梯度多胞材料的动态力学性能分析与设计研究综述

常白雪 张元瑞 王少华 彭克锋 虞吉林 郑志军

常白雪, 张元瑞, 王少华, 彭克锋, 虞吉林, 郑志军. 梯度多胞材料的动态力学性能分析与设计研究综述[J]. 爆炸与冲击, 2024, 44(8): 081411. doi: 10.11883/bzycj-2024-0086
引用本文: 常白雪, 张元瑞, 王少华, 彭克锋, 虞吉林, 郑志军. 梯度多胞材料的动态力学性能分析与设计研究综述[J]. 爆炸与冲击, 2024, 44(8): 081411. doi: 10.11883/bzycj-2024-0086
CHANG Baixue, ZHANG Yuanrui, WANG Shaohua, PENG Kefeng, YU Jilin, ZHENG Zhijun. Review on dynamic mechanical analysis and design of graded cellular materials[J]. Explosion And Shock Waves, 2024, 44(8): 081411. doi: 10.11883/bzycj-2024-0086
Citation: CHANG Baixue, ZHANG Yuanrui, WANG Shaohua, PENG Kefeng, YU Jilin, ZHENG Zhijun. Review on dynamic mechanical analysis and design of graded cellular materials[J]. Explosion And Shock Waves, 2024, 44(8): 081411. doi: 10.11883/bzycj-2024-0086

梯度多胞材料的动态力学性能分析与设计研究综述

doi: 10.11883/bzycj-2024-0086
基金项目: 国家自然科学基金(12102429,12272375,11872360);中央高校基本科研业务费专项资金(WK2090000066)
详细信息
    作者简介:

    常白雪(1992- ),女,博士,副研究员,bxchang@ustc.edu.cn

    通讯作者:

    郑志军(1979- ),男,博士,副教授,zjzheng@ustc.edu.cn

  • 中图分类号: O347

Review on dynamic mechanical analysis and design of graded cellular materials

  • 摘要: 多胞材料是一种内部含有大量空穴和胞元的结构,具有轻质、高比吸能等特性,广泛应用于航空航天、交通运输和人体防护等碰撞/爆炸防护领域。引入梯度设计可实现多胞材料的有序耗能和载荷调控,满足不同情形和工况下的防护需求。对梯度多胞材料动态力学行为和设计的研究进展进行了综述,着重介绍了梯度多胞材料/结构在抗冲击、抗爆炸和模拟爆炸载荷加载3个方面的应用案例。首先,介绍了梯度多胞材料的分类,较系统地总结了梯度多胞材料在动态加载下的变形特征、冲击波模型、防护性能等方面的研究,阐明了梯度多胞材料的密度/强度梯度与惯性效应存在的竞争机制。其次,以冲击波模型为力学原理指导梯度多胞材料/结构设计,介绍了梯度多胞材料耐撞性反向设计、多种抗爆炸夹芯结构设计、计及弹靶耦合效应的爆炸载荷模拟器设计等策略,实现了最佳防护效果或载荷精准控制,为抗冲击/抗爆炸防护设计和快速评估提供理论基础和技术支撑。最后,展望了梯度多胞材料在极端环境加载、大能量冲击和强非线性载荷调控等需求下冲击防护领域的应用前景。
  • 图  1  自然界中典型的梯度多胞材料[8, 32, 38, 41-43]

    Figure  1.  Typical graded cellular materials in nature[8, 32, 38, 41-43]

    图  2  常见的梯度多胞材料[46, 51-52, 56-57, 62]

    Figure  2.  Common graded cellular materials[46, 51-52, 56-57, 62]

    图  3  分层和连续梯度多胞材料[64, 68-69, 75, 79, 81, 84]

    Figure  3.  Layered and continuous gradient cellular materials[64, 68-69, 75, 79, 81, 84]

    图  4  强度与密度梯度[85, 95]

    Figure  4.  Strength and density gradient types[85, 95]

    图  5  传统工艺制备的梯度多胞材料及其密度梯度分布[96, 100-102]

    Figure  5.  Schematic diagrams of graded cellular materials and their density gradient distributions prepared by traditional process[96, 100-102]

    图  6  3D打印梯度多胞材料示意图[62, 77, 103, 105, 108]

    Figure  6.  Schematic diagrams of 3D printed graded cellular materials[62, 77, 103, 105, 108]

    图  7  梯度多胞材料的变形模式[115]

    Figure  7.  Deformation patterns of graded cellular materials[115]

    图  8  梯度Voronoi蜂窝的压溃变形模式[80, 95]

    Figure  8.  Collapse deformation modes for graded Voronoi honeycombs[80, 95]

    图  9  冲击波模型示意图[80, 137]

    Figure  9.  Schematic diagram of shock models[80, 137]

    图  10  质量块撞击和爆炸加载下梯度多胞材料的力学性能分析[113, 137]

    Figure  10.  Mechanical properties analysis of graded cellular materials under mass impact and blast loading[113, 137]

    图  11  质量块初速度撞击下梯度多胞材料的耐撞性设计策略[76-77, 148]

    Figure  11.  Crashworthiness design strategies for graded cellular materials[76-77, 148]

    图  12  梯度泡沫结构的抗爆炸分析[109, 112, 138]

    Figure  12.  Anti-blast analysis of graded foam structures[109, 112, 138]

    图  13  模拟爆炸载荷加载的梯度多胞子弹的设计与验证[78]

    Figure  13.  Design and verification of graded cellular projectiles to simulate blast loading[78]

    表  1  不同冲击工况下梯度多胞材料的动态响应理论模型

    Table  1.   Theoretical models of the dynamic response for graded cellular materials under different impact scenarios

    变形模式 质量块初速度撞击[80, 95] 爆炸加载[112]
    单波 $ \left\{ \begin{gathered} \dot \varPhi = \dfrac{v}{{{\varepsilon _{\text{B}}}(\rho (\varPhi ))}} \\ {\sigma _{\text{B}}} = {\sigma _{\text{0}}} + {\rho _{\text{s}}}\rho (\varPhi )\dfrac{{{v^2}}}{{{\varepsilon _{\text{B}}}(\rho (\varPhi ))}} \\ \dot v = \dfrac{{ - {\sigma _{\text{B}}}}}{{m + {\rho _{\text{s}}}\displaystyle\int_0^\varPhi {\rho (X){\rm{d}}X} }} \\ \end{gathered} \right. $ $ \left\{ \begin{gathered} \dot \varPhi = \dfrac{v}{{{\varepsilon _{\text{B}}}(\rho (\varPhi ))}} \\ {\sigma _{\text{B}}} = {\sigma _{\text{0}}} + {\rho _{\text{s}}}\rho (\varPhi )\dfrac{{{v^2}}}{{{\varepsilon _{\text{B}}}(\rho (\varPhi ))}} \\ \dot v = \dfrac{{p(t) - {\sigma _{\text{B}}}}}{{m + {\rho _{\text{s}}}\displaystyle\int_0^\varPhi {\rho (X){\rm{d}}X} }} \\ \end{gathered} \right. $
    双波 $ \left\{ \begin{gathered} {{\dot \varPhi }_1} = \dfrac{{{v_1} - {v_2}}}{{{\varepsilon _{\text{B}}}(\rho ({\varPhi _1}))}} \\ {{\dot \varPhi }_2} = \dfrac{{ - {v_2}}}{{{\varepsilon _{\text{B}}}(\rho ({\varPhi _2}))}} \\ {\sigma _{{\text{B,1}}}} = {\sigma _{\text{0}}}(\rho ({\varPhi _1})) + {\rho _{\text{s}}}\rho ({\varPhi _1})\dfrac{{{{({v_1} - {v_2})}^2}}}{{{\varepsilon _{\text{B}}}(\rho ({\varPhi _1}))}} \\ {\sigma _{{\text{B,2}}}} = {\sigma _{\text{0}}}(\rho ({\varPhi _2})) + {\rho _{\text{s}}}\rho ({\varPhi _2})\dfrac{{{v_2}^2}}{{{\varepsilon _{\text{B}}}(\rho ({\varPhi _2}))}} \\ {{\dot v}_1} = \dfrac{{ - {\sigma _{{\text{B,1}}}}}}{{m + {\rho _{\text{s}}}\displaystyle\int_0^{{\varPhi _1}} {\rho (X){\text{d}}X} }} \\ {{\dot v}_2} = \dfrac{{{\sigma _{\text{0}}}(\rho ({\varPhi _1})) - {\sigma _{\text{0}}}(\rho ({\varPhi _2}))}}{{{\rho _{\text{s}}}\displaystyle\int_{{\varPhi _1}}^{{\varPhi _2}} {\rho (X){\text{d}}X} }} \\ \end{gathered} \right. $ $ \left\{ \begin{gathered} {{\dot \varPhi }_1} = \dfrac{{{v_1} - {v_2}}}{{{\varepsilon _{\text{B}}}(\rho ({\varPhi _1}))}} \\ {{\dot \varPhi }_2} = \dfrac{{ - {v_2}}}{{{\varepsilon _{\text{B}}}(\rho ({\varPhi _2}))}} \\ {\sigma _{{\text{B,1}}}} = {\sigma _{\text{0}}}(\rho ({\varPhi _1})) + {\rho _{\text{s}}}\rho ({\varPhi _1})\dfrac{{{{({v_1} - {v_2})}^2}}}{{{\varepsilon _{\text{B}}}(\rho ({\varPhi _1}))}} \\ {\sigma _{{\text{B,2}}}} = {\sigma _{\text{0}}}(\rho ({\varPhi _2})) + {\rho _{\text{s}}}\rho ({\varPhi _2})\dfrac{{{v_2}^2}}{{{\varepsilon _{\text{B}}}(\rho ({\varPhi _2}))}} \\ {{\dot v}_1} = \dfrac{{p(t) - {\sigma _{{\text{B,1}}}}}}{{m + {\rho _{\text{s}}}\displaystyle\int_0^{{\varPhi _1}} {\rho (X){\text{d}}X} }} \\ {{\dot v}_2} = \dfrac{{{\sigma _{\text{0}}}(\rho ({\varPhi _1})) - {\sigma _{\text{0}}}(\rho ({\varPhi _2}))}}{{{\rho _{\text{s}}}\displaystyle\int_{{\varPhi _1}}^{{\varPhi _2}} {\rho (X){\text{d}}X} }} \\ \end{gathered} \right. $
    三波 $ \left\{ \begin{gathered} {{\dot \varPhi }_1} = \dfrac{{{v_1} - {v_2}}}{{{\varepsilon _{\text{B}}}(\rho ({\varPhi _1}))}} \\ {{\dot \varPhi }_2} = \dfrac{{{v_2} - {v_3}}}{{{\varepsilon _{\text{B}}}(\rho ({\varPhi _2}))}} \\ {{\dot \varPhi }_3} = \dfrac{{{v_3}}}{{{\varepsilon _{\text{B}}}(\rho ({\varPhi _3}))}} \\ {\sigma _{{\text{B,1}}}} = {\sigma _{\text{0}}}(\rho ({\varPhi _1})) + {\rho _{\text{s}}}\rho ({\varPhi _1})\dfrac{{{{({v_1} - {v_2})}^2}}}{{{\varepsilon _{\text{B}}}(\rho ({\varPhi _1}))}} \\ {\sigma _{{\text{B,2}}}} = {\sigma _{\text{0}}}(\rho ({\varPhi _2})) + {\rho _{\text{s}}}\rho ({\varPhi _2})\dfrac{{{{({v_2} - {v_3})}^2}}}{{{\varepsilon _{\text{B}}}(\rho ({\varPhi _2}))}} \\ {\sigma _{{\text{B,3}}}} = {\sigma _{\text{0}}}(\rho ({\varPhi _3})) + {\rho _{\text{s}}}\rho ({\varPhi _3})\dfrac{{{v_3}^2}}{{{\varepsilon _{\text{B}}}(\rho ({\varPhi _3}))}} \\ {{\dot v}_1} = \dfrac{{ - {\sigma _{{\text{B,1}}}}(\rho ({\varPhi _1}))}}{{m + {\rho _{\text{s}}}\displaystyle\int_0^{{\varPhi _1}} {\rho (X){\rm{d}}X} }} \\ {{\dot v}_2} = \dfrac{{{\sigma _{\text{0}}}(\rho ({\varPhi _1})) - {\sigma _{\text{0}}}(\rho ({\varPhi _2}))}}{{{\rho _{\text{s}}}\displaystyle\int_{{\varPhi _1}}^{{\varPhi _2}} {\rho (X){\rm{d}}X} }} \\ {{\dot v}_3} = \dfrac{{{\sigma _{{\text{B,3}}}}(\rho ({\varPhi _2})) - {\sigma _{{\text{B,2}}}}(\rho ({\varPhi _3}))}}{{{\rho _{\text{s}}}\displaystyle\int_{{\varPhi _2}}^{{\varPhi _3}} {\rho (X){\rm{d}}X} }} \\ \end{gathered} \right. $ $ \left\{ \begin{gathered} {{\dot \varPhi }_1} = \dfrac{{{v_1} - {v_2}}}{{{\varepsilon _{\text{B}}}(\rho ({\varPhi _1}))}} \\ {{\dot \varPhi }_2} = \dfrac{{{v_2} - {v_3}}}{{{\varepsilon _{\text{B}}}(\rho ({\varPhi _2}))}} \\ {{\dot \varPhi }_3} = \dfrac{{{v_3}}}{{{\varepsilon _{\text{B}}}(\rho ({\varPhi _3}))}} \\ {\sigma _{{\text{B,1}}}} = {\sigma _{\text{0}}}(\rho ({\varPhi _1})) + {\rho _{\text{s}}}\rho ({\varPhi _1})\dfrac{{{{({v_1} - {v_2})}^2}}}{{{\varepsilon _{\text{B}}}(\rho ({\varPhi _1}))}} \\ {\sigma _{{\text{B,2}}}} = {\sigma _{\text{0}}}(\rho ({\varPhi _2})) + {\rho _{\text{s}}}\rho ({\varPhi _2})\dfrac{{{{({v_2} - {v_3})}^2}}}{{{\varepsilon _{\text{B}}}(\rho ({\varPhi _2}))}} \\ {\sigma _{{\text{B,3}}}} = {\sigma _{\text{0}}}(\rho ({\varPhi _3})) + {\rho _{\text{s}}}\rho ({\varPhi _3})\dfrac{{{v_3}^2}}{{{\varepsilon _{\text{B}}}(\rho ({\varPhi _3}))}} \\ {{\dot v}_1} = \dfrac{{p(t) - {\sigma _{{\text{B,1}}}}(\rho ({\varPhi _1}))}}{{m + {\rho _{\text{s}}}\displaystyle\int_0^{{\varPhi _1}} {\rho (X){\rm{d}}X} }} \\ {{\dot v}_2} = \dfrac{{{\sigma _{\text{0}}}(\rho ({\varPhi _1})) - {\sigma _{\text{0}}}(\rho ({\varPhi _2}))}}{{{\rho _{\text{s}}}\displaystyle\int_{{\varPhi _1}}^{{\varPhi _2}} {\rho (X){\rm{d}}X} }} \\ {{\dot v}_3} = \dfrac{{{\sigma _{{\text{B,3}}}}(\rho ({\varPhi _2})) - {\sigma _{{\text{B,2}}}}(\rho ({\varPhi _3}))}}{{{\rho _{\text{s}}}\displaystyle\int_{{\varPhi _2}}^{{\varPhi _3}} {\rho (X){\rm{d}}X} }} \\ \end{gathered} \right. $
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  • [1] ZHANG Z Q, YANG J L. Improving safety of runway overrun through foamed concrete aircraft arresting system: an experimental study [J]. International Journal of Crashworthiness, 2015, 20(5): 448–463. DOI: 10.1080/13588265.2015.1033971.
    [2] YANG X F, YANG J L, ZHANG Z Q, et al. A review of civil aircraft arresting system for runway overruns [J]. Progress in Aerospace Sciences, 2018, 102: 99–121. DOI: 10.1016/j.paerosci.2018.07.006.
    [3] 田斌, 李如江, 赵家骏, 等. 钢板与泡沫铝复合板弹药包装箱的对比研究 [J]. 兵器装备工程学报, 2019, 40(10): 190–194. DOI: 10.11809/bqzbgcxb2019.10.040.

    TIAN B, LI R J, ZHAO J J, et al. Comparative study of steel plate and foam aluminum composite plate ammunition packaging box [J]. Journal of Ordnance Equipment Engineering, 2019, 40(10): 190–194. DOI: 10.11809/bqzbgcxb2019.10.040.
    [4] 张凯, 张庆明, 贾伟. 多层圆管夹芯结构的装甲车底板防爆设计 [J]. 安全与环境学报, 2017, 17(3): 969–974. DOI: 10.13637/j.issn.1009-6094.2017.03.030.

    ZHANG K, ZHANG Q M, JIA W. On the safety design of the multilayer circular-tube structure of the armored vehicle plate under the explosion loading [J]. Journal of Safety and Environment, 2017, 17(3): 969–974. DOI: 10.13637/j.issn.1009-6094.2017.03.030.
    [5] 张钱城, 郝方楠, 李裕春, 等. 爆炸冲击载荷作用下车辆和人员的损伤与防护 [J]. 力学与实践, 2014, 36(5): 527–539. DOI: 10.6052/1000-0879-13-539.

    ZHANG Q C, HAO F N, LI Y C, et al. Research progress in the injury and protection to vehicle and passengers under explosive shock loading [J]. Mechanics in Engineering, 2014, 36(5): 527–539. DOI: 10.6052/1000-0879-13-539.
    [6] 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.
    [7] GROSSER D, LIESE W. On the anatomy of Asian bamboos, with special reference to their vascular bundles [J]. Wood Science and Technology, 1971, 5(4): 290–312. DOI: 10.1007/BF00365061.
    [8] 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.
    [9] ASHBY M F. The properties of foams and lattices [J]. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2006, 364(1838): 15–30. DOI: 10.1098/rsta.2005.1678.
    [10] CHEN L M, ZHANG J, DU B, et al. Dynamic crushing behavior and energy absorption of graded lattice cylindrical structure under axial impact load [J]. Thin-Walled Structures, 2018, 127: 333–343. DOI: 10.1016/j.tws.2017.10.048.
    [11] WANG Z G. Recent advances in novel metallic honeycomb structure [J]. Composites Part B: Engineering, 2019, 166: 731–741. DOI: 10.1016/j.compositesb.2019.02.011.
    [12] BACIGALUPO A, DE BELLIS M L, MISSERONI D. Design of tunable acoustic metamaterials with periodic piezoelectric microstructure [J]. Extreme Mechanics Letters, 2020, 40: 100977. DOI: 10.1016/j.eml.2020.100977.
    [13] WANG Z G, ZHOU Y, WANG X X, et al. Compression behavior of strut-reinforced hierarchical lattice—experiment and simulation [J]. International Journal of Mechanical Sciences, 2021, 210: 106749. DOI: 10.1016/j.ijmecsci.2021.106749.
    [14] SUN Z P, GUO Y B, SHIM V P W. Deformation and energy absorption characteristics of additively-manufactured polymeric lattice structures—effects of cell topology and material anisotropy [J]. Thin-Walled Structures, 2021, 169: 108420. DOI: 10.1016/j.tws.2021.108420.
    [15] XIAO L J, XU X, FENG G Z, et al. Compressive performance and energy absorption of additively manufactured metallic hybrid lattice structures [J]. International Journal of Mechanical Sciences, 2022, 219: 107093. DOI: 10.1016/j.ijmecsci.2022.107093.
    [16] 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.
    [17] ELNASRI I, PATTOFATTO S, ZHAO H, et al. Shock enhancement of cellular structures under impact loading: part Ⅰ experiments [J]. Journal of the Mechanics and Physics of Solids, 2007, 55(12): 2652–2671. DOI: 10.1016/j.jmps.2007.04.005.
    [18] LIU Y D, YU J L, ZHENG Z J, et al. A numerical study on the rate sensitivity of cellular metals [J]. International Journal of Solids and Structures, 2009, 46(22/23): 3988–3998. DOI: 10.1016/j.ijsolstr.2009.07.024.
    [19] 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.
    [20] SUN Y L, LI Q M, MCDONALD S A, et al. Determination of the constitutive relation and critical condition for the shock compression of cellular solids [J]. Mechanics of Materials, 2016, 99: 26–36. DOI: 10.1016/j.mechmat.2016.04.004.
    [21] WANG H R, LI S Q, LIU Z F, et al. Investigation on the dynamic response of circular sandwich panels with the bio-inspired gradient core [J]. Thin-Walled Structures, 2020, 149: 106667. DOI: 10.1016/j.tws.2020.106667.
    [22] LAZARUS B S, CHADHA C, VELASCO-HOGAN A, et al. Engineering with keratin: a functional material and a source of bioinspiration [J]. iScience, 2021, 24(8): 102798. DOI: 10.1016/j.isci.2021.102798.
    [23] LIU Z Q, MEYERS M A, ZHANG Z F, et al. Functional gradients and heterogeneities in biological materials: design principles, functions, and bioinspired applications [J]. Progress in Materials Science, 2017, 88: 467–498. DOI: 10.1016/j.pmatsci.2017.04.013.
    [24] LE BARBENCHON L, GIRARDOT J, KOPP J B, et al. Multi-scale foam: 3D structure/compressive behaviour relationship of agglomerated cork [J]. Materialia, 2019, 5: 100219. DOI: 10.1016/j.mtla.2019.100219.
    [25] LAUNEY M E, BUEHLER M J, RITCHIE R O. On the mechanistic origins of toughness in bone [J]. Annual Review of Materials Research, 2010, 40: 25–53. DOI: 10.1146/annurev-matsci-070909-104427.
    [26] SARANATHAN V, OSUJI C O, MOCHRIE S G J, et al. Structure, function, and self-assembly of single network gyroid (I4132) photonic crystals in butterfly wing scales [J]. Proceedings of the National Academy of Sciences of the United States of America, 2010, 107(26): 11676–11681. DOI: 10.1073/pnas.0909616107.
    [27] GIBSON L J, ASHBY M F. Cellular solids: structure and properties [M]. Cambridge: Cambridge University Press, 1988.
    [28] WESTER T. Nature teaching structures [J]. International Journal of Space Structures, 2002, 17(2/3): 135–147. DOI: 10.1260/026635102320321789.
    [29] HELFMAN COHEN Y, REICH Y, GREENBERG S. Biomimetics: structure-function patterns approach [J]. Journal of Mechanical Design, 2014, 136(11): 111108. DOI: 10.1115/1.4028169.
    [30] TAVSAN C, TAVSAN F, SONMEZ E. Biomimicry in architectural design education [J]. Procedia-Social and Behavioral Sciences, 2015, 182: 489–496. DOI: 10.1016/j.sbspro.2015.04.832.
    [31] AZIZ M S, EL SHERIF A Y. Biomimicry as an approach for bio-inspired structure with the aid of computation [J]. Alexandria Engineering Journal, 2016, 55(1): 707–714. DOI: 10.1016/j.aej.2015.10.015.
    [32] BUCKWALTER J A, GLIMCHER M J, COOPER R R, et al. Bone biology. Ⅰ: structure, blood supply, cells, matrix, and mineralization [J]. Instructional Course Lectures, 1996, 45: 371–386.
    [33] NOGATA F, TAKAHASHI H. Intelligent functionally graded material: bamboo [J]. Composites Engineering, 1995, 5(7): 743–751. DOI: 10.1016/0961-9526(95)00037-N.
    [34] AMADA S, MUNEKATA T, NAGASE Y, et al. The mechanical structures of bamboos in viewpoint of functionally gradient and composite materials [J]. Journal of Composite Materials, 1996, 30(7): 800–819. DOI: 10.1177/002199839603000703.
    [35] RAY A K, DAS S K, MONDAL S, et al. Microstructural characterization of bamboo [J]. Journal of Materials Science, 2004, 39(3): 1055–1060. DOI: 10.1023/B:JMSC.0000012943.27090.8f.
    [36] SILVA E C N, WALTERS M C, PAULINO G H. Modeling bamboo as a functionally graded material: lessons for the analysis of affordable materials [J]. Journal of Materials Science, 2006, 41(21): 6991–7004. DOI: 10.1007/s10853-006-0232-3.
    [37] HABIBI M K, SAMAEI A T, GHESHLAGHI B, et al. Asymmetric flexural behavior from bamboo’s functionally graded hierarchical structure: underlying mechanisms [J]. Acta Biomaterialia, 2015, 16: 178–186. DOI: 10.1016/j.actbio.2015.01.038.
    [38] WEGST U G K, BAI H, SAIZ E, et al. Bioinspired structural materials [J]. Nature Materials, 2015, 14(1): 23–36. DOI: 10.1038/nmat4089.
    [39] EDER M, JUNGNIKL K, BURGERT I. A close-up view of wood structure and properties across a growth ring of Norway spruce (Picea abies [L] Karst. ) [J]. Trees, 2009, 23(1): 79-84. DOI: 10.1007/s00468-008-0256-1.
    [40] SPECK T, BURGERT I. Plant stems: functional design and mechanics [J]. Annual Review of Materials Research, 2011, 41: 169–193. DOI: 10.1146/annurev-matsci-062910-100425.
    [41] BOROWSKA-WYKRĘT D, RYPIEŃ A, DULSKI M, et al. Gradient of structural traits drives hygroscopic movements of scarious bracts surrounding Helichrysum bracteatum capitulum [J]. Annals of Botany, 2017, 119(8): 1365–1383. DOI: 10.1093/aob/mcx015.
    [42] DENG K, KOVALEV A, RAJABI H, et al. The damping properties of the foam-filled shaft of primary feathers of the pigeon Columba livia [J]. The Science of Nature, 2021, 109(1): 1. DOI: 10.1007/s00114-021-01773-7.
    [43] YANG T, CHEN H S, JIA Z A, et al. A damage-tolerant, dual-scale, single-crystalline microlattice in the knobby starfish, Protoreaster nodosus [J]. Science, 2022, 375(6581): 647–652. DOI: 10.1126/science.abj9472.
    [44] EVANS A G, HUTCHINSON J W, FLECK N A, et al. The topological design of multifunctional cellular metals [J]. Progress in Materials Science, 2001, 46(3/4): 309–327. DOI: 10.1016/S0079-6425(00)00016-5.
    [45] 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.
    [46] YAO R Y, PANG T, HE S Y, et al. A bio-inspired foam-filled multi-cell structural configuration for energy absorption [J]. Composites Part B: Engineering, 2022, 238: 109801. DOI: 10.1016/j.compositesb.2022.109801.
    [47] ZHANG Y, HE S Y, LIU J G, et al. Density gradient tailoring of aluminum foam-filled tube [J]. Composite Structures, 2019, 220: 451–459. DOI: 10.1016/j.compstruct.2019.04.026.
    [48] BROTHERS A H, DUNAND D C. Density-graded cellular aluminum [J]. Advanced Engineering Materials, 2006, 8(9): 805–809. DOI: 10.1002/adem.200600074.
    [49] 张新春, 刘颖. 密度梯度蜂窝材料动力学性能研究 [J]. 工程力学, 2012, 29(8): 372–377. DOI: 10.6052/j.issn.1000-4750.2010.12.0872.

    ZHANG X C, LIU Y. Research on the dynamic crushing of honeycombs with density gradient [J]. Engineering Mechanics, 2012, 29(8): 372–377. DOI: 10.6052/j.issn.1000-4750.2010.12.0872.
    [50] LIU H, NG B F. Dynamic response of density-graded foam subjected to soft impact [J]. Composite Structures, 2022, 284: 115145. DOI: 10.1016/j.compstruct.2021.115145.
    [51] PAGLIOCCA N, YOUSSEF G, KOOHBOR B. In-plane mechanical and failure responses of honeycombs with syntactic foam cell walls [J]. Composite Structures, 2022, 295: 115866. DOI: 10.1016/j.compstruct.2022.115866.
    [52] JEFFERSON A J, SCHNEIDER J, SCHIFFER A, et al. Dynamic crushing of tailored honeycombs realized via additive manufacturing [J]. International Journal of Mechanical Sciences, 2022, 219: 107126. DOI: 10.1016/j.ijmecsci.2022.107126.
    [53] 吴鹤翔, 刘颖. 梯度变化对密度梯度蜂窝材料力学性能的影响 [J]. 爆炸与冲击, 2013, 33(2): 163–168. DOI: 10.11883/1001-1455(2013)02-0163-06.

    WU H X, LIU Y. Influences of density gradient variation on mechanical performances of density-graded honeycomb materials [J]. Explosion and Shock Waves, 2013, 33(2): 163–168. DOI: 10.11883/1001-1455(2013)02-0163-06.
    [54] FENG G Z, LI S, XIAO L J, et al. Energy absorption performance of honeycombs with curved cell walls under quasi-static compression [J]. International Journal of Mechanical Sciences, 2021, 210: 106746. DOI: 10.1016/j.ijmecsci.2021.106746.
    [55] ZENG Y, SUN L J, YAO H H, et al. Fabrication of alumina ceramics with functional gradient structures by digital light processing 3D printing technology [J]. Ceramics International, 2022, 48(8): 10613–10619. DOI: 10.1016/j.ceramint.2021.12.275.
    [56] BAI L, GONG C, CHEN X H, et al. Mechanical properties and energy absorption capabilities of functionally graded lattice structures: experiments and simulations [J]. International Journal of Mechanical Sciences, 2020, 182: 105735. DOI: 10.1016/j.ijmecsci.2020.105735.
    [57] JIN M X, FENG Q X, FAN X J, et al. Investigation on the mechanical properties of TPMS porous structures fabricated by laser powder bed fusion [J]. Journal of Manufacturing Processes, 2022, 76: 559–574. DOI: 10.1016/j.jmapro.2022.02.035.
    [58] QIU N, ZHANG J Z, YUAN F Q, et al. Mechanical performance of triply periodic minimal surface structures with a novel hybrid gradient fabricated by selective laser melting [J]. Engineering Structures, 2022, 263: 114377. DOI: 10.1016/j.engstruct.2022.114377.
    [59] ZHANG J F, CHEN X H, SUN Y X, et al. Design of a biomimetic graded TPMS scaffold with quantitatively adjustable pore size [J]. Materials & Design, 2022, 218: 110665. DOI: 10.1016/j.matdes.2022.110665.
    [60] AL-KETAN O, ABU AL-RUB R K. Multifunctional mechanical metamaterials based on triply periodic minimal surface lattices [J]. Advanced Engineering Materials, 2019, 21(10): 1900524. DOI: 10.1002/adem.201900524.
    [61] FENG G Z, LI S, XIAO L J, et al. Mechanical properties and deformation behavior of functionally graded TPMS structures under static and dynamic loading [J]. International Journal of Impact Engineering, 2023, 176: 104554. DOI: 10.1016/j.ijimpeng.2023.104554.
    [62] AL-KETAN O, ABU AL-RUB R K. MSLattice: a free software for generating uniform and graded lattices based on triply periodic minimal surfaces [J]. Material Design & Processing Communications, 2021, 3(6): e205. DOI: 10.1002/mdp2.205.
    [63] KOOHBOR B, RAVINDRAN S, KIDANE A. In situ deformation characterization of density-graded foams in quasi-static and impact loading conditions [J]. International Journal of Impact Engineering, 2021, 150: 103820. DOI: 10.1016/j.ijimpeng.2021.103820.
    [64] KOOHBOR B, KIDANE A. Design optimization of continuously and discretely graded foam materials for efficient energy absorption [J]. Materials & Design, 2016, 102: 151–161. DOI: 10.1016/j.matdes.2016.04.031.
    [65] KOOHBOR B, KIDANE A, LU W Y, et al. Investigation of the dynamic stress-strain response of compressible polymeric foam using a non-parametric analysis [J]. International Journal of Impact Engineering, 2016, 91: 170–182. DOI: 10.1016/j.ijimpeng.2016.01.007.
    [66] ZHANG J H, CHEN L, WU H, et al. Experimental and mesoscopic investigation of double-layer aluminum foam under impact loading [J]. Composite Structures, 2020, 241: 110859. DOI: 10.1016/j.compstruct.2019.04.031.
    [67] ZHANG J J, WEI H, WANG Z H, et al. Dynamic crushing of uniform and density graded cellular structures based on the circle arc model [J]. Latin American Journal of Solids and Structures, 2015, 12(6): 1102–1125. DOI: 10.1590/1679-78251630.
    [68] FAN J H, ZHANG J J, WANG Z H, et al. Dynamic crushing behavior of random and functionally graded metal hollow sphere foams [J]. Materials Science and Engineering: A, 2013, 561: 352–361. DOI: 10.1016/j.msea.2012.10.026.
    [69] ZHANG J J, WANG Z H, ZHAO L M. Dynamic response of functionally graded cellular materials based on the Voronoi model [J]. Composites Part B: Engineering, 2016, 85: 176–187. DOI: 10.1016/j.compositesb.2015.09.045.
    [70] LIANG M Z, LI X Y, LIN Y L, et al. Dynamic compressive behaviors of two-layer graded aluminum foams under blast loading [J]. Materials, 2019, 12(9): 1445. DOI: 10.3390/ma12091445.
    [71] LIU Y, WU H X, WANG B. Gradient design of metal hollow sphere (MHS) foams with density gradients [J]. Composites Part B: Engineering, 2012, 43(3): 1346–1352. DOI: 10.1016/j.compositesb.2011.11.057.
    [72] KARAGIOZOVA D, ALVES M. Compaction of a double-layered metal foam block impacting a rigid wall [J]. International Journal of Solids and Structures, 2014, 51(13): 2424–2438. DOI: 10.1016/j.ijsolstr.2014.03.012.
    [73] KARAGIOZOVA D, ALVES M. Stress waves in layered cellular materials—dynamic compaction under axial impact [J]. International Journal of Mechanical Sciences, 2015, 101/102: 196–213. DOI: 10.1016/j.ijmecsci.2015.07.024.
    [74] 张健, 赵桂平, 卢天健. 梯度泡沫金属的冲击吸能特性 [J]. 工程力学, 2016, 33(8): 211–220. DOI: 10.6052/j.issn.1000-4750.2014.09.0755.

    ZHANG J, ZHAO G P, LU T J. Energy absorption behaviour of density-graded metallic foam under impact loading [J]. Engineering Mechanics, 2016, 33(8): 211–220. DOI: 10.6052/j.issn.1000-4750.2014.09.0755.
    [75] YANG J, WANG S L, DING Y Y, et al. Crashworthiness of graded cellular materials: a design strategy based on a nonlinear plastic shock model [J]. Materials Science and Engineering: A, 2017, 680: 411–420. DOI: 10.1016/j.msea.2016.11.010.
    [76] CHANG B X, ZHENG Z J, ZHANG Y L, et al. Crashworthiness design of graded cellular materials: an asymptotic solution considering loading rate sensitivity [J]. International Journal of Impact Engineering, 2020, 143: 103611. DOI: 10.1016/j.ijimpeng.2020.103611.
    [77] CHANG B X, ZHENG Z J, ZHANG Y R, et al. Crashworthiness design of graded cellular materials: experimental verification of the backward design strategy [J]. International Journal of Impact Engineering, 2023, 171: 104366. DOI: 10.1016/j.ijimpeng.2022.104366.
    [78] ZHANG Y R, ZHU Y D, CHANG B X, et al. Blast-loading simulators: multiscale design of graded cellular projectiles considering projectile-beam coupling effect [J]. Journal of the Mechanics and Physics of Solids, 2023, 180: 105402. DOI: 10.1016/j.jmps.2023.105402.
    [79] WANG X K, ZHENG Z J, YU J L, et al. Impact resistance and energy absorption of functionally graded cellular structures [J]. Applied Mechanics and Materials, 2011, 69: 73–78. DOI: 10.4028/www.scientific.net/AMM.69.73.
    [80] ZHENG J, QIN Q H, WANG T J. Impact plastic crushing and design of density-graded cellular materials [J]. Mechanics of Materials, 2016, 94: 66–78. DOI: 10.1016/j.mechmat.2015.11.014.
    [81] SHEN C J, LU G, YU T X, et al. Dynamic response of a cellular block with varying cross-section [J]. International Journal of Impact Engineering, 2015, 79: 53–64. DOI: 10.1016/j.ijimpeng.2014.08.017.
    [82] SHEN C J, LU G, RUAN D, et al. Propagation of the compaction waves in a cellular block with varying cross-section [J]. International Journal of Solids and Structures, 2016, 88/89: 319–336. DOI: 10.1016/j.ijsolstr.2016.01.014.
    [83] 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.
    [84] RAPAKA S D, PANDEY M, ANNABATTULA R K. Effect of combined gradation in cross-sectional area and density on the dynamic compressive behavior of foams for moderate impact velocities [J]. Mechanics of Materials, 2022, 172: 104381. DOI: 10.1016/j.mechmat.2022.104381.
    [85] SHEN C J, YU T X, LU G. 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.
    [86] DUAN Y, DING Y, LIU Z Y, et al. Effects of cell size vs. cell-wall thickness gradients on compressive behavior of additively manufactured foams [J]. Composites Science and Technology, 2020, 199: 108339. DOI: 10.1016/j.compscitech.2020.108339.
    [87] DUAN Y, ZHAO X H, DU B, et al. Quasi-static compressive behavior and constitutive model of graded foams [J]. International Journal of Mechanical Sciences, 2020, 177: 105603. DOI: 10.1016/j.ijmecsci.2020.105603.
    [88] DUAN Y, ZHAO X H, LIU Z Y, et al. Dynamic response of additively manufactured graded foams [J]. Composites Part B: Engineering, 2020, 183: 107630. DOI: 10.1016/j.compositesb.2019.107630.
    [89] BAI L, GONG C, CHEN X H, et al. Quasi-static compressive responses and fatigue behaviour of Ti-6Al-4V graded lattice structures fabricated by laser powder bed fusion [J]. Materials & Design, 2021, 210: 110110. DOI: 10.1016/j.matdes.2021.110110.
    [90] DE WAAL L, LU G X, ZHANG J J, et al. Dynamic behaviour of graded origami honeycomb [J]. International Journal of Impact Engineering, 2021, 157: 103976. DOI: 10.1016/j.ijimpeng.2021.103976.
    [91] YANG J X, CHEN X H, SUN Y X, et al. Compressive properties of bidirectionally graded lattice structures [J]. Materials & Design, 2022, 218: 110683. DOI: 10.1016/j.matdes.2022.110683.
    [92] ZAMANI M H, HEIDARI-RARANI M, TORABI K. Optimal design of a novel graded auxetic honeycomb core for sandwich beams under bending using digital image correlation (DIC) [J]. Composite Structures, 2022, 286: 115310. DOI: 10.1016/j.compstruct.2022.115310.
    [93] 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.
    [94] LIU H, ZHANG E T, NG B F. In-plane dynamic crushing of a novel honeycomb with functionally graded fractal self-similarity [J]. Composite Structures, 2021, 270: 114106. DOI: 10.1016/j.compstruct.2021.114106.
    [95] WANG X K, ZHENG Z J, YU J L. Crashworthiness design of density-graded cellular metals [J]. Theoretical and Applied Mechanics Letters, 2013, 3(3): 031001. DOI: 10.1063/2.1303101.
    [96] 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.
    [97] MATSUMOTO Y, BROTHERS A H, STOCK S R, et al. Uniform and graded chemical milling of aluminum foams [J]. Materials Science and Engineering: A, 2007, 447(1/2): 150–157. DOI: 10.1016/j.msea.2006.10.049.
    [98] POLLIEN A, CONDE Y, PAMBAGUIAN L, et al. Graded open-cell aluminium foam core sandwich beams [J]. Materials Science and Engineering: A, 2005, 404(1/2): 9–18. DOI: 10.1016/j.msea.2005.05.096.
    [99] HASSANI A, HABIBOLAHZADEH A, BAFTI H. Production of graded aluminum foams via powder space holder technique [J]. Materials & Design, 2012, 40: 510–515. DOI: 10.1016/j.matdes.2012.04.024.
    [100] HE S Y, ZHANG Y, DAI G, et al. Preparation of density-graded aluminum foam [J]. Materials Science and Engineering: A, 2014, 618: 496–499. DOI: 10.1016/j.msea.2014.08.087.
    [101] HE S Y, LV Y N, CHEN S T, et al. Gradient regulation and compressive properties of density-graded aluminum foam [J]. Materials Science and Engineering: A, 2020, 772: 138658. DOI: 10.1016/j.msea.2019.138658.
    [102] ZHANG Y, ZANG X Y, WANG K, et al. Fabrication of functionally radial graded metallic foam [J]. Materials Letters, 2020, 264: 127292. DOI: 10.1016/j.matlet.2019.127292.
    [103] JIANG H, COOMES A, ZHANG Z N, et al. Tailoring 3D printed graded architected polymer foams for enhanced energy absorption [J]. Composites Part B: Engineering, 2021, 224: 109183. DOI: 10.1016/j.compositesb.2021.109183.
    [104] ABDELMAGEED M, CANTWELL W, ZAKI W. Energy absorption and mechanical response of graded face-centered cubic structures [J]. International Journal of Mechanical Sciences, 2024, 273: 109232. DOI: 10.1016/j.ijmecsci.2024.109232.
    [105] YU S X, SUN J X, BAI J M. Investigation of functionally graded TPMS structures fabricated by additive manufacturing [J]. Materials & Design, 2019, 182: 108021. DOI: 10.1016/j.matdes.2019.108021.
    [106] BI S R, CHEN E Z, GAITANAROS S. Additive manufacturing and characterization of brittle foams [J]. Mechanics of Materials, 2020, 145: 103368. DOI: 10.1016/j.mechmat.2020.103368.
    [107] MASKERY I, ABOULKHAIR N T, AREMU A O, et al. A mechanical property evaluation of graded density Al-Si10-Mg lattice structures manufactured by selective laser melting [J]. Materials Science and Engineering: A, 2016, 670: 264–274. DOI: 10.1016/j.msea.2016.06.013.
    [108] XIAO L J, SONG W D. Additively-manufactured functionally graded Ti-6Al-4V lattice structures with high strength under static and dynamic loading: experiments [J]. International Journal of Impact Engineering, 2018, 111: 255–272. DOI: 10.1016/j.ijimpeng.2017.09.018.
    [109] LIAO S F, ZHENG Z J, YU J L, et al. A design guide of double-layer cellular claddings for blast alleviation [J]. International Journal of Aerospace and Lightweight Structures, 2013, 3(1): 109–133. DOI: 10.3850/S201042862013000550.
    [110] LIAO S F, ZHENG Z J, YU J L. On the local nature of the strain field calculation method for measuring heterogeneous deformation of cellular materials [J]. International Journal of Solids and Structures, 2014, 51(2): 478–490. DOI: 10.1016/j.ijsolstr.2013.10.019.
    [111] DING Y Y, ZHENG Z J, WANG Y G, et al. Impact resistance and design of graded cellular cladding [J]. International Journal of Applied Mechanics, 2018, 10(10): 1850107. DOI: 10.1142/s1758825118501077.
    [112] 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.
    [113] DING Y Y, ZHENG Y X, ZHENG Z J, et al. Blast alleviation of sacrificial cladding with graded and uniform cellular materials [J]. Materials, 2020, 13(24): 5616. DOI: 10.3390/ma13245616.
    [114] WANG P, WANG X K, ZHENG Z J, et al. Stress distribution in graded cellular materials under dynamic compression [J]. Latin American Journal of Solids and Structures, 2017, 14(7): 1251–1272. DOI: 10.1590/1679-78253428.
    [115] 虞吉林, 余同希, 周风华. 材料和结构的动态吸能 [M]. 合肥: 中国科学技术大学出版社, 2015.

    YU J L, YU T X, ZHOU F H. Dynamic energy absorption of materials and structures [M]. Hefei: University of Science and Technology of China Press, 2015.
    [116] CHEN J Y, ZHANG P, CHENG Y S, et al. On the crushing response of the functionally graded metallic foams based on 3D Voronoi model [J]. Thin-Walled Structures, 2020, 157: 107085. DOI: 10.1016/j.tws.2020.107085.
    [117] LIU Y, WU H X, LU G X, et al. Dynamic properties of density graded thin-walled metal hollow sphere arrays [J]. Mechanics of Advanced Materials and Structures, 2013, 20(6): 478–488. DOI: 10.1080/15376494.2011.627642.
    [118] SHEN C J, LU G, 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.
    [119] KARAGIOZOVA D, ZHANG J J, CHEN P W, et al. Response of graded Miura-Ori metamaterials to quasi-static and dynamic in-plane compression [J]. Journal of Aerospace Engineering, 2022, 35(4). DOI: 10.1061/(asce)as.1943-5525.0001416.
    [120] 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.
    [121] 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.
    [122] 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.
    [123] PATTOFATTO S, ELNASRI I, ZHAO H, et al. Shock enhancement of cellular structures under impact loading: part Ⅱ analysis [J]. Journal of the Mechanics and Physics of Solids, 2007, 55(12): 2672–2686. DOI: 10.1016/j.jmps.2007.04.004.
    [124] ZHENG Z J, YU J L, WANG C F, et al. Dynamic crushing of cellular materials: a unified framework of plastic shock wave models [J]. International Journal of Impact Engineering, 2013, 53: 29–43. DOI: 10.1016/j.ijimpeng.2012.06.012.
    [125] LOPATNIKOV S L, GAMA B A, JAHIRUL HAQUE M, et al. Dynamics of metal foam deformation during Taylor cylinder-Hopkinson bar impact experiment [J]. Composite Structures, 2003, 61(1/2): 61–71. DOI: 10.1016/S0263-8223(03)00039-4.
    [126] LOPATNIKOV S L, GAMA B A, HAQUE M J, et al. High-velocity plate impact of metal foams [J]. International Journal of Impact Engineering, 2004, 30(4): 421–445. DOI: 10.1016/S0734-743X(03)00066-6.
    [127] LOPATNIKOV S L, GAMA B A, GILLESPIE JR J W. Modeling the progressive collapse behavior of metal foams [J]. International Journal of Impact Engineering, 2007, 34(3): 587–595. DOI: 10.1016/j.ijimpeng.2005.12.004.
    [128] HARRIGAN J J, REID S R, YAGHOUBI A S. The correct analysis of shocks in a cellular material [J]. International Journal of Impact Engineering, 2010, 37(8): 918–927. DOI: 10.1016/j.ijimpeng.2009.03.011.
    [129] WANG S L, DING Y Y, WANG C F, et al. Dynamic material parameters of closed-cell foams under high-velocity impact [J]. International Journal of Impact Engineering, 2017, 99: 111–121. DOI: 10.1016/j.ijimpeng.2016.09.013.
    [130] 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.
    [131] DING Y Y, WANG S L, ZHENG Z J, et al. Dynamic crushing of cellular materials: a unique dynamic stress-strain state curve [J]. Mechanics of Materials, 2016, 100: 219–231. DOI: 10.1016/j.mechmat.2016.07.001.
    [132] BARNES A T, RAVI-CHANDAR K, KYRIAKIDES S, et al. Dynamic crushing of aluminum foams: part Ⅰ—experiments [J]. International Journal of Solids and Structures, 2014, 51(9): 1631–1645. DOI: 10.1016/j.ijsolstr.2013.11.019.
    [133] GAITANAROS S, KYRIAKIDES S. Dynamic crushing of aluminum foams: part Ⅱ—analysis [J]. International Journal of Solids and Structures, 2014, 51(9): 1646–1661. DOI: 10.1016/j.ijsolstr.2013.11.020.
    [134] GAITANAROS S, KYRIAKIDES S. On the effect of relative density on the crushing and energy absorption of open-cell foams under impact [J]. International Journal of Impact Engineering, 2015, 82: 3–13. DOI: 10.1016/j.ijimpeng.2015.03.011.
    [135] WANG S L, ZHENG Z J, ZHU C F, et al. Crushing and densification of rapid prototyping polylactide foam: meso-structural effect and a statistical constitutive model [J]. Mechanics of Materials, 2018, 127: 65–76. DOI: 10.1016/j.mechmat.2018.09.003.
    [136] MA G W, YE Z Q. Energy absorption of double-layer foam cladding for blast alleviation [J]. International Journal of Impact Engineering, 2007, 34(2): 329–347. DOI: 10.1016/j.ijimpeng.2005.07.012.
    [137] SHEN C J, LU G, 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.
    [138] ZHANG H, CHANG B X, PENG K F, et al. Anti-blast analysis and design of a sacrificial cladding with graded foam-filled tubes [J]. Thin-Walled Structures, 2023, 182: 110313. DOI: 10.1016/j.tws.2022.110313.
    [139] LIU H, DING S R, NG B F. Impact response and energy absorption of functionally graded foam under temperature gradient environment [J]. Composites Part B: Engineering, 2019, 172: 516–532. DOI: 10.1016/j.compositesb.2019.05.072.
    [140] GUPTA V, KIDANE A, SUTTON M. Closed-form solution for shock wave propagation in density-graded cellular material under impact [J]. Theoretical and Applied Mechanics Letters, 2021, 11(5): 100288. DOI: 10.1016/j.taml.2021.100288.
    [141] RAPAKA S D, PANDEY M, ANNABATTULA R K. Theoretical analysis on the dynamic compressive behavior of cellular solids with non-linear variation in cross-sectional area [J]. International Journal of Impact Engineering, 2021, 155: 103921. DOI: 10.1016/j.ijimpeng.2021.103921.
    [142] CHENG Q, YIN J F, WEN J H, et al. Triply periodic minimal surface structures: energy absorption performance under impact loading and their graded design [J]. Mechanics of Advanced Materials and Structures. DOI: 10.1080/15376494.2024.2311237.
    [143] CUI L, KIERNAN S, GILCHRIST M D. Designing the energy absorption capacity of functionally graded foam materials [J]. Materials Science and Engineering: A, 2009, 507(1/2): 215–225. DOI: 10.1016/j.msea.2008.12.011.
    [144] AJDARI A, NAYEB-HASHEMI H, VAZIRI A. Dynamic crushing and energy absorption of regular, irregular and functionally graded cellular structures [J]. International Journal of Solids and Structures, 2011, 48(3/4): 506–516. DOI: 10.1016/j.ijsolstr.2010.10.018.
    [145] ZHANG X, ZHANG H. Optimal design of functionally graded foam material under impact loading [J]. International Journal of Mechanical Sciences, 2013, 68: 199–211. DOI: 10.1016/j.ijmecsci.2013.01.016.
    [146] YANG J, WANG S L, ZHENG Z J, et al. Impact resistance of graded cellular metals using cell-based finite element models [J]. Key Engineering Materials, 2016, 703: 400–405. DOI: 10.4028/www.scientific.net/KEM.703.400.
    [147] LIU H, ZHANG Z Q, LIU H, et al. Theoretical investigation on impact resistance and energy absorption of foams with nonlinearly varying density [J]. Composites Part B: Engineering, 2017, 116: 76–88. DOI: 10.1016/j.compositesb.2017.02.012.
    [148] 常白雪, 郑志军, 赵凯, 等. 梯度多胞材料耐撞性设计的简化模型和渐近解 [J]. 中国科学: 物理学 力学 天文学, 2018, 48(9): 094615. DOI: 10.1360/SSPMA2018-00162.

    CHANG B X, ZHENG Z J, ZHAO K, et al. A simplified model and its asymptotic solution for the crashworthiness design of graded cellular material [J]. Scientia Sinica Physica, Mechanica & Astronomica, 2018, 48(9): 094615. DOI: 10.1360/SSPMA2018-00162.
    [149] 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.
    [150] RAVINDRAN S, KOOHBOR B, MALCHOW P, et al. Experimental characterization of compaction wave propagation in cellular polymers [J]. International Journal of Solids and Structures, 2018, 139/140: 270–282. DOI: 10.1016/j.ijsolstr.2018.02.003.
    [151] LIU J G, HOU B, LU F Y, et al. A theoretical study of shock front propagation in the density graded cellular rods [J]. International Journal of Impact Engineering, 2015, 80: 133–142. DOI: 10.1016/j.ijimpeng.2015.02.001.
    [152] 常白雪, 郑志军, 赵凯, 等. 具有恒定冲击载荷的梯度泡沫金属材料设计 [J]. 爆炸与冲击, 2019, 39(4): 041101. DOI: 10.11883/bzycj-2018-0431.

    CHANG B X, ZHENG Z J, ZHAO K, et al. Design of gradient foam metal materials with a constant impact load [J]. Explosion and Shock Waves, 2019, 39(4): 041101. DOI: 10.11883/bzycj-2018-0431.
    [153] LI D, HOU H L, CHEN C H, et al. Experimental study on the combined damage of multi-layered composite structures subjected to close-range explosion of simulated warheads [J]. International Journal of Impact Engineering, 2018, 114: 133–146. DOI: 10.1016/j.ijimpeng.2017.12.007.
    [154] 赵著杰, 侯海量, 李典. 填充多胞元抗冲击防护结构动力学特性及防护性能研究进展 [J]. 中国舰船研究, 2021, 16(3): 96–111. DOI: 10.19693/j.issn.1673-3185.02053.

    ZHAO Z J, HOU H L, LI D. Research progress on dynamic characteristics and protective performance of multicellular filled impact resistant protective structure [J]. Chinese Journal of Ship Research, 2021, 16(3): 96–111. DOI: 10.19693/j.issn.1673-3185.02053.
    [155] ZHOU H Y, WANG Y H, WANG X J, et al. Energy absorption of graded foam subjected to blast: a theoretical approach [J]. Materials & Design, 2015, 84: 351–358. DOI: 10.1016/j.matdes.2015.06.124.
    [156] XIA Y, WU C Q, LIU Z X, et al. Protective effect of graded density aluminium foam on RC slab under blast loading—an experimental study [J]. Construction and Building Materials, 2016, 111: 209–222. DOI: 10.1016/j.conbuildmat.2016.02.092.
    [157] YIN C Y, JIN Z Y, CHEN Y, et al. The underwater blast resistance of sacrificial claddings with stepwise graded cellular cores [J]. Journal of Offshore Mechanics and Arctic Engineering, 2017, 139(2): 021602. DOI: 10.1115/1.4034922.
    [158] LIANG M Z, LI Z B, LU F Y, et al. Theoretical and numerical investigation of blast responses of continuous-density graded cellular materials [J]. Composite Structures, 2017, 164: 170–179. DOI: 10.1016/j.compstruct.2016.12.065.
    [159] LAN X K, FENG S S, HUANG Q, et al. Blast response of continuous-density graded cellular material based on the 3D Voronoi model [J]. Defence Technology, 2018, 14(5): 433–440. DOI: 10.1016/j.dt.2018.06.003.
    [160] LIANG M Z, LI X Y, LIN Y L, et al. Compaction wave propagation in layered cellular materials under air-blast [J]. International Journal of Applied Mechanics, 2019, 11(1): 1950003. DOI: 10.1142/S1758825119500030.
    [161] PENG C X, TRAN P. Bioinspired functionally graded gyroid sandwich panel subjected to impulsive loadings [J]. Composites Part B: Engineering, 2020, 188: 107773. DOI: 10.1016/j.compositesb.2020.107773.
    [162] NOVAK N, BOROVINŠEK M, AL-KETAN O, et al. Impact and blast resistance of uniform and graded sandwich panels with TPMS cellular structures [J]. Composite Structures, 2022, 300: 116174. DOI: 10.1016/j.compstruct.2022.116174.
    [163] RADFORD D D, DESHPANDE V S, FLECK N A. The use of metal foam projectiles to simulate shock loading on a structure [J]. International Journal of Impact Engineering, 2005, 31(9): 1152–1171. DOI: 10.1016/j.ijimpeng.2004.07.012.
    [164] CHEN A, KIM H, ASARO R J, et al. Non-explosive simulated blast loading of balsa core sandwich composite beams [J]. Composite Structures, 2011, 93(11): 2768–2784. DOI: 10.1016/j.compstruct.2011.05.027.
    [165] LI L, ZHANG Q C, ZHANG R, et al. A laboratory experimental technique for simulating combined blast and impact loading [J]. International Journal of Impact Engineering, 2019, 134: 103382. DOI: 10.1016/j.ijimpeng.2019.103382.
    [166] RADFORD D D, FLECK N A, DESHPANDE V S. The response of clamped sandwich beams subjected to shock loading [J]. International Journal of Impact Engineering, 2006, 32(6): 968–987. DOI: 10.1016/j.ijimpeng.2004.08.007.
    [167] RADFORD D D, MCSHANE G J, DESHPANDE V S, et al. The response of clamped sandwich plates with metallic foam cores to simulated blast loading [J]. International Journal of Solids and Structures, 2006, 43(7/8): 2243–2259. DOI: 10.1016/j.ijsolstr.2005.07.006.
    [168] 敬霖, 王志华, 赵隆茂, 等. 撞击载荷下泡沫铝夹芯梁的塑性动力响应 [J]. 爆炸与冲击, 2010, 30(6): 561–568. DOI: 10.11883/1001-1455(2010)06-0561-08.

    JING L, WANG Z H, ZHAO L M, et al. Dynamic plastic response of foam sandwich beams subjected to impact loading [J]. Explosion and Shock Waves, 2010, 30(6): 561–568. DOI: 10.11883/1001-1455(2010)06-0561-08.
    [169] 宋延泽, 王志华, 赵隆茂, 等. 撞击载荷下泡沫铝夹层板的动力响应 [J]. 爆炸与冲击, 2010, 30(3): 301–307. DOI: 10.11883/1001-1455(2010)03-0301-07.

    SONG Y Z, WANG Z H, ZHAO L M, et al. Dynamic response of foam sandwich plates subjected to impact loading [J]. Explosion and Shock Waves, 2010, 30(3): 301–307. DOI: 10.11883/1001-1455(2010)03-0301-07.
    [170] JING L, WANG Z H, NING J G, et al. The mechanical response of metallic sandwich beams under foam projectile impact loading [J]. Latin American Journal of Solids and Structures, 2011, 8(1): 107–120. DOI: 10.1590/S1679-78252011000100006.
    [171] JING L, WANG Z H, NING J G, et al. The dynamic response of sandwich beams with open-cell metal foam cores [J]. Composites Part B: Engineering, 2011, 42(1): 1–10. DOI: 10.1016/j.compositesb.2010.09.024.
    [172] XIE Q H, JING L, WANG Z H, et al. Deformation and failure of clamped shallow sandwich arches with foam core subjected to projectile impact [J]. Composites Part B: Engineering, 2013, 44(1): 330–338. DOI: 10.1016/j.compositesb.2012.04.070.
    [173] JING L, WANG Z H, ZHAO L M. Response of metallic cylindrical sandwich shells subjected to projectile impact—experimental investigations [J]. Composite Structures, 2014, 107: 36–47. DOI: 10.1016/j.compstruct.2013.07.011.
    [174] JING L, WANG Z H, ZHAO L M. The dynamic response of sandwich panels with cellular metal cores to localized impulsive loading [J]. Composites Part B: Engineering, 2016, 94: 52–63. DOI: 10.1016/j.compositesb.2016.03.035.
    [175] LI X, LI S Q, WANG Z H, et al. Response of aluminum corrugated sandwich panels under foam projectile impact—experiment and numerical simulation [J]. Journal of Sandwich Structures & Materials, 2017, 19(5): 595–615. DOI: 10.1177/1099636216630503.
    [176] LI X, ZHANG P W, LI S Q, et al. Dynamic response of aluminum honeycomb sandwich panels under foam projectile impact [J]. Mechanics of Advanced Materials and Structures, 2018, 25(8): 637–646. DOI: 10.1080/15376494.2017.1308595.
    [177] 叶楠, 张伟, 黄威, 等. PVC夹芯板在冲击载荷下的动态响应与失效模式 [J]. 爆炸与冲击, 2017, 37(1): 37–45. DOI: 10.11883/1001-1455(2017)01-0037-09.

    YE N, ZHANG W, HUANG W, et al. Dynamic response and failure mode of PVC sandwich plates subjected to impact loading [J]. Explosion and Shock Waves, 2017, 37(1): 37–45. DOI: 10.11883/1001-1455(2017)01-0037-09.
    [178] YE N, ZHANG W, LI D C, et al. Dynamic response and failure of sandwich plates with PVC foam core subjected to impulsive loading [J]. International Journal of Impact Engineering, 2017, 109: 121–130. DOI: 10.1016/j.ijimpeng.2017.06.005.
    [179] XIAO D B, CHEN X Q, LI Y, et al. The structure response of sandwich beams with metallic auxetic honeycomb cores under localized impulsive loading—experiments and finite element analysis [J]. Materials & Design, 2019, 176: 107840. DOI: 10.1016/j.matdes.2019.107840.
    [180] LI Y, CHEN Z H, XIAO D B, et al. The Dynamic response of shallow sandwich arch with auxetic metallic honeycomb core under localized impulsive loading [J]. International Journal of Impact Engineering, 2020, 137: 103442. DOI: 10.1016/j.ijimpeng.2019.103442.
    [181] 熊飞扬, 高松林, 李晓彬, 等. 局部冲击载荷作用下星形蜂窝夹芯梁的动态响应研究 [J]. 武汉理工大学学报(交通科学与工程版), 2020, 44(2): 388–392. DOI: 10.3963/j.issn.2095-3844.2020.02.036.

    XIONG F Y, GAO S L, LI X B, et al. Study on dynamic response of star honeycomb sandwich beam under local impact load [J]. Journal of Wuhan University of Technology (Transportation Science & Engineering), 2020, 44(2): 388–392. DOI: 10.3963/j.issn.2095-3844.2020.02.036.
    [182] CHEN Z H, LIU L W, GAO S L, et al. Dynamic response of sandwich beam with star-shaped reentrant honeycomb core subjected to local impulsive loading [J]. Thin-Walled Structures, 2021, 161: 107420. DOI: 10.1016/j.tws.2020.107420.
    [183] 张元瑞, 朱玉东, 郑志军, 等. 泡沫子弹冲击固支单梁的耦合分析模型 [J]. 力学学报, 2022, 54(8): 2161–2172. DOI: 10.6052/0459-1879-22-223.

    ZHANG Y R, ZHU Y D, ZHENG Z J, et al. A coupling analysis model of clamped monolithic beam impacted by foam projectiles [J]. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(8): 2161–2172. DOI: 10.6052/0459-1879-22-223.
    [184] LI L, HAN B, HE S Y, et al. Shock loading simulation using density-graded metallic foam projectiles [J]. Materials & Design, 2019, 164: 107546. DOI: 10.1016/j.matdes.2018.107546.
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  • 收稿日期:  2024-03-29
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