复合材料层板高速冲击损伤研究
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摘要
纤维增强复合材料以其优异的综合力学性能，在航空航天以及防护装甲等领域得到了广泛的应用，深入研究其弹道性能和高速冲击损伤特性，详细分析侵彻破坏过程及失效机理，不仅是结构生存力研究的主要内容，而且是结构抗战伤设计的重要基础，已成为当前复合材料领域的研究重点和热点之一。本文采用理论分析与数值计算相结合的方法，围绕复合材料层板动态本构模型、抗弹性能和损伤特性展开系统的研究,主要内容包括：
（1）针对任意角度铺层的复合材料层合薄板，基于高速冲击过程中的能量守恒，建立了复合材料层板高速冲击问题的力学分析模型。该模型考虑了纤维断裂，基体裂纹和分层三种主要损伤形式。根据高应变率下单层板的本构关系，采用一维应力波的传播理论，计算复合材料层板冲击后的变形区尺寸和层板应变场，利用能量守恒迭代求解弹体的冲击剩余速度和弹靶接触力等参量，着重研究了复合材料层合薄板高速冲击中的损伤面积和形状，探讨了冲击速度、弹体直径以及靶板铺层情况对损伤形状和大小的影响规律。
（2）根据纤维增强复合材料的宏观和细观结构，基于纤维的线弹性假设和基体的粘弹性假设，推导了单向纤维增强复合材料层板材料主方向上的应力应变关系。在此基础上，结合三维Hashin失效准则，建立了单向复合材料三维粘弹性损伤本构模型。针对复合材料层合薄板，采用复合材料板壳理论，推导了高应变率下的一阶剪切层板理论，结合二维Hashin失效准则，建立了复合材料层板二维粘弹性损伤本构模型。
（3）在二维粘弹性损伤本构的基础上，采用非线性有限元方法，应用ABAQUS软件及其材料用户子程序VUMAT建立复合材料薄板高速冲击损伤有限元分析模型。模型中考虑了复合材料在高速冲击过程中的应变率强化效应，结合Hashin失效准则，模拟了复合材料层板高速冲击损伤破坏过程，通过数值分析深入探讨了相关参数对弹道性能和损伤特性的影响规律。
（4）从复合材料层板的细观结构出发，在有限元建模中引入界面单元模拟层板的层间分层，采用三维粘弹性损伤本构模型模拟单层板的力学特性，建立了复合材料层合厚板高速冲击损伤三维有限元分析模型。深入研究高速冲击下复合材料层板的弹道性能和损伤特征，重点分析了高速冲击损伤沿厚度方向上的变化规律。通过数值分析深入探讨了相关参数对复合材料层板弹道性能和损伤特征的影响规律，获得了一些有价值的结论。
（5）基于ABAQUS软件平台，建立复合材料加筋壁板高速冲击损伤有限元分析模型，分析不同结构形式下复合材料加筋壁板高速冲击后的损伤特性和抗弹性能，详细讨论结构参数对损伤结果的影响。
Fiber-reinforced composites are used extensively in defense engineering, aeronautics andastronautics industry due to their extraordinary mechanical properties, which greatly contribute toreduce the structure weight and improve the ballistic resistant capability. Study of the ballisticperformance and falilure mechanism of composites under high velocity impact loading are importantcontent of the survivability research of aircraft, which would lay a solid foundation for optimizationof aircraft structure design. Therefore, the damage analysis of composites under high velocity hasbeen focoused by many international researchers in the domain of composites mechanics. In thisthesis, systemic studies including dynamic constitutive equation, engineering analyses and numericalsimulations on ballistic performance and damage characteristics of composite laminates under highvelocity impact are conducted. The main contents are as follow:
(1)Based on conservation of energy，a simple model to analyze the high velocity impact damageof thin angular plied composite laminates was established by the analytical approach, coupled withthe existed experimental observation. In the model, different damage and energy absorbingmechanisms, such as tensile failure of primary yarns, matrix cracking, delamination, conedeformation and deformation of secondary yarns during penetration were identified. The strain wavetheory was used for calculating the size of the deformation area and the strain field of compositelaminates. Then, energy absorbed in each time interval and the residual velocity of the projectile weredetermined. The influences of the impact velocity, the projectile diameter and the layer angle ofcomposite laminates to damage characteristic were detailedly discussed.
(2)According to macroscopic and microscopic structure of composite laminates, a rate-dependentconstitutive equation for composite laminates was deduced by by considering the fibre as linearelastic rate-independent and the matrix as viscoelastic. By combining with Hashin failure criteria, a3D rate-depengdent continuum damage constitutive model(CDM) was established for modeling thedynamic properties of unidirectional fiber-reinforced composite laminate. The first-order sheardeformathion laminate theory under high strain rate was developed for modeling thin compositelaminate. By combined with2D Hashin Failure Criteria, a2D rate-depengdent continuum damageconstitutive model(CDM) was established.
(3)Based on2D rate-dependent CDM, a numericial model to simulate ballistic performance anddamage characteristic of thin composite laminate was established by using nonlinear FEM method and coupled with ABAQUS software and the material user subroutine VUMAT. In this FEM model,the strain rate effect of composite material properties under high-velocity impact was considered, andcombined with Hashin Failure Criteria, the damage process of the laminate during the ballistic impactwas simulated. The influences of related parameters on the ballistic proformance and damagecharacteristics of composite laminate wass discussed.
(4)Considering the microstructure of composite laminates, interface unit is introduced into theFEM model to stimulate the delamination of composite laminates. By using the strain rate-depentdent3D-CDM to model the dynamic properties of composite laminates, a3D FEM model was establishedunder ABAQUS software platform for analyzing the ballistic performance and damage characteristicsof thick composite laminates. Results from the numerical simulations were used to analyze theballistic damage mechanisms.The influence of related parameters on ballistic resistance of laminatewas analyzed and discussed by aseries numerical calculationgs.Some valuable conclusions areobtained, which is valuable for the target design and material improvement.
(5)Based on ABAQUS software platform, FEM model for analyzing damage of stiffenedcomposite panel under high velocity impact are constructed.The influence of stiffener’s parameters onballistic resistance and the damage characteristics of the stiffened composite panel were investigateddetailedly.
（1）针对任意角度铺层的复合材料层合薄板，基于高速冲击过程中的能量守恒，建立了复合材料层板高速冲击问题的力学分析模型。该模型考虑了纤维断裂，基体裂纹和分层三种主要损伤形式。根据高应变率下单层板的本构关系，采用一维应力波的传播理论，计算复合材料层板冲击后的变形区尺寸和层板应变场，利用能量守恒迭代求解弹体的冲击剩余速度和弹靶接触力等参量，着重研究了复合材料层合薄板高速冲击中的损伤面积和形状，探讨了冲击速度、弹体直径以及靶板铺层情况对损伤形状和大小的影响规律。
（2）根据纤维增强复合材料的宏观和细观结构，基于纤维的线弹性假设和基体的粘弹性假设，推导了单向纤维增强复合材料层板材料主方向上的应力应变关系。在此基础上，结合三维Hashin失效准则，建立了单向复合材料三维粘弹性损伤本构模型。针对复合材料层合薄板，采用复合材料板壳理论，推导了高应变率下的一阶剪切层板理论，结合二维Hashin失效准则，建立了复合材料层板二维粘弹性损伤本构模型。
（3）在二维粘弹性损伤本构的基础上，采用非线性有限元方法，应用ABAQUS软件及其材料用户子程序VUMAT建立复合材料薄板高速冲击损伤有限元分析模型。模型中考虑了复合材料在高速冲击过程中的应变率强化效应，结合Hashin失效准则，模拟了复合材料层板高速冲击损伤破坏过程，通过数值分析深入探讨了相关参数对弹道性能和损伤特性的影响规律。
（4）从复合材料层板的细观结构出发，在有限元建模中引入界面单元模拟层板的层间分层，采用三维粘弹性损伤本构模型模拟单层板的力学特性，建立了复合材料层合厚板高速冲击损伤三维有限元分析模型。深入研究高速冲击下复合材料层板的弹道性能和损伤特征，重点分析了高速冲击损伤沿厚度方向上的变化规律。通过数值分析深入探讨了相关参数对复合材料层板弹道性能和损伤特征的影响规律，获得了一些有价值的结论。
（5）基于ABAQUS软件平台，建立复合材料加筋壁板高速冲击损伤有限元分析模型，分析不同结构形式下复合材料加筋壁板高速冲击后的损伤特性和抗弹性能，详细讨论结构参数对损伤结果的影响。
Fiber-reinforced composites are used extensively in defense engineering, aeronautics andastronautics industry due to their extraordinary mechanical properties, which greatly contribute toreduce the structure weight and improve the ballistic resistant capability. Study of the ballisticperformance and falilure mechanism of composites under high velocity impact loading are importantcontent of the survivability research of aircraft, which would lay a solid foundation for optimizationof aircraft structure design. Therefore, the damage analysis of composites under high velocity hasbeen focoused by many international researchers in the domain of composites mechanics. In thisthesis, systemic studies including dynamic constitutive equation, engineering analyses and numericalsimulations on ballistic performance and damage characteristics of composite laminates under highvelocity impact are conducted. The main contents are as follow:
(1)Based on conservation of energy，a simple model to analyze the high velocity impact damageof thin angular plied composite laminates was established by the analytical approach, coupled withthe existed experimental observation. In the model, different damage and energy absorbingmechanisms, such as tensile failure of primary yarns, matrix cracking, delamination, conedeformation and deformation of secondary yarns during penetration were identified. The strain wavetheory was used for calculating the size of the deformation area and the strain field of compositelaminates. Then, energy absorbed in each time interval and the residual velocity of the projectile weredetermined. The influences of the impact velocity, the projectile diameter and the layer angle ofcomposite laminates to damage characteristic were detailedly discussed.
(2)According to macroscopic and microscopic structure of composite laminates, a rate-dependentconstitutive equation for composite laminates was deduced by by considering the fibre as linearelastic rate-independent and the matrix as viscoelastic. By combining with Hashin failure criteria, a3D rate-depengdent continuum damage constitutive model(CDM) was established for modeling thedynamic properties of unidirectional fiber-reinforced composite laminate. The first-order sheardeformathion laminate theory under high strain rate was developed for modeling thin compositelaminate. By combined with2D Hashin Failure Criteria, a2D rate-depengdent continuum damageconstitutive model(CDM) was established.
(3)Based on2D rate-dependent CDM, a numericial model to simulate ballistic performance anddamage characteristic of thin composite laminate was established by using nonlinear FEM method and coupled with ABAQUS software and the material user subroutine VUMAT. In this FEM model,the strain rate effect of composite material properties under high-velocity impact was considered, andcombined with Hashin Failure Criteria, the damage process of the laminate during the ballistic impactwas simulated. The influences of related parameters on the ballistic proformance and damagecharacteristics of composite laminate wass discussed.
(4)Considering the microstructure of composite laminates, interface unit is introduced into theFEM model to stimulate the delamination of composite laminates. By using the strain rate-depentdent3D-CDM to model the dynamic properties of composite laminates, a3D FEM model was establishedunder ABAQUS software platform for analyzing the ballistic performance and damage characteristicsof thick composite laminates. Results from the numerical simulations were used to analyze theballistic damage mechanisms.The influence of related parameters on ballistic resistance of laminatewas analyzed and discussed by aseries numerical calculationgs.Some valuable conclusions areobtained, which is valuable for the target design and material improvement.
(5)Based on ABAQUS software platform, FEM model for analyzing damage of stiffenedcomposite panel under high velocity impact are constructed.The influence of stiffener’s parameters onballistic resistance and the damage characteristics of the stiffened composite panel were investigateddetailedly.
引文
[1]沈观林.复合材料力学.北京:清华大学出版社,1994.
[2]张楠.飞机战伤分析与实弹打击试验系统研究.[博士论文],南京:南京航空航天大学,2006.
[3]王元博.纤维增强层合材料的抗弹性能和破坏机理研究.[博士论文],合肥:中国科学技术大学,2006.
[4] Hopkinson B. A method of measuring the pressure produced in the detonation of high explosivesor by the impact of bullets. Philosophical Transactions of the Royal Society of London, Series A,Containing Papers of a Mathematical or Physical Character,1914,213:437-456.
[5] Kolsky H. An investigation of the mechanical properties of materials at very high rates of loading.In: Proceedings of the Royal Society A-Mathematical Physical and Engineering Sciences.1949,62:676-700.
[6] Davies E D H, Hunter S C. The dynamic compression testing of solids by the method of the splitHopkinson pressure bar. Journal of Mechanics and Physics of Solids,1963,11(3):155-179.
[7] Lindholm U S. Some experiments with the split hopkinson pressure bar. Journal of Mechanicsand Physics of Solids,1964,12(5):317-335.
[8] Hauser F E. Technique for measuring stress-strain relations at high strain rates. ExperimentalMechanics,1966,8(6):395-402.
[9] Woldesenbet E, Vinson J R. Specimen geometry effects on high strain rate testing ofgraphite/epoxy composites. AIAA Journal,1999,37(9):1102-1106.
[10]宋孝浜,王春霞.纤维增强复合材料应变率效应研究进展.广西纺织科技,2006,35(4):31-34.
[11] Chen W, Zhou B. Constitutive behavior of Epon828/T-403at various strain rate. Mechanics ofTime-Dependent Materials,1998,2(2):103-111.
[12] Gilat A, Goldberg R K, Roberts G D. Experimental study of strain-rate-dependent behavior ofcarbon/epoxy composite. Composites Science and Technology,2002,62(10-11):1469-1476.
[13] EI-Habak A M A. Mechanical behaviour of woven glass fibre reinforced composites underimpact compression load. Composites,1991,22(2):129-134.
[14] EI-Habak A M A. Compressive resistance of unidirectional GFRP under high rate of loading.Journal of Composites Technology and Research,1993,15(4):311-317.
[15]韩小平,韩省亮,李华,等.复合材料率相关本构模型的研究.机械科学与技术,1999,18(1):125-126.
[16] Segreti M, Rusinek A, Klepaczko J R. Experimental study on puncture of PMMA at low andhigh velocities: effect on the failure mode. Polymer Testing,2004,23(6):703-718.
[17]尚嘉兰,白以龙,沈乐天,等.酚醛玻璃钢动态本构关系的实验研究.爆炸与冲击.1990,10(1):1-13.
[18]姜春兰,李明,王在成,等.聚乙烯纤维增强复合材料的动态力学响应特性.北京理工大学学报,2001,21(2):163-167.
[19]夏源明,王兴,杨报昌.单向玻璃纤维增强环氧树脂在冲击拉伸时的一维本构方程.复合材料学报,1994,11(4):110-116.
[20]许沭华,王肖钧,张刚明,等. Kevlar纤维增强复合材料动态压缩力学性能实验研究.实验力学,2001,16(1):26-33.
[21]张华鹏.防弹材料冲击破坏机理及其纤维的衰减规律.[博士论文],上海:东华大学,2002.
[22] Wang Y, Xia Y M. The effects of strain rate on the mechanical behaviour of Kevlar fibre bundles:an experimental and theoretical study. Composites Part A,1998,29(11):1411-1415.
[23] Zhou Y X, Xia Y M. In situ strength distuibution of carbon fibers in unidirectional metal-matrixcomposites-wires. Composites Science and Technology,2001,61(14):2017-2023.
[24] Hsiao H M, Daniel I M. Strain rate behaviour of composite materials. Composites Patr B,1998,29(5):521-533.
[25] Ochola R O, Marcus K, Nurick G N, Franz T. Mechanical behaviour of glass and carbon fibrereinforced composites at varying strain rates. Composite Structures,2004,63(3-4):455-467.
[26] Zaretsky E, Debotton G, Perl M. The response of a glass fibers reinforced epoxy composite to animpact loading. International Journal of Solids and Structures,2004,41(2):569-584.
[27] Hosur M V, Alexander J, Vaidya U K, et al. High strain rate compression response ofcarbon/epoxy laminate. Composite Structures,2001,52(3-4):405-417.
[28] Hosur M V, Alexander J, Vaidya U K, et al. Studies on the off-axis high strain rate compressionloading of satin weave carbon/epoxy composites. Composite Structures,2004,63(1):75-85.
[29] Jadhav A, Woldesenbet E, Pang S S. High strain rate properties of balanced angle-plygraphite/epoxy composites. Composites Part B,2003,34(4):339-346.
[30] Jiang C L, Li M, Zhang Q M, et al. Impact responses of carbon fiber fabric reinforced composites.Journal of Beijing Institute of Technology,2000,9(3):225-230.
[31] Naik N K, Kavala V R. High strain rate behavior of woven fabric composites under compressiveloading. Materials Science and Engineering A,2008,474(1-2):301-311.
[32] Hosur M V, Adya M, Vaidya U K, et al. Effect of stitching and weave architecture on the highstrain rate compression response of affordable woven carbon/epoxy composite. CompositeStructures,2003,59(4):507-523.
[33] Hosur M V, Vaidya U K, Ulven C, et al. Performance of stitched/unstitched woven carbon/epoxycomposites under high velocity impact loading. Composite Structures,2004,64(3-4):455-466.
[34]陈思颖,黄晨光,段祝平.几种高性能纤维束的冲击动力学性能实验研究.爆炸与冲击,2003,23(4):355-359.
[35] Tay T E, Ang H G, Shim V P W. An empirical strain rate-dependent constitutive relationship forglass-fibre reinforced epoxy and pure epoxy. Composite Structures,1995,33(4):201-210.
[36] Xia Y M, Wang X. Constitutive equation for unidirectional composites under tensile impact.Composites Science and Technology,1996,56(2):155-160.
[37] Wang Y, Xia Y M. A modified constitutive equation for unidirectional composites under tensileimpact and the dynamic tensile properties of KFRP. Composites Science and Technology,2000,60(4):591-596.
[38]汪洋,夏源明.单向KFRP的应变率相关的本构方程.爆炸与冲击,2000,20(3):193-199.
[39] Hayhurst C J, Hiermaier S J, Clegg R A, et al. Development of material models for Nextel andKevlar/epoxy for high pressures and strain rates. International Journal of Impact Engineering,1999,23(1):365-376.
[40]刘占芳,姚国文,詹先义.高速冲击条件下玻璃中破坏波的损伤累积模拟.应用数学和力学,2001,22(9):983-987.
[41] Maimí P, Camanho P P, Mayugo J A, et al. A continuum damage model for composite laminates.Part I: Constitutive model. Mechanics of materials,2007,39(10):897-908.
[42] Aminjikarai B S, Tabiei A. A strain-rate dependent3-D micromechanical model for finiteelement simulations of plain weave composite structures. Composite Structures,2007,81(3):407-418.
[43]许沭华.钨合金杆弹侵彻复合靶板的实验和数值研究.[博士学位论文],合肥:中国科技大学,2000.
[44] Chen J L, Sun C T. A plastic potential function suitable for anisotropic fiber composites. Journalof Composite Materials,1993,27(14):1379-1391.
[45] Thiruppukuzhi S V, Sun C T. Testing and modeling high strain rate behavior of polymericcomposites. Composites Part B,1998,29(5):535-546.
[46] Thiruppukuzhi S V, Sun C T. Models for the strain-rate-dependent behavior of polymericcomposites. Composites Science and Technology,2001,61(1):1-12.
[47]孙紫建,王礼立.高应变率大变形下的聚丙烯/尼龙共混高聚物损伤型本构特性.爆炸与冲击,2006,26(6):492-497.
[48] Wang W, Makarov G, Shenoi R A. An analytical model for assessing strain rate sensitivity ofunidirectional composite laminates. Composite Structures,2005,69(1):45-54.
[49] Wang W B, Shenoi R A. Investigating high strain rate behaviour of unidirectional composites bya visco-elastic model. Journal of Ship Mechanics,2009,13(3):406-415.
[50] Karim M R. Constitutive modeling and failure criteria of carbon-fiber reinforced polymers underhigh strain rate.[Dissertation for the degree of doctor of philosophy], USA: University of Akron,2005.
[51] Hill R. A theory of the yielding and plastic flow of anisotropic metals. Proceedings of the RoyalSociety of London, Series A, Mathematical and Physical Sciences,1948,193(1033):281-297.
[52] Tsai S W, Wu E M. A general theory of strength for anisotropic materials. Journal of CompositeMaterials,1971,5(1):58-80.
[53] Yamada S E, Sun C T. Analysis of laminate strength and its distribution. Journal of CompositeMaterials,1978,12:275-284.
[54] Chang F K, Chang K Y. A progressive damage model for laminated composites containing stressconcentrations. Journal of Composite Materials,1987,21(9):834-855.
[55] Hashin Z. Failure Criteria for Unidirectional Fiber Composites. Journal of Applied Mechanics,1980,47(2):329–334.
[56] Hart-Smith L J. Should fibrous composite failure modes be interacted or superimposed.Composites,1993,24(1):53-55.
[57] Kroll L, Hufenbach W. Physically based failure criterion for dimensioning of thick-walledlaminates. Applied Composite Materials,1997,4(5):321-332.
[58] Echabi J, Trochu F. Failure mode dependent strength criteria for composite laminates. Journal ofReinforced Plastics&Composites,1997,16(10):926-945.
[59] Akil O, Yildirim U, Guden M. Effect of strain rate on the compression behavior of a wovenfabric S2-glass fiber reinforced vinylester composite. Polymer Testing,2003,22(8):883-887.
[60] Dorey G. An overview of impact damage in composites. Mechanical Properties of Materials atHigh Rates of Strain, Proceedings of Fourth International Conference,1989,395-402.
[61] Kim H, Welch D A, Kedward K T. Experimental investigation of high velocity ice impacts onwoven carbon/epoxy composite panels. Composites Part A,2003,34(1):25-41.
[62]金子明,沈峰,曲志敏,等.纤维增强复合材料抗弹性能研究.纤维复合材料,1999,16(3):5-9.
[63] Zhu G, Goldsmith W, Dharan C K H. Penetration of laminated Kevlar by projectiles－IExperimental investigation. International Journal of Solids and Structures,1992,29(4):399-420.
[64] Zhu G, Goldsmith W, Dharan C K H. Penetration of laminated Kevlar by projectiles－IIAnalytical model. International Journal of Solids and Structures,1992,29(4):421-436.
[65]刘国权,杨大峰,梅树清.防弹用纤维复合材料最佳树脂含量研究.玻璃钢/复合材料,2001,1(2):13-15.
[66] Fujii K, Aoki M, Kiuchi N, et al. Impact perforation behavior of CFRPs using high-velocity steelsphere. International Journal of Impact Engineering,2002,27(5):497-508.
[67] Kim J K, Sham M L. Impact and delamination failure of woven-fabric composites. CompositesScience and Technology,2000,60(5):745-761.
[68]黄英,刘晓辉,李郁忠. S-玻纤织物增强复合材料层合板冲击损伤特性研究.机械科学与技术.1999,18(3):483-485.
[69]黄英,刘晓辉,李郁忠. Kevlar织物增强复合材料层板冲击损伤特性研究.西北工业大学学报.2002,20(3):486-491.
[70] Villanueva G R, Cantwell W J. The high velocity impact response of composite andFML-reinforced sandwich structures. Composites Science and Technology,2004,64(1):35-54.
[71] Lee B L, Song L W, Ward I E. Failure of spectra polyethylene fiber-reinforced composites underballistic impact loading. Journal of Composite Materials,1994,28(13):1202-1226.
[72] Yew C H, Kendrick R B. A study of damage in composite panels produced by hypervelocityimpact. International Journal of Impact Engineering,1987,5(1-4):729-738.
[73] Nunes L M, Paciornik S, Almeida J R M. Evaluation of the damaged area of glass-fiber-reinforced epoxy-matrix composite materials submitted to ballistic impacts. CompositesScience and Technology,2004,64(7-8):945-954.
[74] Morye S S, Hine P J, Duckett R A, et al. Modeling of the energy absorption by polymercomposites upon ballistic impact. Composites Science and Technology,2000,60:2631-2642.
[75] Gellert E P, Cimpoeru S J, Woodward R L. A study of the effect of target thickness on theballistic perforation of glass-fibre-reinforced plasic composites. International Journal of ImpactEngineering,2004,24(5):445-456.
[76] Cheng W L, Jen K C, Itoh S. Failure of ceramics due to impact loading. Journal of the JapanExplosives Society,2002,63(6):388-396.
[77] López-Puente J, Zaera R, Navarro C. Experimental and numerical analysis of normal and obliqueballistic impacts on thin carbon/epoxy woven laminates. Composites Part A,2008,39(2):374-387.
[78] Wambua P, Vangrimde B, Lomov S, et al. The response of natural fibre composites to ballisticimpact by fragment simulating projectiles. Composite Structures,2007,77(2):232-240.
[79]顾伯洪.织物弹道贯穿性能分析计算.复合材料学报,2002,19(6):92-96.
[80] Gu B. Analytical modeling for the ballistic perforation of planar plain-woven fabric target byprojectile. Composites Part B,2003,34(4):361-371.
[81] Naik N K, Shrirao P. Composite structures under ballistic impact. Composite Structures,2004,66(1-4):579-590.
[82] Naik N K, Shrirao P, Reddy B C K. Ballistic impact behavior of woven fabric composites:Parametric studies. Materials Science and Engineering: A,2005,412(1-2):104-116.
[83]杜忠华,赵国志,王晓鸣,等.复合材料层合板抗弹性的工程分析模型.兵器材料科学与工程,2002,25(1):8-10.
[84]杜忠华,王戈冰,沈培辉,等.陶瓷/Kevlar复合材料靶板抗弹性能分析模型.弹道学报,2003,15(2):44-48.
[85] Wen H M. Predicting the penetration and perforation of FRP laminates struck normally byprojectiles with different nose shapes. Composite Structures,2000,49(3):321-329.
[86] Wen H M. Penetration and perforation of thick FRP laminates. Composites Science andTechnology,2001,61(8):1163-1172.
[87]覃悦,文鹤鸣,何涛.卵形弹丸撞击下FRP层合板的侵彻和穿透.复合材料学报,2007,24(2):131-136.
[88] Johnson W E, Anderson C E. History and application of hydrocodes in hypervelocity impact.International Journal of Impact Engineering,1987,5(1-4):423-439.
[89] Hamouda A M S, Hashmi M S J. Modelling the impact and penetration events of modernengineering materials: characteristics of computer codes and material models. Journal ofMaterials Processing Technology,1996,56(1-4):847-862.
[90] Nandlall D, Williams K, Vaziri R. Numerical simulation of the ballistic response of GRP plates.Composites Science and Technology.1998,58(9):1463-1469.
[91] Lim C T, Shim V P W, Ng Y H. Finite-element modeling of the ballistic impact of fabric armor.International Journal of Impact Engineering,2003,28(1):13-31.
[92] Cheng W L, Langlie S, Itoh S. High velocity impact of thick composites. International Journal ofImpact Engineering.2003,29(1-10):167-184.
[93] Kollegal G M, Sridharan S. A simplified model for plain woven fabrics. Journal of CompositeMaterials,2000,34(20):1756-1786.
[94] Guan H, Gibson R F. Micromechanical models for damping in woven fabric-reinforced polymermatrix composites. Journal of Composite Materials,2001,35(16):1417-1434.
[95] Jovicic J, Zavaliangos A, Ko F. Modelling of the ballistic behavior of gradient design compositearmors. Composites Part A,2000,31(8):773-784.
[96] Allix O. A composite damage meso-model for impact problems. Composites Science andTechnology.2001,61(15):2193-2205.
[97]梅志远,朱锡,刘燕红.混杂纤维增强材料板抗侵彻数值仿真及实验验证.兵工学报.2003,24(3):373-377.
[98]韩永要,赵国志,方清,等.动能弹侵彻多层陶瓷靶板数值模拟研究.工程力学,2006,23(8):182-186.
[99]何建,肖玉凤,杨世全,等.单层板壳穿甲数值仿真分析.哈尔滨大学工程学报，2006，27(3):382-385.
[100] Libersky L D, Petschek A G. Smooth particle hydrodynamics with strength of materials. LectureNotes in Physics,1990,395,248–257.
[101] Johnson G R, Beissel S R. Normalized smoothed function for SPH impact computations.International Journal for Numerical Methods in Engineering,1996,39(16):2725-2741
[102] Campbell J, Vignjevic R, Libersky L D. A contact algorithm for smoothed particlehydrodynamics. Computer Methods in Applied Mechanics and Engineering,2000,184(1):49-65.
[103] Parshikov A N, Medin S A. Smoothed particle hydrodynamics using interparticle contactalgorithms. Journal of Computational Physics,2002,180(1):358–382.
[104] Parshikov A N, Medin S A, Loukashenko I I, et al. Improvements in SPH method by means ofinterparticle contact algorithm and analysis of perforation tests at moderate projectile velocities.International Journal of Impact Engineering,2000,24(8):779-796.
[105] Vuyst T D, Vignjevic R, Campbell J C. Coupling between meshless and finite element methods.International Journal of Impact Engineering,2005,31(8):1054-1064.
[106] Anghileri M, Castelletti L M L, Fabio I, et al. A survey of numerical models for hail impactanalysis using explicit finite element codes. International Journal of Impact Engineering,2005,31(8):929-944.
[107] Roylance D. Stress wave damage in graphite/epoxy laminate. Composite Materials,1980,14(2):111-119.
[108] Parga L B, Vlegels S, Hernandez O F, et al. Analytical simulation of stress wave propagation incomposite materials. Composite Structures,1999,45(2):125-129.
[109] Smith J C, McCrackin F L, Schiefer H F. Stress-strain relationships in yarns subjected to rapidimpact loading, Part V: Wave propagation in long textile yarns impacted transversely. TextileResearch Journal,1958,28(4):288-302.
[110] Chen J L, Sun C T. A plastic potential function suitable for anisotropic fiber composites. Journalof Composite Materials,1993,27(14):1379-1390.
[111] Weeks C A, Sun C T. Modeling non-linear rate-dependent behavior in fiber-reinforcedcomposites. Composites Science and Technology,1998,58(3-4):603-611.
[112] Thiruppukuzhi S V, Sun C T. Models for the strain-rate-dependent behavior of polymericcomposites. Composites Science and technology,2001,61(1):1-12.
[113] Wang Y, Xia Y M. Experimental and theoretical study on the strain rate and temperaturedependence of mechanical behavior of Kevlar fiber. Composite Part A,1999,30(11):1251-1257.
[114] Noor A K, Peters J M. A posteriori estimates for the shear correction factors in multi-layeredcomposite cylinders. Journal of Engineering Mechanics,1989,115(6):1225-1244.
[115] Huang N N. Influence of shear correction factors in the higher-order deformation laminated shelltheory. International Journal of Solids and Structures,1994,31(9):1263-1277.
[116] Paris F. A study of failure criteria of fibrous composite materials. NASA/CR-2001-210661,2001.
[117] Camanho P P, Davila C G. Mixed-mode decohesion finite elements for the simulation ofdelamination in composite materials. NASA/TM-2002-211737,2002.
[118] Benzeggagh M L, Kenane M. Measurement of mixed-mode delamination fracture toughness ofUnidirectional glass/epoxy composites with mixed-mode bending apparatus. Composites Scienceand Technology,1996,56(4):439-449.
[119]李迎九.钨合金长杆高速侵彻有限厚钢靶的数值模拟.[博士学位论文],南京:南京理工大学,1998.
[120] Borvik T, Hopperstad O S, Berstad T, et al. Numerical simulation of plugging failure in ballisticpenetration. International Journal of Solids and Structures,2001,38(34-35):6241-6264.
[121] Gupta N K, Iqbal M A, Sekhon G S. Experimental and numerical studies on the behavior of thinaluminum plates subjected to impact by blunt and hemispherical nose projectiles. InternationalJournal of Impact Engineering,2006,32(12):1921-1944.
[122]王峰.有限元方法及其在高速碰撞中的应用.[博士学位论文],合肥:中国科学技术大学，2007.
[123] Jacobs M J, Dingenen J V. Ballistic protection mechanisms in personal armor. Journal ofMaterials Science,2001,36(13):3137-3142.
[2]张楠.飞机战伤分析与实弹打击试验系统研究.[博士论文],南京:南京航空航天大学,2006.
[3]王元博.纤维增强层合材料的抗弹性能和破坏机理研究.[博士论文],合肥:中国科学技术大学,2006.
[4] Hopkinson B. A method of measuring the pressure produced in the detonation of high explosivesor by the impact of bullets. Philosophical Transactions of the Royal Society of London, Series A,Containing Papers of a Mathematical or Physical Character,1914,213:437-456.
[5] Kolsky H. An investigation of the mechanical properties of materials at very high rates of loading.In: Proceedings of the Royal Society A-Mathematical Physical and Engineering Sciences.1949,62:676-700.
[6] Davies E D H, Hunter S C. The dynamic compression testing of solids by the method of the splitHopkinson pressure bar. Journal of Mechanics and Physics of Solids,1963,11(3):155-179.
[7] Lindholm U S. Some experiments with the split hopkinson pressure bar. Journal of Mechanicsand Physics of Solids,1964,12(5):317-335.
[8] Hauser F E. Technique for measuring stress-strain relations at high strain rates. ExperimentalMechanics,1966,8(6):395-402.
[9] Woldesenbet E, Vinson J R. Specimen geometry effects on high strain rate testing ofgraphite/epoxy composites. AIAA Journal,1999,37(9):1102-1106.
[10]宋孝浜,王春霞.纤维增强复合材料应变率效应研究进展.广西纺织科技,2006,35(4):31-34.
[11] Chen W, Zhou B. Constitutive behavior of Epon828/T-403at various strain rate. Mechanics ofTime-Dependent Materials,1998,2(2):103-111.
[12] Gilat A, Goldberg R K, Roberts G D. Experimental study of strain-rate-dependent behavior ofcarbon/epoxy composite. Composites Science and Technology,2002,62(10-11):1469-1476.
[13] EI-Habak A M A. Mechanical behaviour of woven glass fibre reinforced composites underimpact compression load. Composites,1991,22(2):129-134.
[14] EI-Habak A M A. Compressive resistance of unidirectional GFRP under high rate of loading.Journal of Composites Technology and Research,1993,15(4):311-317.
[15]韩小平,韩省亮,李华,等.复合材料率相关本构模型的研究.机械科学与技术,1999,18(1):125-126.
[16] Segreti M, Rusinek A, Klepaczko J R. Experimental study on puncture of PMMA at low andhigh velocities: effect on the failure mode. Polymer Testing,2004,23(6):703-718.
[17]尚嘉兰,白以龙,沈乐天,等.酚醛玻璃钢动态本构关系的实验研究.爆炸与冲击.1990,10(1):1-13.
[18]姜春兰,李明,王在成,等.聚乙烯纤维增强复合材料的动态力学响应特性.北京理工大学学报,2001,21(2):163-167.
[19]夏源明,王兴,杨报昌.单向玻璃纤维增强环氧树脂在冲击拉伸时的一维本构方程.复合材料学报,1994,11(4):110-116.
[20]许沭华,王肖钧,张刚明,等. Kevlar纤维增强复合材料动态压缩力学性能实验研究.实验力学,2001,16(1):26-33.
[21]张华鹏.防弹材料冲击破坏机理及其纤维的衰减规律.[博士论文],上海:东华大学,2002.
[22] Wang Y, Xia Y M. The effects of strain rate on the mechanical behaviour of Kevlar fibre bundles:an experimental and theoretical study. Composites Part A,1998,29(11):1411-1415.
[23] Zhou Y X, Xia Y M. In situ strength distuibution of carbon fibers in unidirectional metal-matrixcomposites-wires. Composites Science and Technology,2001,61(14):2017-2023.
[24] Hsiao H M, Daniel I M. Strain rate behaviour of composite materials. Composites Patr B,1998,29(5):521-533.
[25] Ochola R O, Marcus K, Nurick G N, Franz T. Mechanical behaviour of glass and carbon fibrereinforced composites at varying strain rates. Composite Structures,2004,63(3-4):455-467.
[26] Zaretsky E, Debotton G, Perl M. The response of a glass fibers reinforced epoxy composite to animpact loading. International Journal of Solids and Structures,2004,41(2):569-584.
[27] Hosur M V, Alexander J, Vaidya U K, et al. High strain rate compression response ofcarbon/epoxy laminate. Composite Structures,2001,52(3-4):405-417.
[28] Hosur M V, Alexander J, Vaidya U K, et al. Studies on the off-axis high strain rate compressionloading of satin weave carbon/epoxy composites. Composite Structures,2004,63(1):75-85.
[29] Jadhav A, Woldesenbet E, Pang S S. High strain rate properties of balanced angle-plygraphite/epoxy composites. Composites Part B,2003,34(4):339-346.
[30] Jiang C L, Li M, Zhang Q M, et al. Impact responses of carbon fiber fabric reinforced composites.Journal of Beijing Institute of Technology,2000,9(3):225-230.
[31] Naik N K, Kavala V R. High strain rate behavior of woven fabric composites under compressiveloading. Materials Science and Engineering A,2008,474(1-2):301-311.
[32] Hosur M V, Adya M, Vaidya U K, et al. Effect of stitching and weave architecture on the highstrain rate compression response of affordable woven carbon/epoxy composite. CompositeStructures,2003,59(4):507-523.
[33] Hosur M V, Vaidya U K, Ulven C, et al. Performance of stitched/unstitched woven carbon/epoxycomposites under high velocity impact loading. Composite Structures,2004,64(3-4):455-466.
[34]陈思颖,黄晨光,段祝平.几种高性能纤维束的冲击动力学性能实验研究.爆炸与冲击,2003,23(4):355-359.
[35] Tay T E, Ang H G, Shim V P W. An empirical strain rate-dependent constitutive relationship forglass-fibre reinforced epoxy and pure epoxy. Composite Structures,1995,33(4):201-210.
[36] Xia Y M, Wang X. Constitutive equation for unidirectional composites under tensile impact.Composites Science and Technology,1996,56(2):155-160.
[37] Wang Y, Xia Y M. A modified constitutive equation for unidirectional composites under tensileimpact and the dynamic tensile properties of KFRP. Composites Science and Technology,2000,60(4):591-596.
[38]汪洋,夏源明.单向KFRP的应变率相关的本构方程.爆炸与冲击,2000,20(3):193-199.
[39] Hayhurst C J, Hiermaier S J, Clegg R A, et al. Development of material models for Nextel andKevlar/epoxy for high pressures and strain rates. International Journal of Impact Engineering,1999,23(1):365-376.
[40]刘占芳,姚国文,詹先义.高速冲击条件下玻璃中破坏波的损伤累积模拟.应用数学和力学,2001,22(9):983-987.
[41] Maimí P, Camanho P P, Mayugo J A, et al. A continuum damage model for composite laminates.Part I: Constitutive model. Mechanics of materials,2007,39(10):897-908.
[42] Aminjikarai B S, Tabiei A. A strain-rate dependent3-D micromechanical model for finiteelement simulations of plain weave composite structures. Composite Structures,2007,81(3):407-418.
[43]许沭华.钨合金杆弹侵彻复合靶板的实验和数值研究.[博士学位论文],合肥:中国科技大学,2000.
[44] Chen J L, Sun C T. A plastic potential function suitable for anisotropic fiber composites. Journalof Composite Materials,1993,27(14):1379-1391.
[45] Thiruppukuzhi S V, Sun C T. Testing and modeling high strain rate behavior of polymericcomposites. Composites Part B,1998,29(5):535-546.
[46] Thiruppukuzhi S V, Sun C T. Models for the strain-rate-dependent behavior of polymericcomposites. Composites Science and Technology,2001,61(1):1-12.
[47]孙紫建,王礼立.高应变率大变形下的聚丙烯/尼龙共混高聚物损伤型本构特性.爆炸与冲击,2006,26(6):492-497.
[48] Wang W, Makarov G, Shenoi R A. An analytical model for assessing strain rate sensitivity ofunidirectional composite laminates. Composite Structures,2005,69(1):45-54.
[49] Wang W B, Shenoi R A. Investigating high strain rate behaviour of unidirectional composites bya visco-elastic model. Journal of Ship Mechanics,2009,13(3):406-415.
[50] Karim M R. Constitutive modeling and failure criteria of carbon-fiber reinforced polymers underhigh strain rate.[Dissertation for the degree of doctor of philosophy], USA: University of Akron,2005.
[51] Hill R. A theory of the yielding and plastic flow of anisotropic metals. Proceedings of the RoyalSociety of London, Series A, Mathematical and Physical Sciences,1948,193(1033):281-297.
[52] Tsai S W, Wu E M. A general theory of strength for anisotropic materials. Journal of CompositeMaterials,1971,5(1):58-80.
[53] Yamada S E, Sun C T. Analysis of laminate strength and its distribution. Journal of CompositeMaterials,1978,12:275-284.
[54] Chang F K, Chang K Y. A progressive damage model for laminated composites containing stressconcentrations. Journal of Composite Materials,1987,21(9):834-855.
[55] Hashin Z. Failure Criteria for Unidirectional Fiber Composites. Journal of Applied Mechanics,1980,47(2):329–334.
[56] Hart-Smith L J. Should fibrous composite failure modes be interacted or superimposed.Composites,1993,24(1):53-55.
[57] Kroll L, Hufenbach W. Physically based failure criterion for dimensioning of thick-walledlaminates. Applied Composite Materials,1997,4(5):321-332.
[58] Echabi J, Trochu F. Failure mode dependent strength criteria for composite laminates. Journal ofReinforced Plastics&Composites,1997,16(10):926-945.
[59] Akil O, Yildirim U, Guden M. Effect of strain rate on the compression behavior of a wovenfabric S2-glass fiber reinforced vinylester composite. Polymer Testing,2003,22(8):883-887.
[60] Dorey G. An overview of impact damage in composites. Mechanical Properties of Materials atHigh Rates of Strain, Proceedings of Fourth International Conference,1989,395-402.
[61] Kim H, Welch D A, Kedward K T. Experimental investigation of high velocity ice impacts onwoven carbon/epoxy composite panels. Composites Part A,2003,34(1):25-41.
[62]金子明,沈峰,曲志敏,等.纤维增强复合材料抗弹性能研究.纤维复合材料,1999,16(3):5-9.
[63] Zhu G, Goldsmith W, Dharan C K H. Penetration of laminated Kevlar by projectiles－IExperimental investigation. International Journal of Solids and Structures,1992,29(4):399-420.
[64] Zhu G, Goldsmith W, Dharan C K H. Penetration of laminated Kevlar by projectiles－IIAnalytical model. International Journal of Solids and Structures,1992,29(4):421-436.
[65]刘国权,杨大峰,梅树清.防弹用纤维复合材料最佳树脂含量研究.玻璃钢/复合材料,2001,1(2):13-15.
[66] Fujii K, Aoki M, Kiuchi N, et al. Impact perforation behavior of CFRPs using high-velocity steelsphere. International Journal of Impact Engineering,2002,27(5):497-508.
[67] Kim J K, Sham M L. Impact and delamination failure of woven-fabric composites. CompositesScience and Technology,2000,60(5):745-761.
[68]黄英,刘晓辉,李郁忠. S-玻纤织物增强复合材料层合板冲击损伤特性研究.机械科学与技术.1999,18(3):483-485.
[69]黄英,刘晓辉,李郁忠. Kevlar织物增强复合材料层板冲击损伤特性研究.西北工业大学学报.2002,20(3):486-491.
[70] Villanueva G R, Cantwell W J. The high velocity impact response of composite andFML-reinforced sandwich structures. Composites Science and Technology,2004,64(1):35-54.
[71] Lee B L, Song L W, Ward I E. Failure of spectra polyethylene fiber-reinforced composites underballistic impact loading. Journal of Composite Materials,1994,28(13):1202-1226.
[72] Yew C H, Kendrick R B. A study of damage in composite panels produced by hypervelocityimpact. International Journal of Impact Engineering,1987,5(1-4):729-738.
[73] Nunes L M, Paciornik S, Almeida J R M. Evaluation of the damaged area of glass-fiber-reinforced epoxy-matrix composite materials submitted to ballistic impacts. CompositesScience and Technology,2004,64(7-8):945-954.
[74] Morye S S, Hine P J, Duckett R A, et al. Modeling of the energy absorption by polymercomposites upon ballistic impact. Composites Science and Technology,2000,60:2631-2642.
[75] Gellert E P, Cimpoeru S J, Woodward R L. A study of the effect of target thickness on theballistic perforation of glass-fibre-reinforced plasic composites. International Journal of ImpactEngineering,2004,24(5):445-456.
[76] Cheng W L, Jen K C, Itoh S. Failure of ceramics due to impact loading. Journal of the JapanExplosives Society,2002,63(6):388-396.
[77] López-Puente J, Zaera R, Navarro C. Experimental and numerical analysis of normal and obliqueballistic impacts on thin carbon/epoxy woven laminates. Composites Part A,2008,39(2):374-387.
[78] Wambua P, Vangrimde B, Lomov S, et al. The response of natural fibre composites to ballisticimpact by fragment simulating projectiles. Composite Structures,2007,77(2):232-240.
[79]顾伯洪.织物弹道贯穿性能分析计算.复合材料学报,2002,19(6):92-96.
[80] Gu B. Analytical modeling for the ballistic perforation of planar plain-woven fabric target byprojectile. Composites Part B,2003,34(4):361-371.
[81] Naik N K, Shrirao P. Composite structures under ballistic impact. Composite Structures,2004,66(1-4):579-590.
[82] Naik N K, Shrirao P, Reddy B C K. Ballistic impact behavior of woven fabric composites:Parametric studies. Materials Science and Engineering: A,2005,412(1-2):104-116.
[83]杜忠华,赵国志,王晓鸣,等.复合材料层合板抗弹性的工程分析模型.兵器材料科学与工程,2002,25(1):8-10.
[84]杜忠华,王戈冰,沈培辉,等.陶瓷/Kevlar复合材料靶板抗弹性能分析模型.弹道学报,2003,15(2):44-48.
[85] Wen H M. Predicting the penetration and perforation of FRP laminates struck normally byprojectiles with different nose shapes. Composite Structures,2000,49(3):321-329.
[86] Wen H M. Penetration and perforation of thick FRP laminates. Composites Science andTechnology,2001,61(8):1163-1172.
[87]覃悦,文鹤鸣,何涛.卵形弹丸撞击下FRP层合板的侵彻和穿透.复合材料学报,2007,24(2):131-136.
[88] Johnson W E, Anderson C E. History and application of hydrocodes in hypervelocity impact.International Journal of Impact Engineering,1987,5(1-4):423-439.
[89] Hamouda A M S, Hashmi M S J. Modelling the impact and penetration events of modernengineering materials: characteristics of computer codes and material models. Journal ofMaterials Processing Technology,1996,56(1-4):847-862.
[90] Nandlall D, Williams K, Vaziri R. Numerical simulation of the ballistic response of GRP plates.Composites Science and Technology.1998,58(9):1463-1469.
[91] Lim C T, Shim V P W, Ng Y H. Finite-element modeling of the ballistic impact of fabric armor.International Journal of Impact Engineering,2003,28(1):13-31.
[92] Cheng W L, Langlie S, Itoh S. High velocity impact of thick composites. International Journal ofImpact Engineering.2003,29(1-10):167-184.
[93] Kollegal G M, Sridharan S. A simplified model for plain woven fabrics. Journal of CompositeMaterials,2000,34(20):1756-1786.
[94] Guan H, Gibson R F. Micromechanical models for damping in woven fabric-reinforced polymermatrix composites. Journal of Composite Materials,2001,35(16):1417-1434.
[95] Jovicic J, Zavaliangos A, Ko F. Modelling of the ballistic behavior of gradient design compositearmors. Composites Part A,2000,31(8):773-784.
[96] Allix O. A composite damage meso-model for impact problems. Composites Science andTechnology.2001,61(15):2193-2205.
[97]梅志远,朱锡,刘燕红.混杂纤维增强材料板抗侵彻数值仿真及实验验证.兵工学报.2003,24(3):373-377.
[98]韩永要,赵国志,方清,等.动能弹侵彻多层陶瓷靶板数值模拟研究.工程力学,2006,23(8):182-186.
[99]何建,肖玉凤,杨世全,等.单层板壳穿甲数值仿真分析.哈尔滨大学工程学报，2006，27(3):382-385.
[100] Libersky L D, Petschek A G. Smooth particle hydrodynamics with strength of materials. LectureNotes in Physics,1990,395,248–257.
[101] Johnson G R, Beissel S R. Normalized smoothed function for SPH impact computations.International Journal for Numerical Methods in Engineering,1996,39(16):2725-2741
[102] Campbell J, Vignjevic R, Libersky L D. A contact algorithm for smoothed particlehydrodynamics. Computer Methods in Applied Mechanics and Engineering,2000,184(1):49-65.
[103] Parshikov A N, Medin S A. Smoothed particle hydrodynamics using interparticle contactalgorithms. Journal of Computational Physics,2002,180(1):358–382.
[104] Parshikov A N, Medin S A, Loukashenko I I, et al. Improvements in SPH method by means ofinterparticle contact algorithm and analysis of perforation tests at moderate projectile velocities.International Journal of Impact Engineering,2000,24(8):779-796.
[105] Vuyst T D, Vignjevic R, Campbell J C. Coupling between meshless and finite element methods.International Journal of Impact Engineering,2005,31(8):1054-1064.
[106] Anghileri M, Castelletti L M L, Fabio I, et al. A survey of numerical models for hail impactanalysis using explicit finite element codes. International Journal of Impact Engineering,2005,31(8):929-944.
[107] Roylance D. Stress wave damage in graphite/epoxy laminate. Composite Materials,1980,14(2):111-119.
[108] Parga L B, Vlegels S, Hernandez O F, et al. Analytical simulation of stress wave propagation incomposite materials. Composite Structures,1999,45(2):125-129.
[109] Smith J C, McCrackin F L, Schiefer H F. Stress-strain relationships in yarns subjected to rapidimpact loading, Part V: Wave propagation in long textile yarns impacted transversely. TextileResearch Journal,1958,28(4):288-302.
[110] Chen J L, Sun C T. A plastic potential function suitable for anisotropic fiber composites. Journalof Composite Materials,1993,27(14):1379-1390.
[111] Weeks C A, Sun C T. Modeling non-linear rate-dependent behavior in fiber-reinforcedcomposites. Composites Science and Technology,1998,58(3-4):603-611.
[112] Thiruppukuzhi S V, Sun C T. Models for the strain-rate-dependent behavior of polymericcomposites. Composites Science and technology,2001,61(1):1-12.
[113] Wang Y, Xia Y M. Experimental and theoretical study on the strain rate and temperaturedependence of mechanical behavior of Kevlar fiber. Composite Part A,1999,30(11):1251-1257.
[114] Noor A K, Peters J M. A posteriori estimates for the shear correction factors in multi-layeredcomposite cylinders. Journal of Engineering Mechanics,1989,115(6):1225-1244.
[115] Huang N N. Influence of shear correction factors in the higher-order deformation laminated shelltheory. International Journal of Solids and Structures,1994,31(9):1263-1277.
[116] Paris F. A study of failure criteria of fibrous composite materials. NASA/CR-2001-210661,2001.
[117] Camanho P P, Davila C G. Mixed-mode decohesion finite elements for the simulation ofdelamination in composite materials. NASA/TM-2002-211737,2002.
[118] Benzeggagh M L, Kenane M. Measurement of mixed-mode delamination fracture toughness ofUnidirectional glass/epoxy composites with mixed-mode bending apparatus. Composites Scienceand Technology,1996,56(4):439-449.
[119]李迎九.钨合金长杆高速侵彻有限厚钢靶的数值模拟.[博士学位论文],南京:南京理工大学,1998.
[120] Borvik T, Hopperstad O S, Berstad T, et al. Numerical simulation of plugging failure in ballisticpenetration. International Journal of Solids and Structures,2001,38(34-35):6241-6264.
[121] Gupta N K, Iqbal M A, Sekhon G S. Experimental and numerical studies on the behavior of thinaluminum plates subjected to impact by blunt and hemispherical nose projectiles. InternationalJournal of Impact Engineering,2006,32(12):1921-1944.
[122]王峰.有限元方法及其在高速碰撞中的应用.[博士学位论文],合肥:中国科学技术大学，2007.
[123] Jacobs M J, Dingenen J V. Ballistic protection mechanisms in personal armor. Journal ofMaterials Science,2001,36(13):3137-3142.