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Article(id=1241838627647459334, tenantId=1146029695717560320, journalId=1241755870837649424, issueId=1241838624241681037, articleNumber=null, orderNo=null, doi=10.19636/j.cnki.cjsm42-1250/o3.2024.048, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1730217600000, receivedDateStr=2024-10-30, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1774007001077, onlineDateStr=2026-03-20, pubDate=1740672000000, pubDateStr=2025-02-28, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1774007001077, onlineIssueDateStr=2026-03-20, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1774007001077, creator=13701087609, updateTime=1774007001077, updator=13701087609, issue=Issue{id=1241838624241681037, tenantId=1146029695717560320, journalId=1241755870837649424, year='2025', volume='46', issue='1', pageStart='1', pageEnd='148', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1774007000265, creator=13701087609, updateTime=1774007104623, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1241839062017966445, tenantId=1146029695717560320, journalId=1241755870837649424, issueId=1241838624241681037, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1241839062017966446, tenantId=1146029695717560320, journalId=1241755870837649424, issueId=1241838624241681037, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=93, endPage=104, ext={EN=ArticleExt(id=1241838629211934733, articleId=1241838627647459334, tenantId=1146029695717560320, journalId=1241755870837649424, language=EN, title=In-Plane Oblique Loading Impact Failure and Energy Absorption of Gradient Bimaterial Honeycomb Structures with Negative Poisson's Ratios, columnId=1241831201674171363, journalTitle=Chinese Journal of Solid Mechanics, columnName=Research Papers, runingTitle=null, highlight=null, articleAbstract=

Materials with negative Poisson's ratios, as typical mechanical metamaterials, exhibit indentation resistance when impacted, significantly enhancing their impact resistance while remaining lightweight and capable of high energy absorption. Previous research primarily focused on the mechanical properties of honeycomb structures under forward impacts, with limited studies on the dynamic response of multi-cell structures with negative Poisson's ratios—particularly those made of double material cells—under inclined loads. However, structural failures from inclined load impacts are unavoidable in engineering practice. This study integrates gradient design in multicellular structures with inclined load impacts to analyze energy absorption and crushing deformation modes of structures. We propose a gradient bimaterial negative Poisson's ratio honeycomb structure featuring a curved edge concave bimaterial cell. By changing the materials of the transverse and longitudinal curved bars, we design four types of material gradient honeycomb structures: positive gradient, negative gradient, symmetrical positive gradient, and symmetrical negative gradient. Using numerical methods, we examine the dynamic behavior of each gradient structure under in-plane oblique impact loading. It is found that the honeycomb structure with a negative gradient bimaterial arrangement performs best in energy absorption during oblique impacts. We detail the deformation mode, nominal stress-strain curve, and energy absorption of the negative gradient structure at different impact velocities and impact oblique angles. Results indicate that both impact velocity and impact oblique angle significantly affect energy absorption. Regardless of speed, the smaller the impact oblique angle, the better the energy absorption of the honeycomb structure, meaning crashworthiness decreases as the impact oblique angle increases.

, correspAuthors=Junhua Xiao, 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=Wuju Wan, Junhua Xiao, Zhixi Guo), CN=ArticleExt(id=1241838634287042667, articleId=1241838627647459334, tenantId=1146029695717560320, journalId=1241755870837649424, language=CN, title=梯度双材料负泊松比蜂窝结构的面内倾斜冲击失效与吸能研究, columnId=1241831201896469478, journalTitle=固体力学学报, columnName=研究论文, runingTitle=null, highlight=null, articleAbstract=

本文提出了基于曲边内凹双材料胞元的梯度负泊松比蜂窝结构，通过改变横纵向曲杆材料，设计了正梯度、负梯度、对称正梯度和对称负梯度四种材料递变泊松比梯度蜂窝结构. 利用数值方法研究了各梯度结构的面内斜向冲击载荷作用时的动力学性能. 研究发现，在斜向碰撞时下负梯度双材料排列模式的蜂窝结构吸能效果最好. 针对负梯度双材料蜂窝结构，具体讨论了在不同冲击速度和冲击倾斜角度时的压溃变形模式、名义应力应变曲线与能量吸收效果的变化规律. 结果表明，冲击速度和冲击倾斜角度对模式吸能效果的影响非常大；无论在何种速度下，倾斜角度越小，结构的吸能效果越好，即结构的耐撞性随碰撞倾斜角度的增大而减小.

, correspAuthors=肖俊华, authorNote=null, correspAuthorsNote=
**E-mail：.
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figureFileSmall=Q+EBqxtGFjV0KaTbiA3O9A==, figureFileBig=RINCZOGRRfzW+/yi3YvJrQ==, tableContent=null), ArticleFig(id=1241838642017145149, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1241838627647459334, language=CN, label=图9, caption=不同速度时梯度蜂窝结构的名义应力-应变及单位质量能量吸收值, figureFileSmall=Q+EBqxtGFjV0KaTbiA3O9A==, figureFileBig=RINCZOGRRfzW+/yi3YvJrQ==, tableContent=null), ArticleFig(id=1241838642222666050, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1241838627647459334, language=EN, label=Table 1, caption=

Material parameter

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材料密度（g·cm-3）弹性模量（GPa）泊松比屈服强度（MPa）
铝2.7690.3376
合金铜8.931380.3490
1010钢7.8452070.27207
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材料参数

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材料密度（g·cm-3）弹性模量（GPa）泊松比屈服强度（MPa）
铝2.7690.3376
合金铜8.931380.3490
1010钢7.8452070.27207
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Bimaterial combination

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弹性模量比k=E1/E2纵/横向材料
k1=1.51010钢/合金铜
k2=1合金铜/合金铜
k3=0.5铝/合金铜
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双材料组合

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弹性模量比k=E1/E2纵/横向材料
k1=1.51010钢/合金铜
k2=1合金铜/合金铜
k3=0.5铝/合金铜
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梯度双材料负泊松比蜂窝结构的面内倾斜冲击失效与吸能研究
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万武举 1, 2 , 肖俊华 1, 2, ** , 郭之熙 3
固体力学学报 | 研究论文 2025,46(1): 93-104
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固体力学学报 | 研究论文 2025, 46(1): 93-104
梯度双材料负泊松比蜂窝结构的面内倾斜冲击失效与吸能研究
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万武举1, 2, 肖俊华1, 2, ** , 郭之熙3
作者信息
  • 1燕山大学工程力学系，秦皇岛，066004
  • 2燕山大学河北省重型装备与大型结构力学可靠性重点实验室，秦皇岛，066004
  • 3河海大学工程力学系，南京，211100

通讯作者:

In-Plane Oblique Loading Impact Failure and Energy Absorption of Gradient Bimaterial Honeycomb Structures with Negative Poisson's Ratios
Wuju Wan1, 2, Junhua Xiao1, 2, ** , Zhixi Guo3
Affiliations
  • 1Department of Engineering Mechanics, Yanshan University, Qinhuangdao, 066004
  • 2Hebei Key Laboratory of Mechanical Reliability for Heavy Equipments and Large Structures, Yanshan University, Qinhuangdao, 066004
  • 3Department of Engineering Mechanics, Hohai University, Nanjing, 211100
出版时间: 2025-02-28 doi: 10.19636/j.cnki.cjsm42-1250/o3.2024.048
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摘要
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本文提出了基于曲边内凹双材料胞元的梯度负泊松比蜂窝结构，通过改变横纵向曲杆材料，设计了正梯度、负梯度、对称正梯度和对称负梯度四种材料递变泊松比梯度蜂窝结构. 利用数值方法研究了各梯度结构的面内斜向冲击载荷作用时的动力学性能. 研究发现，在斜向碰撞时下负梯度双材料排列模式的蜂窝结构吸能效果最好. 针对负梯度双材料蜂窝结构，具体讨论了在不同冲击速度和冲击倾斜角度时的压溃变形模式、名义应力应变曲线与能量吸收效果的变化规律. 结果表明，冲击速度和冲击倾斜角度对模式吸能效果的影响非常大；无论在何种速度下，倾斜角度越小，结构的吸能效果越好，即结构的耐撞性随碰撞倾斜角度的增大而减小.

负泊松比  /  双材料胞元  /  梯度结构  /  失效变形模式  /  能量吸收  /  斜向加载

Materials with negative Poisson's ratios, as typical mechanical metamaterials, exhibit indentation resistance when impacted, significantly enhancing their impact resistance while remaining lightweight and capable of high energy absorption. Previous research primarily focused on the mechanical properties of honeycomb structures under forward impacts, with limited studies on the dynamic response of multi-cell structures with negative Poisson's ratios—particularly those made of double material cells—under inclined loads. However, structural failures from inclined load impacts are unavoidable in engineering practice. This study integrates gradient design in multicellular structures with inclined load impacts to analyze energy absorption and crushing deformation modes of structures. We propose a gradient bimaterial negative Poisson's ratio honeycomb structure featuring a curved edge concave bimaterial cell. By changing the materials of the transverse and longitudinal curved bars, we design four types of material gradient honeycomb structures: positive gradient, negative gradient, symmetrical positive gradient, and symmetrical negative gradient. Using numerical methods, we examine the dynamic behavior of each gradient structure under in-plane oblique impact loading. It is found that the honeycomb structure with a negative gradient bimaterial arrangement performs best in energy absorption during oblique impacts. We detail the deformation mode, nominal stress-strain curve, and energy absorption of the negative gradient structure at different impact velocities and impact oblique angles. Results indicate that both impact velocity and impact oblique angle significantly affect energy absorption. Regardless of speed, the smaller the impact oblique angle, the better the energy absorption of the honeycomb structure, meaning crashworthiness decreases as the impact oblique angle increases.

negative Poisson's ratio  /  bimaterial cell  /  gradient structure  /  failure deformation mode  /  energy absorption  /  oblique loading
万武举, 肖俊华, 郭之熙. 梯度双材料负泊松比蜂窝结构的面内倾斜冲击失效与吸能研究. 固体力学学报, 2025 , 46 (1) : 93 -104 . DOI: 10.19636/j.cnki.cjsm42-1250/o3.2024.048
Wuju Wan, Junhua Xiao, Zhixi Guo. In-Plane Oblique Loading Impact Failure and Energy Absorption of Gradient Bimaterial Honeycomb Structures with Negative Poisson's Ratios[J]. Chinese Journal of Solid Mechanics, 2025 , 46 (1) : 93 -104 . DOI: 10.19636/j.cnki.cjsm42-1250/o3.2024.048
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0　引言
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超材料是指由人工设计结构并呈现出天然材料所不具备物理性质的特殊材料，负泊松比材料作为一种典型的机械超材料，在受拉压时呈现出的独特的物理性质，具有轻质高吸能的特点，其在受冲击时会出现压痕阻力现象[1]，使得材料的抗冲击性能显著提升，所以被广泛应用于医疗、航空航天、车辆等各个领域[2,3].
负泊松比结构的力学性能主要取决于其胞元的设计，1987年Lakes[4]首次成功合成一种负泊松比泡沫材料，自此关于负泊松比结构的研究蓬勃发展. Gibson等[5]首次提出了二维内凹六边形蜂窝结构. 根据胞元形状的不同，目前常见的负泊松比结构有重入凹角结构、手性/反手性结构、旋转刚体结构等[2]. Qiao等[6]提出一种以正弦曲线作为棱边形状的多胞结构，计算了结构的等效力学性能. 卢子兴等[7]结合星型与内凹三角形胞元，提出了一种新型拉胀蜂窝模型. 魏路路等[8]将六边形内凹结构和手性结构相结合，设计出一种内凹-反手性结构. 王梁和刘海涛[9]结合星型和内凹六边形设计出一种新型内凹蜂窝结构. Zhao等[10]对内凹六边形和星形结构的等效泊松比和等效弹性模量进行了理论推导. 蒋伟等[11]在内凹六边形胞元设计中引入了曲杆，构建了一种具有负泊松比效应的环形内凹结构. 随后沈建邦和肖俊华[12]在该结构的基础上提出可变弧角环形负泊松比蜂窝结构. 尤泽华等[13]基于星形结构提出一种四边曲边内凹负泊松比胞元，构造三维结构并用有限元方法研究了该结构的冲击力学性能.
不仅改变胞元的微结构几何参数会影响其力学性能，不同材料及排布模式也会对胞元的力学性能产生显著影响. 超材料单胞的多材料设计可以将不同材料组合的优异特性结合，从而使得胞元的力学性能得到提升. 同时，梯度设计的胞元结构能够在降低初始力峰值、增强抗冲击性能和能量吸收能力等方面发挥较大的优势. Wang等[14]结合双材料3D打印工艺，研究不同材料选择和刚性材料分数对泊松比、等效杨氏模量的影响，并考察了结构的最大体积缩小率. Li等[15]由双材料制成了一种二维四边形蜂窝结构，并通过实验和数值模拟对其热变形行为进行了研究. 马芳武等[16]提出了一种双材料双箭头负泊松比结构，在保证胞元几何参数不变的前提下，讨论了其余不同参数对面内抗冲击能力和能量吸收能力的影响. He等[17]在双材料三角形网格单元的基础上，设计了一种新的单元结构. Jiang等[18]通过增材制造制备了聚乳酸基负泊松比结构，并基于各位置的几何变形给出了结构的泊松比计算经验公式. Lim等[19]将梯度设计方法与负泊松比材料结合，改变了材料的变形模式，对负泊松比材料的性能进一步优化. Li等[20]结合模拟和实验研究了沿横向呈逐层梯度变化的多层蜂窝结构的抗冲击性能. Xiao等[21]研究了梯度金属负泊松比蜂窝结构的准静态压缩性能，并对比了单向梯度和双向梯度排布的蜂窝结构的能量耗散特性. Zhang等[22]通过改变几何参数和物理参数构建了四种梯度负泊松比蜂窝结构，有限元方法研究了四种梯度负泊松比蜂窝的动态响应. Xu等[23]提出了一种受自然启发的负泊松比超材料设计策略，利用天然多孔材料所具有的独特双梯度结构，通过在多孔结构中引入双梯度变化即可得到负泊松比效应，从而制备负泊松比超材料.
负泊松比结构有着优异的抗冲吸能特性，诸多学者对负泊松比材料的动力学冲击性能进行了广泛研究. Zhang等[24]建立了三维负泊松比多胞结构的轴向冲击模型，分析了胞元几何参数和冲击速度对能量吸收效果的影响. Zhang等[25]采用有限元方法研究了具有负泊松比效应的开孔泡沫铝的动态冲击压溃行为，探讨了其平台应力，比能量吸收率和变形模式. Zhao等[26]提出了一种新的三维星形结构，讨论了该结构在承受冲击载荷时的响应. Wei等[27]结合星形和三角形提出了一种新的混合结构，并数值模拟研究了该结构的变形模式. 实际工程中，结构不单会承受正面冲击，往往还伴随着斜向受载. 马芳武等[28]以内凹三角形负泊松比材料为研究对象，数值分析了冲击倾角与冲击速度对内凹三角形负泊松比材料面内冲击的变形模态和动力响应的影响. 刘海涛等[29]设计了两类角度梯度变化的内凹蜂窝有限元模型，将其与传统蜂窝结构进行准静态压缩试验对比，并研究了面内倾斜冲击载荷作用下两类角度梯度内凹蜂窝结构的变形模式、平台应力和能量吸收特性. 王振等[30]探讨了碳纤维增强树脂铝合金-泡沫铝混杂管件在轴向和斜向荷载下的压溃变形特性和能量耗散机制.
以往研究大多针对蜂窝结构的正向冲击时的力学性能进行分析，对于具有负泊松比多胞结构，尤其是由双材料单胞构建成的多胞结构在倾斜荷载下的动力学响应研究非常有限，然而工程实际中倾斜载荷冲击引起的结构失效无法避免（如汽车碰撞），本文将多胞结构的梯度设计与倾斜载荷冲击相结合，研究结构的吸能及压溃变形模式，更加符合多胞结构作为防护材料在实际工况中的场景. 本文基于作者提出的曲边内凹双材料负泊松比胞元[31]，通过改变胞元纵/横向曲杆材料，设计了正梯度、负梯度、对称正梯度和对称负梯度四种梯度双材料负泊松比蜂窝结构，在面内施加倾斜冲击载荷，讨论了倾斜冲击作用下不同排列梯度双材料负泊松比蜂窝结构的冲击失效模式和吸能特性.
1　梯度双材料负泊松比蜂窝结构
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图1为双材料曲边内凹胞元示意图[31]，h1表示胞元纵向曲边在坐标轴投影半长，h2是横向胞元曲边在坐标轴投影半长，m为胞元连接杆伸出长度. 胞元中横向和纵向材料不同，上下曲杆（黑色）材料弹性模量为E1，弧角为θ1，半径r1=h1/sin（θ1/2），左右曲杆（蓝色）材料弹性模量为E2，弧角为θ2，半径r2=h2/sin（θ2/2），面内厚度为t，面外厚度为b.
蜂窝结构由胞元阵列而成，定义材料模量比E1/E2=k，选取材料及胞元内材料匹配见表1[32]和表2，k分别取值为1.5、1和0.5进行构建梯度双材料负泊松比蜂窝结构.
建立的正梯度、负梯度、对称正梯度和对称负梯度双材料负泊松比蜂窝结构如图2所示，四种梯度多胞结构质量相同，蜂窝结构为胞元18×19阵列而成，k在结构纵向发生变化，胞元结构几何参数为θ1=30°，θ2=60°，h1=3 mm，h2=6 mm，m1=m2=3 mm，t=0.2 mm和b=2 mm. 四种梯度结构的等效密度为：
其中表示模量比为ki层的等效密度.
采用ABAQUS显式动力学方法研究结构的面内倾斜冲击动力学性能. 选择壳单元，在壁厚方向设置5个积分点，设置蜂窝结构材料为理想弹塑性，边界条件如图3. 蜂窝结构放置于上下两块薄板之间，限制结构面外位移，下端薄板完全固定，限制其所有方向的位移，上端薄板以恒定速度沿Y轴负方向冲击结构. 两块薄板设置为解析刚体，避免板变形对结构变形产生影响. 结构与板之间设置绑定约束以限制结构与板之间的横向位移. 为了避免发生穿透，整体采用通用接触，纵向设置硬接触.
2　梯度模式对蜂窝结构能量吸收的影响
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图4给出了四种不同梯度双材料负泊松比蜂窝结构受斜向载荷时单位质量能量吸收的曲线，其中冲击速度v=25 m/s，冲击角度θ=10°. 由图可知，四种梯度结构的能量吸收值都随着应变的增大而增大. 负梯度排布模式结构在压缩前期表现出良好的吸能效果，随着压缩的进行，在压缩中期负梯度和对称正梯度模式能量吸收值趋于一致，并明显优于另外两种模式，最后四种模式的能量吸收值趋于一致. 可知，在相同质量、相同材料、相同构成及相同密度的情况下，负梯度结构能显著增强结构的吸能特性.
在下面研究中，选取负梯度双材料蜂窝结构，进一步讨论冲击速度和冲击角度对蜂窝结构变形模式、动力响应曲线与能量吸收效果的影响.
3　面内倾斜压溃变形失效
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图5给出了负梯度双材料蜂窝结构在低速（v=9 m/s）倾斜冲击时的变形失效模式. 由图可知，初期变形时冲击端均发生横向收缩现象. 在小角度倾斜荷载下，随着冲击的进行，结构的变形向下传递，结构中梯度变化层首先发生变形，这是由于下端材料模量比（k=E1/E2）较小，结构的纵向等效弹性模量较小. 随后结构下端被压溃且发生局部横向收缩变形. 随着冲击角度的增加，远离冲击端的胞元变形越来越小. 结构随着施加荷载倾斜角度的增大，变形传递效果越来越不明显.
图6给出了中速（v=25 m/s）冲击作用下的变形失效模式. 冲击初期的变形主要发生在冲击端，结构出现横向扩张现象，随着冲击的进行结构下部发生“”型变形，结构变化层出现横向收缩，且冲击载荷的倾斜角度越小，此现象越明显.
图7给出了结构在中高速（v=36 m/s）倾斜冲击下的变形压溃模式. 在此速度下，结构变形的传递效果已不再明显，仅在结构顶部密实化之后，冲击的中后期发生“”型变形，且随着倾斜角度的增大，变形也不再明显.
图8给出了结构在高速（v=72 m/s）冲击下的变形失效模式. 在高速冲击载荷作用下，不同的冲击角度时结构表现出几乎一致的变形规律. 由于惯性效应，结构的变形区域主要集中在冲击端，变形区域的胞元密实化程度较高，蜂窝材料被逐层压溃，结构负泊松比效应不明显. 随着角度的增大，结构顶部的胞元受挤压而外扩的现象越来越明显.
4　动力响应曲线与能量吸收特性
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应力-应变曲线与横坐标轴围成的面积代表了结构的吸收能量. 单位质量能量吸收值是评估材料在冲击下吸能效果的一个重要指标，其表达式为[33]：
其中E为单位质量的能量吸收值，WV为体能量吸收值，ρc为结构的等效密度，εd与σ（ε）分别表示锁定应变与名义应力. 对于蜂窝结构，可以利用能量吸收效率法确定它的锁定应变[34]：
W为蜂窝结构的能效参数，定义为同一应变下体能量吸收率和应力之比值，即：
图9给出了不同冲击速度、不同角度冲击时蜂窝结构的名义应力-应变曲线和单位质量能量吸收曲线. 可以看出，相同冲击速度时，无论冲击角度如何变化，结构的能量吸收值都随着应变的增大而增大；随着冲击速度的增大，不同冲击角度下的吸能效果差异越来越明显. 低速冲击时，结构的能量吸收曲线波动较大，冲击末期，承受小倾斜角度冲击时的结构能量吸收会有明显的提升（图9（a）），原因为低速小角度冲击时，结构的横向变形传递效果较为明显. 倾角θ=5°与10°的曲线变化趋势较为相似，都位于θ=20°的曲线之上，即荷载倾角越大结构内部的受力越小，结构的抗冲击能力变弱. 当承受高速冲击时，角度对曲线的影响体现在结构的整体吸能效果，动力响应曲线波动趋势几乎一致，三种倾斜角度下结构的能量吸收曲线几乎都呈线性增长. 不论何种冲击速度，结构的吸能效果都随着冲击倾角的增大而减小，即蜂窝结构在斜载荷作用下的耐撞性随冲击倾角的增大而变弱.
5　结论
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本文基于曲边内凹双材料胞元结构，通过改变胞元纵/横向材料性能，构建了梯度双材料负泊松比蜂窝结构，数值研究了倾斜荷载下正梯度、负梯度、对称正梯度及对称负梯度排布的能量吸收特性，讨论了负梯度蜂窝结构在不同速度与不同倾斜角度冲击荷载时的变形失效模式与单位质量能量吸收值. 主要结论如下：
（1）在相同质量、相同材料、相同构成及相同密度的情况下，负梯度结构能显著增强结构的吸能特性.
（2）低速冲击时，负梯度双材料蜂窝结构内部存在大量未变形胞元，结构出现分层变形，在材料模量比变化处首先出现横向收缩现象；随着冲击倾角的增大，变形传递效果逐渐变弱. 高速冲击时，蜂窝结构的变形区域主要在冲击端，胞元不再出现仅旋转不变形，变形区域密实化后，结构被逐层压溃.
（3）负梯度双材料蜂窝结构的应力和能量吸收值随速度的增加而增大. 冲击速度对结构的变形模式会产生很大影响. 随着冲击速度的增加，结构的变形失效模式由整体变形逐渐向局部变形转变，结构的负泊松比效应逐渐不明显.
（4）相同冲击速度时，荷载倾角越小负梯度双材料蜂窝结构的能量吸收值越大，结构的耐撞性越好. 相同冲击角度时，速度越大能量吸收曲线越平稳.
基金
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  • 中央引导地方科技发展资金项目(236Z1009G)
文献
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2025年第46卷第1期
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doi: 10.19636/j.cnki.cjsm42-1250/o3.2024.048
  • 接收时间：2024-10-30
  • 首发时间：2026-03-20
  • 出版时间：2025-02-28
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  • 收稿日期：2024-10-30
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中央引导地方科技发展资金项目(236Z1009G)
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    1燕山大学工程力学系，秦皇岛，066004
    2燕山大学河北省重型装备与大型结构力学可靠性重点实验室，秦皇岛，066004
    3河海大学工程力学系，南京，211100

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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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