结构冲击动力学进展(2010-2020)

余同希 朱凌 许骏

余同希, 朱凌, 许骏. 结构冲击动力学进展(2010-2020)[J]. 爆炸与冲击, 2021, 41(12): 121401. doi: 10.11883/bzycj-2021-0113
引用本文: 余同希, 朱凌, 许骏. 结构冲击动力学进展(2010-2020)[J]. 爆炸与冲击, 2021, 41(12): 121401. doi: 10.11883/bzycj-2021-0113
YU Tongxi, ZHU Ling, XU Jun. Progress in structural impact dynamics during 2010−2020[J]. Explosion And Shock Waves, 2021, 41(12): 121401. doi: 10.11883/bzycj-2021-0113
Citation: YU Tongxi, ZHU Ling, XU Jun. Progress in structural impact dynamics during 2010−2020[J]. Explosion And Shock Waves, 2021, 41(12): 121401. doi: 10.11883/bzycj-2021-0113

结构冲击动力学进展(2010-2020)

doi: 10.11883/bzycj-2021-0113
详细信息
    作者简介:

    余同希(1941- ),男,博士,教授,metxyu@ust.hk

  • 中图分类号: O385

Progress in structural impact dynamics during 2010−2020

  • 摘要: 本文综述结构冲击动力学的国内外研究进展,在时间区间上聚焦于2010—2020这十来年发表的文献,同时提及在此之前的奠基性工作。在内容上,首先着眼于结构冲击动力学的基本科学问题,如概念、模型和工具,它们源于和用于结构在爆炸与冲击下的塑性动力响应、失效和重复受载等;也介绍典型薄壁结构件的动力行为,以及运动的物体和结构物对固壁的撞击和反弹。注意到近十多年来由于轻质材料(如多胞材料、3D打印的超材料等)和以它们为芯层的轻质结构的大量涌现,以及对生物材料和仿生结构的极大兴趣,对这些材料和结构的冲击动力学行为的研究构成了本文的后半部分。最后指出,在多尺度框架下以更全面的视角研究材料-结构-性能的内在规律,已成为推动冲击动力学继续发展的一个强大的新趋势。
  • 图  1  理想刚塑性固支方板在LRED脉冲载荷作用下的响应区域划分图[29]

    Figure  1.  Response map for a fully clamped rigid-perfectly plastic square plate subjected to an LRED pressure pulse[29]

    图  2  膜力因子法与饱和分析结合得到的方板在脉冲载荷下的塑性动力响应[30-31]

    Figure  2.  Dynamic plastic response of square plates under pulse loading analysed by the combination of the membrane factor method (MFM) and the saturation analysis (SA)[30-31]

    图  3  任意形状脉冲的Youngdahl等效技术[49]

    Figure  3.  Demonstration of Youngdahl equivalent method for a pulse of arbitrary shape[49]

    图  4  3种脉冲等效技术的对比(图中$\lambda $为载荷比)[26]

    Figure  4.  Comparison of three equivalent methods (EMs) with $\lambda $being the loading ratio[26]

    图  5  基于饱和分析的脉冲等效技术在舱室内爆中的应用[52]

    Figure  5.  Application of the saturation equivalent method in cabin explosion[52]

    图  6  脉冲载荷下固支方板的失效模式[81]

    Figure  6.  Failure modes of fully-constrained square plates under impulsive loadings[81]

    图  7  矩形脉冲载荷作用下的固支方板拉伸失效p-I(超压-冲量)图[28]

    Figure  7.  p-I diagram on tensile failure of fully clamped square plates under rectangular pulse loading[28]

    图  8  无量纲饱和冲量叠加在载荷参数空间上的等值线[107]

    Figure  8.  Contours of non-dimensional saturated impulse superimposed on the loading parameters space[107]

    图  9  脉冲和准静态加载下钢/铜板中心点变形量与脉冲载荷作用次数的关系[110]

    Figure  9.  Variation of the midpoint displacement of steel and copper plates with the number of loading impulses[110]

    图  10  结构遭受刚性质块反复碰撞实验

    Figure  10.  Repeated impact experiments of structures impinged by a rigid indenter

    图  11(a)  板塑性变形的刚塑性理论方法对比结果[130]

    Figure  11(a).  Comparison of plastic deformation obtained from different methods[130]

    11(b)  反复碰撞载荷下刚度变形特性[124]

    11(b).  Variation of stiffness under repeated impact loading[124]

    图  12  室温和低温环境下结构永久变形值随碰撞次数的变化关系[126]

    Figure  12.  Relationship of permanent deformation at room and low temperatures versus the number of impacts[126]

    图  13  嵌套的薄圆环组承受横向冲击后的变形形态[137]

    Figure  13.  Deformed configurations of a nested ring under transverse impact[137]

    图  14  在轴向冲击下的折板胞元的串列[147]

    Figure  14.  A chain of pre-bent plates under axial impact[147]

    图  15  受到30 m/s子弹撞击后的圆管[163]

    Figure  15.  Circular tubes after impact by a bullet traveling at 30 m/s[163]

    图  16  圆管梁承受横向均布矩形压力脉冲及其截面的畸变模式[169-170]

    Figure  16.  A beam of circular tubular cross-section subjected to transverse pressure as rectangular pulse as well as its cross-section distortion mode[169-170]

    图  17  对圆管施加横向爆炸载荷的实验装置[171]

    Figure  17.  Experimental setup for a circular tube subjected to explosion in its lateral direction[171]

    图  18(a)  准静态加载和动态加载下球冠变形剖面的比较[195]

    Figure  18(a).  Deformed profiles of a spherical shell under quasi-static and dynamic loadings[195]

    18(b)  加载速度为30 m/s时力随位移的变化[195]

    18(b).  Variation of the force with the displacement under the loading speed of 30 m/s[195]

    图  19  考虑局部剪切变形区的球冠动态变形模型[196]

    Figure  19.  Dynamic deformation model of a spherical shell with local shear region being considered[196]

    图  20  撞击接触时间和恢复系数随撞击速度的变化[226]

    Figure  20.  Contact time and restitution coefficient varying with impact velocity[226]

    图  21  摆锤撞击玻璃板[234]

    Figure  21.  A glass panel impacted by a pendulum[234]

    图  22  圆环撞击固壁后的动态变形模式[243]

    Figure  22.  Dynamic deformation modes of a circular ring after it impinged onto a rigid wall[243]

    图  23  圆环对固壁的撞击实验结果和数值模拟结果的比较[246]

    Figure  23.  Comparisons of experiments and numerical simulations for a circular ring impinging onto a rigid wall[246]

    图  24  乒乓球撞击厚板的实验装置[247]

    Figure  24.  Experimental setup for a ping-pong ball impinging onto a thick plate[247]

    图  25  不同撞击速度(速度由左向右递增)产生的撞击区的顶视图[248]

    Figure  25.  Top-views of the collided region after collision at various velocities (the velocity increased from the left to the right)[248]

    图  26(a)  直杆对线弹簧的撞击与反弹[258]

    Figure  26(a).  Collision and rebounding of a straight rod on a linear spring[258]

    26(b)  恢复系数(COR)和无量纲的反弹时间(NRT)随刚度比$ \bar k $的变化[258]

    26(b).  Coefficient of restitution (COR) and non-dimensional rebounding time (NRT) varying with the rigidity ratio $ \bar k $[258]

    图  27  梁对理想弹簧的横向撞击[258]

    Figure  27.  Collision of beams onto ideally elastic springs[258]

    图  28(a)  二自由度质量-弹簧系统[259]

    Figure  28(a).  A two-degree-of-freedom mass-spring system[259]

    28(b)  恢复系数随质量比的变化[259]

    28(b).  COR varying with the mass ratio[259]

    图  29  六角形蜂窝材料[265]

    Figure  29.  Hexagonal honeycomb materials[265]

    图  30  蜂窝材料面内压缩变形模式[269]

    Figure  30.  Deformation modes of honeycombs under in-plane crushing[269]

    图  31(a)  八角点阵材料[324]

    Figure  31(a).  Octet-truss lattice[324]

    31(b)  锥形点阵材料[328]

    31(b).  Pyramidal lattice[328]

    31(c)  体心立方堆积(BCC)点阵材料[325]

    31(c).  Body-centered cubic (BCC) lattice[325]

    31(d)  具有不同胞元的锥形点阵材料应力-应变曲线(相对密度0.2)[328]

    31(d).  Stress-strain curves of pyramidal lattice with different unit cells (relative density 0.2)[328]

    31(e)  当相对密度变化时,BCC点阵材料应力-应变曲线[329]

    31(e).  Stress-strain curves of BCC lattice as the variation of relative density[329]

    图  32  典型shellular material[340]

    Figure  32.  Typical shellular material[340]

    图  33  传统点阵材料与shellular material压溃时应力-应变曲线对比[342]

    Figure  33.  Comparison of the stress-strain curves under crushing between traditional lattice material and shellular material[342]

    图  34(a)  周期性层状结构[344]

    Figure  34(a).  1D periodic structure[344]

    34(b)  典型共振单元[345]

    34(b).  The basic unit cell of a locally resonant sonic crystal[345]

    34(c)  声学超材料能带结构图[345]

    34(c).  Transmission characteristics of a sonic crystal[345]

    图  35(a)  一维颗粒晶体的基本构型[360]

    Figure  35(a).  The basic configuration of 1D granular crystal [360]

    35(b)  空心椭圆环颗粒晶体中应力波的衰减[376]

    35(b).  Stress wave attenuation in a 1D granular crystal composed of elliptical rings[376]

    图  36  复合材料夹层板在低速((4.8±0.2) m/s)[392]和高速((170.8±1.9) m/s)[393]冲击下的动态响应

    Figure  36.  Dynamic responses of sandwich structures under a low impact speed ((4.8±0.2) m/s)[392] and high impact speed ((170.8±1.9) m/s)[393]

    图  37(a)  泡沫金属夹芯板重复加卸载过程[415]

    Figure  37(a).  Repeated impacts of aluminum foam sandwich plates[415]

    37(b)  泡沫金属夹芯板破坏模式[415]

    37(b).  Repeated impact induced damage in aluminum foam sandwich plates[415]

    37(c)  上面板的塑性变形值随碰撞次数的变化关系[420]

    37(c).  Relationship between front face deflection and impact number[420]

    图  38  复合材料薄壁管渐进式压溃常见失效模式

    Figure  38.  Progressive crushing of composite tubes

    图  39  甲虫前翅微观结构[439-440]

    Figure  39.  Microstructures of beetle forewings[439-440]

    图  40  (a)螳螂虾趾肢的螺旋层状复合结构[449]和(b)结构断面的扫描电子显微镜图片[449]

    Figure  40.  (a) Illustration of a 3D helicoid[449] and (b) SEM figure of the chitin fibril helicoidal structural motif on dactyl clubs[449]

    图  41  趾肢表面纳米颗粒涂层的(a)扫描电子显微镜和(b)透射电子显微镜图片[451]

    Figure  41.  Nanoparticle coating on the dactyl club of mantis shrimps (a) SEM and (b) TEM images[451]

    图  42  山毛榉树干正交平面示意图以及在0.001 s−1应变率下山毛榉样品的切向和轴向压缩曲线[462]

    Figure  42.  Cut planes of the trunk tree and tangential and longitudinal responses of beech samples at the strain rate of 0.001 s−1[462]

    图  43  柚子皮微观结构

    Figure  43.  Microstructures of pomelo peel

    图  44  甲虫前翅启发得到的蜂窝材料[444]

    Figure  44.  Bionic honeycombs inspired by the internal structure of elytra[444]

    图  45  啄木鸟喙角蛋白间的波浪形缝线结构[455]和波浪形蜂窝材料胞元示意图

    Figure  45.  A cross-section view of a wavy suture line on woodpeckers’ beaks[455] and the unit cell of a wavy honeycomb

    图  46  面外加载时,波浪形蜂窝材料的变形模式[485]

    Figure  46.  The deformation mode of the wavy honeycomb under out-of-plane crushing[485]

    图  47(a)  柚子皮微观结构启发得到的多层级蜂窝材料[265]

    Figure  47(a).  Hierarchical honeycombs inspired by the microstructures of pomelo peel[265]

    47(b)  骨骼肌启发的多层级管状材料[486]

    47(b).  Muscle-inspired hierarchical structure[486]

    图  48  传统复合材料与仿生螺旋复合材料示意图[495]

    Figure  48.  Illustration of traditional composites and bio-inspired helicoidal composites[495]

    表  1  矩形脉冲载荷下不同结构的饱和参数

    Table  1.   Saturation parameters for different structures under rectangular pulse loading

    结构类型边界条件${\left(\dfrac{ { {W_0} } }{H}\right)_{ {\rm{sat} } } } $$ {\bar I_{ {\rm{sat} } } } $$ \lambda $$ {p_{\rm{y} } } $
    简支$\dfrac{1}{2}\lambda - \dfrac{1}{2}$$\dfrac{\text{π} }{ {\sqrt 6 } }\lambda$$(1,3]$$\dfrac{ { {\text{2} }{M_0} } }{ { {L^2} } }$
    固支$\lambda - 1$$\dfrac{\text{π} }{ {\sqrt 3 } }\lambda$$(1,3]$$\dfrac{ { {\text{4} }{M_0} } }{ { {L^2} } }$
    圆板简支$\lambda - 1$$\dfrac{\text{π} }{2}\lambda$$(1,2]$$\dfrac{ { {\text{6} }{M_0} } }{ { {R^2} } }$
    方板简支$\lambda - 1$$\dfrac{\text{π} }{2}\lambda$$(1,2]$$\dfrac{ {6{M_0} } }{ { {L^2} } }$
    方板固支$2\lambda - 2$$\dfrac{\text{π} }{ {\sqrt 2 } }\lambda$$(1,2]$$\dfrac{ {12{M_0} } }{ { {L^2} } }$
    圆柱壳等距刚性加固$\dfrac{1}{2}\lambda - \dfrac{1}{2}$$\dfrac{\text{π} }{ {\sqrt 6 } }\lambda$$(1,3]$$\dfrac{ { {N_0} } }{R}{\text{ + } }\dfrac{ {4{M_0} } }{ { {L^2} } }$
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  • [1] QIU X M, YU T X. Some topics in recent advances and applications of structural impact dynamics [J]. Applied Mechanics Reviews, 2011, 64(3): 030801. DOI: 10.1115/1.4005571.
    [2] 朱建士, 胡晓棉, 王裴, 等. 爆炸与冲击动力学若干问题研究进展 [J]. 力学进展, 2010, 40(4): 400–423. DOI: 10.6052/1000-0992-2010-4-j2009-144.

    ZHU J S, HU X M, WANG P, et al. A review on research progress in explosion mechanics and impact dynamics [J]. Advances in Mechanics, 2010, 40(4): 400–423. DOI: 10.6052/1000-0992-2010-4-j2009-144.
    [3] JONES N. Structural impact [M]. New York: Cambridge University Press, 2011.
    [4] STRONGE W J, YU T X. Dynamic models for structural plasticity [M]. London: Springer Science and Business Media, 2012.
    [5] 余同希, 邱信明. 冲击动力学 [M]. 北京: 清华大学出版社, 2011.
    [6] JOHNSON W. Impact strength of materials [M]. London: Hodder Arnold, 1983.
    [7] BAROUTAJI A, SAJJIA M, OLABI A G. On the crashworthiness performance of thin-walled energy absorbers: recent advances and future developments [J]. Thin-Walled Structures, 2017, 118: 137–163. DOI: 10.1016/j.tws.2017.05.018.
    [8] 余同希, 卢国兴, 张雄. 能量吸收: 结构与材料的力学行为和塑性分析 [M]. 北京: 科学出版社, 2019.
    [9] YANG X F, MA J X, WEN D S, et al. Crashworthy design and energy absorption mechanisms for helicopter structures: a systematic literature review [J]. Progress in Aerospace Sciences, 2020, 114: 100618. DOI: 10.1016/j.paerosci.2020.100618.
    [10] 刘小川, 王彬文, 白春玉, 等. 航空结构冲击动力学技术的发展与展望 [J]. 航空科学技术, 2020, 31(3): 1–14. DOI: 10.19452/j.issn1007-5453.2020.03.001.

    LIU X C, WANG B W, BAI C Y, et al. Progress and prospect of aviation structure impact dynamics [J]. Aeronautical Science and Technology, 2020, 31(3): 1–14. DOI: 10.19452/j.issn1007-5453.2020.03.001.
    [11] PHAM T M, CHEN W S, HAO H. Review on impact response of reinforced concrete beams: contemporary understanding and unsolved problems [J]. Advances in Structural Engineering, 2021, 24(10). DOI: 10.1177/1369433221997716.
    [12] SYMONDS P S, MENTEL T J. Impulsive loading of plastic beams with axial constraints [J]. Journal of the Mechanics and Physics of Solids, 1958, 6(3): 186–202. DOI: 10.1016/0022-5096(58)90025-5.
    [13] KOMAROV K L, NEMIROVSKII Y V. Dynamic behavior of rigid-plastic rectangular plates [J]. Soviet Applied Mechanics, 1985, 21(7): 683–690. DOI: 10.1007/BF00888115.
    [14] MARTIN J B, SYMONDS P S. Mode approximations for impulsively-loaded rigid-plastic structures [J]. Journal of the Engineering Mechanics Division, 1966, 92(5): 43–66. DOI: 10.1061/JMCEA3.0000787.
    [15] NURICK G N, MARTIN J B. Deformation of thin plates subjected to impulsive loading: a review: Part Ⅰ: theoretical considerations [J]. International Journal of Impact Engineering, 1989, 8(2): 159–170. DOI: 10.1016/0734-743X(89)90014-6.
    [16] NURICK G N, MARTIN J B. Deformation of thin plates subjected to impulsive loading: a review: Part Ⅱ: experimental studies [J]. International Journal of Impact Engineering, 1989, 8(2): 171–186. DOI: 10.1016/0734-743X(89)90015-8.
    [17] JONES N. Dynamic inelastic response of strain rate sensitive ductile plates due to large impact, dynamic pressure and explosive loadings [J]. International Journal of Impact Engineering, 2014, 74: 3–15. DOI: 10.1016/j.ijimpeng.2013.05.003.
    [18] JONES N. Slamming damage [J]. Journal of Ship Research, 1973, 17(2): 80–86. DOI: 10.5957/jsr.1973.17.2.80.
    [19] SHEN W Q, JONES N. The pseudo-shakedown of beams and plates when subjected to repeated dynamic loads [J]. Journal of Applied Mechanics, 1992, 59(1): 168–175. DOI: 10.1115/1.2899423.
    [20] ZHAO Y P, YU T X, FANG J. Large dynamic plastic deflection of a simply supported beam subjected to rectangular pressure pulse [J]. Archive of Applied Mechanics, 1994, 64(3): 223–232. DOI: 10.1007/BF00806819.
    [21] ZHAO Y P, YU T X, FANG J. Saturation impulses for dynamically loaded structures with finite-deflections [J]. Structural Engineering and Mechanics, 1995, 3(6): 583–592. DOI: 10.12989/sem.1995.3.6.583.
    [22] 赵亚溥. 冲击载荷下结构塑性动力响应与失效的若干问题研究 [D]. 北京: 北京大学, 1994.
    [23] ZHU L, YU T X. Saturated impulse for pulse-loaded elastic-plastic square plates [J]. International Journal of Solids and Structures, 1997, 34(14): 1709–1718. DOI: 10.1016/S0020-7683(96)00111-4.
    [24] 席丰, 杨嘉陵. 强脉冲载荷作用下弹-塑性薄圆板的大挠度动力响应 [J]. 爆炸与冲击, 2000, 20(4): 379–384.

    XI F, YANG J L. Dynamic response analysis of elastic-plastic thin circular plates under impulse loading with consideration of large deflection [J]. Explosion and Shock Waves, 2000, 20(4): 379–384.
    [25] 席丰, 张云. 脉冲载荷作用下钢梁动力响应及反常行为的应变率效应 [J]. 爆炸与冲击, 2012, 32(1): 34–42. DOI: 10.11883/1001-1455(2012)01-0034-09.

    XI F, ZHANG Y. The effects of strain rate on the dynamic response and abnormal behavior of steel beams under pulse loading [J]. Explosion and Shock Waves, 2012, 32(1): 34–42. DOI: 10.11883/1001-1455(2012)01-0034-09.
    [26] ZHU L, BAI X Y, YU T X. The saturated impulse of fully clamped square plates subjected to linearly decaying pressure pulse [J]. International Journal of Impact Engineering, 2017, 110: 198–207. DOI: 10.1016/j.ijimpeng.2016.12.012.
    [27] BAI X Y, ZHU L, YU T X. Saturated impulse for pulse-loaded rectangular plates with various boundary conditions [J]. Thin-Walled Structures, 2017, 119: 166–177. DOI: 10.1016/j.tws.2017.03.030.
    [28] 白雪玉. 船体板在脉冲载荷下的饱和冲量研究 [D]. 武汉: 武汉理工大学, 2018.
    [29] BAI X Y, ZHU L, YU T X. Saturated impulse for fully clamped square plates under blast loading [J]. International Journal of Mechanical Sciences, 2018, 146−147: 417–431. DOI: 10.1016/j.ijmecsci.2017.08.047.
    [30] TIAN L R, CHEN F L, ZHU L, et al. Saturated analysis of pulse-loaded beams based on Membrane Factor Method [J]. International Journal of Impact Engineering, 2019, 131: 17–26. DOI: 10.1016/j.ijimpeng.2019.04.021.
    [31] TIAN L R, CHEN F L, ZHU L, et al. Large deformation of square plates under pulse loading by combined saturation analysis and membrane factor methods [J]. International Journal of Impact Engineering, 2020, 140: 103546. DOI: 10.1016/j.ijimpeng.2020.103546.
    [32] ZHU L, HE X, YU T X, et al. Scaling effect on saturated impulse for square plates under rectangular pulse loading [C]// Proceedings of the ASME 35th International Conference on Ocean, Offshore and Arctic Engineering. Busan: ASME, 2016. DOI: 10.1115/OMAE2016-54366.
    [33] HE X, ZHU L, CHEN F L, et al. Saturated impulse of pulse loaded square plates made of steels with various yield stresses [C]// Proceedings of the 27th International Ocean and Polar Engineering Conference. San Francisco: International Society of Offshore and Polar Engineers, 2017.
    [34] ZHU L, HE X, CHEN F L, et al. Effects of the strain rate sensitivity and strain hardening on the saturated impulse of plates [J]. Latin American Journal of Solids and Structures, 2017, 14(7): 1273–1292. DOI: 10.1590/1679-78253664.
    [35] JONES N. A theoretical study of the dynamic plastic behavior of beams and plates with finite-deflections [J]. International Journal of Solids and Structures, 1971, 7(8): 1007–1029. DOI: 10.1016/0020-7683(71)90078-3.
    [36] YU T X, STRONGE W J. Large deflections of a rigid-plastic beam-on-foundation from impact [J]. International Journal of Impact Engineering, 1990, 9(1): 115–126. DOI: 10.1016/0734-743X(90)90025-Q.
    [37] 余同希, 陈发良. 用“膜力因子法”分析简支刚塑性圆板的大挠度动力响应 [J]. 力学学报, 1990, 22(5): 555–565. DOI: 10.6052/0459-1879-1990-5-1995-984.

    YU T X, CHEN F L. Analysis of the large deflection dynamic response of simply-supported circular plates by the “membrane factor method” [J]. Acta Mechanica Sinica, 1990, 22(5): 555–565. DOI: 10.6052/0459-1879-1990-5-1995-984.
    [38] 陈发良, 余同希. 正多边形板的塑性动力响应: 小挠度分析和大挠度分析 [J]. 爆炸与冲击, 1991, 11(2): 106–116.

    CHEN F L, YU T X. Dynamic plastic response of regular polygonal plates [J]. Explosion and Shock Waves, 1991, 11(2): 106–116.
    [39] YU T X, CHEN F L. The large deflection dynamic plastic response of rectangular plates [J]. International Journal of Impact Engineering, 1992, 12(4): 605–616. DOI: 10.1016/0734-743X(92)90261-Q.
    [40] 颜丰, 刘敬喜. 爆炸载荷下固支矩形板的大挠度塑性动力响应 [J]. 中国舰船研究, 2013, 8(1): 47–53. DOI: 10.3969/j.issn.1673-3185.2013.01.008.

    YAN F, LIU J X. The large deflection dynamic plastic response of rectangular plates subjected to blast load [J]. Chinese Journal of Ship Research, 2013, 8(1): 47–53. DOI: 10.3969/j.issn.1673-3185.2013.01.008.
    [41] 王鑫. 爆炸作用下钢筋混凝土板的塑性动力响应 [D]. 哈尔滨: 哈尔滨工程大学, 2014. DOI: 10.7666/d.D595676.
    [42] 王喆. 加筋板结构爆炸冲击下塑性动力响应分析 [D]. 哈尔滨: 哈尔滨工程大学, 2014. DOI: 10.7666/d.D595610.
    [43] 郭君, 张文启, 郭建军, 等. 水下爆炸冲击波作用下单向加筋板的大挠度塑性变形 [J]. 兵工学报, 2015, 36(S1): 163–168.

    GUO J, ZHANG W Q, GUO J J, et al. Large plastic deformation of stiffened plate subjected to blast load [J]. Acta Armamentarii, 2015, 36(S1): 163–168.
    [44] QIN Q H, WANG T J, ZHAO S Z. Large deflections of metallic sandwich and monolithic beams under locally impulsive loading [J]. International Journal of Mechanical Sciences, 2009, 51(11−12): 752–773. DOI: 10.1016/j.ijmecsci.2009.08.008.
    [45] QIN Q H, WANG T J. A theoretical analysis of the dynamic response of metallic sandwich beam under impulsive loading [J]. European Journal of Mechanics: A/Solids, 2009, 28(5): 1014–1025. DOI: 10.1016/j.euromechsol.2009.04.002.
    [46] QIN Q H, XIANG C P, ZHANG J X, et al. On low-velocity impact response of metal foam core sandwich beam: a dual beam model [J]. Composite Structures, 2017, 176: 1039–1049. DOI: 10.1016/j.compstruct.2017.06.038.
    [47] SYMONDS P S. Dynamic load characteristics in plastic bending of beams [J]. Journal of Applied Mechanics, 1953, 20(4): 475–481.
    [48] HODGE P G. The influence of blast characteristics on the final deformation of circular cylindrical shells [M]. Brooklyn: Department of Aeronautical Engineering, Polytechnic Institute of Brooklyn, 1954.
    [49] YOUNGDAHL C K. Correlation parameters for eliminating the effect of pulse shape on dynamic plastic deformation [J]. Journal of Applied Mechanics, 1970, 37(3): 744–752. DOI: 10.1115/1.3408605.
    [50] ZHU G, HUANG Y G, YU T X, et al. Estimation of the plastic structural response under impact [J]. International Journal of Impact Engineering, 1986, 4(4): 271–282. DOI: 10.1016/0734-743X(86)90018-7.
    [51] LI Q M, MENG H. Pulse loading shape effects on pressure-impulse diagram of an elastic-plastic, single-degree-of-freedom structural model [J]. International Journal of Mechanical Sciences, 2002, 44(9): 1985–1998. DOI: 10.1016/S0020-7403(02)00046-2.
    [52] 朱凌, 田岚仁, 李德聪, 等. 饱和冲量及其等效方法在舱室内爆炸中的应用 [J]. 中国舰船研究, 2021, 16(2): 99–107. DOI: 10.19693/j.issn.1673-3185.01876.

    ZHU L, TIAN L R, LI D C, et al. Saturated impulse and application of saturation equivalent method in cabin explosion [J]. Chinese Journal of Ship Research, 2021, 16(2): 99–107. DOI: 10.19693/j.issn.1673-3185.01876.
    [53] 赵亚溥, 余同希, 方竞. 关于结构塑性动力失效若干问题的研究进展 [J]. 力学进展, 1995, 25(4): 549–561. DOI: 10.6052/1000-0992-1995-4-J1995-009.

    ZHAO Y P, YU T X, FANG J. On the some advances in studies of structural dynamic plastic failure [J]. Advances in Mechanics, 1995, 25(4): 549–561. DOI: 10.6052/1000-0992-1995-4-J1995-009.
    [54] YU T X, CHEN F L. Failure of plastic structures under intense dynamic loading: modes, criteria and thresholds [J]. International Journal of Mechanical Sciences, 2000, 42(8): 1537–1554. DOI: 10.1016/S0020-7403(99)00089-2.
    [55] MENKES S B, OPAT H J. Broken beams [J]. Experimental Mechanics, 1973, 13(11): 480–486. DOI: 10.1007/BF02322734.
    [56] ZHU L. Transient deformation modes of square plates subjected to explosive loadings [J]. International Journal of Solids and Structures, 1996, 33(3): 301–314. DOI: 10.1016/0020-7683(95)00037-B.
    [57] NURICK G N, SHAVE G C. The deformation and tearing of thin square plates subjected to impulsive loads: an experimental study [J]. International Journal of Impact Engineering, 1996, 18(1): 99–116. DOI: 10.1016/0734-743X(95)00018-2.
    [58] RAMAJEYATHILAGAM K, VENDHAN C P. Deformation and rupture of thin rectangular plates subjected to underwater shock [J]. International Journal of Impact Engineering, 2004, 30(6): 699–719. DOI: 10.1016/j.ijimpeng.2003.01.001.
    [59] JACOB N, YUEN S C K, NURICK G N, et al. Scaling aspects of quadrangular plates subjected to localised blast loads: experiments and predictions [J]. International Journal of Impact Engineering, 2004, 30(8−9): 1179–1208. DOI: 10.1016/j.ijimpeng.2004.03.012.
    [60] JACOB N, NURICK G N, LANGDON G S. The effect of stand-off distance on the failure of fully clamped circular mild steel plates subjected to blast loads [J]. Engineering Structures, 2007, 29(10): 2723–2736. DOI: 10.1016/j.engstruct.2007.01.021.
    [61] YUEN S C K, NURICK G N. Experimental and numerical studies on the response of quadrangular stiffened plates: Part Ⅰ: subjected to uniform blast load [J]. International Journal of Impact Engineering, 2005, 31(1): 55–83. DOI: 10.1016/j.ijimpeng.2003.09.048.
    [62] LANGDON G S,YUEN S C K, NURICK G N. Experimental and numerical studies on the response of quadrangular stiffened plates: Part Ⅱ: localised blast loading [J]. International Journal of Impact Engineering, 2005, 31(1): 85–111. DOI: 10.1016/j.ijimpeng.2003.09.050.
    [63] ZHAO N, YAO S J, ZHANG D, et al. Experimental and numerical studies on the dynamic response of stiffened plates under confined blast loads [J]. Thin-Walled Structures, 2020, 154: 106839. DOI: 10.1016/j.tws.2020.106839.
    [64] 牟金磊, 朱锡, 张振华, 等. 水下爆炸载荷作用下加筋板变形及开裂试验研究 [J]. 振动与冲击, 2008, 27(1): 57–60. DOI: 10.3969/j.issn.1000-3835.2008.01.013.

    MU J L, ZHU X, ZHANG Z H, et al. Experimental study on deformation and rupture of stiffened plates subjected to underwater shock [J]. Journal of Vibration and Shock, 2008, 27(1): 57–60. DOI: 10.3969/j.issn.1000-3835.2008.01.013.
    [65] BONORCHIS D, NURICK G N. The analysis and simulation of welded stiffener plates subjected to localised blast loading [J]. International Journal of Impact Engineering, 2010, 37(3): 260–273. DOI: 10.1016/j.ijimpeng.2009.08.004.
    [66] YUAN Y, TAN P J. Deformation and failure of rectangular plates subjected to impulsive loadings [J]. International Journal of Impact Engineering, 2013, 59: 46–59. DOI: 10.1016/j.ijimpeng.2013.03.009.
    [67] MICALLEF K, FALLAH A S, POPE D J, et al. Dynamic performance of simply supported rigid plastic circular thick steel plates subjected to localized blast loading [J]. Journal of Engineering Mechanics, 2014, 140(1): 159–171. DOI: 10.1061/(ASCE)EM.1943-7889.0000645.
    [68] MEHREGANIAN N, FALLAH A S, LOUCA L A. Plastic dynamic response of simply supported thick square plates subject to localised blast loading [J]. International Journal of Impact Engineering, 2019, 126: 85–100. DOI: 10.1016/j.ijimpeng.2018.12.010.
    [69] AUNE V, VALSAMOS G, CASADEI F, et al. Numerical study on the structural response of blast-loaded thin aluminium and steel plates [J]. International Journal of Impact Engineering, 2017, 99: 131–144. DOI: 10.1016/j.ijimpeng.2016.08.010.
    [70] YUAN Y, TAN P J. On large deformation, damage and failure of ductile plates to blast loading [J]. International Journal of Impact Engineering, 2019, 132: 103330. DOI: 10.1016/j.ijimpeng.2019.103330.
    [71] 纪冲, 徐全军, 万文乾, 等. 钢质圆柱壳在侧向爆炸荷载下的动力响应 [J]. 爆炸与冲击, 2014, 34(2): 137–144. DOI: 10.11883/1001-1455(2014)02-0137-08.

    JI C, XU Q J, WAN W Q, et al. Dynamic responses of steel cylindrical shells under lateral explosion loading [J]. Explosion and Shock Waves, 2014, 34(2): 137–144. DOI: 10.11883/1001-1455(2014)02-0137-08.
    [72] WIERZBICKI T, BAO Y B, LEE Y W, et al. Calibration and evaluation of seven fracture models [J]. International Journal of Mechanical Sciences, 2005, 47(4−5): 719–743. DOI: 10.1016/j.ijmecsci.2005.03.003.
    [73] JOHNSON G R, COOK W H. Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures [J]. Engineering Fracture Mechanics, 1985, 21(1): 31–48. DOI: 10.1016/0013-7944(85)90052-9.
    [74] ZHU L, ATKINS A G. Failure criteria for ship collision and grounding [C]//Proceedings of the 7th International Symposium on Practical Design of Ships and Mobile Units. The Hague: Elsevier, 1998.
    [75] RUDRAPATNA N S, VAZIRI R, OLSON M D. Deformation and failure of blast-loaded stiffened plates [J]. International Journal of Impact Engineering, 2000, 24(5): 457–474. DOI: 10.1016/S0734-743X(99)00172-4.
    [76] BAO Y B, WIERZBICKI T. A comparative study on various ductile crack formation criteria [J]. Journal of Engineering Materials and Technology, 2004, 126(3): 314–324. DOI: 10.1115/1.1755244.
    [77] BAI Y L, WIERZBICKI T. Application of extended Mohr-Coulomb criterion to ductile fracture [J]. International Journal of Fracture, 2010, 161(1): 1. DOI: 10.1007/s10704-009-9422-8.
    [78] STORHEIM M, ALSOS H S, HOPPERSTAD O S, et al. A damage-based failure model for coarsely meshed shell structures [J]. International Journal of Impact Engineering, 2015, 83: 59–75. DOI: 10.1016/j.ijimpeng.2015.04.009.
    [79] YANG L, PENG Z L, WANG D Y. Experimental and numerical investigation of material failure criterion with high-strength hull steel under biaxial stress [J]. Ocean Engineering, 2018, 155: 24–41. DOI: 10.1016/j.oceaneng.2018.02.022.
    [80] WANG Z P, HU Z Q, LIU K, et al. Application of a material model based on the Johnson-Cook and Gurson-Tvergaard-Needleman model in ship collision and grounding simulations [J]. Ocean Engineering, 2020, 205: 106768. DOI: 10.1016/j.oceaneng.2019.106768.
    [81] MORIELLO D S, BOSI F, TORII R, et al. Failure and detachment path of impulsively loaded plates [J]. Thin-Walled Structures, 2020, 155: 106871. DOI: 10.1016/j.tws.2020.106871.
    [82] NEEDLEMAN A, TVERGAARD V. An analysis of ductile rupture in notched bars [J]. Journal of the Mechanics and Physics of Solids, 1984, 32(6): 461–490. DOI: 10.1016/0022-5096(84)90031-0.
    [83] JARRETT D E. Derivation of the British explosives safety distances [J]. Annals of the New York Academy of Sciences, 1968, 152(1): 18–35. DOI: 10.1111/j.1749-6632.1968.tb11963.x.
    [84] 李天华. 爆炸荷载下钢筋混凝土板的动态响应及损伤评估 [D]. 西安: 长安大学, 2012. DOI: 10.7666/d.D234344.
    [85] PARLIN N J, DAVIDS W G, NAGY E, et al. Dynamic response of lightweight wood-based flexible wall panels to blast and impulse loading [J]. Construction and Building Materials, 2014, 50: 237–245. DOI: 10.1016/j.conbuildmat.2013.09.046.
    [86] STOLZ A, FISCHER K, ROLLER C, et al. Dynamic bearing capacity of ductile concrete plates under blast loading [J]. International Journal of Impact Engineering, 2014, 69: 25–38. DOI: 10.1016/j.ijimpeng.2014.02.008.
    [87] COTSOVOS D M. A simplified approach for assessing the load-carrying capacity of reinforced concrete beams under concentrated load applied at high rates [J]. International Journal of Impact Engineering, 2010, 37(8): 907–917. DOI: 10.1016/j.ijimpeng.2010.01.005.
    [88] COTSOVOS D M, PAVLOVIĆ M N. Modelling of RC beams under impact loading [J]. Proceedings of the Institution of Civil Engineers-Structures and Buildings, 2012, 165(2): 77–94. DOI: 10.1680/stbu.2012.165.2.77.
    [89] 汪维. 钢筋混凝土构件在爆炸载荷作用下的毁伤效应及评估方法研究 [D]. 长沙: 国防科学技术大学, 2012.
    [90] 师吉浩, 朱渊, 陈国明, 等. 基于p-I模型的爆炸载荷下波纹板防爆墙抗爆能力评估 [J]. 振动与冲击, 2017, 36(6): 188–195. DOI: 10.13465/j.cnki.jvs.2017.06.029.

    SHI J H, ZHU Y, CHEN G M, et al. Assessment of blast resistance capacities of corrugated blast walls based on the p-I Model [J]. Journal of Vibration and Shock, 2017, 36(6): 188–195. DOI: 10.13465/j.cnki.jvs.2017.06.029.
    [91] 丁阳, 陈晔, 师燕超. 室内爆炸与火灾联合作用下约束钢柱损伤评估 [J]. 振动与冲击, 2017, 36(5): 79–86. DOI: 10.13465/j.cnki.jvs.2017.05.013.

    DING Y, CHEN Y, SHI Y C. Damage evaluation of a restrained steel column subjected to indoor blast and fire [J]. Journal of Vibration and Shock, 2017, 36(5): 79–86. DOI: 10.13465/j.cnki.jvs.2017.05.013.
    [92] 陈赟, 冯顺山, 王芳, 等. 爆炸冲击波作用下的金属板损伤p-I图仿真 [J]. 科技导报, 2010, 28(18): 52–56.

    CHEN Y, FENG S S, WANG F, et al. Numerical methods of pressure-impulse diagrams for damages of plates under blast loads [J]. Science and Technology Review, 2010, 28(18): 52–56.
    [93] ABRAHAMSON G R, LINDBERG H E. Peak load-impulse characterization of critical pulse loads in structural dynamics [J]. Nuclear Engineering and Design, 1976, 37(1): 35–46. DOI: 10.1016/0029-5493(76)90051-0.
    [94] LI Q M, MENG H. Pressure-impulse diagram for blast loads based on dimensional analysis and single-degree-of-freedom model [J]. Journal of Engineering Mechanics, 2002, 128(1): 87–92. DOI: 10.1061/(ASCE)0733-9399(2002)128:1(87).
    [95] FALLAH A S, NWANKWO E, LOUCA L A. Pressure-impulse diagrams for blast loaded continuous beams based on dimensional analysis [J]. Journal of Applied Mechanics, 2013, 80(5): 11. DOI: 10.1115/1.4023639.
    [96] DRAGOS J, WU C Q. A new general approach to derive normalised pressure impulse curves [J]. International Journal of Impact Engineering, 2013, 62: 1–12. DOI: 10.1016/j.ijimpeng.2013.05.005.
    [97] DRAGOS J, WU C Q. Single-degree-of-freedom approach to incorporate axial load effects on pressure impulse curves for steel columns [J]. Journal of Engineering Mechanics, 2015, 141(1): 04014098. DOI: 10.1061/(ASCE)EM.1943-7889.0000818.
    [98] TSAI Y K. Energy based load-impulse diagrams for structural elements [D]. Gainesville: University of Florida, 2015.
    [99] TSAI Y K, KRAUTHAMMER T. Energy based load-impulse diagrams [J]. Engineering Structures, 2017, 149: 64–77. DOI: 10.1016/j.engstruct.2016.10.042.
    [100] TSAI Y K, KRAUTHAMMER T. Energy based load-impulse diagrams with multiple failure modes for blast-loaded reinforced concrete structural elements [J]. Engineering Failure Analysis, 2019, 104: 830–843. DOI: 10.1016/j.engfailanal.2019.06.023.
    [101] 陈俊杰, 高康华, 孙敖. 爆炸条件下结构超压-冲量曲线简化计算研究 [J]. 振动与冲击, 2016, 35(13): 224–232. DOI: 10.13465/j.cnki.jvs.2016.13.036.

    CHEN J J, GAO K H, SUN A. Simplified calculation method for pressure-impulse curve of a structure under blast load [J]. Journal of Vibration and Shock, 2016, 35(13): 224–232. DOI: 10.13465/j.cnki.jvs.2016.13.036.
    [102] 潘建军, 陈万祥, 郭志昆, 等. 基于p-I曲线的火灾后钢管RPC柱抗爆损伤评估方法 [J]. 防护工程, 2018, 40(5): 16–26.

    PAN J J, CHEN W X, GUO Z K, et al. Evaluation of fire and blast-damaged RPC-FST column based on pressure-impulse diagram [J]. Protective Engineering, 2018, 40(5): 16–26.
    [103] SHI Y J. Characterization with scaling techniques on response energy of a single degree of freedom system subject to blast loading [J]. International Journal of Impact Engineering, 2021, 148: 103764. DOI: 10.1016/j.ijimpeng.2020.103764.
    [104] 汪维, 张舵, 卢芳云, 等. 爆炸荷载作用下钢筋混凝土板跨高比对两种失效模式p-I图的影响 [J]. 防护工程, 2015, 37(1): 44–49.

    WANG W, ZHANG D, LU F Y, et al. The influence of span length to height ratio of reinforced concrete slabs on pressure-impulse diagram with multiple failure modes under blast loading [J]. Protective Engineering, 2015, 37(1): 44–49.
    [105] YU R Q, ZHANG D D, CHEN L, et al. Non-dimensional pressure-impulse diagrams for blast-loaded reinforced concrete beam columns referred to different failure modes [J]. Advances in Structural Engineering, 2018, 21(14): 2114–2129. DOI: 10.1177/1369433218768085.
    [106] YU R Q, CHEN L, FANG Q, et al. Generation of pressure-impulse diagrams for failure modes of RC columns subjected to blast loads [J]. Engineering Failure Analysis, 2019, 100: 520–535. DOI: 10.1016/j.engfailanal.2019.02.001.
    [107] YUAN Y, ZHU L, BAI X Y, et al. Pressure-impulse diagrams for elastoplastic beams subjected to pulse-pressure loading [J]. International Journal of Solids and Structures, 2019, 160: 148–157. DOI: 10.1016/j.ijsolstr.2018.10.021.
    [108] CHERNIN L, VILNAY M, SHUFRIN I, et al. Pressure-impulse diagram method: a fundamental review [J]. Proceedings of the Institution of Civil Engineers:Engineering and Computational Mechanics, 2019, 172(2): 55–69. DOI: 10.1680/jencm.17.00017.
    [109] YUHARA T. Fundamental study of wave impact loads on ship bow: 3rd report: simulation of bow damage [J]. Journal of the Society of Naval Architects of Japan, 1975(137): 240–245.
    [110] STOFFEL M. Limit states of elastic-viscoplastic plate deformations caused by repeated shock wave-loadings: Part 1: experimental observation [J]. Mechanics Research Communications, 2006, 33(6): 771–774. DOI: 10.1016/j.mechrescom.2006.03.004.
    [111] STOFFEL M. Limit states of elastic-viscoplastic plate deformations caused by repeated shock wave-loadings: Part 2: theoretical modelling [J]. Mechanics Research Communications, 2006, 33(6): 775–779. DOI: 10.1016/j.mechrescom.2006.03.005.
    [112] SHIN H, SEO B, CHO S R. Experimental investigation of slamming impact acted on flat bottom bodies and cumulative damage [J]. International Journal of Naval Architecture and Ocean Engineering, 2018, 10(3): 294–306. DOI: 10.1016/j.ijnaoe.2017.06.004.
    [113] HENCHIE T F, YUEN S C K, NURICK G N, et al. The response of circular plates to repeated uniform blast loads: an experimental and numerical study [J]. International Journal of Impact Engineering, 2014, 74: 36–45. DOI: 10.1016/j.ijimpeng.2014.02.021.
    [114] KUMAR M, GOEL M D, MATSAGAR V A, et al. Response of semi-buried structures subjected to multiple blast loading considering soil-structure interaction [J]. Indian Geotechnical Journal, 2015, 45(3): 243–253. DOI: 10.1007/s40098-014-0143-1.
    [115] ZHOU Y, JI C, LONG Y, et al. Experimental studies on the deformation and damage of steel cylindrical shells subjected to double-explosion loadings [J]. Thin-Walled Structures, 2018, 127: 469–482. DOI: 10.1016/j.tws.2018.02.019.
    [116] YUEN S C K, BUTLER A, BORNSTEIN H, et al. The influence of orientation of blast loading on quadrangular plates [J]. Thin-Walled Structures, 2018, 131: 827–837. DOI: 10.1016/j.tws.2018.08.004.
    [117] CHENG L Y, JI C, GAO F Y, et al. Deformation and damage of liquid-filled cylindrical shell composite structures subjected to repeated explosion loads: experimental and numerical study [J]. Composite Structures, 2019, 220: 386–401. DOI: 10.1016/j.compstruct.2019.03.083.
    [118] REZASEFAT M, MOSTOFI T M, OZBAKKALOGLU T. Repeated localized impulsive loading on monolithic and multi-layered metallic plates [J]. Thin-Walled Structures, 2019, 144: 106332. DOI: 10.1016/j.tws.2019.106332.
    [119] ZIYA-SHAMAMI M, BABAEI H, MOSTOFI T M, et al. Structural response of monolithic and multi-layered circular metallic plates under repeated uniformly distributed impulsive loading: an experimental study [J]. Thin-Walled Structures, 2020, 157: 107024. DOI: 10.1016/j.tws.2020.107024.
    [120] ZHU L. Dynamic inelastic behaviour of ship plates in collision [D]. Glasgow: University of Glasgow, 1990.
    [121] ZHU L, FAULKNER D. Damage estimate for plating of ships and platforms under repeated impacts [J]. Marine Structures, 1996, 9(7): 697–720. DOI: 10.1016/0951-8339(95)00018-6.
    [122] HUANG Z Q, CHEN Q S, ZHANG W T. Pseudo-shakedown in the collision mechanics of ships [J]. International Journal of Impact Engineering, 2000, 24(1): 19–31. DOI: 10.1016/S0734-743X(99)00041-X.
    [123] JONES N. Pseudo-shakedown phenomenon for the mass impact loading of plating [J]. International Journal of Impact Engineering, 2014, 65: 33–39. DOI: 10.1016/j.ijimpeng.2013.10.009.
    [124] ZHU L. Modeling of repeated impacts on ships and offshore platforms [C]//Proceedings of the International Conference on Safety and Reliability of Ship, Offshore and Subsea Structures. Glasgow, 2014.
    [125] DUAN F J, LIU J X, WANG G, et al. Dynamic behaviour of aluminium alloy plates with surface cracks subjected to repeated impacts [J]. Ships and Offshore Structures, 2019, 14(5): 478–491. DOI: 10.1080/17445302.2018.1507088.
    [126] CHO S R, TRUONG D D, SHIN H K. Repeated lateral impacts on steel beams at room and sub-zero temperatures [J]. International Journal of Impact Engineering, 2014, 72: 75–84. DOI: 10.1016/j.ijimpeng.2014.05.010.
    [127] TRUONG D D, JUNG H J, SHIN H K, et al. Response of low-temperature steel beams subjected to single and repeated lateral impacts [J]. International Journal of Naval Architecture and Ocean Engineering, 2018, 10(6): 670–682. DOI: 10.1016/j.ijnaoe.2017.10.002.
    [128] 黄震球. 船舶结构力学中的“伪安定”问题 [J]. 上海交通大学学报, 1998, 32(11): 51–55. DOI: 10.16183/j.cnki.jsjtu.1998.11.011.

    HUANG Z Q. Pseudo shakedown in structural mechanics of ships [J]. Journal of Shanghai Jiaotong University, 1998, 32(11): 51–55. DOI: 10.16183/j.cnki.jsjtu.1998.11.011.
    [129] TRUONG D D, SHIN H K, CHO S R. Repeated lateral impacts on steel grillage structures at room and sub-zero temperatures [J]. International Journal of Impact Engineering, 2018, 113: 40–53. DOI: 10.1016/j.ijimpeng.2017.11.007.
    [130] ZHU L, SHI S Y, JONES N. Dynamic response of stiffened plates under repeated impacts [J]. International Journal of Impact Engineering, 2018, 117: 113–122. DOI: 10.1016/j.ijimpeng.2018.03.006.
    [131] HAO Q M, YIN X C, QIAN P B, et al. Transient impact analysis of elastic-plastic beam with strain-rate sensitivity [J]. International Journal of Impact Engineering, 2021, 153: 103865. DOI: 10.1016/j.ijimpeng.2021.103865.
    [132] HE X, SOARES C G. Experimental study on the dynamic behavior of beams under repeated impacts [J]. International Journal of Impact Engineering, 2021, 147: 103724. DOI: 10.1016/j.ijimpeng.2020.103724.
    [133] OWENS R H. Plastic deformations of a free ring under concentrated dynamic loading [R]. Providence, RI: Division of Applied Mathematics, Brown University, 1954.
    [134] HASHMI S J, AL-HASSANI S T S, JOHNSON W. Dynamic plastic deformation of rings under impulsive load [J]. International Journal of Mechanical Sciences, 1972, 14(12): 823–826. DOI: 10.1016/0020-7403(72)90043-4.
    [135] WANG H B, YANG J L, LIU H. Lateral crushing of circular rings under wedge impact [J]. International Journal of Applied Mechanics, 2016, 8(3): 1650031. DOI: 10.1142/S1758825116500319.
    [136] FAN Z H, SHEN J H, LU G X, et al. Dynamic lateral crushing of empty and sandwich tubes [J]. International Journal of Impact Engineering, 2013, 53: 3–16. DOI: 10.1016/j.ijimpeng.2012.09.006.
    [137] WANG H B, YANG J L, LIU H, et al. Internally nested circular tube system subjected to lateral impact loading [J]. Thin-Walled Structures, 2015, 91: 72–81. DOI: 10.1016/j.tws.2015.02.014.
    [138] BAROUTAJI A, GILCHRIST M D, OLABI A G. Quasi-static, impact and energy absorption of internally nested tubes subjected to lateral loading [J]. Thin-Walled Structures, 2016, 98: 337–350. DOI: 10.1016/j.tws.2015.10.001.
    [139] YU Z L, XUE P, CHEN Z. Reprint of: nested tube system applicable to protective structures against blast shock [J]. International Journal of Impact Engineering, 2017, 105: 13–23. DOI: 10.1016/j.ijimpeng.2017.03.025.
    [140] VIRGIN L N, GILIBERTO J V, PLAUT R H. Deformation and vibration of compressed, nested, elastic rings on rigid base [J]. Thin-Walled Structures, 2018, 132: 167–175. DOI: 10.1016/j.tws.2018.08.015.
    [141] USTA F, TÜRKMEN H S. Experimental and numerical investigation of impact behavior of nested tubes with and without honeycomb filler [J]. Thin-Walled Structures, 2019, 143: 106256. DOI: 10.1016/j.tws.2019.106256.
    [142] SHABANI B, RAD S G, ALIJANI A, et al. Dynamic plastic behavior of single and nested rings under lateral impact [J]. Thin-Walled Structures, 2021, 160: 107373. DOI: 10.1016/j.tws.2020.107373.
    [143] REID S R, REDDY T Y. Experimental investigation of inertia effects in one-dimensional metal ring systems subjected to end impact: Ⅰ: fixed-ended systems [J]. International Journal of Impact Engineering, 1983, 1(1): 85–106. DOI: 10.1016/0734-743X(83)90014-3.
    [144] REID S R, BELL W W, BARR R A. Structural plastic shock model for one-dimensional ring systems [J]. International Journal of Impact Engineering, 1983, 1(2): 175–191. DOI: 10.1016/0734-743X(83)90005-2.
    [145] REID S R, BELL W W. Response of one-dimensional metal ring systems to end impact [C]//Institute of Physics Conference Series, 1984: 471-478.
    [146] GAO Z Y, YU T X, LU G. A study on type Ⅱ structures: Part Ⅰ: a modified one-dimensional mass-spring model [J]. International Journal of Impact Engineering, 2005, 31(7): 895–910. DOI: 10.1016/j.ijimpeng.2004.04.015.
    [147] GAO Z Y, YU T X, LU G. A study on type Ⅱ structures: Part Ⅱ: dynamic behavior of a chain of pre-bent plates [J]. International Journal of Impact Engineering, 2005, 31(7): 911–926. DOI: 10.1016/j.ijimpeng.2004.04.014.
    [148] YU T X, LU G, GAO Z Y, et al. Dynamic behaviour and energy absorption of 1D and 2D regularly packed cells [J]. International Journal of Vehicle Design, 2005, 37(2−3): 199–223. DOI: 10.1504/IJVD.2005.006657.
    [149] LIU K, ZHAO K, GAO Z Y, et al. Dynamic behavior of ring systems subjected to pulse loading [J]. International Journal of Impact Engineering, 2005, 31(10): 1209–1222. DOI: 10.1016/j.ijimpeng.2004.08.005.
    [150] GAO Z Y, YU T X. One-dimensional analysis on the dynamic response of cellular chains to pulse loading [J]. Proceedings of the Institution of Mechanical Engineers: Part C: Journal of Mechanical Engineering Science, 2006, 220(5): 679–689. DOI: 10.1243/09544062C07505.
    [151] SHIM V P W, LAN R, GUO Y B, et al. Elastic wave propagation in cellular systems: experiments on single rings and ring systems [J]. International Journal of Impact Engineering, 2007, 34(10): 1565–1584. DOI: 10.1016/j.ijimpeng.2006.08.007.
    [152] FLORENCE A L, GOODIER J N. Dynamic plastic buckling of cylindrical shells in sustained axial compressive flow [J]. Journal of Applied Mechanics, 1968, 35(1): 80–86. DOI: 10.1115/1.3601178.
    [153] ABRAMOWICZ W, JONES N. Dynamic axial crushing of circular tubes [J]. International Journal of Impact Engineering, 1984, 2(3): 263–281. DOI: 10.1016/0734-743X(84)90010-1.
    [154] GUPTA N K. Some aspects of axial collapse of cylindrical thin-walled tubes [J]. Thin-Walled Structures, 1998, 32(1−3): 111–126. DOI: 10.1016/S0263-8231(98)00029-9.
    [155] KARAGIOZOVA D, JONES N. Dynamic effects on buckling and energy absorption of cylindrical shells under axial impact [J]. Thin-Walled Structures, 2001, 39(7): 583–610. DOI: 10.1016/S0263-8231(01)00015-5.
    [156] KARAGIOZOVA D, JONES N. On dynamic buckling phenomena in axially loaded elastic-plastic cylindrical shells [J]. International Journal of Non-linear Mechanics, 2002, 37(7): 1223–1238. DOI: 10.1016/S0020-7462(01)00146-9.
    [157] KARAGIOZOVA D, JONES N. Influence of stress waves on the dynamic progressive and dynamic plastic buckling of cylindrical shells [J]. International Journal of Solids and Structures, 2001, 38(38−39): 6723–6749. DOI: 10.1016/S0020-7683(01)00111-1.
    [158] KARAGIOZOVA D, ALVES M. Transition from progressive buckling to global bending of circular shells under axial impact: Part Ⅰ: experimental and numerical observations [J]. International Journal of Solids and Structures, 2004, 41(5−6): 1565–1580. DOI: 10.1016/j.ijsolstr.2003.10.005.
    [159] KARAGIOZOVA D, JONES N. Dynamic buckling of elastic-plastic square tubes under axial impact: Ⅱ: structural response [J]. International Journal of Impact Engineering, 2004, 30(2): 167–192. DOI: 10.1016/S0734-743X(03)00062-9.
    [160] ABDUL-LATIF A, BALEH R. Dynamic biaxial plastic buckling of circular shells [J]. Journal of Applied Mechanics, 2008, 75(3): 31013. DOI: 10.1115/1.2839686.
    [161] WILLIAMS B W, SIMHA C H M, ABEDRABBO N, et al. Effect of anisotropy, kinematic hardening, and strain-rate sensitivity on the predicted axial crush response of hydroformed aluminium alloy tubes [J]. International Journal of Impact Engineering, 2010, 37(6): 652–661. DOI: 10.1016/J.IJIMPENG.2009.10.010.
    [162] RAJABIEHFARD R, DARVIZEH A, DARVIZEH M, et al. Theoretical and experimental analysis of elastic-plastic cylindrical shells under two types of axial impacts [J]. Thin-Walled Structures, 2016, 107: 315–326. DOI: 10.1016/j.tws.2015.12.014.
    [163] KULEYIN H, GÜMRÜK R. Pressure wave propagation in pressurized thin-walled circular tubes under axial impact [J]. International Journal of Impact Engineering, 2019, 130: 138–152. DOI: 10.1016/J.IJIMPENG.2019.04.015.
    [164] ZHANG X W, YU T X. Energy absorption of pressurized thin-walled circular tubes under axial crushing [J]. International Journal of Mechanical Sciences, 2009, 51(5): 335–349. DOI: 10.1016/j.ijmecsci.2009.03.002.
    [165] ZHANG X, ZHANG H, YANG C Y, et al. Static and dynamic axial crushing of self-locking multi-cell tubes [J]. International Journal of Impact Engineering, 2019, 127: 17–30. DOI: 10.1016/j.ijimpeng.2019.01.002.
    [166] BAMBACH M R. Behaviour and design of aluminium hollow sections subjected to transverse blast loads [J]. Thin-Walled Structures, 2008, 46(12): 1370–1381. DOI: 10.1016/j.tws.2008.03.010.
    [167] JAMA H H, NURICK G N, BAMBACH M R, et al. Steel square hollow sections subjected to transverse blast loads [J]. Thin-Walled Structures, 2012, 53: 109–122. DOI: 10.1016/j.tws.2012.01.007.
    [168] KARAGIOZOVA D, YU T X, LU G. Transverse blast loading of hollow beams with square cross-sections [J]. Thin-Walled Structures, 2013, 62: 169–178. DOI: 10.1016/j.tws.2012.09.004.
    [169] KARAGIOZOVA D, YU T X, LU G, et al. Response of a circular metallic hollow beam to an impulsive loading [J]. Thin-Walled Structures, 2014, 80: 80–90. DOI: 10.1016/j.tws.2014.02.021.
    [170] KARAGIOZOVA D M A. On the saturated impulse for a circular hollow beam under pressure pulse loading [J]. International Journal of Impact Engineering, 2021, 156(2): 103958. DOI: 10.1016/j.ijimpeng.2021.103958.
    [171] LI S Q, YU B L, KARAGIOZOVA D, et al. Experimental, numerical, and theoretical studies of the response of short cylindrical stainless steel tubes under lateral air blast loading [J]. International Journal of Impact Engineering, 2019, 124: 48–60. DOI: 10.1016/j.ijimpeng.2018.10.004.
    [172] 陈勇, 纪冲, 龙源, 等. 爆炸荷载下不同壁厚圆柱壳动力学行为的研究 [J]. 高压物理学报, 2014, 28(5): 525–532. DOI: 10.11858/gywlxb.2014.05.003.

    CHEN Y, JI C, LONG Y, et al. Research on dynamic behaviors of cylindrical shells with different wall-thickness under explosion loading [J]. Chinese Journal of High Pressure Physics, 2014, 28(5): 525–532. DOI: 10.11858/gywlxb.2014.05.003.
    [173] 宋克健, 龙源, 纪冲, 等. 薄壁方管结构在爆炸荷载作用下动力响应及破坏模式分析 [J]. 振动与冲击, 2016, 35(10): 133–138. DOI: 10.13465/j.cnki.jvs.2016.10.021.

    SONG K J, LONG Y, JI C, et al. Dynamic responses and damage modes of thin-walled square tubes subjected to explosion loading [J]. Journal of Vibration and Shock, 2016, 35(10): 133–138. DOI: 10.13465/j.cnki.jvs.2016.10.021.
    [174] 余洋, 纪冲, 周游, 等. 侧向局部爆炸荷载下钢质方管的损伤破坏及影响因素研究 [J]. 振动与冲击, 2018, 37(15): 191–198. DOI: 10.13465/j.cnki.jvs.2018.15.027.

    YU Y, JI C, ZHOU Y, et al. Damage and failure of steel square tubes under lateral local explosion loading and their influencing factors [J]. Journal of Vibration and Shock, 2018, 37(15): 191–198. DOI: 10.13465/j.cnki.jvs.2018.15.027.
    [175] JONES N, BIRCH R S. Low-velocity impact of pressurised pipelines [J]. International Journal of Impact Engineering, 2010, 37(2): 207–219. DOI: 10.1016/j.ijimpeng.2009.05.006.
    [176] ZEINODDINI M, HARDING J E, PARKE G A R. Axially pre-loaded steel tubes subjected to lateral impacts: a numerical simulation [J]. International Journal of Impact Engineering, 2008, 35(11): 1267–1279. DOI: 10.1016/j.ijimpeng.2007.08.002.
    [177] KRISTOFFERSEN M, CASADEI F, BØRVIK T, et al. Impact against empty and water-filled X65 steel pipes: experiments and simulations [J]. International Journal of Impact Engineering, 2014, 71: 73–88. DOI: 10.1016/J.IJIMPENG.2014.04.004.
    [178] MADULIAT S, NGO T D, TRAN P, et al. Performance of hollow steel tube bollards under quasi-static and lateral impact load [J]. Thin-Walled Structures, 2015, 88: 41–47. DOI: 10.1016/j.tws.2014.11.024.
    [179] ZHU L, LIU Q Y, JONES N, et al. Experimental study on the deformation of fully clamped pipes under lateral impact [J]. International Journal of Impact Engineering, 2018, 111: 94–105. DOI: 10.1016/j.ijimpeng.2017.09.008.
    [180] ZHANG R, ZHI X D, FAN F. Plastic behavior of circular steel tubes subjected to low-velocity transverse impact [J]. International Journal of Impact Engineering, 2018, 114: 1–19. DOI: 10.1016/j.ijimpeng.2017.12.003.
    [181] DO Q T, MUTTAQIE T, SHIN H K, et al. Dynamic lateral mass impact on steel stringer-stiffened cylinders [J]. International Journal of Impact Engineering, 2018, 116: 105–126. DOI: 10.1016/j.ijimpeng.2018.02.007.
    [182] LU G Y, ZHANG S Y, LEI J P, et al. Dynamic responses and damages of water-filled pre-pressurized metal tube impacted by mass [J]. International Journal of Impact Engineering, 2007, 34(10): 1594–1601. DOI: 10.1016/j.ijimpeng.2006.07.006.
    [183] LU G Y, LEI J P, HAN Z J, et al. Denting and failure of liquid-filled tubes under lateral impact [J]. Acta Mechanica Solida Sinica, 2012, 25(6): 609–615. DOI: 10.1016/S0894-9166(12)60056-1.
    [184] REN Y T, QIU X M, YU T X. Theoretical analysis of the static and dynamic response of tensor skin [J]. International Journal of Impact Engineering, 2014, 64: 75–90. DOI: 10.1016/j.ijimpeng.2013.10.006.
    [185] REN Y T, QIU X M, YU T X. The sensitivity analysis of a geometrically unstable structure under various pulse loading [J]. International Journal of Impact Engineering, 2014, 70: 62–72. DOI: 10.1016/j.ijimpeng.2014.03.005.
    [186] GUPTA N K, VENKATESH. Experimental and numerical studies of dynamic axial compression of thin walled spherical shells [J]. International Journal of Impact Engineering, 2004, 30(8−9): 1225–1240. DOI: 10.1016/J.IJIMPENG.2004.03.009.
    [187] GUPTA N K, MOHAMED SHERIFF N, VELMURUGAN R. Experimental and numerical investigations into collapse behaviour of thin spherical shells under drop hammer impact [J]. International Journal of Solids and Structures, 2007, 44(10): 3136–3155. DOI: 10.1016/j.ijsolstr.2006.09.014.
    [188] 路国运, 秦斌, 张国权, 等. 冲击作用下夹层充液薄壁半球壳组合结构的动力响应 [J]. 爆炸与冲击, 2012, 32(6): 561–567. DOI: 10.11883/1001-1455(2012)06-0561-07.

    LU G Y, QIN B, ZHANG G Q, et al. Dynamic responses of liquid-filled thin-wall hemispherical shells under impact [J]. Explosion and Shock Waves, 2012, 32(6): 561–567. DOI: 10.11883/1001-1455(2012)06-0561-07.
    [189] YANG H W, GUAN W B, LU G Y. Experimental and numerical investigations into collapse behavior of hemispherical shells under drop hammer impact [J]. Thin-Walled Structures, 2018, 124: 48–57. DOI: 10.1016/j.tws.2017.11.034.
    [190] ZHANG Y H, WU X D, LU G Y, et al. Experimental and numerical studies on dynamic responses of liquid-filled hemispherical shell under axial impact [J]. Thin-Walled Structures, 2018, 131: 606–618. DOI: 10.1016/j.tws.2018.07.003.
    [191] 刘文祥, 张德志, 钟方平, 等. 爆炸下球壳变形空间周期分布的理论计算方法 [J]. 爆炸与冲击, 2020, 40(6): 064201. DOI: 10.11883/bzycj-2019-0340.

    LIU W X, ZHANG D Z, ZHONG F P, et al. A theoretical method for calculating spatial periodic distribution of deformation of a spherical shell under explosive loading [J]. Explosion and Shock Waves, 2020, 40(6): 064201. DOI: 10.11883/bzycj-2019-0340.
    [192] RUAN H H, GAO Z Y, YU T X. Crushing of thin-walled spheres and sphere arrays [J]. International Journal of Mechanical Sciences, 2006, 48(2): 117–133. DOI: 10.1016/j.ijmecsci.2005.08.006.
    [193] DONG X L, GAO Z Y, YU T X. Dynamic crushing of thin-walled spheres: an experimental study [J]. International Journal of Impact Engineering, 2008, 35(8): 717–726. DOI: 10.1016/j.ijimpeng.2007.11.004.
    [194] ZHANG X W, YU T X. Experimental and numerical study on the dynamic buckling of ping-pong balls under impact loading [J]. International Journal of Nonlinear Sciences and Numerical Simulation, 2012, 13(1): 81–92.
    [195] KARAGIOZOVA D, ZHANG X W, YU T X. Static and dynamic snap-through behaviour of an elastic spherical shell [J]. Acta Mechanica Sinica, 2012, 28(3): 695–710. DOI: 10.1007/s10409-012-0065-z.
    [196] LI J Q, REN H L, NING J G. Deformation and failure of thin spherical shells under dynamic impact loading: experiment and analytical model [J]. Thin-Walled Structures, 2021, 161: 107403. DOI: 10.1016/j.tws.2020.107403.
    [197] HU J X, LU G Y, YANG H W, et al. Dynamic response of internally nested hemispherical shell system to impact loading [J]. Thin-Walled Structures, 2017, 120: 29–37. DOI: 10.1016/j.tws.2017.08.009.
    [198] 翟希梅, 王永辉. 爆炸荷载下网壳结构的动力响应及泄爆措施 [J]. 爆炸与冲击, 2012, 32(4): 404–410. DOI: 10.11883/1001-1455(2012)04-0404-07.

    ZHAI X M, WANG Y H. Dynamic response and explosion relief of reticulated shell under blast loading [J]. Explosion and Shock Waves, 2012, 32(4): 404–410. DOI: 10.11883/1001-1455(2012)04-0404-07.
    [199] 王多智, 范峰, 支旭东, 等. 冲击荷载下单层球面网壳的失效机理 [J]. 爆炸与冲击, 2010, 30(2): 169–177. DOI: 10.11883/1001-1455(2010)02-0169-09.

    WANG D Z, FAN F, ZHI X D, et al. Failure mechanism of single-layer reticulated domes subjected to impact loads [J]. Explosion And Shock Waves, 2010, 30(2): 169–177. DOI: 10.11883/1001-1455(2010)02-0169-09.
    [200] 王多智, 范峰, 支旭东, 等. 冲击荷载下网壳结构的失效模式及其动力响应特性 [J]. 工程力学, 2014, 31(5): 180–189. DOI: 10.6052/j.issn.1000-4750.2012.12.0950.

    WANG D Z, FAN F, ZHI X D, et al. Failure modes and characteristics of dynamic response for reticulated shells under impact [J]. Engineering Mechanics, 2014, 31(5): 180–189. DOI: 10.6052/j.issn.1000-4750.2012.12.0950.
    [201] DONG Q, LI Q M, ZHENG J Y. Further study on strain growth in spherical containment vessels subjected to internal blast loading [J]. International Journal of Impact Engineering, 2010, 37(2): 196–206. DOI: 10.1016/j.ijimpeng.2009.09.001.
    [202] DONG Q, LI Q M, ZHENG J Y. Interactive mechanisms between the internal blast loading and the dynamic elastic response of spherical containment vessels [J]. International Journal of Impact Engineering, 2010, 37(4): 349–358. DOI: 10.1016/j.ijimpeng.2009.10.004.
    [203] CHEN Y J, WU X D, ZHENG J Y, et al. Dynamic responses of discrete multi-layered explosion containment vessels with the consideration of strain-hardening and strain-rate effects [J]. International Journal of Impact Engineering, 2010, 37(7): 842–853. DOI: 10.1016/j.ijimpeng.2009.11.011.
    [204] LANGDON G S, OZINSKY A, YUEN S C K. The response of partially confined right circular stainless steel cylinders to internal air-blast loading [J]. International Journal of Impact Engineering, 2014, 73: 1–14. DOI: 10.1016/j.ijimpeng.2014.05.002.
    [205] 刘文祥, 谭书舜, 景吉勇, 等. 球形爆炸容器的内部载荷和响应特性 [J]. 爆炸与冲击, 2013, 33(6): 594–600. DOI: 10.11883/1001-1455(2013)06-0594-07.

    LIU W X, TAN S S, JING J Y, et al. Internal loads and structure responses of spherical explosive vessel [J]. Explosion and Shock Waves, 2013, 33(6): 594–600. DOI: 10.11883/1001-1455(2013)06-0594-07.
    [206] 崔云霄, 胡永乐, 王春明, 等. 内部爆炸作用下多层钢筒的动态响应 [J]. 爆炸与冲击, 2015, 35(6): 820–824. DOI: 10.11883/1001-1455(2015)06-0820-05.

    CUI Y X, HU Y L, WANG C M, et al. Dynamic response of multi-layer steel cylinder under internal intense blast loading [J]. Explosion and Shock Waves, 2015, 35(6): 820–824. DOI: 10.11883/1001-1455(2015)06-0820-05.
    [207] 姚术健, 张舵, 郑监, 等. 内部爆炸作用下钢箱结构变形规律性实验 [J]. 爆炸与冲击, 2017, 37(5): 964–968. DOI: 10.11883/1001-1455(2017)05-0964-05.

    YAO S J, ZHANG D, ZHENG J, et al. Experimental study of deformation of steel box subjected to internal blast loading [J]. Explosion and Shock Waves, 2017, 37(5): 964–968. DOI: 10.11883/1001-1455(2017)05-0964-05.
    [208] WANG X Y, WANG S S, MA F. Experimental study on the expansion of metal cylinders by detonation [J]. International Journal of Impact Engineering, 2018, 114: 147–152. DOI: 10.1016/j.ijimpeng.2017.12.017.
    [209] LIU X, GU W B, LIU J Q, et al. Dynamic response of cylindrical explosion containment vessels subjected to internal blast loading [J]. International Journal of Impact Engineering, 2020, 135: 103389. DOI: 10.1016/j.ijimpeng.2019.103389.
    [210] CHEN Z F, LI X Y, WANG W, et al. Dynamic burst pressure analysis of cylindrical shells based on average shear stress yield criterion [J]. Thin-Walled Structures, 2020, 148: 106498. DOI: 10.1016/j.tws.2019.106498.
    [211] KARAC A, IVANKOVIC A. Investigating the behaviour of fluid-filled polyethylene containers under base drop impact: a combined experimental/numerical approach [J]. International Journal of Impact Engineering, 2009, 36(4): 621–631. DOI: 10.1016/j.ijimpeng.2008.08.007.
    [212] CAO Y, JIN X L. Dynamic response of flexible container during the impact with the ground [J]. International Journal of Impact Engineering, 2010, 37(10): 999–1007. DOI: 10.1016/j.ijimpeng.2010.05.001.
    [213] TILLETT J P A. A study of the impact of spheres on plates [J]. Proceedings of the Physical Society: Section B, 1954, 67(9): 677–688. DOI: 10.1088/0370-1301/67/9/304.
    [214] HUNTER S C. Energy absorbed by elastic waves during impact [J]. Journal of the Mechanics and Physics of Solids, 1957, 5(3): 162–171. DOI: 10.1016/0022-5096(57)90002-9.
    [215] REED J. Energy losses due to elastic wave propagation during an elastic impact [J]. Journal of Physics D: Applied Physics, 1985, 18(12): 2329–2337. DOI: 10.1088/0022-3727/18/12/004.
    [216] HUTCHINGS I M. Energy absorbed by elastic waves during plastic impact [J]. Journal of Physics D: Applied Physics, 1979, 12(11): 1819–1824. DOI: 10.1088/0022-3727/12/11/010.
    [217] THORNTON C. Coefficient of restitution for collinear collisions of elastic-perfectly plastic spheres [J]. Journal of Applied Mechanics, 1997, 64(2): 383–386. DOI: 10.1115/1.2787319.
    [218] WU C Y, LI L Y, THORNTON C. Rebound behaviour of spheres for plastic impacts [J]. International Journal of Impact Engineering, 2003, 28(9): 929–946. DOI: 10.1016/S0734-743X(03)00014-9.
    [219] WU C Y, LI L Y, THORNTON C. Energy dissipation during normal impact of elastic and elastic-plastic spheres [J]. International Journal of Impact Engineering, 2005, 32(1−4): 593–604. DOI: 10.1016/j.ijimpeng.2005.08.007.
    [220] VU-QUOC L, ZHANG X. An elastoplastic contact force-displacement model in the normal direction: displacement-driven version [J]. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 1999, 455(1991): 4013–4044. DOI: 10.1098/rspa.1999.0488.
    [221] VU-QUOC L, ZHANG X, LESBURG L. A normal force-displacement model for contacting spheres accounting for plastic deformation: force-driven formulation [J]. Journal of Applied Mechanics, 2000, 67(2): 363–371. DOI: 10.1115/1.1305334.
    [222] ZHANG X, VU-QUOC L. Modeling the dependence of the coefficient of restitution on the impact velocity in elasto-plastic collisions [J]. International Journal of Impact Engineering, 2002, 27(3): 317–341. DOI: 10.1016/S0734-743X(01)00052-5.
    [223] STRONGE W J. Theoretical coefficient of restitution for planer impact of rough elasto-plastic bodies: CONF-950686-TRN: 95: 006111-0385 [R]. Los Angeles, CA, United States: University of California, 1995.
    [224] STRONGE W J. Impact mechanics [M]. Cambridge: Cambridge University Press, 2000.
    [225] MINAMOTO H, KAWAMURA S. Effects of material strain rate sensitivity in low speed impact between two identical spheres [J]. International Journal of Impact Engineering, 2009, 36(5): 680–686. DOI: 10.1016/j.ijimpeng.2008.10.001.
    [226] MINAMOTO H, KAWAMURA S. Moderately high speed impact of two identical spheres [J]. International Journal of Impact Engineering, 2011, 38(2−3): 123–129. DOI: 10.1016/J.IJIMPENG.2010.09.005.
    [227] ARGATOV I I. Asymptotic modeling of the impact of a spherical indenter on an elastic half-space [J]. International Journal of Solids and Structures, 2008, 45(18−19): 5035–5048. DOI: 10.1016/J.IJSOLSTR.2008.05.003.
    [228] DU Y C, WANG S L, ZHANG J L. Energy dissipation in collision of two balls covered by fine particles [J]. International Journal of Impact Engineering, 2010, 37(3): 309–316. DOI: 10.1016/j.ijimpeng.2009.06.011.
    [229] JACKSON R L, GREEN I, MARGHITU D B. Predicting the coefficient of restitution of impacting elastic-perfectly plastic spheres [J]. Nonlinear Dynamics, 2010, 60(3): 217–229. DOI: 10.1007/s11071-009-9591-z.
    [230] MURAKAMI R, HAYAKAWA H. Effect of elastic vibrations on normal head-on collisions of isothermal spheres [J]. Physical Review E, 2014, 89(1): 012205. DOI: 10.1103/PhysRevE.89.012205.
    [231] MÜLLER P, HECKEL M, SACK A, et al. Complex velocity dependence of the coefficient of restitution of a bouncing ball [J]. Physical Review Letters, 2013, 110(25): 254301. DOI: 10.1103/PhysRevLett.110.254301.
    [232] BÖTTCHER R, MÜLLER P, TRÜE M, et al. Energy dissipation due to flexural waves during impacts [J]. Chemie Ingenieur Technik, 2016, 88(7): 1002–1011. DOI: 10.1002/cite.201500155.
    [233] BOETTCHER R, KUNIK M, EICHMANN S, et al. Revisiting energy dissipation due to elastic waves at impact of spheres on large thick plates [J]. International Journal of Impact Engineering, 2017, 104: 45–54. DOI: 10.1016/j.ijimpeng.2017.02.012.
    [234] PARRA J A, ALONSO J, PACIOS A, et al. Effective energy applied to a glass plate during an impact test [J]. International Journal of Impact Engineering, 2019, 130: 11–18. DOI: 10.1016/j.ijimpeng.2019.03.008.
    [235] YU T X, YANG J L, REID S R. Deformable body impact: dynamic plastic behaviour of a moving free-free beam striking the tip of a cantilever beam [J]. International Journal of Solids and Structures, 2001, 38(2): 261–287. DOI: 10.1016/S0020-7683(00)00019-6.
    [236] YANG J L, YU T X. Dynamic plastic behavior of a free-rotating hinged beam striking a cantilever beam [J]. Mechanics of Structures and Machines, 2001, 29(3): 391–409. DOI: 10.1081/SME-100105657.
    [237] RUAN H H, YU T X. Local deformation models in analyzing beam-on-beam collisions [J]. International Journal of Mechanical Sciences, 2003, 45(3): 397–423. DOI: 10.1016/S0020-7403(03)00082-1.
    [238] RUAN H H, YU T X, HUA Y L. Plastic modal approximations in analyzing beam-on-beam collisions [J]. International Journal of Solids and Structures, 2003, 40(12): 2937–2956. DOI: 10.1016/S0020-7683(03)00098-2.
    [239] RUAN H H, YU T X. Collision between a ring and a beam [J]. International Journal of Mechanical Sciences, 2003, 45(10): 1751–1780. DOI: 10.1016/j.ijmecsci.2003.09.025.
    [240] RUAN H H, YU T X. Collision between mass-spring systems [J]. International Journal of Impact Engineering, 2005, 31(3): 267–288. DOI: 10.1016/j.ijimpeng.2003.11.003.
    [241] RUAN H H, YU T X. Experimental study of collision between a free-free beam and a simply supported beam [J]. International Journal of Impact Engineering, 2005, 32(1−4): 416–443. DOI: 10.1016/j.ijimpeng.2005.03.003.
    [242] YANG J L, LU G Y, YU T X, et al. Experimental study and numerical simulation of pipe-on-pipe impact [J]. International Journal of Impact Engineering, 2009, 36(10−11): 1259–1268. DOI: 10.1016/j.ijimpeng.2009.05.001.
    [243] BAO R H, YU T X. Impact and rebound of an elastic–plastic ring on a rigid target [J]. International Journal of Mechanical Sciences, 2015, 91: 55–63. DOI: 10.1016/j.ijmecsci.2014.03.031.
    [244] 李凤云, 吴志鹏, 郑宇轩, 等. 弹性圆环在刚壁上的撞击回弹 [J]. 振动与冲击, 2018, 37(11): 12–17; 26. DOI: 10.13465/j.cnki.jvs.2018.11.003.

    LI F Y, WU Z P, ZHENG Y X, et al. An elastic ring impacting against a rigid wall and rebounding [J]. Journal of Vibration and Shock, 2018, 37(11): 12–17; 26. DOI: 10.13465/j.cnki.jvs.2018.11.003.
    [245] WANG Y, YANG Y L, WANG S, et al. Dynamic behavior of circular ring impinging on ideal elastic wall: analytical model and experimental validation [J]. International Journal of Impact Engineering, 2018, 122: 148–160. DOI: 10.1016/J.IJIMPENG.2018.07.009.
    [246] XU S Q, RUAN D, LU G X, et al. Collision and rebounding of circular rings on rigid target [J]. International Journal of Impact Engineering, 2015, 79: 14–21. DOI: 10.1016/j.ijimpeng.2014.07.005.
    [247] ZHANG X W, FU R, YU T X. Experimental study on static/dynamic local buckling of ping pong balls compressed onto a rigid plate [C]//Proceedings of SPIE 7522, Fourth International Conference on Experimental Mechanics. Singapore: SPIE, 2010: 75220Z. DOI: 10.1117/12.851435.
    [248] BAO R H, YU T X. Collision and rebound of ping pong balls on a rigid target [J]. Materials and Design, 2015, 87: 278–286. DOI: 10.1016/j.matdes.2015.08.019.
    [249] CROSS R. The bounce of a ball [J]. American Journal of Physics, 1999, 67(3): 222–227. DOI: 10.1119/1.19229.
    [250] CROSS R. Measurements of the horizontal coefficient of restitution for a superball and a tennis ball [J]. American Journal of Physics, 2002, 70(5): 482–489. DOI: 10.1119/1.1450571.
    [251] CROSS R. Impact behavior of hollow balls [J]. American Journal of Physics, 2014, 82(3): 189–195. DOI: 10.1119/1.4839055.
    [252] CROSS R. Impact of sports balls with striking implements [J]. Sports Engineering, 2014, 17(1): 3–22. DOI: 10.1007/s12283-013-0132-0.
    [253] CROSS R. Impact behavior of a superball [J]. American Journal of Physics, 2015, 83(3): 238–248. DOI: 10.1119/1.4898312.
    [254] HUBBARD M, STRONGE W J. Bounce of hollow balls on flat surfaces [J]. Sports Engineering, 2001, 4(2): 49–61. DOI: 10.1046/j.1460-2687.2001.00073.x.
    [255] ZHAO Y F, SUN Z L, YU Z L. Procedure for studying the repeated contacts and separations in an axial impact involving a non-uniform elastic bar [J]. International Journal of Impact Engineering, 2016, 95: 133–140. DOI: 10.1016/j.ijimpeng.2016.05.006.
    [256] LUNDBERG B, RASTEMO T, HUO J. Effect of pre-impact waves in an elastic rod on coefficient of restitution [J]. International Journal of Impact Engineering, 2021, 151: 103816. DOI: 10.1016/j.ijimpeng.2021.103816.
    [257] GHEADNIA H, CERMIK O, MARGHITU D B. Experimental and theoretical analysis of the elasto-plastic oblique impact of a rod with a flat [J]. International Journal of Impact Engineering, 2015, 86: 307–317. DOI: 10.1016/j.ijimpeng.2015.08.007.
    [258] WANG S, WANG Y, HUANG Z L, et al. Dynamic behavior of elastic bars and beams impinging on ideal springs [J]. Journal of Applied Mechanics, 2016, 83(3): 031002. DOI: 10.1115/1.4032048.
    [259] RUAN H H, YU T X. The unexpectedly small coefficient of restitution of a two-degree-of-freedom mass-spring system and its implications [J]. International Journal of Impact Engineering, 2016, 88: 1–11. DOI: 10.1016/j.ijimpeng.2015.09.005.
    [260] KUNINAKA H, HAYAKAWA H. Anomalous behavior of the coefficient of normal restitution in oblique impact [J]. Physical Review Letters, 2004, 93(15): 154301. DOI: 10.1103/PhysRevLett.93.154301.
    [261] KUNINAKA H, HAYAKAWA H. Simulation of cohesive head-on collisions of thermally activated nanoclusters [J]. Physical Review E, 2009, 79(3): 031309. DOI: 10.1103/PhysRevE.79.031309.
    [262] XU F X, ZHANG X, ZHANG H. A review on functionally graded structures and materials for energy absorption [J]. Engineering Structures, 2018, 171: 309–325. DOI: 10.1016/j.engstruct.2018.05.094.
    [263] SUN Y L, LI Q M. Dynamic compressive behaviour of cellular materials: a review of phenomenon, mechanism and modelling [J]. International Journal of Impact Engineering, 2018, 112: 74–115. DOI: 10.1016/j.ijimpeng.2017.10.006.
    [264] WANG Y L, YU Y, WANG C Y, et al. On the out-of-plane ballistic performances of hexagonal, reentrant, square, triangular and circular honeycomb panels [J]. International Journal of Mechanical Sciences, 2020, 173: 105402. DOI: 10.1016/j.ijmecsci.2019.105402.
    [265] ZHANG W, YIN S, YU T X, et al. Crushing resistance and energy absorption of pomelo peel inspired hierarchical honeycomb [J]. International Journal of Impact Engineering, 2019, 125: 163–172. DOI: 10.1016/j.ijimpeng.2018.11.014.
    [266] GALEHDARI S A, KADKHODAYAN M, HADIDI-MOUD S. Low velocity impact and quasi-static in-plane loading on a graded honeycomb structure; experimental, analytical and numerical study [J]. Aerospace Science and Technology, 2015, 47: 425–433. DOI: 10.1016/j.ast.2015.10.010.
    [267] WANG X, ZHANG P, LUDWICK S, et al. Natural frequency optimization of 3D printed variable-density honeycomb structure via a homogenization-based approach [J]. Additive Manufacturing, 2018, 20: 189–198. DOI: 10.1016/j.addma.2017.10.001.
    [268] IMBALZANO G, LINFORTH S, NGO T D, et al. Blast resistance of auxetic and honeycomb sandwich panels: comparisons and parametric designs [J]. Composite Structures, 2018, 183: 242–261. DOI: 10.1016/j.compstruct.2017.03.018.
    [269] RUAN D, LU G X, WANG B, et al. In-plane dynamic crushing of honeycombs: a finite element study [J]. International Journal of Impact Engineering, 2003, 28(2): 161–182. DOI: 10.1016/S0734-743X(02)00056-8.
    [270] WANG H, LU Z X, YANG Z Y, et al. A novel re-entrant auxetic honeycomb with enhanced in-plane impact resistance [J]. Composite Structures, 2019, 208: 758–770. DOI: 10.1016/j.compstruct.2018.10.024.
    [271] LU G X, YU T X. Energy absorption of structures and materials [M]. Cambridge: Woodhead Publishing Limited, 2003.
    [272] SHEN C J, LU G X, YU T X. Dynamic behavior of graded honeycombs: a finite element study [J]. Composite Structures, 2013, 98: 282–293. DOI: 10.1016/j.compstruct.2012.11.002.
    [273] MOUSANEZHAD D, GHOSH R, AJDARI A, et al. Impact resistance and energy absorption of regular and functionally graded hexagonal honeycombs with cell wall material strain hardening [J]. International Journal of Mechanical Sciences, 2014, 89: 413–422. DOI: 10.1016/j.ijmecsci.2014.10.012.
    [274] GIBSON L J, ASHBY M F. Cellular solids: structure and properties [M]. Cambridge, UK: Cambridge University Press, 1997.
    [275] WIERZBICKI T. Crushing analysis of metal honeycombs [J]. International Journal of Impact Engineering, 1983, 1(2): 157–174. DOI: 10.1016/0734-743X(83)90004-0.
    [276] ZHANG X, HUH H. Crushing analysis of polygonal columns and angle elements [J]. International Journal of Impact Engineering, 2010, 37(4): 441–451. DOI: 10.1016/j.ijimpeng.2009.06.009.
    [277] ZHANG X, ZHANG H. Experimental and numerical investigation on crush resistance of polygonal columns and angle elements [J]. Thin-Walled Structures, 2012, 57: 25–36. DOI: 10.1016/j.tws.2012.04.006.
    [278] WIERZBICKI T, ABRAMOWICZ W. On the crushing mechanics of thin-walled structures [J]. Journal of Applied Mechanics, 1983, 50(4a): 727–734. DOI: 10.1115/1.3167137.
    [279] ZHANG X, ZHANG H. Theoretical and numerical investigation on the crush resistance of rhombic and kagome honeycombs [J]. Composite Structures, 2013, 96: 143–152. DOI: 10.1016/j.compstruct.2012.09.028.
    [280] HU L L, HE X L, WU G P, et al. Dynamic crushing of the circular-celled honeycombs under out-of-plane impact [J]. International Journal of Impact Engineering, 2015, 75: 150–161. DOI: 10.1016/j.ijimpeng.2014.08.008.
    [281] ALEXANDER J M. An approximate analysis of the collapse of thin cylindrical shells under axial loading [J]. The Quarterly Journal of Mechanics and Applied Mathematics, 1960, 13(1): 10–15. DOI: 10.1093/qjmam/13.1.10.
    [282] REID S R, PENG C. Dynamic uniaxial crushing of wood [J]. International Journal of Impact Engineering, 1997, 19(5−6): 531–570. DOI: 10.1016/S0734-743X(97)00016-X.
    [283] ZOU Z, REID S R, TAN P J, et al. Dynamic crushing of honeycombs and features of shock fronts [J]. International Journal of Impact Engineering, 2009, 36(1): 165–176. DOI: 10.1016/j.ijimpeng.2007.11.008.
    [284] HU L L, YU T X. Dynamic crushing strength of hexagonal honeycombs [J]. International Journal of Impact Engineering, 2010, 37(5): 467–474. DOI: 10.1016/j.ijimpeng.2009.12.001.
    [285] HU L L, YU T X. Mechanical behavior of hexagonal honeycombs under low-velocity impact: theory and simulations [J]. International Journal of Solids and Structures, 2013, 50(20−21): 3152–3165. DOI: 10.1016/j.ijsolstr.2013.05.017.
    [286] HU L L, YOU F F, YU T X. Effect of cell-wall angle on the in-plane crushing behaviour of hexagonal honeycombs [J]. Materials and Design, 2013, 46: 511–523. DOI: 10.1016/J.MATDES.2012.10.050.
    [287] TAO Y, CHEN M J, PEI Y M, et al. Strain rate effect on mechanical behavior of metallic honeycombs under out-of-plane dynamic compression [J]. Journal of Applied Mechanics, 2015, 82(2). DOI: 10.1115/1.4029471.
    [288] TAO Y, CHEN M J, CHEN H S, et al. Strain rate effect on the out-of-plane dynamic compressive behavior of metallic honeycombs: experiment and theory [J]. Composite Structures, 2015, 132: 644–651. DOI: 10.1016/j.compstruct.2015.06.015.
    [289] TAO Y, DUAN S Y, WEN W B, et al. Enhanced out-of-plane crushing strength and energy absorption of in-plane graded honeycombs [J]. Composites Part B: Engineering, 2017, 118: 33–40. DOI: 10.1016/j.compositesb.2017.03.002.
    [290] QIAO J X, CHEN C Q. Impact resistance of uniform and functionally graded auxetic double arrowhead honeycombs [J]. International Journal of Impact Engineering, 2015, 83: 47–58. DOI: 10.1016/j.ijimpeng.2015.04.005.
    [291] ZHANG Y, CHEN T T, XU X, et al. Out-of-plane mechanical behaviors of a side hierarchical honeycomb [J]. Mechanics of Materials, 2020, 140: 103227. DOI: 10.1016/j.mechmat.2019.103227.
    [292] QIAO J X, CHEN C Q. In-plane crushing of a hierarchical honeycomb [J]. International Journal of Solids and Structures, 2016, 85−86: 57–66. DOI: 10.1016/j.ijsolstr.2016.02.003.
    [293] CHEN W S, HAO H. Experimental investigations and numerical simulations of multi-arch double-layered panels under uniform impulsive loadings [J]. International Journal of Impact Engineering, 2014, 63: 140–157. DOI: 10.1016/j.ijimpeng.2013.08.012.
    [294] MENG Y, LIN Y L, ZHANG Y W, et al. Study on the dynamic response of combined honeycomb structure under blast loading [J]. Thin-Walled Structures, 2020, 157: 107082. DOI: 10.1016/j.tws.2020.107082.
    [295] HATAMI H, RAD M S, JAHROMI A G. A theoretical analysis of the energy absorption response of expanded metal tubes under impact loads [J]. International Journal of Impact Engineering, 2017, 109: 224–239. DOI: 10.1016/j.ijimpeng.2017.06.009.
    [296] 吴文旺, 肖登宝, 孟嘉旭, 等. 负泊松比结构力学设计、抗冲击性能及在车辆工程应用与展望 [J]. 力学学报, 2021, 53(3): 611–638. DOI: 10.6052/0459-1879-20-333.

    WU W W, XIAO D B, MENG J X, et al. Mechanical design, impact energy absorption and applications of auxetic structures in automobile lightweight engineering [J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(3): 611–638. DOI: 10.6052/0459-1879-20-333.
    [297] ZHANG X C, AN L Q, DING H M, et al. The influence of cell micro-structure on the in-plane dynamic crushing of honeycombs with negative Poisson’s ratio [J]. Journal of Sandwich Structures and Materials, 2015, 17(1): 26–55. DOI: 10.1177/1099636214554180.
    [298] BAERTSCH F, AMELI A, MAYER T. Finite-element modeling and optimization of 3D-printed auxetic reentrant structures with stiffness gradient under low-velocity impact [J]. Journal of Engineering Mechanics, 2021, 147(7): 04021036. DOI: 10.1061/(ASCE)EM.1943-7889.0001923.
    [299] QIAO J X, CHEN C Q. Analyses on the in-plane impact resistance of auxetic double arrowhead honeycombs [J]. Journal of Applied Mechanics, 2015, 82(5): 051007. DOI: 10.1115/1.4030007.
    [300] GAO D W, WANG S H, ZHANG M Z, et al. Experimental and numerical investigation on in-plane impact behaviour of chiral auxetic structure [J]. Composite Structures, 2021, 267: 113922. DOI: 10.1016/j.compstruct.2021.113922.
    [301] DESHPANDE V S, FLECK N A. Isotropic constitutive models for metallic foams [J]. Journal of the Mechanics and Physics of Solids, 2000, 48(6−7): 1253–1283. DOI: 10.1016/S0022-5096(99)00082-4.
    [302] TAN P J, REID S R, HARRIGAN J J, et al. Dynamic compressive strength properties of aluminium foams: Part Ⅰ: experimental data and observations [J]. Journal of the Mechanics and Physics of Solids, 2005, 53(10): 2174–2205. DOI: 10.1016/j.jmps.2005.05.007.
    [303] TAN P J, REID S R, HARRIGAN J J, et al. Dynamic compressive strength properties of aluminium foams: Part Ⅱ: ‘shock’ theory and comparison with experimental data and numerical models [J]. Journal of the Mechanics and Physics of Solids, 2005, 53(10): 2206–2230. DOI: 10.1016/J.JMPS.2005.05.003.
    [304] HARRIGAN J J, REID S R, TAN P J, et al. High rate crushing of wood along the grain [J]. International Journal of Mechanical Sciences, 2005, 47(4−5): 521–544. DOI: 10.1016/j.ijmecsci.2004.12.013.
    [305] ZHENG Z J, LIU Y D, YU J L, et al. Dynamic crushing of cellular materials: continuum-based wave models for the transitional and shock modes [J]. International Journal of Impact Engineering, 2012, 42: 66–79. DOI: 10.1016/j.ijimpeng.2011.09.009.
    [306] DING Y Y, WANG S L, ZHAO K, et al. Blast alleviation of cellular sacrificial cladding: a nonlinear plastic shock model [J]. International Journal of Applied Mechanics, 2016, 8(4): 1650057. DOI: 10.1142/S1758825116500575.
    [307] 蔡正宇, 丁圆圆, 王士龙, 等. 梯度多胞牺牲层的抗爆炸分析 [J]. 爆炸与冲击, 2017, 37(3): 396–404. DOI: 10.11883/1001-1455(2017)03-0396-09.

    CAI Z Y, DING Y Y, WANG S L, et al. Anti-blast analysis of graded cellular sacrificial cladding [J]. Explosion and Shock Waves, 2017, 37(3): 396–404. DOI: 10.11883/1001-1455(2017)03-0396-09.
    [308] KADER M A, ISLAM M A, HAZELL P J, et al. Modelling and characterization of cell collapse in aluminium foams during dynamic loading [J]. International Journal of Impact Engineering, 2016, 96: 78–88. DOI: 10.1016/j.ijimpeng.2016.05.020.
    [309] LIAO S F, ZHENG Z J, YU J L. Dynamic crushing of 2D cellular structures: local strain field and shock wave velocity [J]. International Journal of Impact Engineering, 2013, 57: 7–16. DOI: 10.1016/j.ijimpeng.2013.01.008.
    [310] ZHENG Z J, WANG C F, YU J L, et al. Dynamic stress-strain states for metal foams using a 3D cellular model [J]. Journal of the Mechanics and Physics of Solids, 2014, 72: 93–114. DOI: 10.1016/j.jmps.2014.07.013.
    [311] LI Z Q, ZHANG J J, FAN J H, et al. On crushing response of the three-dimensional closed-cell foam based on Voronoi model [J]. Mechanics of Materials, 2014, 68: 85–94. DOI: 10.1016/j.mechmat.2013.08.009.
    [312] KOOHBOR B, KIDANE A. Design optimization of continuously and discretely graded foam materials for efficient energy absorption [J]. Materials and Design, 2016, 102: 151–161. DOI: 10.1016/J.MATDES.2016.04.031.
    [313] GUPTA N. A functionally graded syntactic foam material for high energy absorption under compression [J]. Materials Letters, 2007, 61(4−5): 979–982. DOI: 10.1016/j.matlet.2006.06.033.
    [314] ZENG H B, PATTOFATTO S, ZHAO H, et al. Impact behaviour of hollow sphere agglomerates with density gradient [J]. International Journal of Mechanical Sciences, 2010, 52(5): 680–688. DOI: 10.1016/j.ijmecsci.2009.11.012.
    [315] SHEN C J, YU T X, LU G X. Double shock mode in graded cellular rod under impact [J]. International Journal of Solids and Structures, 2013, 50(1): 217–233. DOI: 10.1016/j.ijsolstr.2012.09.021.
    [316] SHEN C J, LU G X, YU T X. Investigation into the behavior of a graded cellular rod under impact [J]. International Journal of Impact Engineering, 2014, 74: 92–106. DOI: 10.1016/j.ijimpeng.2014.02.015.
    [317] ZHANG J J, LU G X, RUAN D, et al. Experimental observations of the double shock deformation mode in density graded honeycombs [J]. International Journal of Impact Engineering, 2019, 134: 103386. DOI: 10.1016/j.ijimpeng.2019.103386.
    [318] 范华林, 杨卫. 轻质高强点阵材料及其力学性能研究进展 [J]. 力学进展, 2007, 37(1): 99–112. DOI: 10.3321/j.issn:1000-0992.2007.01.012.

    FAN H L, YANG W. Development of lattice materials with high specific stiffness and strength [J]. Advances in Mechanics, 2007, 37(1): 99–112. DOI: 10.3321/j.issn:1000-0992.2007.01.012.
    [319] 易建坤, 马翰宇, 朱建生, 等. 点阵金属夹芯结构抗爆炸冲击问题研究的综述 [J]. 兵器材料科学与工程, 2014, 37(2): 116–120. DOI: 10.14024/j.cnki.1004-244x.2014.02.010.

    YI J K, MA H Y, ZHU J S, et al. Review of explosion and shock wave resistance of metallic lattice sandwich structure [J]. Ordnance Material Science and Engineering, 2014, 37(2): 116–120. DOI: 10.14024/j.cnki.1004-244x.2014.02.010.
    [320] HUANG W, FAN Z H, ZHANG W, et al. Impulsive response of composite sandwich structure with tetrahedral truss core [J]. Composites Science and Technology, 2019, 176: 17–28. DOI: 10.1016/j.compscitech.2019.03.020.
    [321] DESHPANDE V S, ASHBY M F, FLECK N A. Foam topology: bending versus stretching dominated architectures [J]. Acta Materialia, 2001, 49(6): 1035–1040. DOI: 10.1016/S1359-6454(00)00379-7.
    [322] QIU X M, ZHANG J, YU T X. Collapse of periodic planar lattices under uniaxial compression: part Ⅰ: quasi-static strength predicted by limit analysis [J]. International Journal of Impact Engineering, 2009, 36(10−11): 1223–1230. DOI: 10.1016/J.IJIMPENG.2009.05.011.
    [323] QIU X M, ZHANG J, YU T X. Collapse of periodic planar lattices under uniaxial compression: part Ⅱ: dynamic crushing based on finite element simulation [J]. International Journal of Impact Engineering, 2009, 36(10−11): 1231–1241. DOI: 10.1016/J.IJIMPENG.2009.05.010.
    [324] DESHPANDE V S, FLECK N A, ASHBY M F. Effective properties of the octet-truss lattice material [J]. Journal of the Mechanics and Physics of Solids, 2001, 49(8): 1747–1769. DOI: 10.1016/S0022-5096(01)00010-2.
    [325] JIN N, WANG F C, WANG Y W, et al. Failure and energy absorption characteristics of four lattice structures under dynamic loading [J]. Materials and Design, 2019, 169: 107655. DOI: 10.1016/J.MATDES.2019.107655.
    [326] WALLACH J C, GIBSON L J. Mechanical behavior of a three-dimensional truss material [J]. International Journal of Solids and Structures, 2001, 38(40−41): 7181–7196. DOI: 10.1016/S0020-7683(00)00400-5.
    [327] HYUN S, KARLSSON A M, TORQUATO S, et al. Simulated properties of Kagomé and tetragonal truss core panels [J]. International Journal of Solids and Structures, 2003, 40(25): 6989–6998. DOI: 10.1016/S0020-7683(03)00350-0.
    [328] HAMMETTER C I, RINALDI R G, ZOK F W. Pyramidal lattice structures for high strength and energy absorption [J]. Journal of Applied Mechanics, 2013, 80(4): 041015. DOI: 10.1115/1.4007865.
    [329] TANCOGNE-DEJEAN T, MOHR D. Stiffness and specific energy absorption of additively-manufactured metallic BCC metamaterials composed of tapered beams [J]. International Journal of Mechanical Sciences, 2018, 141: 101–116. DOI: 10.1016/j.ijmecsci.2018.03.027.
    [330] OZDEMIR Z, HERNANDEZ-NAVA E, TYAS A, et al. Energy absorption in lattice structures in dynamics: experiments [J]. International Journal of Impact Engineering, 2016, 89: 49–61. DOI: 10.1016/j.ijimpeng.2015.10.007.
    [331] TANCOGNE-DEJEAN T, SPIERINGS A B, MOHR D. Additively-manufactured metallic micro-lattice materials for high specific energy absorption under static and dynamic loading [J]. Acta Materialia, 2016, 116: 14–28. DOI: 10.1016/j.actamat.2016.05.054.
    [332] EVANS A G, HE M Y, DESHPANDE V S, et al. Concepts for enhanced energy absorption using hollow micro-lattices [J]. International Journal of Impact Engineering, 2010, 37(9): 947–959. DOI: 10.1016/j.ijimpeng.2010.03.007.
    [333] YIN S, CHEN H Y, LI J N, et al. Effects of architecture level on mechanical properties of hierarchical lattice materials [J]. International Journal of Mechanical Sciences, 2019, 157−158: 282–292. DOI: 10.1016/j.ijmecsci.2019.04.051.
    [334] YIN S, WANG H T, HU J X, et al. Fabrication and anti-crushing performance of hollow honeytubes [J]. Composites Part B: Engineering, 2019, 179: 107522. DOI: 10.1016/j.compositesb.2019.107522.
    [335] WENDY GU X, GREER J R. Ultra-strong architected Cu meso-lattices [J]. Extreme Mechanics Letters, 2015, 2: 7–14. DOI: 10.1016/j.eml.2015.01.006.
    [336] MEZA L R, DAS S, GREER J R. Strong, lightweight, and recoverable three-dimensional ceramic nanolattices [J]. Science, 2014, 345(6202): 1322–1326. DOI: 10.1126/science.1255908.
    [337] SCHAEDLER T A, JACOBSEN A J, TORRENTS A, et al. Ultralight metallic microlattices [J]. Science, 2011, 334(6058): 962–965. DOI: 10.1126/science.1211649.
    [338] ZHANG X, VYATSKIKH A, GAO H J, et al. Lightweight, flaw-tolerant, and ultrastrong nanoarchitected carbon [J]. Proceedings of the National Academy of Sciences of the United States of America, 2019, 116(14): 6665–6672. DOI: 10.1073/pnas.1817309116.
    [339] HE Z Z, WANG F C, ZHU Y B, et al. Mechanical properties of copper octet-truss nanolattices [J]. Journal of the Mechanics and Physics of Solids, 2017, 101: 133–149. DOI: 10.1016/j.jmps.2017.01.019.
    [340] HAN S C, LEE J W, KANG K. A new type of low density material: shellular [J]. Advanced Materials, 2015, 27(37): 5506–5511. DOI: 10.1002/adma.201501546.
    [341] LEE M G, LEE J W, HAN S C, et al. Mechanical analyses of “Shellular”, an ultralow-density material [J]. Acta Materialia, 2016, 103: 595–607. DOI: 10.1016/j.actamat.2015.10.040.
    [342] CHEN X Y, JI Q X, WEI J Z, et al. Light-weight shell-lattice metamaterials for mechanical shock absorption [J]. International Journal of Mechanical Sciences, 2020, 169: 105288. DOI: 10.1016/j.ijmecsci.2019.105288.
    [343] KUSHWAHA M S, HALEVI P, DOBRZYNSKI L, et al. Acoustic band structure of periodic elastic composites [J]. Physical Review Letters, 1993, 71(13): 2022–2025. DOI: 10.1103/PhysRevLett.71.2022.
    [344] 张研, 韩林, 蒋林华, 等. 声子晶体的计算方法与带隙特性 [M]. 北京: 科学出版社, 2015.
    [345] LIU Z Y, ZHANG X X, MAO Y W, et al. Locally resonant sonic materials [J]. Science, 2000, 289(5485): 1734–1736. DOI: 10.1126/science.289.5485.1734.
    [346] DEYMIER P A. Acoustic metamaterials and phononic crystals [M]. Berlin Heidelberg: Springer, 2013. DOI: 10.1007/978-3-642-31232-8.
    [347] LIU J Y, GUO H B, WANG T. A review of acoustic metamaterials and phononic crystals [J]. Crystals, 2020, 10(4): 305. DOI: 10.3390/cryst10040305.
    [348] CUMMER S A, CHRISTENSEN J, ALÙ A. Controlling sound with acoustic metamaterials [J]. Nature Reviews Materials, 2016, 1(3): 16001. DOI: 10.1038/natrevmats.2016.1.
    [349] WANG Y F, WANG Y Z, WU B, et al. Tunable and active phononic crystals and metamaterials [J]. Applied Mechanics Reviews, 2020, 72(4): 040801. DOI: 10.1115/1.4046222.
    [350] TAN K T, HUANG H H, SUN C T. Optimizing the band gap of effective mass negativity in acoustic metamaterials [J]. Applied Physics Letters, 2012, 101(24): 241902. DOI: 10.1063/1.4770370.
    [351] XU X C, LI P, ZHOU X M, et al. Experimental study on acoustic subwavelength imaging based on zero-mass metamaterials [J]. EPL (Europhysics Letters), 2015, 109(2): 28001. DOI: 10.1209/0295-5075/109/28001.
    [352] TAN K T, HUANG H H, SUN C T. Blast-wave impact mitigation using negative effective mass density concept of elastic metamaterials [J]. International Journal of Impact Engineering, 2014, 64: 20–29. DOI: 10.1016/j.ijimpeng.2013.09.003.
    [353] XU X C, BARNHART M V, LI X P, et al. Tailoring vibration suppression bands with hierarchical metamaterials containing local resonators [J]. Journal of Sound and Vibration, 2019, 442: 237–248. DOI: 10.1016/j.jsv.2018.10.065.
    [354] CHEN Y Y, BARNHART M V, CHEN J K, et al. Dissipative elastic metamaterials for broadband wave mitigation at subwavelength scale [J]. Composite Structures, 2016, 136: 358–371. DOI: 10.1016/j.compstruct.2015.09.048.
    [355] XU X C, BARNHART M V, FANG X, et al. A nonlinear dissipative elastic metamaterial for broadband wave mitigation [J]. International Journal of Mechanical Sciences, 2019, 164: 105159. DOI: 10.1016/j.ijmecsci.2019.105159.
    [356] AIROLDI L, RUZZENE M. Design of tunable acoustic metamaterials through periodic arrays of resonant shunted piezos [J]. New Journal of Physics, 2011, 13(11): 113010. DOI: 10.1088/1367-2630/13/11/113010.
    [357] XIAO X, HE Z C, LI E, et al. A lightweight adaptive hybrid laminate metamaterial with higher design freedom for wave attenuation [J]. Composite Structures, 2020, 243: 112230. DOI: 10.1016/j.compstruct.2020.112230.
    [358] NING S W, YANG F Y, LUO C C, et al. Low-frequency tunable locally resonant band gaps in acoustic metamaterials through large deformation [J]. Extreme Mechanics Letters, 2020, 35: 100623. DOI: 10.1016/j.eml.2019.100623.
    [359] NESTERENKO V F. Propagation of nonlinear compression pulses in granular media [J]. Journal of Applied Mechanics and Technical Physics, 1983, 24(5): 733–743. DOI: 10.1007/BF00905892.
    [360] PORTER M A, KEVREKIDIS P G, DARAIO C. Granular crystals: nonlinear dynamics meets materials engineering [J]. Physics Today, 2015, 68(11): 44–50. DOI: 10.1063/PT.3.2981.
    [361] NGO D, GRIFFITHS S, KHATRI D, et al. Highly nonlinear solitary waves in chains of hollow spherical particles [J]. Granular Matter, 2013, 15(2): 149–155. DOI: 10.1007/s10035-012-0377-5.
    [362] NGO D, KHATRI D, DARAIO C. Highly nonlinear solitary waves in chains of ellipsoidal particles [J]. Physical Review E, 2011, 84(2): 026610. DOI: 10.1103/PhysRevE.84.026610.
    [363] KHATRI D, NGO D, DARAIO C. Highly nonlinear solitary waves in chains of cylindrical particles [J]. Granular Matter, 2012, 14(1): 63–69. DOI: 10.1007/s10035-011-0297-9.
    [364] BOECHLER N, THEOCHARIS G, JOB S, et al. Discrete breathers in one-dimensional diatomic granular crystals [J]. Physical Review Letters, 2010, 104(24): 244302. DOI: 10.1103/PhysRevLett.104.244302.
    [365] DARAIO C, NESTERENKO V F, HERBOLD E B, et al. Strongly nonlinear waves in a chain of Teflon beads [J]. Physical Review E, 2005, 72(1): 016603. DOI: 10.1103/PhysRevE.72.016603.
    [366] PORTER M A, DARAIO C, SZELENGOWICZ I, et al. Highly nonlinear solitary waves in heterogeneous periodic granular media [J]. Physica D: Nonlinear Phenomena, 2009, 238(6): 666–676. DOI: 10.1016/j.physd.2008.12.010.
    [367] LEONARD A, DARAIO C, AWASTHI A, et al. Effects of weak disorder on stress-wave anisotropy in centered square nonlinear granular crystals [J]. Physical Review E, 2012, 86(3): 031305. DOI: 10.1103/PhysRevE.86.031305.
    [368] BURGOYNE H A, NEWMAN J A, JACKSON W C, et al. Guided impact mitigation in 2D and 3D granular crystals [J]. Procedia Engineering, 2015, 103: 52–59. DOI: 10.1016/j.proeng.2015.04.008.
    [369] LIN W H, DARAIO C. Wave propagation in one-dimensional microscopic granular chains [J]. Physical Review E, 2016, 94(5): 052907. DOI: 10.1103/PhysRevE.94.052907.
    [370] WANG W J, ZHU Z G. Two kinds of dissipation in sheared granular materials [J]. EPL (Europhysics Letters), 2008, 82(2): 24004. DOI: 10.1209/0295-5075/82/24004.
    [371] MORGADO W A M, OPPENHEIM I. Energy dissipation for quasielastic granular particle collisions [J]. Physical Review E, 1997, 55(2): 1940–1945. DOI: 10.1103/PhysRevE.55.1940.
    [372] WANG E, ON T, LAMBROS J. An experimental study of the dynamic elasto-plastic contact behavior of dimer metallic granules [J]. Experimental Mechanics, 2013, 53(5): 883–892. DOI: 10.1007/s11340-012-9696-z.
    [373] HERBOLD E B, NESTERENKO V F. The role of dissipation on wave shape and attenuation in granular chains [J]. Physics Procedia, 2010, 3(1): 465–471. DOI: 10.1016/j.phpro.2010.01.061.
    [374] YANG J, GONZALEZ M, KIM E, et al. Attenuation of solitary waves and localization of breathers in 1D granular crystals visualized via high speed photography [J]. Experimental Mechanics, 2014, 54(6): 1043–1057. DOI: 10.1007/s11340-014-9866-2.
    [375] NESTERENKO V F. Waves in strongly nonlinear discrete systems [J]. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2018, 376(2127): 20170130. DOI: 10.1098/rsta.2017.0130.
    [376] KIM H, KIM E, CHONG C, et al. Demonstration of dispersive rarefaction shocks in hollow elliptical cylinder chains [J]. Physical Review Letters, 2018, 120(19): 194101. DOI: 10.1103/PhysRevLett.120.194101.
    [377] ZHANG W, XU J. Tunable traveling wave properties in one-dimensional chains composed from hollow cylinders: from compression to rarefaction waves [J]. International Journal of Mechanical Sciences, 2021, 191: 106073. DOI: 10.1016/j.ijmecsci.2020.106073.
    [378] 彭克锋, 崔世堂, 潘昊, 等. 冲击载荷作用下柱壳链中的弹性波传播简化模型及其解析解 [J]. 爆炸与冲击, 2021, 41(1): 011403. DOI: 10.11883/bzycj-2020-0246.

    PENG K F, CUI S T, PAN H, et al. Simplified model of elastic wave propagation in cylindrical shell chain under impact load and its analytical solution [J]. Explosion and Shock Waves, 2021, 41(1): 011403. DOI: 10.11883/bzycj-2020-0246.
    [379] ZHANG W, XU J. Universal design law of equivalent systems for Nesterenko solitary waves transmission [J]. Granular Matter, 2020, 22(2): 46. DOI: 10.1007/S10035-020-1011-6.
    [380] ZHANG W, XU J. Toward understanding solitary wave propagation in composite-cylinders-based 1D granular crystals [J]. Extreme Mechanics Letters, 2021, 43: 101156. DOI: 10.1016/j.eml.2020.101156.
    [381] YIN S, CHEN D H, XU J. Novel propagation behavior of impact stress wave in one-dimensional hollow spherical structures [J]. International Journal of Impact Engineering, 2019, 134: 103368. DOI: 10.1016/j.ijimpeng.2019.103368.
    [382] ZHANG W, XU J. Quantitatively solitary wave tuning strategies based on one-dimensional cylindrical granular chains [J]. Extreme Mechanics Letters, 2020, 40: 100972. DOI: 10.1016/j.eml.2020.100972.
    [383] CHONG C, PORTER M A, KEVREKIDIS P G, et al. Nonlinear coherent structures in granular crystals [J]. Journal of Physics: Condensed Matter, 2017, 29(41): 413003. DOI: 10.1088/1361-648X/aa7672.
    [384] KIM E, YANG J. Review: wave propagation in granular metamaterials [J]. Functional Composites and Structures, 2019, 1(1): 012002. DOI: 10.1088/2631-6331/ab0c7e.
    [385] SEN S, HONG J, BANG J, et al. Solitary waves in the granular chain [J]. Physics Reports, 2008, 462(2): 21–66. DOI: 10.1016/j.physrep.2007.10.007.
    [386] KEVREKIDIS P G. Non-linear waves in lattices: past, present, future [J]. IMA Journal of Applied Mathematics, 2011, 76(3): 389–423. DOI: 10.1093/imamat/hxr015.
    [387] 李威, 郭权锋. 碳纤维复合材料在航天领域的应用 [J]. 中国光学, 2011, 4(3): 201–212. DOI: 10.3969/j.issn.2095-1531.2011.03.001.

    LI W, GUO Q F. Application of carbon fiber composites to cosmonautic fields [J]. Chinese Optics, 2011, 4(3): 201–212. DOI: 10.3969/j.issn.2095-1531.2011.03.001.
    [388] SHAH S Z H, KARUPPANAN S, MEGAT-YUSOFF P S M, et al. Impact resistance and damage tolerance of fiber reinforced composites: a review [J]. Composite Structures, 2019, 217: 100–121. DOI: 10.1016/j.compstruct.2019.03.021.
    [389] SADIGHI M, ALDERLIESTEN R C, BENEDICTUS R. Impact resistance of fiber-metal laminates: a review [J]. International Journal of Impact Engineering, 2012, 49: 77–90. DOI: 10.1016/j.ijimpeng.2012.05.006.
    [390] SHYR T W, PAN Y H. Impact resistance and damage characteristics of composite laminates [J]. Composite Structures, 2003, 62(2): 193–203. DOI: 10.1016/S0263-8223(03)00114-4.
    [391] OLIVEIRA L, LUIZ M, TONATTO P, et al. Experimental and numerical assessment of sustainable bamboo core sandwich panels under low-velocity impact [J]. Construction and Building Materials, 2021, 292(5): 123437. DOI: 10.1016/j.conbuildmat.2021.123437.
    [392] ZHANG D H, JIANG D, FEI Q, et al. Experimental and numerical investigation on indentation and energy absorption of a honeycomb sandwich panel under low-velocity impact [J]. Finite Elements in Analysis and Design, 2016, 117−118: 21–30. DOI: 10.1016/j.finel.2016.04.003.
    [393] SUN G Y, CHEN D D, WANG H X, et al. High-velocity impact behaviour of aluminium honeycomb sandwich panels with different structural configurations [J]. International Journal of Impact Engineering, 2018, 122: 119–136. DOI: 10.1016/j.ijimpeng.2018.08.007.
    [394] FOO C C, CHAI G B, SEAH L K. A model to predict low-velocity impact response and damage in sandwich composites [J]. Composites Science and Technology, 2008, 68(6): 1348–1356. DOI: 10.1016/j.compscitech.2007.12.007.
    [395] QIN Q H, WANG T J. Low-velocity heavy-mass impact response of slender metal foam core sandwich beam [J]. Composite Structures, 2011, 93(6): 1526–1537. DOI: 10.1016/j.compstruct.2010.11.018.
    [396] XIANG C P, QIN Q H, WANG F F, et al. Impulsive response of rectangular metal sandwich plate with a graded foam core [J]. International Journal of Applied Mechanics, 2018, 10(6): 1850064. DOI: 10.1142/S1758825118500643.
    [397] ZHANG J X, YE Y, QIN Q H. On dynamic response of rectangular sandwich plates with fibre-metal laminate face-sheets under blast loading [J]. Thin-Walled Structures, 2019, 144: 106288. DOI: 10.1016/J.TWS.2019.106288.
    [398] ZHANG J X, QIN Q H, WANG T J. Compressive strengths and dynamic response of corrugated metal sandwich plates with unfilled and foam-filled sinusoidal plate cores [J]. Acta Mechanica, 2013, 224(4): 759–775. DOI: 10.1007/s00707-012-0770-5.
    [399] ZHANG J X, LIU K, YE Y, et al. Low-velocity impact of rectangular multilayer sandwich plates [J]. Thin-Walled Structures, 2019, 141: 308–318. DOI: 10.1016/j.tws.2019.04.033.
    [400] WANG Z J, QIN Q H, ZHANG J X, et al. Low-velocity impact response of geometrically asymmetric slender sandwich beams with metal foam core [J]. Composite Structures, 2013, 98: 1–14. DOI: 10.1016/j.compstruct.2012.10.054.
    [401] CRUPI V, EPASTO G, GUGLIELMINO E. Collapse modes in aluminium honeycomb sandwich panels under bending and impact loading [J]. International Journal of Impact Engineering, 2012, 43: 6–15. DOI: 10.1016/j.ijimpeng.2011.12.002.
    [402] LIU J J, ZHU W Q, YU Z L, et al. Dynamic shear-lag model for understanding the role of matrix in energy dissipation in fiber-reinforced composites [J]. Acta Biomaterialia, 2018, 74: 270–279. DOI: 10.1016/j.actbio.2018.04.031.
    [403] LIU J J, HAI X S, WEI X D. Design the wave attenuation property of nacreous composites [J]. Extreme Mechanics Letters, 2020, 40: 100875. DOI: 10.1016/J.EML.2020.100875.
    [404] TAN C Y, AKIL H M. Impact response of fiber metal laminate sandwich composite structure with polypropylene honeycomb core [J]. Composites Part B: Engineering, 2012, 43(3): 1433–1438. DOI: 10.1016/j.compositesb.2011.08.036.
    [405] SUN G Y, CHEN D D, HUO X T, et al. Experimental and numerical studies on indentation and perforation characteristics of honeycomb sandwich panels [J]. Composite Structures, 2018, 184: 110–124. DOI: 10.1016/j.compstruct.2017.09.025.
    [406] ZHOU Q, LIU S D. Mechanisms of diverting out-of-plane impact to transverse response in plate structures [J]. International Journal of Impact Engineering, 2019, 133: 103346. DOI: 10.1016/j.ijimpeng.2019.103346.
    [407] HA N S, LU G X. Thin-walled corrugated structures: a review of crashworthiness designs and energy absorption characteristics [J]. Thin-Walled Structures, 2020, 157: 106995. DOI: 10.1016/j.tws.2020.106995.
    [408] HUANG W, ZHANG W, YE N, et al. Dynamic response and failure of PVC foam core metallic sandwich subjected to underwater impulsive loading [J]. Composites Part B: Engineering, 2016, 97: 226–238. DOI: 10.1016/j.compositesb.2016.05.015.
    [409] HUANG W, ZHANG W, HUANG X L, et al. Dynamic response of aluminum corrugated sandwich subjected to underwater impulsive loading: experiment and numerical modeling [J]. International Journal of Impact Engineering, 2017, 109: 78–91. DOI: 10.1016/j.ijimpeng.2017.06.002.
    [410] CHEN G C, CHENG Y S, ZHANG P, et al. Contact underwater explosion response of metallic sandwich panels with different face-sheet configurations and core materials [J]. Thin-Walled Structures, 2020, 157: 107126. DOI: 10.1016/j.tws.2020.107126.
    [411] WANG E H, WRIGHT J, SHUKLA A. Analytical and experimental study on the fluid structure interaction during air blast loading [J]. Journal of Applied Physics, 2011, 110(11): 114901. DOI: 10.1063/1.3662948.
    [412] TEICH M, GEBBEKEN N. Analysis of FSI effects of blast loaded flexible structures [J]. Engineering Structures, 2013, 55: 73–79. DOI: 10.1016/j.engstruct.2011.12.003.
    [413] GHOSHAL R, MITRA N. High-intensity air-explosion-induced shock loading of structures: consideration of a real gas in modelling a nonlinear compressible medium [J]. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2015, 471(2176): 20140825. DOI: 10.1098/rspa.2014.0825.
    [414] WANG C, CHEN Z, SILBERSCHMIDT V V, et al. Damage accumulation in braided textiles-reinforced composites under repeated impacts: experimental and numerical studies [J]. Composite Structures, 2018, 204: 256–267. DOI: 10.1016/j.compstruct.2018.07.084.
    [415] GUO K L, ZHU L, LI Y G, et al. Experimental investigation on the dynamic behaviour of aluminum foam sandwich plate under repeated impacts [J]. Composite Structures, 2018, 200: 298–305. DOI: 10.1016/j.compstruct.2018.05.148.
    [416] GUO K L, ZHU L, LI Y, et al. Numerical study on mechanical behavior of foam core sandwich plates under repeated impact loadings [J]. Composite Structures, 2019, 224: 111030. DOI: 10.1016/j.compstruct.2019.111030.
    [417] WU Z Y, SHI L, PAN Z X, et al. Damage assessment of braided composite tube subjected to repeated transverse impact [J]. Thin-Walled Structures, 2020, 156: 107004. DOI: 10.1016/j.tws.2020.107004.
    [418] ZHOU J J, WEN P H, WANG S N. Numerical investigation on the repeated low-velocity impact behavior of composite laminates [J]. Composites Part B: Engineering, 2020, 185: 107771. DOI: 10.1016/j.compositesb.2020.107771.
    [419] ZHANG Y, LI Y G, GUO K L, et al. Dynamic mechanical behaviour and energy absorption of aluminium honeycomb sandwich panels under repeated impact loads [J]. Ocean Engineering, 2021, 219: 108344. DOI: 10.1016/j.oceaneng.2020.108344.
    [420] ZHU L, GUO K L, LI Y G, et al. Experimental study on the dynamic behaviour of aluminium foam sandwich plates under single and repeated impacts at low temperature [J]. International Journal of Impact Engineering, 2018, 114: 123–132. DOI: 10.1016/j.ijimpeng.2017.12.001.
    [421] SUPIAN A B M, SAPUAN S M, ZUHRI M Y M, et al. Effect of winding orientation on energy absorption and failure modes of filament wound kenaf/glass fibre reinforced epoxy hybrid composite tubes under intermediate-velocity impact (IVI) load [J]. Journal of Materials Research and Technology, 2021, 10: 1–14. DOI: 10.1016/j.jmrt.2020.11.103.
    [422] HULL D. Axial crushing of fibre reinforced composite tubes [M]//JONES N, WEIRZBICKI T. Structural Crashworthiness. London: Butterworths, 1983: 118−135.
    [423] TONG Y, XU Y M. Improvement of crash energy absorption of 2D braided composite tubes through an innovative chamfer external triggers [J]. International Journal of Impact Engineering, 2018, 111: 11–20. DOI: 10.1016/j.ijimpeng.2017.08.002.
    [424] KIM J, JEONG M, BÖHM H, et al. Experimental investigation into static and dynamic axial crush of composite tubes of glass-fiber mat/PA6 laminates [J]. Composites Part B: Engineering, 2020, 181: 107590. DOI: 10.1016/j.compositesb.2019.107590.
    [425] GUPTA N K, VELMURUGAN R, GUPTA S K. An analysis of axial crushing of composite tubes [J]. Journal of Composite Materials, 1997, 31(13): 1262–1286. DOI: 10.1177/002199839703101301.
    [426] HANEFI E H, WIERZBICKI T. Axial resistance and energy absorption of externally reinforced metal tubes [J]. Composites Part B: Engineering, 1996, 27(5): 387–394. DOI: 10.1016/1359-8368(96)00002-9.
    [427] SONG H W, WAN Z M, XIE Z M, et al. Axial impact behavior and energy absorption efficiency of composite wrapped metal tubes [J]. International Journal of Impact Engineering, 2000, 24(4): 385–401. DOI: 10.1016/S0734-743X(99)00165-7.
    [428] MAHDI E, HAMOUDA A M S, SEBAEY T A. The effect of fiber orientation on the energy absorption capability of axially crushed composite tubes [J]. Materials and Design (1980-2015), 2014, 56: 923–928. DOI: 10.1016/J.MATDES.2013.12.009.
    [429] MIRZAEI M, SHAKERI M, SADIGHI M, et al. Experimental and analytical assessment of axial crushing of circular hybrid tubes under quasi-static load [J]. Composite Structures, 2012, 94(6): 1959–1966. DOI: 10.1016/j.compstruct.2012.01.003.
    [430] MAMALIS A G, MANOLAKOS D E, DEMOSTHENOUS G A, et al. The static and dynamic axial crumbling of thin-walled fibreglass composite square tubes [J]. Composites Part B: Engineering, 1997, 28(4): 439–451. DOI: 10.1016/S1359-8368(96)00066-2.
    [431] BORIA S, PETTINARI S, GIANNONI F. Theoretical analysis on the collapse mechanisms of thin-walled composite tubes [J]. Composite Structures, 2013, 103: 43–49. DOI: 10.1016/j.compstruct.2013.03.020.
    [432] HUSSEIN R D, RUAN D, LU G X. An analytical model of square CFRP tubes subjected to axial compression [J]. Composites Science and Technology, 2018, 168: 170–178. DOI: 10.1016/j.compscitech.2018.09.019.
    [433] 邢运, 杨嘉陵. 动物进化的抗冲击策略及其仿生机理研究 [J]. 力学进展, 2021, 51(2): 295–341. DOI: 10.6052/1000-0992-20-027.

    XING Y, YANG J L. Research progress of impact-resistance strategies and biomimetic mechanism in animal evolution [J]. Advances in Mechanics, 2021, 51(2): 295–341. DOI: 10.6052/1000-0992-20-027.
    [434] LAZARUS B S, VELASCO-HOGAN A, GÓMEZ-DEL RÍO T, et al. A review of impact resistant biological and bioinspired materials and structures [J]. Journal of Materials Research and Technology, 2020, 9(6): 15705–15738. DOI: 10.1016/j.jmrt.2020.10.062.
    [435] HA N S, LU G X. A review of recent research on bio-inspired structures and materials for energy absorption applications [J]. Composites Part B: Engineering, 2020, 181: 107496. DOI: 10.1016/j.compositesb.2019.107496.
    [436] CHEN J X, XIE J, WU Z S, et al. Review of beetle forewing structures and their biomimetic applications in China: Ⅰ: on the structural colors and the vertical and horizontal cross-sectional structures [J]. Materials Science and Engineering: C, 2015, 55: 605–619. DOI: 10.1016/j.msec.2015.05.064.
    [437] COMSTOCK J H, NEEDHAM J G. The wings of insects [J]. The American Naturalist, 1899, 33(395): 845–860. DOI: 10.1086/277462.
    [438] VINCENT J F. Insect cuticle: a paradigm for natural composites [J]. Symposia of the Society for Experimental Biology, 1980, 34: 183–210.
    [439] CHEN J X, XIE J, ZHU H, et al. Integrated honeycomb structure of a beetle forewing and its imitation [J]. Materials Science and Engineering: C, 2012, 32(3): 613–618. DOI: 10.1016/j.msec.2011.12.020.
    [440] CHEN J X, GU C L, GUO S J, et al. Integrated honeycomb technology motivated by the structure of beetle forewings [J]. Materials Science and Engineering: C, 2012, 32(7): 1813–1817. DOI: 10.1016/j.msec.2012.04.067.
    [441] XIANG J W, DU J X, LI D C, et al. Functional morphology and structural characteristics of wings of the ladybird beetle, Coccinella septempunctata (L.): wings of the ladybird beetle [J]. Microscopy Research and Technique, 2016, 79(6): 550–556. DOI: 10.1002/jemt.22669.
    [442] LOMAKIN J, HUBER P A, EICHLER C, et al. Mechanical properties of the beetle elytron, a biological composite material [J]. Biomacromolecules, 2011, 12(2): 321–335. DOI: 10.1021/bm1009156.
    [443] CHEN J X, DAI G Z, XU Y L, et al. Basic study of biomimetic composite materials in the forewings of beetles [J]. Materials Science and Engineering: A, 2008, 483−484: 625–628. DOI: 10.1016/j.msea.2006.09.180.
    [444] HAO P, DU J X. Energy absorption characteristics of bio-inspired honeycomb column thin-walled structure under impact loading [J]. Journal of the Mechanical Behavior of Biomedical Materials, 2018, 79: 301–308. DOI: 10.1016/j.jmbbm.2018.01.001.
    [445] PATEK S N, KORFF W L, CALDWELL R L. Deadly strike mechanism of a mantis shrimp [J]. Nature, 2004, 428(6985): 819–820. DOI: 10.1038/428819a.
    [446] YARAGHI N A, KISAILUS D. Biomimetic structural materials: inspiration from design and assembly [J]. Annual Review of Physical Chemistry, 2018, 69: 23–57. DOI: 10.1146/annurev-physchem-040215-112621.
    [447] AMINI S, TADAYON M, IDAPALAPATI S, et al. The role of quasi-plasticity in the extreme contact damage tolerance of the stomatopod dactyl club [J]. Nature Materials, 2015, 14(9): 943–950. DOI: 10.1038/nmat4309.
    [448] GRUNENFELDER L K, MILLIRON G, HERRERA S, et al. Ecologically driven ultrastructural and hydrodynamic designs in stomatopod cuticles [J]. Advanced Materials, 2018, 30(9): 1705295. DOI: 10.1002/adma.201705295.
    [449] WEAVER J C, MILLIRON G W, MISEREZ A, et al. The stomatopod dactyl club: a formidable damage-tolerant biological hammer [J]. Science, 2012, 336(6086): 1275–1280. DOI: 10.1126/science.1218764.
    [450] YARAGHI N A, GUARÍN-ZAPATA N, GRUNENFELDER L K, et al. A sinusoidally architected helicoidal biocomposite [J]. Advanced Materials, 2016, 28(32): 6835–6844. DOI: 10.1002/adma.201600786.
    [451] HUANG W, SHISHEHBOR M, GUARÍN-ZAPATA N, et al. A natural impact-resistant bicontinuous composite nanoparticle coating [J]. Nature Materials, 2020, 19(11): 1236–1243. DOI: 10.1038/s41563-020-0768-7.
    [452] MAY P R A, FUSTER J M, HABER J, et al. Woodpecker drilling behavior: an endorsement of the rotational theory of impact brain injury [J]. Archives of Neurology, 1979, 36(6): 370–373. DOI: 10.1001/archneur.1979.00500420080011.
    [453] WANG L Z, CHEUNG J T M, PU F, et al. Why do woodpeckers resist head impact injury: a biomechanical investigation [J]. PLoS One, 2011, 6(10): e26490. DOI: 10.1371/journal.pone.0026490.
    [454] WANG L Z, ZHANG H Q, FAN Y B. Comparative study of the mechanical properties, micro-structure, and composition of the cranial and beak bones of the great spotted woodpecker and the lark bird [J]. Science China Life Sciences, 2011, 54(11): 1036–1041. DOI: 10.1007/s11427-011-4242-2.
    [455] LEE N, HORSTEMEYER M F, RHEE H, et al. Hierarchical multiscale structure-property relationships of the red-bellied woodpecker (Melanerpes carolinus) beak [J]. Journal of the Royal Society Interface, 2014, 11(96): 20140274. DOI: 10.1098/RSIF.2014.0274.
    [456] LIU Z Q, ZHANG Z F, RITCHIE R O. On the materials science of nature’s arms race [J]. Advanced Materials, 2018, 30(32): 1705220. DOI: 10.1002/adma.201705220.
    [457] LIU Y Z, QIU X M, MA H L, et al. A study of woodpecker’s pecking process and the impact response of its brain [J]. International Journal of Impact Engineering, 2017, 108: 263–271. DOI: 10.1016/j.ijimpeng.2017.05.016.
    [458] JUNG J Y, NALEWAY S E, YARAGHI N A, et al. Structural analysis of the tongue and hyoid apparatus in a woodpecker [J]. Acta Biomaterialia, 2016, 37: 1–13. DOI: 10.1016/j.actbio.2016.03.030.
    [459] JUNG J Y, PISSARENKO A, TRIKANAD A A, et al. A natural stress deflector on the head? Mechanical and functional evaluation of the woodpecker skull bones [J]. Advanced Theory and Simulations, 2019, 2(4): 1800152. DOI: 10.1002/adts.201800152.
    [460] NEUMANN M, HERTER J, DROSTE B O, et al. Compressive behaviour of axially loaded spruce wood under large deformations at different strain rates [J]. European Journal of Wood and Wood Products, 2011, 69(3): 345–357. DOI: 10.1007/s00107-010-0442-x.
    [461] EISENACHER G, SCHEIDEMANN R, NEUMANN M, et al. Dynamic crushing characteristics of spruce wood under large deformations [J]. Wood Science and Technology, 2013, 47(2): 369–380. DOI: 10.1007/s00226-012-0508-5.
    [462] WOUTS J, HAUGOU G, OUDJENE M, et al. Strain rate effects on the compressive response of wood and energy absorption capabilities: Part A: experimental investigations [J]. Composite Structures, 2016, 149: 315–328. DOI: 10.1016/j.compstruct.2016.03.058.
    [463] WOUTS J, HAUGOU G, OUDJENE M, et al. Strain rate effects on the compressive response of wood and energy absorption capabilities: Part B: experimental investigation under rigid lateral confinement [J]. Composite Structures, 2018, 204: 95–104. DOI: 10.1016/j.compstruct.2018.07.001.
    [464] HEPWORTH D G, VINCENT J F, STRINGER G, et al. Variations in the morphology of wood structure can explain why hardwood species of similar density have very different resistances to impact and compressive loading [J]. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2002, 360(1791): 255–272. DOI: 10.1098/rsta.2001.0927.
    [465] MATSUSHITA A K, GONZALEZ D, WANG M, et al. Beyond density: mesostructural features of impact resistant wood [J]. Materials Today Communications, 2020, 22: 100697. DOI: 10.1016/J.MTCOMM.2019.100697.
    [466] GROSS J, TIMBERG R, GRAEF M. Pigment and ultrastructural changes in the developing pummelo Citrus grandis ‘Goliath’ [J]. Botanical Gazette, 1983, 144(3): 401–406. DOI: 10.1086/337389.
    [467] MORTON J F. Fruits of warm climates [M]. Miami: Creative Resource Systems Inc, 1987.
    [468] FISCHER S F, THIELEN M, LOPRANG R R, et al. Pummelos as concept generators for biomimetically inspired low weight structures with excellent damping properties [J]. Advanced Engineering Materials, 2010, 12(12): B658–B663. DOI: 10.1002/adem.201080065.
    [469] BÜHRIG-POLACZEK A, FLECK C, SPECK T, et al. Biomimetic cellular metals: using hierarchical structuring for energy absorption [J]. Bioinspiration and Biomimetics, 2016, 11(4): 045002. DOI: 10.1088/1748-3190/11/4/045002.
    [470] THIELEN M, SPECK T, SEIDEL R. The ecological relevance of the pomelo (Citrus maxima) peel acting as an effective impact protection [C]//Proceedings of the 7th Plant Biomechanics International Conference. Clermont-Ferrand, France, 2012.
    [471] THIELEN M, SPECK T, SEIDEL R. Viscoelasticity and compaction behaviour of the foam-like pomelo (Citrus maxima) peel [J]. Journal of Materials Science, 2013, 48(9): 3469–3478. DOI: 10.1007/s10853-013-7137-8.
    [472] WANG B, PAN B, LUBINEAU G. Morphological evolution and internal strain mapping of pomelo peel using X-ray computed tomography and digital volume correlation [J]. Materials and Design, 2018, 137: 305–315. DOI: 10.1016/J.MATDES.2017.10.038.
    [473] THIELEN M, SCHMITT C N Z, ECKERT S, et al. Structure-function relationship of the foam-like pomelo peel (Citrus maxima): an inspiration for the development of biomimetic damping materials with high energy dissipation [J]. Bioinspiration and Biomimetics, 2013, 8(2): 025001. DOI: 10.1088/1748-3182/8/2/025001.
    [474] HA N S, LU G X, SHU D W, et al. Mechanical properties and energy absorption characteristics of tropical fruit durian (Durio zibethinus) [J]. Journal of the Mechanical Behavior of Biomedical Materials, 2020, 104: 103603. DOI: 10.1016/j.jmbbm.2019.103603.
    [475] GLUDOVATZ B, WALSH F, ZIMMERMANN E A, et al. Multiscale structure and damage tolerance of coconut shells [J]. Journal of the Mechanical Behavior of Biomedical Materials, 2017, 76: 76–84. DOI: 10.1016/j.jmbbm.2017.05.024.
    [476] DARDICK C, CALLAHAN A M. Evolution of the fruit endocarp: molecular mechanisms underlying adaptations in seed protection and dispersal strategies [J]. Frontiers in Plant Science, 2014, 5: 284. DOI: 10.3389/fpls.2014.00284.
    [477] VINCENT J. Structural biomaterials [M]. 3rd ed. Princeton: Princeton University Press, 2012.
    [478] NGUYEN X T, HOU S J, LIU T Q, et al. A potential natural energy absorption material: coconut mesocarp: Part A: experimental investigations on mechanical properties [J]. International Journal of Mechanical Sciences, 2016, 115-116: 564–573. DOI: 10.1016/j.ijmecsci.2016.07.017.
    [479] LU C H, HOU S J, ZHANG Z Y, et al. The mystery of coconut overturns the crashworthiness design of composite materials [J]. International Journal of Mechanical Sciences, 2020, 168: 105244. DOI: 10.1016/j.ijmecsci.2019.105244.
    [480] SCHMIER S, HOSODA N, SPECK T. Hierarchical structure of the Cocos nucifera (Coconut) endocarp: functional morphology and its influence on fracture toughness [J]. Molecules, 2020, 25(1): 223. DOI: 10.3390/molecules25010223.
    [481] SHARAN S, RAIJIWALA D B. Abrasion and drop weight impact resistance of coconut shell ash concrete [J]. International Journal of Civil Engineering and Technology, 2017, 8(2): 383–389.
    [482] GUNASEKARAN K, KUMAR P S, LAKSHMIPATHY M. Mechanical and bond properties of coconut shell concrete [J]. Construction and Building Materials, 2011, 25(1): 92–98. DOI: 10.1016/j.conbuildmat.2010.06.053.
    [483] LIU T Q, HOU S J, NGUYEN X, et al. Energy absorption characteristics of sandwich structures with composite sheets and bio coconut core [J]. Composites Part B: Engineering, 2017, 114: 328–338. DOI: 10.1016/j.compositesb.2017.01.035.
    [484] XIANG J W, DU J X. Energy absorption characteristics of bio-inspired honeycomb structure under axial impact loading [J]. Materials Science and Engineering: A, 2017, 696: 283–289. DOI: 10.1016/j.msea.2017.04.044.
    [485] HA N S, LU G X, XIANG X M. Energy absorption of a bio-inspired honeycomb sandwich panel [J]. Journal of Materials Science, 2019, 54(8): 6286–6300. DOI: 10.1007/s10853-018-3163-x.
    [486] TSANG H H, TSE K M, CHAN K Y, et al. Energy absorption of muscle-inspired hierarchical structure: experimental investigation [J]. Composite Structures, 2019, 226: 111250. DOI: 10.1016/j.compstruct.2019.111250.
    [487] ZHANG Z Q, ZHANG Y W, GAO H J. On optimal hierarchy of load-bearing biological materials [J]. Proceedings of the Royal Society B: Biological Sciences, 2011, 278(1705): 519–525. DOI: 10.1098/rspb.2010.1093.
    [488] CHEN Y Y, JIA Z A, WANG L F. Hierarchical honeycomb lattice metamaterials with improved thermal resistance and mechanical properties [J]. Composite Structures, 2016, 152: 395–402. DOI: 10.1016/j.compstruct.2016.05.048.
    [489] HALDAR S, BRUCK H A. Mechanics of composite sandwich structures with bioinspired core [J]. Composites Science and Technology, 2014, 95: 67–74. DOI: 10.1016/j.compscitech.2014.02.011.
    [490] 王海任, 李世强, 刘志芳, 等. 爆炸载荷下双向梯度仿生夹芯圆板的力学行为 [J]. 爆炸与冲击, 2021, 41(4): 043201. DOI: 10.11883/bzycj-2020-0132.

    WANG H R, LI S Q, LIU Z F, et al. Mechanical behaviors of bi-directional gradient bio-inspired circular sandwich plates under blast loading [J]. Explosion and Shock Waves, 2021, 41(4): 043201. DOI: 10.11883/bzycj-2020-0132.
    [491] CHENG L, THOMAS A, GLANCEY J L, et al. Mechanical behavior of bio-inspired laminated composites [J]. Composites Part A: Applied Science and Manufacturing, 2011, 42(2): 211–220. DOI: 10.1016/j.compositesa.2010.11.009.
    [492] ZIMMERMANN E A, GLUDOVATZ B, SCHAIBLE E, et al. Mechanical adaptability of the Bouligand-type structure in natural dermal armour [J]. Nature Communications, 2013, 4(1): 2634. DOI: 10.1038/ncomms3634.
    [493] NIKOLOV S, PETROV M, LYMPERAKIS L, et al. Revealing the design principles of high-performance biological composites using ab initio and multiscale simulations: the example of lobster cuticle [J]. Advanced Materials, 2010, 22(4): 519–526. DOI: 10.1002/adma.200902019.
    [494] GRUNENFELDER L K, SUKSANGPANYA N, SALINAS C, et al. Bio-inspired impact-resistant composites [J]. Acta Biomaterialia, 2014, 10(9): 3997–4008. DOI: 10.1016/j.actbio.2014.03.022.
    [495] GINZBURG D, PINTO F, IERVOLINO O, et al. Damage tolerance of bio-inspired helicoidal composites under low velocity impact [J]. Composite Structures, 2017, 161: 187–203. DOI: 10.1016/j.compstruct.2016.10.097.
    [496] YIN S, CHEN H Y, YANG R H, et al. Tough nature-inspired helicoidal composites with printing-induced voids [J]. Cell Reports Physical Science, 2020, 1(7): 100109. DOI: 10.1016/j.xcrp.2020.100109.
    [497] YIN S, YANG R H, HUANG Y, et al. Toughening mechanism of coelacanth-fish-inspired double-helicoidal composites [J]. Composites Science and Technology, 2021, 205: 108650. DOI: 10.1016/j.compscitech.2021.108650.
    [498] YIN S, GUO W H, WANG H T, et al. Strong and tough bioinspired additive-manufactured dual-phase mechanical metamaterial composites [J]. Journal of the Mechanics and Physics of Solids, 2021, 149: 104341. DOI: 10.1016/j.jmps.2021.104341.
    [499] LIU J L, SINGH A K, LEE H P, et al. The response of bio-inspired helicoidal laminates to small projectile impact [J]. International Journal of Impact Engineering, 2020, 142: 59–70. DOI: 10.1016/j.ijimpeng.2020.103608.
    [500] ABIR M R, TAY T E, LEE H P. On the improved ballistic performance of bio-inspired composites [J]. Composites Part A: Applied Science and Manufacturing, 2019, 123: 59–70. DOI: 10.1016/j.compositesa.2019.04.021.
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  • 收稿日期:  2021-03-30
  • 修回日期:  2021-05-28
  • 网络出版日期:  2021-10-20
  • 刊出日期:  2021-12-05

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