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Article(id=1241831205922996500, tenantId=1146029695717560320, journalId=1241755870837649424, issueId=1241831200843699167, articleNumber=null, orderNo=null, doi=10.19636/j.cnki.cjsm42-1250/o3.2025.031, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1759075200000, receivedDateStr=2025-09-29, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1774005231600, onlineDateStr=2026-03-20, pubDate=1761494400000, pubDateStr=2025-10-27, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1774005231600, onlineIssueDateStr=2026-03-20, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1774005231600, creator=13701087609, updateTime=1774005231600, updator=13701087609, issue=Issue{id=1241831200843699167, tenantId=1146029695717560320, journalId=1241755870837649424, year='2025', volume='46', issue='5', pageStart='571', pageEnd='706', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=1, specialIssue=null, createTime=1774005230388, creator=13701087609, updateTime=1774005316875, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1241831563734881184, tenantId=1146029695717560320, journalId=1241755870837649424, issueId=1241831200843699167, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1241831563739075489, tenantId=1146029695717560320, journalId=1241755870837649424, issueId=1241831200843699167, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=693, endPage=706, ext={EN=ArticleExt(id=1241831206170460440, articleId=1241831205922996500, tenantId=1146029695717560320, journalId=1241755870837649424, language=EN, title=Research on the Crashworthiness of New Honeycomb Structures, columnId=1241831201674171363, journalTitle=Chinese Journal of Solid Mechanics, columnName=Research Papers, runingTitle=null, highlight=null, articleAbstract=

To improve the impact resistance of metal honeycomb structures, three new types of impact protection structures, namely, closed bent honeycomb, concave filled honeycomb, and star-shaped curved honeycomb, were proposed and analyzed via finite element simulations using ANSYS/LS-DYNA. The deformation patterns and energy absorption capacities were evaluated at different impact velocities. Results showed that deformation patterns were related to the cell element structure and impact velocity. The closed bent honeycomb exhibited superior nominal stress and energy absorption efficiency compared to the other structures. Geometric parameters of honeycomb cell elements do not affect the trend of the nominal stress-strain curves. Increasing the bending angle of the closed bent honeycomb increased platform stress and decreased dense strain. Under medium-velocity impact, the platform stress of the 60° closed bent honeycomb structure increased by 19.5% compared to the 45°structure. Increasing relative density significantly improved energy absorption efficiency; the specific energy absorption of the high-density 60°closed bent honeycomb structure increased by 207.6% compared to the low-density structure.

, correspAuthors=Chengbing Li, authorNote=null, correspAuthorsNote=null, copyrightStatement=null, copyrightOwner=null, extLink=null, articleAbsUrl=null, sourceXml=null, magXml=null, pdfUrl=null, pdf=null, pdfFileSize=null, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=null, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=null, mapNumber=null, authorCompany=null, fund=null, authors=null, authorsList=Chengbing Li, Ke Xiao, Rui Li, Xupeng Feng, Junheng Peng), CN=ArticleExt(id=1241831214970110404, articleId=1241831205922996500, tenantId=1146029695717560320, journalId=1241755870837649424, language=CN, title=新型蜂窝结构的耐撞性能研究, columnId=1241831201896469478, journalTitle=固体力学学报, columnName=研究论文, runingTitle=null, highlight=null, articleAbstract=

为提升金属蜂窝结构抗冲击能力，提出了封闭弯折型蜂窝、内凹填充型蜂窝、星形曲边型蜂窝三种新型抗冲击防护结构. 采用ANSYS/LS-DYNA的有限元仿真进行分析，分析各冲击速度下三种蜂窝的变形特征和能量吸收能力. 研究结果表明：三种蜂窝结构的变形模式与胞元结构和冲击速度有关. 封闭弯折型蜂窝名义应力和能量吸收效率优于其他结构；蜂窝胞元的几何参数不影响名义应力-应变曲线的变化趋势. 封闭弯折型蜂窝弯折角度越大、平台应力值越高，密实应变值降低. 在中速冲击时，60°封闭弯折型蜂窝结构的平台应力相较45°结构提升了19.5%；提高相对密度能有效的提高蜂窝结构的吸能效率，高密度60°封闭弯折型蜂窝结构的比吸能相较于低密度提升了207.6%.

, correspAuthors=李成兵, authorNote=null, correspAuthorsNote=
**E-mail：.
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figureFileSmall=2KCx0mQxog9zg8k9AZhbBA==, figureFileBig=X1+QdgAw+uXXaRFs1vgyMg==, tableContent=null), ArticleFig(id=1241831223740400276, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1241831205922996500, language=EN, label=Table 1, caption=

Model parameters of each specimen

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蜂窝类型L1（mm）L2（mm）t（mm）
封闭弯折型蜂窝116.4101.80.300
内凹填充型蜂窝115.8102.00.280
星形曲边型蜂窝116.699.20.362
六边形蜂窝114.0104.40.575
), ArticleFig(id=1241831223828480662, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1241831205922996500, language=CN, label=表1, caption=

各试件模型参数

, figureFileSmall=null, figureFileBig=null, tableContent=
蜂窝类型L1（mm）L2（mm）t（mm）
封闭弯折型蜂窝116.4101.80.300
内凹填充型蜂窝115.8102.00.280
星形曲边型蜂窝116.699.20.362
六边形蜂窝114.0104.40.575
), ArticleFig(id=1241831223920755351, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1241831205922996500, language=EN, label=Table 2, caption=

Material parameter[14]

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材料ρ（kg•m-3）E（GPa）μσy（MPa）
铝合金2700690.3376
刚性板78452070.27207
), ArticleFig(id=1241831224050778775, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1241831205922996500, language=CN, label=表2, caption=

材料参数[14]

, figureFileSmall=null, figureFileBig=null, tableContent=
材料ρ（kg•m-3）E（GPa）μσy（MPa）
铝合金2700690.3376
刚性板78452070.27207
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Closed bent cellular cell parameters

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蜂窝结构L（mm）α（°）l（mm）t（mm）d（mm）
45°封闭弯折型蜂窝8.5452.070.3521.5
60°封闭弯折型蜂窝8.5601.690.31.5
75°封闭弯折型蜂窝8.5751.520.2581.5
), ArticleFig(id=1241831224222745243, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1241831205922996500, language=CN, label=表3, caption=

封闭弯折型蜂窝胞元参数

, figureFileSmall=null, figureFileBig=null, tableContent=
蜂窝结构L（mm）α（°）l（mm）t（mm）d（mm）
45°封闭弯折型蜂窝8.5452.070.3521.5
60°封闭弯折型蜂窝8.5601.690.31.5
75°封闭弯折型蜂窝8.5751.520.2581.5
), ArticleFig(id=1241831224340185756, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1241831205922996500, language=EN, label=Table 4, caption=

Parameters of closed bent honeycomb structure at each relative density

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Identifierα（°）b（mm）ρ
RD1450.1170.04518
600.100
750.086
RD2450.3500.13554
600.300
750.258
RD3450.5250.20331
600.450
750.388
), ArticleFig(id=1241831224440849053, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1241831205922996500, language=CN, label=表4, caption=

各相对密度下封闭弯折型蜂窝结构参数

, figureFileSmall=null, figureFileBig=null, tableContent=
Identifierα（°）b（mm）ρ
RD1450.1170.04518
600.100
750.086
RD2450.3500.13554
600.300
750.258
RD3450.5250.20331
600.450
750.388
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新型蜂窝结构的耐撞性能研究
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李成兵 1, 2, ** , 肖可 1 , 李锐 3 , 冯旭鹏 1 , 彭俊恒 1
固体力学学报 | 研究论文 2025,46(5): 693-706
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固体力学学报 | 研究论文 2025, 46(5): 693-706
新型蜂窝结构的耐撞性能研究
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李成兵1, 2, ** , 肖可1, 李锐3, 冯旭鹏1, 彭俊恒1
作者信息
  • 1西南石油大学机电工程学院，成都，610500
  • 2石油天然气装备技术四川省科技资源共享服务平台，成都，610500
  • 3成都航天通信设备有限责任公司，成都，610051

通讯作者:

Research on the Crashworthiness of New Honeycomb Structures
Chengbing Li1, 2, ** , Ke Xiao1, Rui Li3, Xupeng Feng1, Junheng Peng1
Affiliations
  • 1College of Mechanical and Electrical Engineering, Southwest Petroleum University, Chengdu, 610500
  • 2Oil and Gas Equipment Technology, Sharing and Service Platform of Sichuan Province, Chengdu, 610500
  • 3Chengdu Aerospace Communication Equipment Co., Ltd., Chengdu, 610051
出版时间: 2025-10-27 doi: 10.19636/j.cnki.cjsm42-1250/o3.2025.031
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摘要
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为提升金属蜂窝结构抗冲击能力，提出了封闭弯折型蜂窝、内凹填充型蜂窝、星形曲边型蜂窝三种新型抗冲击防护结构. 采用ANSYS/LS-DYNA的有限元仿真进行分析，分析各冲击速度下三种蜂窝的变形特征和能量吸收能力. 研究结果表明：三种蜂窝结构的变形模式与胞元结构和冲击速度有关. 封闭弯折型蜂窝名义应力和能量吸收效率优于其他结构；蜂窝胞元的几何参数不影响名义应力-应变曲线的变化趋势. 封闭弯折型蜂窝弯折角度越大、平台应力值越高，密实应变值降低. 在中速冲击时，60°封闭弯折型蜂窝结构的平台应力相较45°结构提升了19.5%；提高相对密度能有效的提高蜂窝结构的吸能效率，高密度60°封闭弯折型蜂窝结构的比吸能相较于低密度提升了207.6%.

蜂窝结构  /  变形模式  /  平台应力  /  能量吸收效率

To improve the impact resistance of metal honeycomb structures, three new types of impact protection structures, namely, closed bent honeycomb, concave filled honeycomb, and star-shaped curved honeycomb, were proposed and analyzed via finite element simulations using ANSYS/LS-DYNA. The deformation patterns and energy absorption capacities were evaluated at different impact velocities. Results showed that deformation patterns were related to the cell element structure and impact velocity. The closed bent honeycomb exhibited superior nominal stress and energy absorption efficiency compared to the other structures. Geometric parameters of honeycomb cell elements do not affect the trend of the nominal stress-strain curves. Increasing the bending angle of the closed bent honeycomb increased platform stress and decreased dense strain. Under medium-velocity impact, the platform stress of the 60° closed bent honeycomb structure increased by 19.5% compared to the 45°structure. Increasing relative density significantly improved energy absorption efficiency; the specific energy absorption of the high-density 60°closed bent honeycomb structure increased by 207.6% compared to the low-density structure.

honeycomb structure  /  deformation pattern  /  platform stress  /  energy absorption efficiency
李成兵, 肖可, 李锐, 冯旭鹏, 彭俊恒. 新型蜂窝结构的耐撞性能研究. 固体力学学报, 2025 , 46 (5) : 693 -706 . DOI: 10.19636/j.cnki.cjsm42-1250/o3.2025.031
Chengbing Li, Ke Xiao, Rui Li, Xupeng Feng, Junheng Peng. Research on the Crashworthiness of New Honeycomb Structures[J]. Chinese Journal of Solid Mechanics, 2025 , 46 (5) : 693 -706 . DOI: 10.19636/j.cnki.cjsm42-1250/o3.2025.031
正文
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0　引言
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蜂窝作为一种常见的多孔材料，具有高强度、轻质量，良好的能量效率和优异的耐撞性能等特征. 在面外冲击和面内冲击时，能够减少材料的损坏，延长使用寿命，在航空航天、船舶、建筑、汽车、包装、电子设备保护等领域广泛应用[1-2].
由于蜂窝结构吸能能力优越，目前关于蜂窝已展开大量的调查. Lee等[3]提出了一种新的抗爆炸自适应夹层BRAS结构（blast resistant adaptive sandwich），发现塑性铰折弯堆叠结构抗冲击性能较为优秀. 亓昌等[4]利用多孔结构对车用动力电池箱底部冲击防护，对比了三种不同芯层结构，对比分析显示，BRAS夹芯板的耐撞性能最佳，是动力电池箱底部防护的理想材料选择. Liu等[5]对内凹六边形蜂窝结构的耐撞性能进行了研究，发现在同等应变下内凹六边形蜂窝结构相较于传统蜂窝结构有更好的吸能效果. 邓小林等[6]提出了一种全参数化正弦曲线蜂窝结构，发现正弦曲线蜂窝结构的轻微拉胀效应可增强其平面内能量吸收能力. 韩会龙等[7]研究了冲击载荷下星形节点周期性蜂窝结构的动力学响应特性，基于能量效率法和一维冲击波理论，给出了星形蜂窝结构密实应变和动态平台应力的经验公式. 张宝庆等[8]研究了旋转负泊松比星形蜂窝结构能量吸收特性，研究表明旋转形结构的胞元在被冲击时具有更强的负泊松比效应. 王腾博等[9]提出了一种具有负泊松比效应的内凹工字形蜂窝结构，发现该结构相比于内凹六边形蜂窝结构，峰值应力更低，平台应力阶段时间更长，并且随着冲击速度的提高，表现出更好的冲击载荷一致性和能量吸收特性. Zhu等[10]结果发现不规则度的引入，可以延长应力-应变曲线的平台阶段且提出和优化了一种幂函数内凹负泊松比结构，结果显示改良后的结构能够有效提高比吸能. 如何结合各结构的优点，提高蜂窝结构的耐撞性能是本文研究的重点.
综上所述，本文将理论与实际相结合，提出了三种抗冲击蜂窝结构，并以此为研究对象. 研究其在不同速度下的面内耐撞性能和变形特征，并与传统蜂窝结构进行比较. 讨论各结构的面内冲击性能和能量吸收效率，得出耐撞性能较为优异的新型蜂窝结构，研究分析各结构参数对该蜂窝冲击动态响应的影响.
1　计算模型
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1.1　胞元几何结构
本文根据BRAS芯层胞元结构[5]，如图1（a）所示，提出了一种封闭式蜂窝胞元结构. 该结构为了满足蜂窝阵列，将蜂窝单元的尖角部分优化为平面设计. 上下由两个弯折的伞状结构组成，填充肋板可以起支撑作用，命名为封闭弯折型蜂窝（Closed bent honeycomb），如图1（b）所示. 其中：主要吸能的三个弯折角度分别为α1、α2、α3；l、l1、l2分别为单胞竖边长度、弯折薄壁长度、上下底长度，t1为胞壁厚度.
封闭弯折型蜂窝胞元体积
式中，H为蜂窝沿Z轴方向的长度，本研究中H=20 mm.
本文在内凹六边形蜂窝结构的基础上[5]，如图2（a）所示，提出了四周胞壁均为弧形结构的内凹蜂窝结构. 该结构由内凹六边形蜂窝和曲线负泊松比蜂窝复合而成，其曲线设计可以使蜂窝结构不易发生应力集中，填充肋板可以减弱其所受载荷发生的波动，命名为内凹填充型蜂窝（Concave filled honeycomb），如图2（b）所示. 其中：l为胞元高度，侧边内凹角度为α1，上下边圆弧角α2，圆弧半径分别为R1、R2，t2为胞壁厚度.
内凹填充型蜂窝结构胞元体积
本文在传统星形蜂窝结构的基础上[6]，如图3（a）所示，提出了一种正弦曲边蜂窝结构. 该结构的四条直线边由正弦曲线替代，命名为星形曲边型蜂窝（Star-shaped curved honeycomb），如图3（b）所示. 其中：l1为四周对称分布的正弦曲边，l为连接杆长度，正弦曲线的基本函数方程为：，t3为胞壁厚度.
星形曲边型蜂窝结构的胞元体积为
1.2　相对密度
相对密度是决定蜂窝结构耐撞性能的关键因素[11]. 蜂窝结构的相对密度越大，蜂窝结构的胞元变得更加紧密，增加了对外力的抵抗能力. 根据多胞材料理论[12]，相对密度Δρ由蜂窝材料实体部分面积与蜂窝材料所围区域面积.
式中：Vs是蜂窝材料实体部分体积，Vtotal是蜂窝材料所围区域体积.
封闭弯折型蜂窝结构相对密度
内凹填充型蜂窝结构相对密度
星形曲边型蜂窝结构相对密度
蜂窝的胞元几何结构不同，导致其相对密度不同，影响其力学性能. 本文通过控制胞壁的厚度控制各类蜂窝的相对密度. 为了探究这几种蜂窝结构的实用性，本文还讨论了传统蜂窝的数值结果与之比较. 表1给出了各试件在相对密度相等下各胞壁的厚度以及试件参数.
1.3　有限元设置
该研究蜂窝结构的有限元计算模型如图4所示，试件长度为L1，高度为L2，中间由各蜂窝结构填充. 加载模型的过程中，上端刚性板沿y轴方向以恒定的速度冲击试件，底部刚性板固定，蜂窝两侧为自由端.
本研究采用显式动力学有限元方法，使用Hypermesh和LS-DYNA平台建立蜂窝试件动态压缩模型. 蜂窝结构自身设置为自接触（AUTOMATIC_SINGLE_SURFACE）来定义自身之间的接触且假定为无摩擦. 其他各部分之间都设置为面接触（AUTOMATIC_SURFACE_TO_SURFACE）摩擦系数均为0.1. 两刚性板用（MAT_RIGID）定义，蜂窝材料采用多段线性弹性模型进行模拟. 采用四节点四边形壳单元进行离散，通过网格收敛性分析和实验数据相比较，设置网格大小为0.5 mm[13]. 在整个模拟过程中，材料参数如表2所示.
1.4　有限元模型验证
为验证有限元模型的有效性，本文使用试件材料ABS，该材料和铝合金都具有显著的塑性变形能力，该材料选择参考文献[15]. 建立试验模型为5* 5封闭弯折型蜂窝模型，进行面内动态力学性能模拟. 利用3D打印技术，将实验模型完整打印. 实验采用万能试验机进行轴向压缩测试，设置应变速率为0.001 s-1（压缩速率4 mm/min）. 图5对比展示了实验与仿真的力-位移曲线及变形模式，结果显示，两者基本吻合，证明了该有限元方法的可靠性.
2　计算结果与讨论
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2.1　变形模式
图6给出了各蜂窝结构在不同冲击速度下宏观变形情况，观察蜂窝结构在各类应变条件下的变形行为. 其本文中名义应变ε的计算方法为：冲击刚性板位移与试件原始高度的比值. 结果显示，在低速冲击时（v=10 m/s），随着刚性板往下压缩，封闭弯折型蜂窝各层胞元先后发生弯折变形，呈现出X形变形带. 在压缩过程中，冲击端和固定端胞元弯折角被压平后向中层胞元坍塌. 这是由于封闭弯折型蜂窝被压平使得结构冲击端和固定端的接触面积大于中间部分，导致其胞元相对比较稳定. 星形曲边型蜂窝的胞元发生卷曲旋转变形且向胞元中心蜷缩，呈负泊松比效应，两侧的变形区域带动中间的胞元发生形变. 这是由于结构边是曲边，在胞元被迅速压溃时，四角方向发生了较大变化，影响后续胞元压溃. 在整个过程中，封闭弯折型蜂窝是冲击端先发生坍塌，而星形曲边型蜂窝和内凹填充型蜂窝是中间部分先发生坍塌. 在中低速冲击时（v=30 m/s），开始出现惯性效应，三种蜂窝结构在冲击端变形明显. 内凹填充型蜂窝的变形模式转变为冲击端先发生变形. 封闭弯折型蜂窝和星形曲边型蜂窝整体结构都在变形，封闭弯折型蜂窝呈现“V”形的变形模式；星形曲边型蜂窝是冲击端的胞元四个角被拉直变形，随后带动下方胞元变形，变形方式与低速有差异. 这是因为内凹填充型蜂窝由于其结构特征，刚度比较大，后续胞元不易发生坍塌，使变形部分集中在冲击端；封闭弯折型蜂窝则是两侧弯折角被拉直后指向中间方向，使变形向中间靠拢. 星形曲边型蜂窝由于其曲边的结构特征，其四周角度容易被压塌，各胞元的四周角被压塌后垂直向下变形. 在中速冲击时（v=50 m/s），此时变形模式主要受到惯性效应的影响. 三种结构在冲击端都出现了“O”形带. 封闭弯折型蜂窝和星形曲边型蜂窝则是蜂窝试件整体同时变形，直至密实，内凹填充型蜂窝则是冲击端完全被压溃，下方胞元才开始变形. 三种结构在各速度冲击下，封闭弯折型蜂窝的变形模式是胞元向两边扩散，水平尺寸增大呈正泊松比；内凹填充型蜂窝则是横向尺寸基本保持不变，应力波竖直向下传递呈零泊松比；星形曲边型蜂窝是沿着四角向内部收缩，横向尺寸在达到密实应变前减小呈负泊松比.
2.2　动态响应曲线
名义应力-应变曲线能够反应在冲击过程中吸收能量的过程. 其中名义应力σ定义为冲击力和试件接触面积之比. 为模拟各工况下不同速度的冲击，本研究讨论低、中低、中、高（v=100 m/s）四种速度. 图7给出了各蜂窝结构在不同速度下的名义应力-应变曲线. 在低速和中低速冲击时，四种结构的动态响应曲线都有明显的缓冲吸能区，应力值比较稳定. 三种蜂窝结构名义应力值相差无几且均略强于普通六边形蜂窝. 随着变形进一步进行，胞元孔壁相互挤压，名义应变逐渐增大，各个胞元结构孔隙被压缩，名义应力也随之增大，直至密实. 在中速和超高速冲击时，名义应力值提高，随着应变率效应的增强[16]，名义应力值显著提升，同时应力-应变曲线呈现明显波动特征. 随着高速冲击产生的应力波在坍塌方向上快速传播，蜂窝试件被压溃在极短试件内坍塌至密实，使封闭弯折型蜂窝结构的名义应力呈周期性变化. 图中每一个凸起的峰值都是一层胞元被压密实的周期. 根据图7（c）（d），封闭弯折型蜂窝和星形曲边型蜂窝的名义应力值高于另外两种结构，说明这两种结构拥有更优越的耐撞性能.
2.3　比吸能
在动态冲击过程中，评估结构的能量吸收能力通常采用比吸能吸收（Esea）[17]这一参数来评估，它反应了结构单位质量所吸收的能量. 即
式中M为蜂窝结构的总质量，Ea为结构的总吸收能量由下式给出
式中：d为蜂窝结构变形的位移，F（x）为在冲击过程中产生的载荷.
比吸能能够直接反应各结构吸收能量的能力. 图8为不同速度下各结构能量吸收比. 在低速冲击时，封闭弯折型蜂窝的Esea略高于其他结构，这是因为其各层结构都发生折叠，具有更强的抵抗坍塌失稳的能力. 在应变ε=0.28时内凹填充型蜂窝的Esea超过了封闭弯折型蜂窝，是因为其结构稳定，抗冲击能力强. 在中低速和中速冲击时，封闭弯折型蜂窝的Esea在变形初始阶段领先于其他结构，分别在ε=0.65和ε=0.76时被星形曲边型蜂窝超过以及在接近ε=0.80时被内凹填充型蜂窝超过. 多孔结构的吸能阶段主要是在平台段，在高应变时，各种结构已经被压密实，没有讨论价值. 在高速时，封闭弯折型蜂窝的比吸能领先星形曲边型蜂窝结构43.5%，而其他两种结构的比吸能则远不如封闭弯折型蜂窝. 综上所述，封闭弯折型蜂窝具有最优的缓冲吸能特性.
随着冲击速度增加，所有蜂窝结构的比吸能都会增加. 这是因为随着冲击速度的提升，惯性效应显著增强，促使蜂窝结构的变形模式发生明显改变，单胞折叠次数增加，从而导致单位质量下吸收能量的能力随速度增加而增加这与文献[18]结论一致.
3　封闭弯折型蜂窝的耐撞性能
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3.1　结构参数化设计
为研究封闭弯折型蜂窝的耐撞性能，对该结构进行参数化设计. 改变胞元的几何参数，得到不同的胞元结构，评估其耐撞性能. 本文将研究弯折角度和相对密度对封闭弯折型蜂窝结构抗冲击性能的影响. 图9给出了各单胞结构示意图，其中，弯折角为α；胞元高度为L，底板宽度为d，弯折边长度为l，厚度为b. 封闭弯折型蜂窝的结构参数如表3所示.
3.2　结果与讨论
图10给出了45°、60°、75°封闭弯折型蜂窝结构的名义应力-应变曲线随冲击速度变化规律. 在低速和中低速冲击时，由于三种结构胞元几何相似性，其应力-应变曲线展现出相近的变化趋势，平台应力波动范围控制在10%以内.60°、75°封闭弯折型蜂窝的名义应力相近且大于45°结构，名义应力急剧上升的时间也早于45°封闭弯折型蜂窝，说明这两种结构的缓冲吸能的时间短于后者. 这是因为45°封闭弯折型蜂窝结构的孔隙率较大，被压密实的时间较长. 在中速和高速冲击时，由于应变率效应的影响，名义应力有较大的波动，且三种封闭弯折型结构的波动周期一致，且每个周期的长度与胞元的高度一致. 这是因为在高速冲击时，其结构的变形特征是逐层依次被压溃.
蜂窝结构在压缩过程中，主要通过蜂窝胞壁发生变形坍塌从而吸收能量. 本文将初始峰值应力至密实时的平均应力称为平台应力σp[19]，平台应力的大小决定结构的吸能能力.
蜂窝平台应力定义为
εs为初始应力达到峰值所对应的名义应变，密实应变εe由能量吸收效率方法确定.
基于能量吸收效率方法，密实应变[20]可表示为
式中，η为多胞试件在冲击过程中吸收的总能量与相应名义应变的比值，即：
如图11所示，为封闭弯折型蜂窝结构的能量吸收效率曲线. 能量吸收效率曲线上最后达到极大值点时刻所对应的应变值定义为蜂窝结构密实应变点.
图12给出了不同冲击速度下三种封闭弯折型蜂窝结构被压溃时所对应的密实应变. 由图12可知，随着冲击速度的提升，密实应变值也随之上升. 这是由于在高速加载中，应力波在传播过程中，会导致局部变形和致密化延迟. 在各种速度下45°封闭弯折型蜂窝的密实应变大于其他两种，这也验证了前文名义应力-应变曲线得到的结论，另外两种结构在各速度下互有高低.
图13给出了封闭弯折型蜂窝结构在不同冲击速度下的能量吸收情况. 从低速到高速冲击，封闭弯折型蜂窝结构的能量吸收曲线展现出相似的变化特征，这种特征与其平台应力的变化行为吻合.60°和75°封闭弯折型蜂窝的比吸能曲线基本一致，高于45°封闭弯折型蜂窝约20%到28%. 这是因为这两种结构相对于后者结构更加紧凑，胞元相对更多，导致抗冲击能力更强，但是也意味着会更早进入致密化阶段. 这也导致这两种结构比吸能Esea急剧上升要快于45°封闭弯折型蜂窝.
相对密度是影响蜂窝结构平台应力的关键因素. 为深入研究不同封闭弯折型蜂窝结构的平台应力与相对密度之间的关系，通过调整结构壁厚，构建了低、中、高三种相对密度水平的模型，其具体结构参数详见表4. 在同一密度下，45°弯折封闭时蜂窝胞元的厚度要高于另外两种.
图14给出了在各相对密度下三种封闭弯折型蜂窝结构在不同速度下的平台应力. 结果显示，在同一密度下，冲击速度提高，平台应力也随之提高，这与文献[21]结论一致. 相对密度的增加会显著增加各结构的平台应力. 在低阶密度时三种结构的应力水平相近，随着密度的增加，弯折角较大的两种结构平台应力值也明显高于45°弯折型蜂窝.
图15给出了在三种相对密度不同结构在（v=30 m/s）下的比吸能Esea. 比吸能随相对密度的增加显著增加.60°封闭弯折型蜂窝在中阶密度（ρ=0.13554）和高阶密度（ρ=0.20331）下的比吸能相对于低阶密度（ρ=0.04518）提高了大约122.5%和207.6%. 在低阶密度时，60°封闭弯折型蜂窝的比吸能效果优于另外两种. 随着相对密度的增加，高弯折角的封闭弯折型蜂窝比吸能的提升速度要快于低弯折角. 说明高弯折角的封闭弯折型蜂窝对相对密度的影响更为敏感.
4　结论
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通过显式动力学有限元方法，对本文提出的三种蜂窝结构的耐撞性能进行了研究得到以下主要结论：
（1）三种蜂窝结构在不同冲击速度的作用下，变形模式与各自的胞元结构有关. 封闭弯折型蜂窝依靠弯曲变形抵抗冲击，变形模式是多层胞元整体发生变形. 内凹填充型蜂窝由于刚度较高，蜂窝胞元则是逐层发生变形. 星形曲边型蜂窝由于负泊松比效应，蜂窝试件向内发生坍塌变形，且变形发生在试件中部.
（2）在相对密度相同的情况下，随着冲击速度的增加，平台应力和比吸能均有增加，封闭弯折型蜂窝的平台应力以及比吸能在各冲击速度下优于其他结构.
（3）弯折角这一参数对封闭弯折型蜂窝的耐撞性有着较大的影响，增大弯折角可以使封闭弯折型蜂窝的平台应力增大，但密实应变会减小，说明平台段吸收能量更多，但是吸能时间较短.
（4）相对密度对封闭弯折型蜂窝的力学性能有着较大的影响. 随着相对密度的增加，高弯折角的封闭弯折型蜂窝比吸能的提升速度要快于低弯折角，相对密度对弯折角较大的封闭弯折型蜂窝影响更为明显.
文献
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2025年第46卷第5期
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doi: 10.19636/j.cnki.cjsm42-1250/o3.2025.031
  • 接收时间：2025-09-29
  • 首发时间：2026-03-20
  • 出版时间：2025-10-27
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  • 收稿日期：2025-09-29
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    1西南石油大学机电工程学院，成都，610500
    2石油天然气装备技术四川省科技资源共享服务平台，成都，610500
    3成都航天通信设备有限责任公司，成都，610051

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2种不同金属材料的力学参数
科
Family		 属数
Number of
genus		 种数
Number of
species		 占总种数比例
Percentage of
total species (%)		 属
Genus		 种数
Number of
species		 占总种数比例
Percentage of total
species (%)
鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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