of five ceramic materials and pyrex. International Journal of Impact Engineering, 23: 771-782.
[168]	Rong G, Huang D W, Yang M C.2012. Penetrating behaviors of Zr-based metallic glass composite rods reinforced by tungsten fibers. Theoretical and Applied Fracture Mechanics, 58: 21-27.
[169]	Rosenberg Z.1993. On the relation between the Hugoniot elastic limit and the yield strength of brittle materials. Journal of Applied Physics, 1: 752-753.
[170]	Rosenberg Z, Ashuach Y, Dekel E.2007. More on the ricochet of eroding long rods—validating the analytical model with 3D simulations. International Journal of Impact Engineering, 34: 942-957.
[171]	Rosenberg Z, Ashuach Y, Yeshurun Y, Dekel E.2009. On the main mechanisms for defeating AP projectiles, long rods and shaped charge jets. International Journal of Impact Engineering, 36: 588-596.
[172]	Rosenberg Z, Dekel E.1994a. The relation between the penetration capability of long rods and their length to diameter ratio. International Journal of Impact Engineering, 15: 125-129.
[173]	Rosenberg Z, Dekel E.1994b. A critical examination of the modified Bernoulli equation using two-dimensional simulations of long rod penetrators. International Journal of Impact Engineering, 15: 711-720.
[174]	Rosenberg Z, Dekel E.1996. A computational study of the influence of projectile strength on the performance of long-rod penetrators. International Journal of Impact Engineering, 18: 671-677.
[175]	Rosenberg Z, Dekel E.1998. A computational study of the relations between material properties of long-rod penetrators and their ballistic performance. International Journal of Impact Engineering, 21: 283-296.
[176]	Rosenberg Z, Dekel E.1999. On the role of nose profile in long-rod penetration. International Journal of Impact Engineering, 22: 551-557.
[177]	Rosenberg Z, Dekel E.2000. Further examination of long rod penetration: the role of penetrator strength at hypervelocity impacts. International Journal of Impact Engineering, 24: 85-102.
[178]	Rosenberg Z, Dekel E.2001a. More on the secondary penetration of long rods. International Journal of Impact Engineering, 26: 639-649.
[179]	Rosenberg Z, Dekel E.2001b. Material similarities in long-rod penetration mechanics. International Journal of Impact Engineering, 25: 361-372.
[180]	Rosenberg Z, Dekel E.2003. Numerical study of the transition from rigid to eroding-rod penetration. Journal De Physique IV, 110: 681-686.
[181]	Rosenberg Z, Dekel E.2004. On the role of material properties in the terminal ballistics of long rods. International Journal of Impact Engineering, 30: 835-851.
[182]	Rosenberg Z, Dekel E.2008. A numerical study of the cavity expansion process and its application to long-rod penetration mechanics. International Journal of Impact Engineering, 35: 147-154.
[183]	Rosenberg Z, Dekel E.2010. On the deep penetration of deforming long rods. International Journal of Solids & Structures, 47: 238-250.
[184]	Rosenberg Z, Dekel E.2012. Terminal Ballistics. Springer Berlin Heidelberg.
[185]	Rosenberg Z, Dekel E, Ashuach Y.2006. More on the penetration of yawed rods. Journal De Physique IV, 134: 397-402.
[186]	Rosenberg Z, Dekel E, Hohler V, Stilp A J, Weber K.1997a. Hypervelocity penetration of tungsten alloy rods into ceramic tiles: experiments and 2-D simulations. International Journal of Impact Engineering, 20: 675-683.
[187]	Rosenberg Z, Dekel E, Hohler V, Stilp A J, Weber K.1998. Penetration of Tungsten-Alloy rods into composite ceramic targets: Experiments and 2-D Simulations//Proceedings of the APS conference on Shock Waves in Condensed Matter, Amherst, Mass: 917-920.
[188]	Rosenberg Z, Dekel E, Yeshurun Y, Bar-On E.1995. Experiments and 2-D simulations of high velocity penetrations into ceramic tiles. International Journal of Impact Engineering, 17: 697-706.
[189]	Rosenberg Z, Kreif R, Dekel E.1997b. A note on the geometric scaling of long-rod penetration. International Journal of Impact Engineering, 19: 277-283.
[190]	Rosenberg Z, Marmor E, Mayseless M.1990. On the hydrodynamic theory of long-rod penetration. International Journal of Impact Engineering, 10: 483-486.
[191]	Rosenberg Z, Tsaliah J.1990. Applying Tate's model for the interaction of long rod projectiles with ceramic targets. International Journal of Impact Engineering, 9: 247-251.
[192]	Rosenberg Z, Yeshurun Y, Mayseless M.1989. On the ricochet of long rod projectiles//Proceedings of the 11th international symposium on ballistics, Brussels: 501-506.
[193]	Rozenberg Z, Yeshurun Y.1988. The relation between ballastic efficiency and compressive strength of ceramic tiles. International Journal of Impact Engineering, 7: 357-362.
[194]	Sadanandan S, Hetherington J G.1997. Characterisation of ceramic/steel and ceramic/aluminium armours subjected to oblique impact. International Journal of Impact Engineering, 19: 811-819.
[195]	Satapathy S.2001. Dynamic spherical cavity expansion in brittle ceramics. International Journal of Solids & Structures, 38: 5833-5845.
[196]	Satapathy S S, Bless S J.2000. Cavity expansion resistance of brittle materials obeying a two-curve pressure--shear behavior. Journal of Applied Physics, 88: 4004-4012.
[197]	Segletes S B, Walters W P.2003. Extensions to the exact solution of the long-rod penetration/erosion equations. International Journal of Impact Engineering, 28: 363-376.
[198]	Senf H, Rothenhausler H, Scharpf F, Both A, Pfang W.1981. Experimental and numerical investigation of the ricocheting of projectiles from metallic surfaces//Proceedings of the 6th international symposium on ballistics, Orlando: 510-521.
[199]	Shin H, Yoo Y.2003. Effect of the velocity of a single flying plate on the protection capability against obliquely impacting long-rod penetrators. Combustion, Explosion, and Shock Waves, 39: 591-600.
[200]	Silsby G F.1984. Penetration of semi-infinite steel targets by tungsten rods at 1.3 to 4.5km/s//Proceedings of the 8th International Symposium on Ballistics.
[201]	Silsby G F, Roszak R J, Giglio-Tos L.1983. BRL's 50mm high pressure powder gun for terminal ballistic testing-the first year's experience. Ballistic Research Laboratory Report No. BRL-MR-03236.
[202]	Song W J, Chen X W, Chen P.2017a. A simplified approximate model of compressible hypervelocity penetration. Acta Mechanica Sinica, doi: 10.1007/s10409-018-0769-9.
[203]	Song W J, Chen X W, Chen P.2017b. The effects of compressibility and strength on penetration of long rod and jet. Defence Technology, 2017, DOI: 10.1016/j.dt.2017.11.010.
[204]	Song W J, Chen X W, Chen P.2018. Effect of compressibility on the hypervelocity penetration. Acta Mechanica Sinica, 34: 82-98.
[205]	Sorensen B R, Kimsey K D, Silsby G F, Scheffler D R, Sherrick T M, de Rosset W S.1991. High velocity penetration of steel targets. International Journal of Impact Engineering, 11: 107-119.
[206]	Steinberg D J.1987. Constitutive model used in computer simulation of time-resolved, shock-wave data. International Journal of Impact Engineering, 5: 603-611.
[207]	Steinberg D J, Cochran S G, Guinan M W.1980. A constitutive model for metals applicable at high-strain rate. Journal of Applied Physics, 51: 1498-1504.
[208]	Steinberg D J, Lund C M.1989. A constitutive model for strain rates from 0.0001 to 1,000,000/s. Journal of Applied Physics, 65: 1528-1533.
[209]	Sternberg J.1989. Material properties determining the resistance of ceramics to high velocity penetration. Journal of Applied Physics, 65: 3417-3424.
[210]	Stilp A J, Hohler V.1990. Experimental methods for terminal ballistics and impact physics//High Velocity Impact Dynamics. Wiley, New York :515-592.
[211]	Stilp A J, Hohler V.1995. Aeroballistic and impact physics research at EMI-an historical overview. International Journal of Impact Engineering, 17: 785-805.
[212]	Subramanian R, Bless S J.1995. Penetration of semi-infinite AD995 alumina targets by tungsten long rod penetrators from 1.5 to 3.5km/s. International Journal of Impact Engineering, 17: 807-816.
[213]	Subramanian R, Bless S J, Cazamias J, Berry D.1995. Reverse impact experiments against tungsten rods and results for aluminum penetration between 1.5 and 4.2km/s. International Journal of Impact Engineering, 17: 817-824.
[214]	Tate A.1967. A theory for the deceleration of long rods after impact. Journal of the Mechanics & Physics of Solids, 15: 387-399.
[215]	Tate A.1969. Further Results in the Theory of Long Rod Penetration. Journal of the Mechanics & Physics of Solids, 17: 141-150.
[216]	Tate A.1979. A simple estimate of the minimum target obliquity required for the ricochet of a high speed long rod projectile. Journal of Physics. D. Applied Physics, 12: 1825-1829.
[217]	Tate A.1986. Long rod penetration models & mdash: Part II. Extensions to the hydrodynamic theory of penetration. International Journal of Mechanical Sciences, 28: 599-612.
[218]	Tate A, Green K E B, Chamberlain P G, Baker R G.1978. Model scale experiments on long rod penetrators//Proceedings of 4th International Symposium on Ballistics, Monterey.
[219]	Tu Z, Lu Y.2010. Modifications of RHT material model for improved numerical simulation of dynamic response of concrete. International Journal of Impact Engineering, 37: 1072-1082.
[220]	Walker D, Anderson Jr C E.1991. The Wilkins' computational ceramic model for CTH. SwRI Report, 4391 (002).
[221]	Walker J D.1999. A model for penetration by very low aspect ratio projectiles. International Journal of Impact Engineering, 23: 957-966.
[222]	Walker J D.1999. An analytical velocity field for back surface bulging//Proceedings of the 18th international symposium on ballistics , Lancaster: Technomic Publishing Co.:1239-1246.
[223]	Walker J D.2001. Ballistic limit of fabrics with resin//Proceedings of the 19th International Symposium on Ballistics, Interlaken, Switzerland: 7-11.
[224]	Walker J D, Anderson Jr. C E, Goodlin D L.2001. Tunsten into steel penetration including velocity, $L/D$, and impact inclination effects//Proceedings of the 19th international symposium on ballistics ,Interlaken Switzerland: 1133-1139.
[225]	Walker J D, Anderson Jr. C E.1994. The influence of initial nose shape in eroding penetration. International Journal of Impact Engineering, 15: 139-148.
[226]	Walker J D, Anderson Jr. C E.1995. A time-dependent model for long-rod penetration. International Journal of Impact Engineering, 16: 19-48.
[227]	Walters W, Williams C, Normandia M.2006. An explicit solution of the Alekseevski--Tate penetration equations. International Journal of Impact Engineering, 33: 837-846.
[228]	Walters W P, Segletes S B.1991. An exact solution of the long rod penetration equations. International Journal of Impact Engineering, 11: 225-231.
[229]	Wang X M, Zhao G Z, Shen P H, Zha H Z.1995. High velocity impact of segmented rods with an aluminum carrier tube. International Journal of Impact Engineering, 17: 915-923.
[230]	Weerheijm J, Van Doormaal J C A M.2007. Tensile failure of concrete at high loading rates: New test data on strength and fracture energy from instrumented spalling tests. International Journal of Impact Engineering, 34: 609-626.
[231]	Wen H M, He Y, Lan B.2010. Analytical model for cratering of semi-infinite metallic targets by long rod penetrators. Science China (Technological Sciences), 53: 3189-3196.
[232]	Wen H M, He Y, Lan B.2011. A combined numerical and theoretical study on the penetration of a jacketed rod into semi-infinite targets. International Journal of Impact Engineering, 38: 1001-1010.
[233]	Wen H M, Lan B.2010. Analytical models for the penetration of semi-infinite targets by rigid, deformable and erosive long rods. Acta Mechanica Sinica, 26: 573-583.
[234]	Westerling L, Lundberg P, Holmberg L, Lundberg B.1997. High velocity penetration of homogeneous, segmented and telescopic projectiles into alumina targets. International Journal of Impact Engineering, 20: 817-827.
[235]	Westerling L, Lundberg P, Lundberg B.2001. Tungsten long-rod penetration into confined cylinders of boron carbide at and above ordnance velocities. International Journal of Impact Engineering, 25: 703-714.
[236]	Yaziv D, Rosenberg G, Patrtom Y.Differential ballistic efficiency of applique armour. Shriveham, UK: 1986.
[237]	Yaziv D, Walker J D, Riegel J P.1992. Analytical model of yawed penetration in the 0 to 90 degrees range//Proceedings of the 13th international symposium on ballistics, Stockholm: 1-3.
[238]	Zaera R, Sánchez-Gálvez V.1998. Analytical modelling of normal and oblique ballistic impact on ceramic/metal lightweight armours. International Journal of Impact Engineering, 21: 133-148.
[239]	Zhang L S, Huang F L.2004. Model for long-rod penetration into semi-infinite targets. Journal of Beijing Institute of Technology, 13: 285-289.
[240]	Zhang X, Serjouei A, Sridhar I.2017. Criterion for interface defeat to penetration transition of long rod projectile impact on ceramic armor. Thin-Walled Structures.
[241]	Zhang X F, Li Y C.2010. On the comparison of the ballistic performance of 10% zirconia toughened alumina and 95% alumina ceramic target. Materials & Design, 31: 1945-1952.
[242]	Zhang X F, Li Y C, Zhang N S.2011. Numerical study on anti-penetration process of alumina ceramic (AD95) to tungsten long rod projectiles. International Journal of Modern Physics B, 25: 2091-2103.
[243]	Zhao J, Chen X W, Jin F N, Xu Y.2010. Depth of penetration of high-speed penetrator with including the effect of mass abrasion. International Journal of Impact Engineering, 37: 971-979.
[244]	Zhou H, Wen H M.2003. Penetration of bilinear strain-hardening targets subjected to impact by ogival-nosed projectiles. Theory and Practice of Energetic Materials, 5: 933-942.