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Article(id=1325146209106670547, tenantId=1146029695717560320, journalId=1255847867265597444, issueId=1325146207672214104, articleNumber=null, orderNo=null, doi=10.11858/gywlxb.20261042, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=research-article, receivedDate=1772726400000, receivedDateStr=2026-03-06, revisedDate=1778688000000, revisedDateStr=2026-05-14, acceptedDate=null, acceptedDateStr=null, onlineDate=1793869076276, onlineDateStr=2026-11-05, pubDate=1783180800000, pubDateStr=2026-07-05, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1793869076276, onlineIssueDateStr=2026-11-05, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1793869076276, creator=13701087609, updateTime=1793869076276, updator=13701087609, issue=Issue{id=1325146207672214104, tenantId=1146029695717560320, journalId=1255847867265597444, year='2026', volume='40', issue='7', pageStart='070101-1', pageEnd='070114-14', issueExtLink='null', onlineDate='null', pubDate='1783180800000', pubDateStr='2026-07-05', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=0, createTime=1793869075935, creator='13701087609', updateTime=1793870526447, updator='13701087609', preIssue=null, nextIssue=null, articleTotal=null, ext={EN=IssueExt(id=1325152292009279913, tenantId=1146029695717560320, journalId=1255847867265597444, issueId=1325146207672214104, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1325152292009279914, tenantId=1146029695717560320, journalId=1255847867265597444, issueId=1325146207672214104, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null, downloadFileDto=null}, startPage=070104-1, endPage=070104-13, ext={EN=ArticleExt(id=1325146209865839572, articleId=1325146209106670547, tenantId=1146029695717560320, journalId=1255847867265597444, language=EN, title=Novel Buffering Metamaterials with a Long Load Plateau: Design and Mechanical Characterization, columnId=1325146208670458457, journalTitle=Chinese Journal of High Pressure Physics, columnName=Mechanical Behavior of Lightweight Composite Protective Materials and Structures, runingTitle=null, highlight=null, articleAbstract=

Metamaterials with both reversible deformation and a long load plateau meet the demand for cyclic buffering, offering great application prospects in protective engineering. However, current metamaterials generally suffer from low material utilization, which limits their load-bearing and energy absorption performance. To address these limitations, a novel buffering metamaterial with a long load plateau is proposed in this work. Composed of bilaterally symmetric double-arc structures and vertically symmetric curved plates, the metamaterial is capable of recoverable large deformation and overall cooperative load-bearing deformation, thereby improving material utilization and optimizing structural load capacity and energy absorption performance. Experimental tests and numerical simulations were conducted to validate the long load plateau and recoverable large deformation characteristics of the metamaterial. The influences of structural geometric parameters on its mechanical behavior were also systematically analyzed. The results indicate that the long load plateau can be effectively tuned by adjusting the thickness of lateral double arcs, the thickness of intermediate curved plates, and the central transverse span. Once the intermediate curved plates are removed, the long load plateau feature disappears, and the force-displacement curve presents an approximately linear variation. Finite element simulations at equal mass confirm that the proposed metamaterial possesses better buffering performance than similar structures without a long load plateau, and the underlying buffering mechanism is clarified. The findings provide a novel design strategy for improving the performance of metamaterials with a long load plateau, and facilitate their application in protective engineering.

, authors=Yixuan YOU, Wenkang YE, Tianpeng ZHANG, Lingling HU, authorsList=Yixuan YOU, Wenkang YE, Tianpeng ZHANG, Lingling HU, authorCompany=null, correspAuthors=Lingling HU, authorNote=null, correspAuthorsNote=null, copyrightStatement=Copyright © 2026 Chinese Journal of High Pressure Physics. All rights reserved., 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, fund=null), CN=ArticleExt(id=1325146220301267961, articleId=1325146209106670547, tenantId=1146029695717560320, journalId=1255847867265597444, language=CN, title=新型长载荷平台缓冲超材料的设计与性能研究, columnId=1325146208871785051, journalTitle=高压物理学报, columnName=轻质复合防护材料与结构的力学行为, runingTitle=null, highlight=null, articleAbstract=

兼具可逆变形与长载荷平台特性的超材料可满足多次缓冲的需求，在防护工程中具有重要的应用潜力。然而，现有的此类超材料普遍存在材料利用率偏低的问题，制约了其承载与缓冲吸能性能的提升。为解决上述不足，提出了一种新型长载荷平台缓冲超材料，它由左右对称双弧与上下对称曲面板组合而成，能够实现可恢复大变形和全结构协同承载变形，大幅提升了材料的利用率，从而优化了承载和缓冲吸能性能。通过试验与数值仿真方法，验证了该超材料的长载荷平台及可恢复大变形特性，同时系统分析了结构几何参数对其力学行为的影响。结果表明：通过调节侧面双弧厚度、中间曲面板厚度以及中部横向跨度，可实现对长载荷平台的有效调控；移除中间曲面板后，长载荷平台特性消失，力-位移曲线呈近似线性变化。同等质量下的有限元仿真对比证实，所设计的超材料的缓冲性能明显优于无长载荷平台特性的同类结构，并揭示了其内在缓冲机理。研究结果为长载荷平台超材料的性能提升提供了新的设计思路，有助于推动其在缓冲工程中的应用。

, authors=尤艺璇, 叶文康, 张天朋, 胡玲玲, authorsList=尤艺璇, 叶文康, 张天朋, 胡玲玲, authorCompany=null, correspAuthors=胡玲玲, authorNote=

尤艺璇（2002－），女，硕士研究生，主要从事缓冲吸能超材料研究. E-mail：

, correspAuthorsNote=
胡玲玲（1980－），女，博士，教授，主要从事冲击动力学研究. E-mail：
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尤艺璇（2002－），女，硕士研究生，主要从事缓冲吸能超材料研究. E-mail：

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尤艺璇（2002－），女，硕士研究生，主要从事缓冲吸能超材料研究. E-mail：

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新型长载荷平台缓冲超材料的设计与性能研究
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尤艺璇 , 叶文康 , 张天朋 , 胡玲玲
高压物理学报 | 轻质复合防护材料与结构的力学行为 2026,40(7): 070104-1-070104-13
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高压物理学报 |轻质复合防护材料与结构的力学行为 2026 , 40 (7) : 070104-1 -070104-13
新型长载荷平台缓冲超材料的设计与性能研究
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[Author(id=1325146220594869246, tenantId=1146029695717560320, journalId=1255847867265597444, articleId=1325146209106670547, orderNo=0, firstName=null, middleName=null, lastName=null, nameCn=null, orcid=null, stid=null, country=null, authorPic=null, dead=0, email=youyx6@mail2.sysu.edu.cn, emailSecond=null, emailThird=null, correspondingAuthor=0, authorType=1, ext={EN=AuthorExt(id=1325146220682949632, tenantId=1146029695717560320, journalId=1255847867265597444, articleId=1325146209106670547, authorId=1325146220594869246, language=EN, stringName=Yixuan YOU, firstName=Yixuan, middleName=null, lastName=YOU, prefix=null, suffix=null, authorComment=null, nameInitials=null, affiliation=null, department=null, xref=null, address=School of Aeronautics and Astronautics, Shenzhen Campus of Sun Yat-Sen University, Shenzhen 518107, Guangdong, China, bio=null, bioImg=null, bioContent=null, aboutCorrespAuthor=null), CN=AuthorExt(id=1325146220750057472, tenantId=1146029695717560320, journalId=1255847867265597444, articleId=1325146209106670547, authorId=1325146220594869246, language=CN, stringName=尤艺璇, firstName=null, middleName=null, lastName=null, prefix=null, suffix=null, authorComment=null, nameInitials=null, affiliation=null, department=null, xref=null, address=中山大学深圳校区航空航天学院, 广东 深圳　518107, bio={"content":"

尤艺璇（2002－），女，硕士研究生，主要从事缓冲吸能超材料研究. E-mail：

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尤艺璇（2002－），女，硕士研究生，主要从事缓冲吸能超材料研究. E-mail：

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尤艺璇 , 叶文康, 张天朋, 胡玲玲
作者信息
  • 中山大学深圳校区航空航天学院, 广东 深圳　518107
通讯作者:
胡玲玲（1980－），女，博士，教授，主要从事冲击动力学研究. E-mail：
作者简介:

尤艺璇（2002－），女，硕士研究生，主要从事缓冲吸能超材料研究. E-mail：

Novel Buffering Metamaterials with a Long Load Plateau: Design and Mechanical Characterization
Yixuan YOU , Wenkang YE, Tianpeng ZHANG, Lingling HU
Affiliations
  • School of Aeronautics and Astronautics, Shenzhen Campus of Sun Yat-Sen University, Shenzhen 518107, Guangdong, China
出版时间: 2026-07-05 doi: 10.11858/gywlxb.20261042
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摘要
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兼具可逆变形与长载荷平台特性的超材料可满足多次缓冲的需求，在防护工程中具有重要的应用潜力。然而，现有的此类超材料普遍存在材料利用率偏低的问题，制约了其承载与缓冲吸能性能的提升。为解决上述不足，提出了一种新型长载荷平台缓冲超材料，它由左右对称双弧与上下对称曲面板组合而成，能够实现可恢复大变形和全结构协同承载变形，大幅提升了材料的利用率，从而优化了承载和缓冲吸能性能。通过试验与数值仿真方法，验证了该超材料的长载荷平台及可恢复大变形特性，同时系统分析了结构几何参数对其力学行为的影响。结果表明：通过调节侧面双弧厚度、中间曲面板厚度以及中部横向跨度，可实现对长载荷平台的有效调控；移除中间曲面板后，长载荷平台特性消失，力-位移曲线呈近似线性变化。同等质量下的有限元仿真对比证实，所设计的超材料的缓冲性能明显优于无长载荷平台特性的同类结构，并揭示了其内在缓冲机理。研究结果为长载荷平台超材料的性能提升提供了新的设计思路，有助于推动其在缓冲工程中的应用。

超材料  /  结构设计  /  长载荷平台  /  可恢复大变形  /  多次缓冲

Metamaterials with both reversible deformation and a long load plateau meet the demand for cyclic buffering, offering great application prospects in protective engineering. However, current metamaterials generally suffer from low material utilization, which limits their load-bearing and energy absorption performance. To address these limitations, a novel buffering metamaterial with a long load plateau is proposed in this work. Composed of bilaterally symmetric double-arc structures and vertically symmetric curved plates, the metamaterial is capable of recoverable large deformation and overall cooperative load-bearing deformation, thereby improving material utilization and optimizing structural load capacity and energy absorption performance. Experimental tests and numerical simulations were conducted to validate the long load plateau and recoverable large deformation characteristics of the metamaterial. The influences of structural geometric parameters on its mechanical behavior were also systematically analyzed. The results indicate that the long load plateau can be effectively tuned by adjusting the thickness of lateral double arcs, the thickness of intermediate curved plates, and the central transverse span. Once the intermediate curved plates are removed, the long load plateau feature disappears, and the force-displacement curve presents an approximately linear variation. Finite element simulations at equal mass confirm that the proposed metamaterial possesses better buffering performance than similar structures without a long load plateau, and the underlying buffering mechanism is clarified. The findings provide a novel design strategy for improving the performance of metamaterials with a long load plateau, and facilitate their application in protective engineering.

metamaterial  /  structural design  /  long load plateau  /  recoverable large deformation  /  cyclic buffering
尤艺璇, 叶文康, 张天朋, 胡玲玲. 新型长载荷平台缓冲超材料的设计与性能研究. 高压物理学报, 2026 , 40 (7) : 070104-1 -070104-13 . DOI: 10.11858/gywlxb.20261042
Yixuan YOU, Wenkang YE, Tianpeng ZHANG, Lingling HU. Novel Buffering Metamaterials with a Long Load Plateau: Design and Mechanical Characterization[J]. Chinese Journal of High Pressure Physics, 2026 , 40 (7) : 070104-1 -070104-13 . DOI: 10.11858/gywlxb.20261042
正文
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缓冲吸能材料在航空航天[1-3]、交通运输[4-5]、建筑安全[6-8]、机械设备[9]等多个领域均展现出广阔的应用前景。传统的缓冲吸能材料如蜂窝结构[10-11]、点阵材料[12]等，主要通过塑性变形来吸收能量，难以多次使用。为了克服这一缺陷，依托弹性变形实现能量储存或耗散的可重复使用缓冲结构逐渐成为缓冲吸能领域的研究热点[13-15]。例如：Hu等[13]对仿DNA双螺旋超材料的低速冲击缓冲特性进行了研究，证实了其具备优异的可恢复性与冲击衰减能力；Shan等[14]借助倾斜弹性梁的双稳态特性设计出一类全新的多稳态超材料，实现了弹性应变能的捕获；Ou等[15]基于压缩-扭转耦合效应，设计了一款可重复使用的缓冲超材料，大幅提升了此类超材料的缓冲效率。上述工作通过多样化构型设计，实现了缓冲超材料的可逆变形与高效吸能，展现出良好的重复使用潜力。具有平缓长载荷平台且可逆变形的结构能够在较低峰值力下保持载荷的稳定输出，并实现持续储能；这一特性与可重复缓冲的多次使用、低峰值力且高效能量吸收的需求相契合，使其在缓冲领域具有较大的应用潜力。
一般来说，构造具有长载荷平台结构的关键在于设计负刚度单元，然后将其与正刚度单元组合。Liu等[16]全面回顾了此类结构的设计途径、优化策略及应用场景。根据目前的研究成果，实现长载荷平台的方法大致分为2类：机构组合和结构设计。机构组合主要包括斜弹簧机构[17-19]、凸轮-滚子-弹簧机构[20-22]、磁性机构[23-24]等。2007年，Carrella等[17]提出了经典的三弹簧结构，其中，2个倾斜的弹簧作为负刚度单元，1个竖直的弹簧作为正刚度单元，通过正、负刚度单元的并联达到长载荷平台的效果。凸轮-滚子-弹簧型结构通过滚子沿凸轮轮廓滚动引发的非线性反力与弹簧的线性恢复力在平衡位置相互抵消来实现长载荷平台特性。磁性结构利用永磁体间的非线性磁力提供负刚度，并与正刚度弹簧组合，构建出长载荷平台本构曲线。
通过机构组合的方式虽然能实现长载荷平台特性，但其结构复杂，质量和体积都偏大，不适用于小型轻量化设备。为了解决此问题，学者们通过人工拓扑与结构设计，使长载荷平台成为结构自身固有的力学特性。例如：Zhou等[25]设计了由一大一小2个固体块通过4根对称的多段弧形细梁连接而成的结构，通过优化细梁形状使结构展现出长载荷平台特性；Pan等[26]借助非均匀B样条曲线，设计了一款轴对称的旋转体，通过调整曲线，使结构在特定压缩区间内呈现出长载荷平台特性；Liu等[27]对截锥壳进行了优化设计，通过调整其几何参数实现了长载荷平台。然而，现有此类结构普遍需要设计质量占比过高的约束构件，致使材料利用率偏低，进而制约结构承载与缓冲吸能性能。此外，当前研究多依托其载荷平台特性开展隔振相关工作，而针对缓冲吸能领域的研究仍较为匮乏。
为此，本研究将设计一种新型长载荷平台缓冲超材料，凭借可恢复大变形且全结构参与承载变形，克服约束结构质量占比过高的缺陷，通过试验和有限元（finite element, FE）仿真对其力学性能和缓冲性能进行研究，具体包括以下3个部分：首先，介绍3种超材料胞元的设计思路，采用细观有限元方法建立胞元结构的数值仿真模型；然后，通过数值仿真研究3种胞元的力学行为，并通过准静态压缩试验对仿真模型进行验证，借助验证后的仿真模型系统，分析几何参数对胞元力学行为的影响，评估其承载能力；最后，对比同等质量下具备与不具备长载荷平台特性超材料的缓冲性能，分析其内在缓冲机理，以期为可重复缓冲超材料的设计与优化提供参考。
1 超材料胞元设计与研究方法
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1.1 胞元结构设计
为了得到兼具可恢复大变形与长载荷平台特性的超材料，本研究共设计了3种胞元结构，如图1所示。胞元1（图1(a)）由一对左右对称的双弧以及上下加载平板组成，其核心几何参数为侧面双弧的厚度a、中部横向跨度c和变形部分的高度$ {h}_{0} $；胞元2通过在第1种胞元的中部嵌入一块厚度为b的平板实现，该平板与周边结构采用一体化成型设计，见图1(b)；胞元3在第1种胞元的基础上，于中间区域增设2块上下对称的曲面板，其厚度为b，同样与周边结构采用一体化成型设计，如图1(c)所示。为了避免胞元结构在压缩时出现面外变形，对胞元结构的面外尺寸进行加厚处理。
1.2 试验设计
3种胞元结构均采用热塑性聚氨酯（thermoplastic polyurethane, TPU）材料，通过熔融沉积成型（fused deposition modeling, FDM）技术制备，关键工艺参数如下：喷嘴挤出温度 230 ℃，加热底板温度 55 ℃，单层打印层厚 0.2 mm，内部填充密度100%，基础打印速度 30 mm/s。制备过程中保持工艺参数一致，保障各组试样的成型精度与力学性能均匀稳定。利用单轴拉伸试验确定其材料参数。根据ISO 37标准，本研究加工并制备了3个2型哑铃状TPU材料试样，共进行3次试验，以验证数据的重复性。对3次试验结果取平均，减小偶然误差，得到的应力-应变曲线如图2所示。图2中，实线代表平均应力-应变曲线，阴影部分代表3次拉伸试验的标准差。可见，标准差较小，说明试验数据的重复性良好。取平均曲线作为材料的本构模型，导入有限元软件，以定义材料特性。
采用INSTRON 10 kN万能试验机，对胞元结构进行准静态压缩试验和120次循环压缩试验，如图3所示。试验通过位移加载控制，在进行准静态压缩试验时，设定位移加载速率为5 mm/min，在进行循环压缩试验时，设定位移加载速率为60 mm/min。试验的最终压缩位移设置为30 mm，既覆盖所有试件的有效承载平台，又保证大部分试件未进入密实阶段。此时，胞元的整体应变为0.6。
1.3 有限元模型建立
采用显式动态有限元软件ABAQUS/Explicit对胞元结构进行仿真。将单轴拉伸试验得到的平均应力-应变曲线输入ABAQUS，选用Mooney-Rivlin、3阶Ogden、Neo Hooke和Yeoh 4种常用的超弹性本构模型，对试验数据进行拟合，结果如图4所示。其中：红色虚线表示试验结果，黑色实线为3阶Ogden模型拟合曲线，2条曲线几乎完全重合，其余曲线则与试验结果存在较大的差距，因此，选用此本构模型进行TPU材料的参数设置。
对胞元结构进行准静态压缩仿真，胞元结构的网格划分、边界条件与加载条件设置如图5(a)和图5(b)所示。采用八节点线性减缩积分六面体单元C3D8R划分网格。设置2块刚性板，令其分别与胞元的上、下表面接触，用于模拟压缩试验机的上、下压缩面板。仿真过程中，在上刚性板的参考点上施加向下的位移，同时，在下刚性板的参考点上施加固定约束。利用切向行为和法向行为来定义面与面接触时的相互作用，切向行为考虑摩擦力，法向行为设置为硬接触。对胞元结构进行网格收敛性分析，设置0.5、0.6、0.8、1.0 mm 4种网格尺寸，提取准静态压缩下结构的力-位移响应，如图5(c)所示。结果表明：1.0 mm的网格过粗，力-位移曲线结果失真；网格细化至0.8、0.6和0.5 mm后，平台段平均力的相对误差均小于5%，说明网格已收敛。为了获得更高的计算精度，最终选用0.5 mm作为仿真网格尺寸。
为研究所提出胞元结构的缓冲性能，将胞元结构周期排列成胞串，对胞串在质量块冲击下的动态响应进行模拟。对胞串的输入端施加质量m=9 g、速度v=15 m/s的质量冲击，限制胞串除加载方向以外的其他方向位移，在输出端施加固定约束，如图6所示。
2 胞元力学行为与性能
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2.1 3种胞元的力学行为
准静态压缩下3种胞元结构的力-位移曲线及变形模式如图7和图8所示。对于胞元结构，设定其几何参数：a=2 mm，c=25 mm，h0=50 mm。图7(a)结果显示，胞元1的力-位移曲线近似为一条直线，其斜率随着位移的增大有轻微的减小，说明胞元具有较弱的刚度软化特性。观察胞元在不同压缩位移下的变形可以发现，胞元发生了对称且均匀的变形：从初始细长双弧形态开始，弧形中心点逐步向外扩张，最终形成上下扁平的弧形结构，此时，胞元的变形进入密实阶段，如图8(a)所示。
在胞元1的中间部分增设平板和曲面板，形成胞元2和胞元3，保持a、c、h0不变（a=2 mm，c=25 mm，h0=50 mm），研究3种不同板厚b下2种胞元的力学行为。为了保证胞元2与胞元3具有相同的质量，胞元2中b取2.0、4.0和5.9 mm，胞元3中b取1.0、2.0和3.0 mm。图7(b)和图8(b)的结果表明，在一定的应变范围内，胞元2呈现出长载荷平台特性，且b的变化几乎不影响胞元的力-位移曲线及变形模式。胞元2在变形过程中出现了左右不对称变形，但这种变形并未对胞元的长平台特性造成影响。
图7(c)和图8(c)的结果表明，胞元3的力-位移曲线先上升后趋于平缓，在0.2～0.6的应变范围内呈现出长载荷平台特性。此外，当b发生变化时，胞元的变形模式基本不受影响。当胞元3的变形达到临界阈值时，原本上下对称的变形模式会转变为非对称变形，胞元3的上下部分中一侧会率先发生大变形，而另一侧则变形滞后。尽管胞元3在变形过程中出现了非对称变形，但是从整体的力学响应来看，这种现象并未破坏胞元3的长载荷平台特性。
胞元3具备长载荷平台的核心原因在于，曲面板的约束作用使双弧结构产生规律的葫芦状变形，进而使结构在压缩过程中产生几乎恒定的力。为了验证该结论，将中间部分设置为刚体，以消除其变形对结构力-位移曲线的干扰，如图9所示，结果显示，此时，仅侧面双弧产生葫芦状变形，即结构产生几乎恒定的力。
2.2 试验验证
对胞元2和胞元3进行准静态压缩试验。针对胞元2，共进行3组试验，b取2.0、4.0、5.9 mm，其余几何参数保持不变，即a=2 mm、c=25 mm、h0=50 mm。对比试验结果与仿真结果，如图10所示，两者吻合良好，说明仿真模型的准确性较高。从图10(d)可以看出，在3种不同平板厚度下，胞元2均发生了明显的左右不对称变形。
针对胞元3，共进行4组试验，即改变试件侧面双弧的厚度a，取2、3、4、5 mm，其余几何参数保持不变，即b=1.0 mm、c=25 mm、h0=50 mm。将试验中采集到的试件的力-位移曲线与仿真结果进行对比，如图11(a)所示，两者的变化趋势具有较好的一致性，证明了所建立的有限元模型具有较高的准确性。同时，试验验证了胞元3具有稳定长载荷平台特性。
在相同质量条件下，胞元2拥有更高的峰值力和平台承载力，但在整个压缩过程中均出现左右非对称变形，空间适配性较差，在需要长期使用的场景中，这种不对称变形易导致局部破坏，影响胞元结构的正常使用；胞元3在压缩完成后能够维持整体对称的变形模式，如图11(c)所示，力学响应稳定，兼具大变形能力与平稳的平台载荷特性，综合变形特征与缓冲性能更具优势，因此，本研究将围绕胞元3开展深入探讨。
胞元3的试验结果与仿真结果存在微小差异，主要体现在试验曲线有2个小波峰，而仿真曲线中该现象并不明显。分析试件的变形模式可以发现：在试验过程中，试件的上下部分在变形之初就出现明显的分层变形现象，上层先发生变形，而后才是下层变形，如图11(c)所示；在仿真结果中，试件在变形之初呈现均匀变形特征，而在较大变形时仅出现轻微的分层变形现象，如图11(d)所示。分析认为，该差异主要源于难以避免的试件加工误差，具体表现在试件上、下部分的尺寸存在偏差。在试验过程中，上、下部分中较为薄弱的部分会先变形，导致试件的实际力学行为与理想的仿真模型结果存在一定的偏差。
为进一步提升仿真模型的准确性，使其更贴合试验情况，对仿真模型的几何参数进行针对性修正：对胞元上、下部分的a引入一定的几何尺寸偏差e，以模拟实际试件的加工误差。结合3D打印的精度±0.15 mm，对修正误差进行敏感性分析，结果如图12所示。结果表明，在0.05～0.15 mm范围内，不同几何偏差对结构仿真结果的影响比较微弱，不同几何尺寸偏差下的仿真结果均与试验结果匹配良好。综合3D打印精度与参数敏感性分析结果，本研究最终选取0.10 mm作为仿真几何偏差。修正后的仿真结果如图11(b)所示，可见，仿真曲线与试验曲线的吻合度显著提升，并且仿真变形过程也更贴近试验中的变形特征，如图11(e)所示。这些结果验证了修正仿真模型的可靠性，为后续相关研究提供了精度更高的仿真结果。
观察不同a值条件下胞元3在压缩过程中的力-位移曲线，如图11(b)所示，结果表明，a的增加会显著提高力的峰值，当a从2 mm增加至5 mm时，胞元结构的变形模式并未发生改变，力的峰值提升819.5%，其原因在于尺寸的增加可显著提升胞元整体刚度与抗变形能力。a的改变也会影响胞元曲线的双峰现象：a为2 mm时，胞元的力-位移曲线较为平滑；当a为3、4和5 mm时，力-位移曲线出现较明显的双峰现象。
2.3 几何参数对胞元力学行为的影响
为了实现胞元结构的优化设计，采用有限元模型，计算和分析了胞元中间曲面板的厚度b和中部横向跨度c对胞元力学行为的影响。
研究b对胞元力学性能的影响时，其他参数保持不变，即a=2 mm、c=25 mm、h0=50 mm，仿真结果如图13(a)所示。b的增加也会增强胞元结构抵抗变形的能力，进而提高力的峰值，b从1.0 mm增加至5.0 mm时，力的峰值提升了约36%，说明b对力峰值的影响程度远不及a对力峰值的影响程度。不同b条件下的曲线斜率均呈先上升后趋于平缓的特征，说明b几乎未对胞元力-位移曲线的变化趋势造成影响。此外，b还会对胞元的密实应变造成影响。当b取1.0、2.0、3.0 mm时，胞元的应变均达到0.6，但随着b的增大，胞元的密实应变逐渐减小；当b=4.0 mm时，胞元的密实应变约为0.568，当b=5.0 mm时，胞元更快进入密实阶段，密实应变为0.522。对于b不同的胞元，其密实应变存在一定的差异，主要原因在于，b越大，压缩过程中构件接触越早，结构越易进入密实化阶段。
设a=2 mm、b=3.0 mm、h0=50 mm，研究c对胞元结构力-位移曲线的影响，结果如图13(b)所示。当c=20 mm时，胞元在压缩位移达到14 mm时发生不可控失稳，产生左右不对称变形，进而影响胞元的力-位移曲线，导致曲线出现异常波动，说明c与胞元的稳定性相关。不同于a和b，c与胞元力-位移曲线中力的峰值呈现显著的负相关关系，即随着c的增大，力的峰值减小。观察不同c下胞元结构的变形，可以发现，这种现象的出现主要源于c决定了曲面板对双弧结构的约束强度：当c较小时，压缩载荷下双弧结构的变形受到明显限制，整体结构刚度更高，力峰值更大；相反，当c较大时，结构的抗弯与抗变形能力下降，力的峰值随之降低。并且，c与胞元进入密实阶段的临界位移成反比，当c分别取30、35和40 mm时，在位移到达28.8、27.3和26.7 mm时力-位移曲线急剧上升，即胞元进入密实阶段，原因在于胞元的上下部分在变形后与上下钢板接触并发生挤压。
分析发现，改变胞元的几何参数会对其力-位移曲线造成影响，包括力的峰值以及曲线的变化趋势。此外，胞元的几何参数还会改变胞元在准静态压缩过程中的密实应变，影响其稳定性。
2.4 承载性能与可重复使用性能分析
基于a=2 mm时的试验结果，计算单位质量胞元的平台承载力，并与同类结构[25–29]进行比较，如图14所示。结果显示，本研究设计的胞元3的单位质量平台承载力为2.70 N/g，是现有同类结构的2.3倍以上，表明其承载能力明显优于现有同类结构。其原因在于，现有的结构为实现长载荷平台，往往需要设计质量占比过高的约束结构，实际参与变形的结构质量占比较低，导致材料的利用率偏低。而胞元3中的侧面双弧与中间曲面板全部参与变形，提升了材料的利用率，克服了以往此类结构约束质量占比过高的问题，提升了结构的承载性能。
为了进一步验证胞元结构的可重复使用性，对胞元3进行了120次循环压缩试验。图15展示了循环压缩试验采集到的试件的压缩和卸载曲线，以及试件在压缩前、后的结构形态。从图15中可以看出，结构在加、卸载过程会出现明显的滞回响应，主要由TPU材料的Mullins效应与其黏弹性耗散共同引起。前80次循环曲线会产生微小的残余变形，主要由TPU材料的Mullins效应引起；当循环次数达到80次后，力学响应逐步趋于稳定，加载曲线基本重合；历经120次循环测试后，试件无明显破损，整体力学性能保持稳定，证明了该结构具备良好的循环稳定性与可重复使用特性。这一结论为其在需要多次承载场景中的应用提供了有力支撑。
3 超材料的缓冲性能与机理
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3.1 缓冲性能分析
共设计了2种不同的胞串，以对比其缓冲性能。这2种胞串中只有第3个胞元的结构存在差异：第1种胞串（胞串S1，见图16(a)）中的第1、2、4和5个胞元都采用a=5 mm、b=3.0 mm、c=25 mm、h0=50 mm的单胞，通过设置第3个胞元的a，保证其与第2种胞串中的第3个胞元具有相同的质量，第3个胞元的其他参数设定为b=0 mm、c=25 mm、h0=50 mm；第2种胞串（胞串S2，见图16(b)）中的第1、2、4和5个胞元与胞串S1保持一致，第3个胞元的参数设置为a=1 mm、b=3.0 mm、c=25 mm、h0=50 mm。
在相同的冲击载荷下，2种胞串的输出端受到的力将反映胞串的缓冲性能。对胞串的输出端力-时间曲线进行对比，如图17所示。可以看出：胞串S1和S2的末端力分别在约5.8和14.0 ms时达到峰值；胞串S1的峰值力高于胞串S2，说明胞串S2的缓冲性能优于胞串S1。此类超材料在冲击载荷作用下发生反弹。考虑到本研究主要探究2种胞串的缓冲性能，重点关注其输出力-时间曲线中的首个压缩波，后续波动并非本研究的重点，故对其予以隐去。
3.2 缓冲机理解析
为了进一步解释胞串S1和S2的缓冲性能差异，对胞串中第3个胞元的力-位移曲线进行分析和对比，如图18(a)所示。对于胞串S1，中间胞元的力-位移曲线近似为一条倾斜直线，这种胞元的能量储存主要集中在行程的后半段，缓冲行程的利用率低；而对于胞串S2，中间胞元拥有长载荷平台段的力-位移曲线，可以在极小的反作用力下产生较大的变形，通过大变形储存和耗散冲击能量，缓冲行程的利用率高，因此，更契合缓冲设计需求。此外，基于仿真结果，获得了胞串中前4个胞元与最后1个胞元的能量演变，如图18(b)和图18(c)所示，以深入探索结构的缓冲机理。对比胞串S1与S2在冲击过程中的能量演变，发现在整个冲击过程中，胞串S2的前4个胞元的能量始终大于胞串S1，传递到最后1个胞元的能量则是胞串S1大于胞串S2。这表明，相较于胞串S1的中间胞元，胞串S2的中间胞元储存冲击能量的能力更强。不同于胞串S1，因结构突变引发的刚度与波阻抗失配，胞串S2中各胞元的几何构型虽然一致，但动态冲击下不同胞元的力学响应存在明显差异。胞串S2中第3个胞元的低幅值、长平台力-位移响应使其动态波阻抗大幅降低，与后续胞元形成更显著的波阻抗差值；该阻抗差异可调控应力波的反射与能量积聚行为，进而使更多冲击能量集中储存于该胞元内。除了结构的弹性储能之外，基材的黏弹性效应可进一步耗散冲击能量，2种机制共同决定结构的防护缓冲性能。因此，与普通的缓冲材料相比，本研究提出的超材料在缓冲应用场景中具有显著的优势。
4 结　论
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提出了一种具有可恢复大变形、长载荷平台特性的新型缓冲超材料，通过试验和有限元仿真，研究了其力学行为和缓冲性能，得到如下主要结论。
(1) 所设计的胞元结构由左右对称双弧与上下对称曲面板组合而成，其力-位移曲线在宽变形区间内呈现稳定的长平台段，可实现应变达0.6左右的可恢复变形。与现有同类结构相比，该胞元能够实现全结构协同承载变形，有效提升了材料利用率与承载性能。
(2) 胞元结构的力学行为可通过几何参数优化实现有效调控：厚度参数可正向提升平台载荷；横向跨度可降低平台载荷，并调控密实位移；中间曲面板是实现长载荷平台特性的关键结构。
(3) 在相同质量条件下，所提出的超材料的缓冲性能显著优于具有近似线性力-位移响应的其他结构，其优异的缓冲特性源于长载荷平台带来的更强波阻抗失配效应，实现了更高效的冲击能量捕获。

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2026年第40卷第7期
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doi: 10.11858/gywlxb.20261042
  • 接收时间：2026-03-06
  • 首发时间：2026-11-05
  • 出版时间：2026-07-05
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  • 收稿日期：2026-03-06
  • 修回日期：2026-05-14
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    中山大学深圳校区航空航天学院, 广东 深圳　518107

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胡玲玲（1980－），女，博士，教授，主要从事冲击动力学研究. E-mail：
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2种不同金属材料的力学参数
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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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