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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  • 收稿日期:  2024-03-29
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