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Article(id=1246031929405976910, tenantId=1146029695717560320, journalId=1241755870837649424, issueId=1246031922707677827, articleNumber=null, orderNo=null, doi=10.19636/j.cnki.cjsm42-1250/o3.2024.011, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1709049600000, receivedDateStr=2024-02-28, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1775006762123, onlineDateStr=2026-04-01, pubDate=1724515200000, pubDateStr=2024-08-25, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1775006762123, onlineIssueDateStr=2026-04-01, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1775006762123, creator=13701087609, updateTime=1775006762123, updator=13701087609, issue=Issue{id=1246031922707677827, tenantId=1146029695717560320, journalId=1241755870837649424, year='2024', volume='45', issue='4', pageStart='427', pageEnd='564', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1775006760527, creator=13701087609, updateTime=1775006830786, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1246032217470779944, tenantId=1146029695717560320, journalId=1241755870837649424, issueId=1246031922707677827, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1246032217470779945, tenantId=1146029695717560320, journalId=1241755870837649424, issueId=1246031922707677827, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=508, endPage=519, ext={EN=ArticleExt(id=1246031929724744016, articleId=1246031929405976910, tenantId=1146029695717560320, journalId=1241755870837649424, language=EN, title=Research on Functional Characteristics of Perceptual Structures Based on Three-unit Configuration, columnId=1244229834482757770, journalTitle=Chinese Journal of Solid Mechanics, columnName=Research Paper, runingTitle=null, highlight=null, articleAbstract=

Using fused deposition modeling (FDM) 3D printing technology, a lattice structure was created. After adhering composite conductive materials to the surface of its structural elements, the 3D lattice structure with sensing capability (LSS) was fabricated. Based on three-unit configurations, a study was conducted to investigate the mechanical properties and piezoresistive characteristics of different lattice structures in LSS. Utilizing the conductive percolation phenomenon in conductive composites, this study explored the patterns of piezoresistive behavior in LSS with varying structures and composites under both small and large strain conditions. Key factors such as stress caused by structural deformation and self-contact between lattice surfaces were identified, leading to the observed three-stage trend in the change of electrical resistance response. By analyzing the experimental data from compression tests, the optimal lattice structure and composite mass fraction for LSS were determined, providing a reliable basis for deformation monitoring in perceptual structures. The approach of creating a 3D structure and then incorporating conductive composites offers benefits such as structural controllability and good mechanical performance. The sensing structure can detect compressive stress in objects and serve as a high-quality buffering or damping material that effectively absorbs vibration and energy. This research demonstrates promising applications in various fields.

, correspAuthors=Jie Zhang, 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=Lihong Kang, Rui Zhu, Guoliang Wu, Daoming Chen, Jie Zhang), CN=ArticleExt(id=1246031934481084875, articleId=1246031929405976910, tenantId=1146029695717560320, journalId=1241755870837649424, language=CN, title=基于三种单元构型的感知结构功能特性研究, columnId=1241831201896469478, journalTitle=固体力学学报, columnName=研究论文, runingTitle=null, highlight=null, articleAbstract=

通过熔融沉积成型（Fused Deposition Modeling，FDM）的3D打印技术，制备了晶格结构，在其结构元素表面粘附复合导电材料后，制备了具有感知功能的3D晶格结构（lattice structure sensor，LSS）. 基于3种单元构型，对不同晶格结构LSS的力学性能与压阻特性展开研究，根据导电复合材料中的导电渗流现象，探究在小范围应变与大变形应变的情况下，不同结构、不同复合材料的LSS压阻特性的规律. 结合实验的压缩应力平台数据，找到最适合的晶格结构与LSS复合材料质量分数值，为实现感知结构的变形监测功能提供了可靠的依据. 采用先生成3D结构再复合导电复合材料的方法形成功能3D结构，具有结构可控且机械性能良好的优势. 其感知结构可用于物体压缩应力的检测，同时也可作为优质缓冲或阻尼材料，有效的吸收振动和能量，因此该研究成果具有较为广阔的应用前景.

, correspAuthors=张婕, authorNote=null, correspAuthorsNote=
** E-mail：.
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2江苏省食品先进制造与装备重点实验室，无锡，214122
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caption=粘附CB/PDMS-10的Octet晶格感知结构能量吸收与变形感知性能, figureFileSmall=+x8oRX/AO8R46F7hxqHwDQ==, figureFileBig=/JkO069sLxId7vjrgzUFtw==, tableContent=null), ArticleFig(id=1246042380030292925, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246031929405976910, language=EN, label=Table 1, caption=

Three lattice structure geometric parameters

, figureFileSmall=null, figureFileBig=null, tableContent=
单元构型名称Octet（O）Kelvin（K）Gyroid（G）
单位晶格周期性边长15 mm
杆件直径*2 mm2.7 mm1 mm
晶格结构缩写晶格O晶格K晶格G
感知结构缩写LSS-OLSS-KLSS-G
), ArticleFig(id=1246042380126761921, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246031929405976910, language=CN, label=表1, caption=

三种晶格结构几何参数

, figureFileSmall=null, figureFileBig=null, tableContent=
单元构型名称Octet（O）Kelvin（K）Gyroid（G）
单位晶格周期性边长15 mm
杆件直径*2 mm2.7 mm1 mm
晶格结构缩写晶格O晶格K晶格G
感知结构缩写LSS-OLSS-KLSS-G
), ArticleFig(id=1246042380219036613, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246031929405976910, language=EN, label=Table 2, caption=

Lattice structure stress platform occupancy rate

, figureFileSmall=null, figureFileBig=null, tableContent=
晶格构型平台应力（kPa）占用率Δε（%）相对密度
Octet21.306410.2089
Kelvin32.058460.2014
Gyroid52.072330.1974
), ArticleFig(id=1246042380349060041, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246031929405976910, language=CN, label=表2, caption=

晶格结构应力平台占用率

, figureFileSmall=null, figureFileBig=null, tableContent=
晶格构型平台应力（kPa）占用率Δε（%）相对密度
Octet21.306410.2089
Kelvin32.058460.2014
Gyroid52.072330.1974
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基于三种单元构型的感知结构功能特性研究
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康利宏 1 , 朱睿 1 , 吴国良 1 , 陈道明 1 , 张婕 1, 2, 3, **
固体力学学报 | 研究论文 2024,45(4): 508-519
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固体力学学报 | 研究论文 2024, 45(4): 508-519
基于三种单元构型的感知结构功能特性研究
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康利宏1, 朱睿1, 吴国良1, 陈道明1, 张婕1, 2, 3, **
作者信息
  • 1江南大学机械工程学院，无锡，214122
  • 2江苏省食品先进制造与装备重点实验室，无锡，214122
  • 3先进技术研究院，无锡，214122

通讯作者:

Research on Functional Characteristics of Perceptual Structures Based on Three-unit Configuration
Lihong Kang1, Rui Zhu1, Guoliang Wu1, Daoming Chen1, Jie Zhang1, 2, 3, **
Affiliations
  • 1School of Mechanical Engineering, Jiangnan University, Wuxi, 214122
  • 2Jiangsu Key Laboratory of Food Advanced Manufacturing and Equipment, Wuxi, 214122
  • 3Advanced Technology Research Institute, Wuxi, 214122
出版时间: 2024-08-25 doi: 10.19636/j.cnki.cjsm42-1250/o3.2024.011
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摘要
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通过熔融沉积成型（Fused Deposition Modeling，FDM）的3D打印技术，制备了晶格结构，在其结构元素表面粘附复合导电材料后，制备了具有感知功能的3D晶格结构（lattice structure sensor，LSS）. 基于3种单元构型，对不同晶格结构LSS的力学性能与压阻特性展开研究，根据导电复合材料中的导电渗流现象，探究在小范围应变与大变形应变的情况下，不同结构、不同复合材料的LSS压阻特性的规律. 结合实验的压缩应力平台数据，找到最适合的晶格结构与LSS复合材料质量分数值，为实现感知结构的变形监测功能提供了可靠的依据. 采用先生成3D结构再复合导电复合材料的方法形成功能3D结构，具有结构可控且机械性能良好的优势. 其感知结构可用于物体压缩应力的检测，同时也可作为优质缓冲或阻尼材料，有效的吸收振动和能量，因此该研究成果具有较为广阔的应用前景.

晶格结构  /  3D打印  /  多孔结构  /  应力平台  /  感知结构  /  压阻传感

Using fused deposition modeling (FDM) 3D printing technology, a lattice structure was created. After adhering composite conductive materials to the surface of its structural elements, the 3D lattice structure with sensing capability (LSS) was fabricated. Based on three-unit configurations, a study was conducted to investigate the mechanical properties and piezoresistive characteristics of different lattice structures in LSS. Utilizing the conductive percolation phenomenon in conductive composites, this study explored the patterns of piezoresistive behavior in LSS with varying structures and composites under both small and large strain conditions. Key factors such as stress caused by structural deformation and self-contact between lattice surfaces were identified, leading to the observed three-stage trend in the change of electrical resistance response. By analyzing the experimental data from compression tests, the optimal lattice structure and composite mass fraction for LSS were determined, providing a reliable basis for deformation monitoring in perceptual structures. The approach of creating a 3D structure and then incorporating conductive composites offers benefits such as structural controllability and good mechanical performance. The sensing structure can detect compressive stress in objects and serve as a high-quality buffering or damping material that effectively absorbs vibration and energy. This research demonstrates promising applications in various fields.

lattice structure  /  3D printing  /  porous structure  /  stress platform  /  sensing structure  /  piezoresistive sensing
康利宏, 朱睿, 吴国良, 陈道明, 张婕. 基于三种单元构型的感知结构功能特性研究. 固体力学学报, 2024 , 45 (4) : 508 -519 . DOI: 10.19636/j.cnki.cjsm42-1250/o3.2024.011
Lihong Kang, Rui Zhu, Guoliang Wu, Daoming Chen, Jie Zhang. Research on Functional Characteristics of Perceptual Structures Based on Three-unit Configuration[J]. Chinese Journal of Solid Mechanics, 2024 , 45 (4) : 508 -519 . DOI: 10.19636/j.cnki.cjsm42-1250/o3.2024.011
正文
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0　引言
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近年来，三维多孔晶格结构备受关注，作为一种性能极佳的多功能结构[1-3]，它们相较于块状实体材料展现出了优越的机械性能，鉴于其复杂的几何结构，通常无法按照传统的生产方法制备. 3D打印技术的快速发展为复杂三维多孔结构的构建提供了更多可能性. 如今，用聚合物[4]、碳化物[5]、或纤维增强复合材料[6]等制备的晶格结构在多个领域中实现应用. 晶格不仅拥有良好的刚度，同时还具备轻量化、能量吸收以及高比强度等特点，可以用于生物医学、热力学以及材料性能改进等领域中，广泛应用于各种结构件、功能件或符合人体工程学的部件中[7]. 在文献中，常见的一些晶格单元构型包括简单立方、Octet（八面体桁架）和Kelvin（十四面体）等结构. 其中，Octet与Kelvin结构的变形模式分别是拉伸主导和弯曲主导[8]. 以拉伸为主的晶格具有较高的特定弹性模量，而以弯曲为主的晶格结构在大变形阶段往往表现出较长的平台应力期[9]，吸能性较好[10]. 上述两种晶格单元构型的基本组成是支柱状结构，与它们不同，以面片状结构为基本组成的单元构型是Gyroid结构[11,7]. 这三种晶格单元构型代表不同的压缩载荷响应模式与不同类别的晶格结构，具有典型性.
传感器件通过压阻、压电、超级电容和摩擦电等[12,13]机制，将机械刺激转化为电信号，从而能够检测结构的变形或损伤情况[14,15]. 晶格结构较高的孔隙率及其内部结构的联通性可以为感知器件提供导电通道，晶格结构的感知功能主要通过两种方式实现：一是将传感元件嵌入材料中，通过传感器的参数变化检测外部环境的改变[16]；二是使用有传感能力的功能材料打印3D结构[17,18]. Yang等[19]通过3D打印技术成功开发出一种轻质智能装甲，这种装甲中的石墨烯纳米片排列整齐，通过其压阻性能实现了损伤感知. Reddy等[20]将多层石墨烯纳米颗粒注入泡沫多孔结构中实现了传感功能，压阻响应性能良好. Pang等[21]提出了一种摩擦纳米发电的自供电传感器，以三周期最小表面（TPMS）为结构基底，表现出典型多孔材料的应力应变特性. 这些研究工作的特点是利用功能性材料构建三维结构，然而，功能改性的需求极大地增加了通过3D打印技术制造复杂结构的难度. 因此，结构与感知性能之间的内在联系尚未得到有效探究.
本文选取三种（Octet、Kelvin、Gyroid）单元构型的晶格结构，通过FDM的3D打印技术制备感知结构的基底，在基底表面粘附导电碳黑（CB）质量分数分别为10%、15%、20%的复合材料，经过一系列处理制得具有感知功能的3D晶格结构（lattice structure sensor，LSS）. 研究三种感知结构的应力平台占用率、应变灵敏度ks、损伤灵敏度kd、比能量吸收、能量吸收效率等参数表征感知结构的性能，探究不同单元构型及表面粘附材料对晶格感知结构的力学和压阻性能的影响，为晶格感知结构在实际的应用中提供指导和方向.
1　实验部分
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1.1　主要原料
3D打印丝材（Thermoplastic Elastomer，TPE），邵氏硬度83 A，密度1.14 g/cm3，易生3D打印耗材公司®；碳黑（carbon black，CB），粒径24 nm，比表面积112 m2/g，卡博特（中国）投资有限公司；聚二甲基硅氧烷（PDMS SYLGARD 1700），美国道康宁公司；二甲基硅油，力辰仪器科技公司；N，N-二甲基甲酰胺（DMF）和乙酸乙酯，分析纯，上海泰坦科技股份有限公司.
1.2　主要设备
3D打印设备（浙江闪铸三维科技有限公司®，Creator Pro2）. 测试设备是自行搭建的测试平台，测试平台包括测力计（乐清市艾德堡仪器有限公司®，HP-500）、程控移动平台（北京北光世纪仪器有限公司®，MVS313），LCR测试仪（HIOKI®，IM3536）. 扫描电子显微镜（德国蔡司®，EVO-8）.
1.3　样品制备
1.3.1　基底结构设计和制造
基底的结构设计基于Octet，Kelvin，Gyroid三维晶格结构，使用nTopology设计模型. 具体参数如表1所示. 基底是由对应的单元结构分别沿X、Y、Z坐标方向进行线性阵列所得，形成2×2×2的3D晶格结构，三种结构的相对密度均为20%，晶格结构模型如图1（a）、（b）、（c）所示.
使用商用FDM的3D打印机制造基底，3D打印机具体参数为：喷头直径0.4 mm，打印精度0.2 mm. 喷头温度240 ℃，平台温度60 ℃，层高0.18 mm，填充密度100%. 热塑性弹性体树脂TPE作为打印材料. 为了保证样品的一致性，本文中的样品全都基于上述打印参数进行，打印成型后，作为基底的结构如图1（d）、（e）、（f）所示，最终样品尺寸为30 mm×30 mm×30 mm.
1.3.2　表面导电复合材料的粘附
为实现晶格结构的感知功能，选择CB/PDMS作为导电复合材料与基底结合. 导电复合材料的制作方式过程如图2所示. 首先，配置CB质量分数为10%、15%、20%的CB/PDMS分散液（记为CB/PDMS-x）. 然后，将使用DMF预处理后的基底结构放入CB/PDMS溶液中静置3分钟，取出后烘箱加热60 ℃固化处理，冷却后制得晶格感知结构（LSS）. 分别将3种单元构型的基底经过上述3种质量分数的CB/PDMS分散液处理，得到9组晶格感知结构样品，每组制作3个.
切取晶格感知结构的支柱部分，利用扫描电子显微镜（SEM）对其截面进行表征. 如图3显示，基底结构表面与复合材料的结合包括三部分，底层部分是相对光滑的基底框架，中间层是由基底和复合导电材料形成的，整体上仍保留着基底的特征，但是呈现一些孔洞. 上层完全由固化后的CB/PDMS大颗粒附着组成.
1.4　性能测试与表征
对制备完成的LSS进行Z轴方向单轴压缩实验，同时探究结构的应力和电阻随着应变变化的关系，实验以5 mm/min的恒定速度进行压缩，测力计和LCR测试仪分别测定材料的受力和电阻变化. 对LSS施加压力之前，剪裁合适尺寸的铜箔并将其粘贴到测力计的压头与平台底面，使用导线将铜箔与LCR测试仪连接. 使用千眼狼X113高速摄像机记录压缩加载过程中晶格结构的形变.
计算LSS的工程应力、应变分别为：
式中：σ为LSS的整体应力大小（kPa）；F为作用在试件上的载荷（N）；A为试件的横截面积（mm2）.
式中，ε为LSS的应变大小（mm/mm）；Δl为LSS的压缩长度，即压缩试验机的位移值；l0为试件的初始高度.
LSS在外部载荷下的电阻变化灵敏度（Resistance Change Sensitivity），其公式为：
式中：R0表示试件在未承受外部载荷时的初始电阻值；R表示LSS在承受外部载荷时的实时电阻值.
所有表征实验均进行3次以上重复，使用python进行统计数据分析，使用Origin2021®进行数据样本可视化.
2　结果与讨论
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2.1　基底框架的力学性能
本节对图1中三种单元构型的晶格O、K、G结构进行压缩实验，对基底框架力学性能进行分析. 由于选用的材料为一种柔性的树脂，并且三维晶格结构孔隙率较大，因此在进行单轴压缩时晶格结构的基底可以实现较大的变形.
为了深入探讨不同晶格结构的变形模式、应力分布以及载荷响应机理，使用ABAQUS进行有限元模拟分析，用于模拟分析的模型按照实际尺寸进行建模. 选择C3D8R单元进行网格划分，平均网格尺寸为0.45 mm. 通过对TPE标准圆柱体进行单轴压缩实验，获取了材料的应力-应变数据，这些数据为有限元模拟提供了关键的材料属性参数，模拟中使用了Mooney-Rivlin本构模型[22]. 为了模拟实验条件，将压缩实验的上下压板定义为刚体并分别设置参考点，在压板之间放置晶格结构模型. 固定底部刚性压板，同时在垂直方向上给予顶部刚性压板向下的位移以压缩试件，位移载荷设置为-22.5 mm. 模型中所有单元之间采取通用接触，法向接触行为选择硬接触，切向接触行为设置罚因子为0.3.
由于在后续实际的单轴压缩实验中，很难清晰观察到结构在受压时及受压后的真实情况，因此本文通过有限元仿真给出了模型的变形及应力云图，这些云图能够直观的展示出每个杆件的真实应力状况以及各节点的受力情况，为后续的分析研究提供了重要的依据，应力云图如图4所示.
为了验证有限元模拟的正确性，本文对上述三种晶格结构的打印件进行了单轴压缩实验，对比了实验与有限元仿真结果. 图5展示了在Z轴压缩载荷作用下，三种晶格结构的实验与仿真应力-应变曲线的对比情况. 从图中可以看出，实验和仿真应力-应变曲线的整体趋势相似，在局部应力/应变存在偏差. 造成这种现象的主要原因有两个方面. 首先，打印设备精度的限制会导致结构在转折点上存在打印线宽误差，导致结构的实际相对密度与理论值存在偏差. 其次，由于打印结构的曲面及杆件的较大跨度，无支撑自由部分可能在固化过程中存在一些变形，从而影响晶格结构的力学性能. 这些因素都会在一定程度上造成实验与仿真结果的偏差. 尽管存在这些偏差，但它们均在可接受范围之内，不会对结果总体趋势的准确性产生影响. 因此，在后续的分析研究中，将以实验所得的应力-应变曲线为主要依据，结合有限元模拟的云图进行综合分析.
结合图4的应力云图，可以观察到应力的主要集中区域位于结构的各杆件连接处以及与平面呈一定倾斜角的杆件处，这些区域在受力时容易产生应力集中现象. 根据压缩实验所得的应力-应变曲线图5，可以将应力响应过程分为三个阶段，第一个阶段是材料在弹性变形段，此时应力随应变的增加而线性增加，材料表现出弹性性质. 第二个阶段是内部胞体逐渐坍塌段（应力平台段），此时应力在持续增加的应变下增加很小. 第三个阶段是内部胞体完全坍塌后产生致密化效应段，此时应力随应变的增加而迅速增加，材料表现出致密化性质.
根据应力-应变曲线图，发现在同等相对密度下，应变相同时，Gyroid晶格结构的承载能力明显强于其他两种结构. 然而，需要注意的是，3D打印的TPE材料是一种柔性树脂，试件整体结构相对较软，所以在这项研究中并不关注结构的承载能力，而更加关注其在受压时内部结构所展现出的力学特性，也就是吸能应力平台[23]，即结构在受压过程中的能量吸收能力. 为了量化这一特性，引入了应力平台占用率（Δε）[23]. 应力平台占用率定义为结构在应力平台段的应变范围与试样整体应变范围的比值.
表2给出了上述三种晶格结构的相对密度以及应力平台的占用率值. 首先，三种结构的相对密度误差不大，这说明它们在原材料使用效率上是相当的. 在同等相对密度下，晶格G的平台占用率与晶格O和晶格K的差距较大，晶格G的平台占用率较小. 这与结构特性有关，其孔隙率较低，由图4应力云图可知，面片状的结构部件之间距离接近，在受压时，很快就到达结构的致密化应变处，因此应力平台的占比相对较小. 从应力-应变曲线（图5）可以看出，在同等应变的状态下，晶格O与晶格K的应力较低，但是它们表现出了更好的应力平台占用率.
虽然三种晶格结构在相对密度上相差不大，但在平台占用率和能量吸收能力方面却表现出明显的差异. Octet与Kelvin结构具有良好的应力平台占用率，能量吸收性能更佳.
2.2　LSS的压阻性能
导电复合材料对3D表面处理后的晶格结构具有应变感知功能，其具有导电性并表现出压阻效应，因此在准静态压缩测试过程中记录了不同导电体含量CB/PDMS-10、CB/PDMS-15、CB/PDMS-20晶格感知结构的电阻值变化，以评估其压阻行为. 其中，对于单元构型与导电体含量的每一种组合，均制作了3个样品进行测试以消除误差.
不同单元构型的应力-应变曲线如图6所示. 所有LSS的电阻值都随着施加压缩应力的增加而下降，这与预期相符. 第一阶段，三种结构的初始压阻响应都接近线性，这主要是因为压缩过程刚发生，导电颗粒之间的距离开始缩小，复合材料内导电网络的迅速建立导致电阻变化率的线性改变. 第二阶段，初始的线性压阻之后，其响应的斜率减小，在此区域中，结构的屈服和逐渐皱褶主导了压阻效应. 在第三阶段，随着致密化开始，观察到-ΔR/R0-ε曲线的斜率增加，这是晶格结构表面彼此接触的时刻（即支柱与面片状结构之间接触的导电网络渗流路径开始形成），从而在晶格结构内部形成了更多的导电路径. 随着压缩载荷的进一步增加，接触渗流现象也不断增强，直至结构几乎完全致密化. 此时，应变达到完全致密化应变（即结构部件之间紧密贴合），结构的电阻到达最小值.
图7显示了试件（CB/PDMS-10，相对密度为20%）在准静态压缩下不同应变水平的图像. 结合图8应力应变曲线可知，所有试件接近完全致密化之前，晶格感知结构没有宏观破坏的行为发生.
LSS对应变的敏感性通过应变灵敏度来衡量，即材料对应力的响应，特别指小范围应变. 即图6电阻变化率曲线的第一阶段所对应的应变区间，在该阶段-ΔR/R0-ε曲线的斜率，由下式给出：
其中，ΔR是在压力作用下的压缩应变范围Δε（压阻线性响应区）内的电阻变化，应变灵敏度ks绘制在图9中.
从图9可以看出，随着导电复合材料中CB浓度的增加，应变敏感性ks提高. CB浓度较高的样品表现出较高的ks. 这是由于CB浓度较高的复合材料内部的导电路径数量（低于或略高于渗流阈值）较多，形成了更密集的、数量处于渗流阈值边缘的导电网络.
不同的结构之间，可以观察到应变敏感性ks的明显区别. LSS-G表现出更高的应变敏感性，其ks值范围为17至22，而LSS-K的ks值平均最低，范围为9至22. LSS-O的应变敏感性受CB浓度的影响更大，因此不在以下讨论之中. 不同基底感知结构的ks值与机械性能表现出对应关系，压阻响应差异可以归因于结构的变形模式. 晶格K以弯曲变形为主，与晶格G相比，其结构受到更多的弯曲. 在拉伸应力作用的区域，电阻值会局部增加，使得LSS-K电阻整体的变化较小.
与LSS-K不同，LSS-G同时受到弯曲和拉伸变形模式的作用. LSS-G的结构受弯曲而产生的拉伸应力的影响较小，同样的应变下，结构的内应力更大，导电路径结合的更加紧密，因此LSS-G的应变敏感性ks较高（范围为17-22）.
此外，还通过损伤灵敏度来描述材料在较大应变时（即图6曲线第一阶段之后的应变区间），电阻对应变的敏感程度，由下式给出：
其中εD是晶格结构致密化的起始应变，εy是晶格结构的初始屈服应变，即图5中应力-应变平台区域的起始点对应的应变. 图10（a）-（c）显示了在非线性压阻区域中计算的kd. 可以看到，CB浓度越小的LSS，其kd越高，LSS-O的kd高于另外两种结构. kd随单元构型、CB浓度的变化而变化. kd表征的区域，处于压阻响应曲线的第二段与第三段，需要注意的是，压阻响应曲线的三个区域的开始点均比应力曲线要更早出现. 由图6可知，相较于第二段，压阻响应的第三阶段，-ΔR/R0-ε曲线的斜率快速增加，这是由于结构体之间全面接触的开始，支柱与面片结构的接触导致新的导电路径的接通，所以第三段压阻曲线斜率大幅增加. 其中，LSS-O的压阻曲线第三部分斜率最大，其性能最佳. 由图4云图可知，这是由于晶格O的结构组织比较密集，结构孔隙率较大，而晶格K与晶格G较疏松，孔隙率较小.
基于上述分析，在小应变时，LSS-O的电阻变化对应变的敏感性受复合材料中CB浓度的影响最大，呈正相关. 在大应变时，LSS-O的kd最高，电阻变化对应变的敏感性最好. 为了较好的实现对结构大变形的感知检测，拟选用晶格O与CB/PDMS-10，组成晶格感知结构的基底与粘附材料.
2.3　LSS吸能性分析
晶格结构的一个重要应用是机械防护与缓冲吸能，其能够降低外部冲击对被保护物的影响，如电子设备、精密仪器等产品的包装吸能性的优劣非常重要. 缓冲材料可以吸收和分散外部冲击产生的能量，从而保护主体结构免受损伤. 因此，晶格结构的能量吸收能力是一个非常重要的性能指标.
根据前两节的研究，发现粘附CB/PDMS-10的LSS-O表现出了良好的压缩性能，其电阻对应变的敏感性最为良好. 以下，进行其吸能性的分析.
由图11可知，粘附不同质量分数CB的复合材料后，晶格感知结构的应力平台占用率相较基底结构变化不大，分别为42.6%、45.07%、42.78%. 说明复合材料的粘附对基底结构的力学性能无显著影响，平台的力学特性仍然由基底结构主导，LSS-O仍然保持良好的吸能性.
为了比较晶格O的基底与LSS-O的力学性能，从能量吸收角度出发，结合式（6）与式（7）分别求出基底晶格O与LSS-O的比吸能和吸能效率η.
式中，x为实时的压缩位移，F为结构承受的力载荷；m为试样的质量，根据电子秤称量得到.
由图12（a），LSS-O的比能量吸收值比基底结构更大，说明复合材料的粘附可以适量增加基底结构的能量吸收能力.
为了表征LSS变形过程中实时的压阻灵敏程度，使用ΔR/R0-ε曲线的瞬时斜率作为衡量指标，即瞬时应变系数（Instantaneous Guage factor，GF），由下式给出：
根据图12（b）所示，与前文分析相同，LSS-O瞬时应变系数k的曲线分为三个阶段. 第一阶段是k快速变化的线性压阻区，第二阶段k保持稳定，电阻缓慢增加，第三阶段结构大变形开始，LSS-O的支柱结构互相接触，新的导电渗流通道形成，电阻变化率再次显著增加. 所以，粘附CB/PDMS-10的LSS-O，电阻变化率的变化受到结构的控制，可根据瞬时量规系数的阶段判断此时结构的变形状态，LSS-O具有良好的感知结构变形的能力.
LSS处于小的应变区间时，其电阻变化率呈现线性，灵敏度较高，可应用于监测持续性、周期性的变形情况. 当处于较大的应变区间时，其电阻变化率虽然不呈现线性，但是会在结构的致密化应变点附近有一个较大的电阻变化率，这一应变区间可用于监测结构受到大的冲击力时，其较大变形情况.
3　结论
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（1）根据选择的三种单元构型，设计多孔晶格结构，通过3D打印技术制备样品. 以晶格结构作为基底，在表面粘附复合材料后，制备了晶格感知结构. 针对所设计的晶格结构，研究了其力学性能以及压缩吸能特性. TPE这种软性材料与CB/PDMS复合材料结合构成的晶格感知结构展现出了良好的力学特点. 其在变形过程中，共经历了弹性变形、应力平台、致密化效应三个变形阶段. 分析比较了三种单元构型组成的晶格结构的吸能特性差异，根据实验结果表明，晶格O与晶格K具有较好的应力平台，晶格G具有良好的承载能力.
（2）晶格感知结构具有感知变形的能力，变形承载所受的应力、晶格表面之间的自接触导致了电阻变化响应的三段趋势；在小范围应变时，同种结构下，随着CB浓度的增加，LSS应变敏感性提高. 不同结构之间比较，LSS-G的电阻变化对应变的敏感性更强，这是因为晶格-G的承载力大，应力更大的LSS应变灵敏度性能更好；在大应变时候，晶格结构表面之间的自接触开始发生，这个行为致使新的导电渗流网络产生. 其中，LSS-O的损伤灵敏度最大，这是由于晶格O结构孔隙率较大，结构表面导电复合材料的自接触面积最多.
（3）通过改变基底的晶格单元构型以及粘附材料，其表现出的力学特性与压阻响应会有区别. LSS性能最佳的晶格结构与复合材料，即Octet晶格与CB/PDMS-10，该晶格感知结构具有良好的吸能性，同时变形感知性能最佳. 根据瞬时应变系数可反映出结构的变形状态，因此，通过LSS-O的电阻变化，可以实现对结构变形状态的实时监测. 可以进行合理的设计将LSS应用到需要缓冲吸能的场景中，利用LSS的应变感知功能监测变形状况，同时，通过结构的改变，能适当控制LSS压阻效应的电阻值变化，根据应用场景进行相应的调控.
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2024年第45卷第4期
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doi: 10.19636/j.cnki.cjsm42-1250/o3.2024.011
  • 接收时间：2024-02-28
  • 首发时间：2026-04-01
  • 出版时间：2024-08-25
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  • 收稿日期：2024-02-28
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    1江南大学机械工程学院，无锡，214122
    2江苏省食品先进制造与装备重点实验室，无锡，214122
    3先进技术研究院，无锡，214122

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2种不同金属材料的力学参数
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鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
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