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Article(id=1241831206245957914, tenantId=1146029695717560320, journalId=1241755870837649424, issueId=1241831200843699167, articleNumber=null, orderNo=null, doi=10.19636/j.cnki.cjsm42-1250/o3.2025.028, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1758124800000, receivedDateStr=2025-09-18, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1774005231676, onlineDateStr=2026-03-20, pubDate=1761494400000, pubDateStr=2025-10-27, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1774005231676, onlineIssueDateStr=2026-03-20, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1774005231676, creator=13701087609, updateTime=1774005231676, 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=667, endPage=680, ext={EN=ArticleExt(id=1241831206585696544, articleId=1241831206245957914, tenantId=1146029695717560320, journalId=1241755870837649424, language=EN, title=Mechanical Properties and Deformation Mechanisms of Lattice Sandwich Structures with a Replaceable Hybrid Core Configuration, columnId=1241831201674171363, journalTitle=Chinese Journal of Solid Mechanics, columnName=Research Papers, runingTitle=null, highlight=null, articleAbstract=

Hybrid lattice configurations that incorporate diverse structural units offer a promising pathway to tailor the mechanical performance of hybrid lattice sandwich structures. A deeper understanding of the underlying mechanisms governing how hybridization influences global structural responses is essential for establishing rational design strategies. In response to the requirements of mechanical performance regulation in hybrid structures, this study investigates the influence mechanisms of core-layer unit hybridization on the mechanical performance and deformation characteristics. Based on the specific modulus and yield stress responses of eight representative lattice structure units, four units with significant geometric and mechanical disparities were strategically selected, and ten substitution-type hybrid core configurations were developed through spatial arrangement optimization. The corresponding lattice sandwich structure specimens were fabricated via fused deposition modeling (FDM). Combined with finite element analysis and compressive experiments, the effects of substitution configuration on load-bearing characteristics and deformation modes were revealed. The results demonstrate that the performance difference between the substitution units and the matrix units dominates the deformation mode transition in hybrid structures. Weak-unit substitution in strong matrices induces premature core-layer activation, reducing overall specific modulus and yield stress of the structure by 41.78% and 25.58%, and 45.19% and 26.07%, respectively, compared to their homogeneous counterparts with all hybrid combinations exhibiting similar mechanical performance at equivalent substitution volume fractions. Conversely, strong-unit substitution in weak matrices delays core densification while enhancing load redistribution to the upper and lower layers. The specific modulus demonstrated maximum and average deviations of 10.5% and 4.2%, respectively, while the yield stress exhibited corresponding maximum and average deviations of 14.0% and 6.6%, respectively. The results provide useful references for the design and optimization of hybrid lattice cores. In particular, the findings highlight that the mechanical performance under large-deformation conditions can be enhanced through selective reinforcement strategies, where stronger units are judiciously introduced into critical regions of the core to replace weaker ones. Such a substitution scheme avoids detrimental weakening effects while promoting improved load-bearing capacity and damage tolerance. These insights offer guidance for engineering hybrid sandwich designs capable of meeting specialized demands in extreme service environments.

, correspAuthors=Sheng Ding, 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=Zhirong Huang, Sheng Ding, Yibo Li), CN=ArticleExt(id=1241831210457039188, articleId=1241831206245957914, tenantId=1146029695717560320, journalId=1241755870837649424, language=CN, title=置换式混杂芯层构型下点阵夹芯结构的力学性能与变形机制, columnId=1241831201896469478, journalTitle=固体力学学报, columnName=研究论文, runingTitle=null, highlight=null, articleAbstract=

本文基于混杂点阵夹芯结构的力学性能调控需求，探究了其芯层点阵结构单元的混杂组合方式对其力学性能和变形机制的影响规律. 基于8种典型点阵结构单元在压缩载荷下的比模量与屈服应力的响应，筛选出几何参数、力学性能差异显著的4种单元，并依据空间排列可行性构建了10种置换式混杂芯层结构. 采用熔融沉积成型（FDM）技术制备了其对应的点阵夹芯结构，结合压缩试验与有限元数值模拟，揭示了置换方式对结构承载特性与变形模式的作用机理. 研究表明：置换单元与基体单元的性能差异主导着混杂结构的变形模式演变，弱单元置换强基体时芯层优先进入承载阶段，较同构基体整体比模量分别下降41.78%和25.58%、屈服应力分别下降45.19%和26.07%，且在相同置换体积分数条件下，各组合的性能表现趋于一致；而强单元置换弱基体则延后了芯层的致密化过程，使上下层承担更多载荷，其比模量最大偏差与平均偏差均不足10.5%和4.2%、屈服应力偏差分别为14.0%和6.6%.

, correspAuthors=丁晟, authorNote=null, correspAuthorsNote=
**E-mail：.
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Process parameters for additive manufacturing

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参数数值
材料短碳纤维增强尼龙（Onyx）
喷嘴温度（℃）275
床身温度（℃）室温
填充模式实体
填充密度（%）100
边缘层数2
层厚（mm）0.1
), ArticleFig(id=1241831216446505479, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1241831206245957914, language=CN, label=表1, caption=

增材制造的工艺参数

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参数数值
材料短碳纤维增强尼龙（Onyx）
喷嘴温度（℃）275
床身温度（℃）室温
填充模式实体
填充密度（%）100
边缘层数2
层厚（mm）0.1
), ArticleFig(id=1241831216542974476, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1241831206245957914, language=EN, label=Table 2, caption=

Mechanical properties of Onyx

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性能Onyx
密度（g/cm3）1.2
杨氏模量（GPa）2.4
泊松比0.3
屈服强度（MPa）40
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Onyx的力学性能

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性能Onyx
密度（g/cm3）1.2
杨氏模量（GPa）2.4
泊松比0.3
屈服强度（MPa）40
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Mechanical property of 8 types of specimens

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类型比模量（MPa•cm3/g）屈服应力（MPa）屈服应变比吸收能（J/g）
ALL-A244.743.530.03846.21
ALL-B353.284.400.033714.27
ALL-C461.767.140.037014.59
ALL-D376.196.490.037614.08
ALL-E442.376.770.035410.94
ALL-F344.835.410.03619.15
ALL-G399.745.400.03109.98
ALL-H324.423.560.027713.31
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8种试样的力学性能

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类型比模量（MPa•cm3/g）屈服应力（MPa）屈服应变比吸收能（J/g）
ALL-A244.743.530.03846.21
ALL-B353.284.400.033714.27
ALL-C461.767.140.037014.59
ALL-D376.196.490.037614.08
ALL-E442.376.770.035410.94
ALL-F344.835.410.03619.15
ALL-G399.745.400.03109.98
ALL-H324.423.560.027713.31
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置换式混杂芯层构型下点阵夹芯结构的力学性能与变形机制
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黄职榮 1, 2 , 丁晟 1, 2, ** , 李毅波 1, 2
固体力学学报 | 研究论文 2025,46(5): 667-680
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固体力学学报 | 研究论文 2025, 46(5): 667-680
置换式混杂芯层构型下点阵夹芯结构的力学性能与变形机制
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黄职榮1, 2, 丁晟1, 2, ** , 李毅波1, 2
作者信息
  • 1中南大学轻合金研究院，长沙，410083
  • 2极端服役性能精准制造全国重点实验室，长沙，410083

通讯作者:

Mechanical Properties and Deformation Mechanisms of Lattice Sandwich Structures with a Replaceable Hybrid Core Configuration
Zhirong Huang1, 2, Sheng Ding1, 2, ** , Yibo Li1, 2
Affiliations
  • 1Light Alloy Research Institute, Central South University, Changsha, 410083
  • 2State Key Laboratory of Precision Manufacturing for Extreme Service Performance, Changsha, 410083
出版时间: 2025-10-27 doi: 10.19636/j.cnki.cjsm42-1250/o3.2025.028
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摘要
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本文基于混杂点阵夹芯结构的力学性能调控需求，探究了其芯层点阵结构单元的混杂组合方式对其力学性能和变形机制的影响规律. 基于8种典型点阵结构单元在压缩载荷下的比模量与屈服应力的响应，筛选出几何参数、力学性能差异显著的4种单元，并依据空间排列可行性构建了10种置换式混杂芯层结构. 采用熔融沉积成型（FDM）技术制备了其对应的点阵夹芯结构，结合压缩试验与有限元数值模拟，揭示了置换方式对结构承载特性与变形模式的作用机理. 研究表明：置换单元与基体单元的性能差异主导着混杂结构的变形模式演变，弱单元置换强基体时芯层优先进入承载阶段，较同构基体整体比模量分别下降41.78%和25.58%、屈服应力分别下降45.19%和26.07%，且在相同置换体积分数条件下，各组合的性能表现趋于一致；而强单元置换弱基体则延后了芯层的致密化过程，使上下层承担更多载荷，其比模量最大偏差与平均偏差均不足10.5%和4.2%、屈服应力偏差分别为14.0%和6.6%.

点阵结构  /  混杂设计  /  熔融沉积成型  /  力学性能  /  变形机制

Hybrid lattice configurations that incorporate diverse structural units offer a promising pathway to tailor the mechanical performance of hybrid lattice sandwich structures. A deeper understanding of the underlying mechanisms governing how hybridization influences global structural responses is essential for establishing rational design strategies. In response to the requirements of mechanical performance regulation in hybrid structures, this study investigates the influence mechanisms of core-layer unit hybridization on the mechanical performance and deformation characteristics. Based on the specific modulus and yield stress responses of eight representative lattice structure units, four units with significant geometric and mechanical disparities were strategically selected, and ten substitution-type hybrid core configurations were developed through spatial arrangement optimization. The corresponding lattice sandwich structure specimens were fabricated via fused deposition modeling (FDM). Combined with finite element analysis and compressive experiments, the effects of substitution configuration on load-bearing characteristics and deformation modes were revealed. The results demonstrate that the performance difference between the substitution units and the matrix units dominates the deformation mode transition in hybrid structures. Weak-unit substitution in strong matrices induces premature core-layer activation, reducing overall specific modulus and yield stress of the structure by 41.78% and 25.58%, and 45.19% and 26.07%, respectively, compared to their homogeneous counterparts with all hybrid combinations exhibiting similar mechanical performance at equivalent substitution volume fractions. Conversely, strong-unit substitution in weak matrices delays core densification while enhancing load redistribution to the upper and lower layers. The specific modulus demonstrated maximum and average deviations of 10.5% and 4.2%, respectively, while the yield stress exhibited corresponding maximum and average deviations of 14.0% and 6.6%, respectively. The results provide useful references for the design and optimization of hybrid lattice cores. In particular, the findings highlight that the mechanical performance under large-deformation conditions can be enhanced through selective reinforcement strategies, where stronger units are judiciously introduced into critical regions of the core to replace weaker ones. Such a substitution scheme avoids detrimental weakening effects while promoting improved load-bearing capacity and damage tolerance. These insights offer guidance for engineering hybrid sandwich designs capable of meeting specialized demands in extreme service environments.

lattice structures  /  hybrid design  /  fused deposition modeling  /  mechanical properties  /  deformation mechanisms
黄职榮, 丁晟, 李毅波. 置换式混杂芯层构型下点阵夹芯结构的力学性能与变形机制. 固体力学学报, 2025 , 46 (5) : 667 -680 . DOI: 10.19636/j.cnki.cjsm42-1250/o3.2025.028
Zhirong Huang, Sheng Ding, Yibo Li. Mechanical Properties and Deformation Mechanisms of Lattice Sandwich Structures with a Replaceable Hybrid Core Configuration[J]. Chinese Journal of Solid Mechanics, 2025 , 46 (5) : 667 -680 . DOI: 10.19636/j.cnki.cjsm42-1250/o3.2025.028
正文
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0　引言
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随着增材制造技术如熔融沉积成型（FDM）的发展，极大地便利了关于复杂点阵结构设计的探索，使得点阵结构在工程领域的应用日益广泛，特别是在轻量化和高性能结构设计中展现出巨大潜力[1-6]. 现有研究中的许多点阵结构及混合设计灵感往往源自于大自然生物的各种微观结构[7-10]. 其中，分层结构设计策略因其兼具理论可行性与工程可实现性的双重优势，已逐步发展为结构设计领域的研究前沿与技术焦点.
近年来，均质点阵结构因空间构型简单备受关注，其力学性能已通过传统分析方法得到广泛研究[11-16]，但针对多种点阵单元的混杂设计研究仍相对匮乏. 现有研究主要分为单元层面和整体结构层面：在单元层面，Ma等[17]融合BCC结构和Octet结构设计新型混杂单元，提升了结构刚度、强度及能量吸收性能；Li等[18,19]结合弯曲主导的Octagonal结构与拉伸主导的简单立方结构（SC），使应力分布更均匀、压缩稳定性增强. 在整体结构层面，Vangelatos等[20]通过策略性结构修饰改变超材料变形和坍塌模式；Lei等[21]发现水平混合的多层点阵结构呈现独特逐层破坏模式；Yang等[22]证实负泊松比n型结构层的位置和数量显著影响整体变形模式. 尽管这些研究有效改善了混杂结构性能，但尚未充分挖掘单元潜力，亟需创新设计策略，实现通过调整点阵单元类型、占比及混杂方式精准定制结构性能.
在力学性能研究范畴内，比模量与屈服应力作为核心评价指标，混杂结构设计对其力学响应的内在作用机制仍需进一步明晰. 尤其是不同比模量和屈服应力组合的点阵单元之间如何协同作用、相互影响，进而塑造整体结构性能，仍是亟待解决的关键问题. 而变形模式作为力学性能的宏观外在体现[23-25]，众多研究已证实从其入手探索结构性能影响机制的有效性：Li等[26]基于压缩结果分析了结构的变形模式与破坏机制，发现了刚度和强度随结构层数的增加而显著降低；Yu等[27]分析了结构在[100]、[110]、[111]三个方向上的变形模式，观察到在压缩方向上对齐的结构有着高强度，而稳定的逐层变形则导致了高的比吸收能；Sun等[28]结合有限元模拟与CT扫描图像，证实了压缩方向对Octet结构与HS拓扑结构应力水平和变形模式的显著影响.
本研究聚焦于点阵夹芯结构的芯层设计，选择了形态及性能差异明显的2种典型点阵结构单元和特征相近的2种单元，形成4组特征组合方式，提出了基于芯层各单元的占比及排布的新型混杂设计方法. 采用短碳纤维增强尼龙（Onyx）线材为原料，通过熔融沉积成型（FDM）方法制备了8种典型点阵结构单元试样及10组混杂点阵夹芯结构. 通过多种试验方法比较并探讨了这些结构的力学性能及变形模式，结果可为混杂结构的设计提供了新的参考.
1　设计与方法
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1.1　点阵结构单元设计
为构建点阵夹芯结构并合理选择其组成单元，本研究首先从众多点阵结构中筛选出8种典型的点阵结构单元，设计并制备相应试样开展性能测试. 这些结构单元在几何构型与力学特性上呈现显著差异，涵盖两类结构形式：其一为5种基础点阵结构单元，分别是体心立方结构（BCC）、面心立方结构（FCC）、金刚石结构（Diamond）、萤石复合结构（Fluorite）及八面体结构（Octet）；其二为3种组合单元，即由BCC与FCC组合而成的BFCC结构、十字形结构（Cross）与BCC组合而成的CBCC结构，以及Cross与FCC组合而成的CFCC结构.
同时计算了各单元对应的麦克斯韦数，麦克斯韦准则常被用于判断点阵结构单元的变形状态[11,29]，当M<0时，表示结构变形为弯曲主导；当M≥0时，表示结构变形为拉伸主导. 将这一数据作为选取点阵结构单元的参考之一，旨在将点阵结构单元的变形特点与其性能联系在一起，更好地研究混杂设计的影响机理.
通过调整各结构的杆径，将相对密度统一设置为30%，有助于在相同条件下比较各结构的性能. 先前的研究表明[26]，三层点阵夹芯结构的各层因受特定边界约束的影响，通常以层为单位发生破坏，而非整体出现剪切带，这使得芯层能够协同承载. 为便于研究，选择了一个由4×4×3个单元组成的点阵夹芯结构，用以评估各点阵结构单元的性能，并进行后续的混杂设计. 上、下面板厚度均为0.5 mm，图1中详细列出了各单元及其对应试样的参数和三维模型.
1.2　置换式混杂芯层设计
为了避免结构因局部单元屈服而在试验中失衡，从而导致性能异常，因此选择了只包含单一单元的点阵夹芯结构作为基体，并对其芯层进行混杂设计，如图2所示. 通过调整置换单元的占比及排布，分析其对整体结构性能的影响.
在设计过程中，根据置换单元在芯层占比的差异，同时考虑整体结构的对称性，将排列方式分为3类（a）低占比，（b）中占比，（c）高占比，如图2所示. 图中展示了每种排列的示意图及命名，两种不同的颜色代表两种点阵结构单元，分别表示X和Y. 例如，XY1表示X为基体单元，Y为置换单元的第1种混杂芯层，其对应的混杂点阵夹芯结构则命名为X-XY1-X.
在具体的混杂结构设计完成后，为实现与对应基体在同等条件下的比较分析，准确把握性能变化的趋势，同时兼顾制造精度和确保整体结构的杆径统一，基于建模软件SOLIDWORKS提供的模型实时体积，对各结构杆径进行统一的参数化调整，以保证其与基体体积的一致性.
1.3　材料与制备
本研究采用增材制造（AM）技术制备结构. 利用熔融沉积成型（FDM）设备（MarkTwo，Markforged，USA）配合设备自带的切片处理网站（Eiger）对所需制造的模型进行切片并逐层打印，工艺参数见表1.
选择短碳纤维增强尼龙（Onyx）作为打印材料是看中其具有高强度和高韧性，能够制造出高质量的点阵结构. 如制造商所称，其纤维体积分数约为9%. 该线材的力学性能表现如表2所示.
1.4　测试方法
为了深入分析所设计的各结构的力学性能，探讨各变量与性能之间的关系，对8种点阵结构单元试样和各单元组合的10种混杂结构进行了单轴压缩实验. 使用设备为万能试验机（CMT-5105GJ，SUST，China），力传感器（DBSL-10t，transcell，USA）最大量程为100 kN，精度为±0.25%，压缩速度依据标准GB/T 1041-2008设定为1 mm/min，同时使用数码相机记录压缩过程中产生的变形模式. 为确保结果的可靠性和可重复性，每种结构均制作了2个试件并分别进行了压缩试验.
为了进一步验证结构的性能与变形模式，以及获得结构的全局应力分布，采用商业有限元软件Abaqus对关键结构进行有限元分析，考虑到大变形加载过程中涉及的非线性问题以及计算收敛性，采用显式动力学分析方法[30]. 在分析设置中，材料非线性设置通过输入拉伸试验获得的弹塑性本构模型来实现[31]；几何非线性设置则通过打开分析步设置中的几何非线性开关来激活. 这种建模方法有效保证了在大变形条件下应力应变响应的计算精度. 划分的网格类型为二次四面体单元（C3D10M），为保证网格质量，经验证，在保证计算精度的前提下兼顾计算效率，网格尺寸设置为结构杆径的1/4. 同时为进行压缩模拟，在模型的顶部和底部分别设置2块平板，下板施加固定约束，上板设置单轴加载速度并限制其余自由度. 由于相对于模型，两板的变形几乎可以忽略不计，因此将其设置为刚体. 考虑到试验中实际的摩擦接触，所有实体之间设置了法向的硬接触和摩擦系数为0.15的切向接触.
2　结果与讨论
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2.1　所打印结构的实际质量及偏差
由于打印模型需要通过Markforged自带的切片处理系统Eiger网站进行自动切片处理，为确保打印成功，系统会根据实际情况对部分位置进行材料补充. 此外，受限于3D打印机的精度，最终打印成品的质量与设计质量之间存在偏差.
图3展示了各组成品的平均质量，为保持直观性，各组合以芯层命名暂时代替混杂结构命名. 与各组的平均值相比，（b）最大偏差为-9.6%，（c）最大偏差为5.4%，（d）最大偏差为-4.3%，（e）最大偏差为-6.9%，（f）最大偏差为-7.5%. 这些偏差处于可接受范围内，表明采用熔融沉积成型（FDM）技术开展点阵结构的相关研究具有技术可行性与实践价值.
2.2　点阵结构单元的力学性能响应
通过对8种试样进行压缩试验，可以处理得到其应力-应变曲线，如图4所示.
从图4中可以看出，所有试样在受压过程中都表现出了相似的总体变形模式，曲线大致分为线弹性响应阶段、非线性损伤阶段和致密化阶段. 在低应变状态下，所有试样都表现出弹性响应，应力随应变线性增大. 在接近屈服应力点时，曲线逐渐进入应力较为稳定的非线性阶段. 在试验过程中可以观察到，该阶段时部分支柱出现了破坏，同时在卸载后试样存在不可逆的变形；从应力-应变曲线上则表现为，曲线斜率逐渐降低，即材料模量发生退化，当应力达到峰值后出现平台化或开始降低，直至下一阶段. 最终试样出现致密化，此时应力随应变急剧增大.
通过比模量、屈服应力、屈服应变和比吸收能四个参数，详细评价了8种试样的力学性能. 其中，比模量代表结构抵抗弹性变形的能力，其数值等于线弹性响应阶段曲线的斜率除于结构表观密度；屈服应力代表结构抵抗明显塑性变形的能力，对于无明显屈服点的材料，采用0.2%偏移法求得；屈服应变代表结构的回弹能力，通常为曲线到达屈服应力点时对应的应变；比吸收能代表结构的韧性，其定义为每单位质量所吸收的能量，可表示为：
式中，为应力对应变的积分，为了计算结构的有效吸收能，积分的端点通常定义为点阵结构的致密化应变. 为便于计算，通常取曲线斜率突变点作为近似值；ρ为结构的表观密度，除以该值主要是为了排除其对各结构比较结果的干扰.
如表3所示，清晰地呈现了各试样在各项力学性能上的大小关系：比模量方面，C>E>G>D>B>F>H>A；屈服应力方面，C>E>D>F>G>B>H>A；屈服应变方面，A>D>C>F>E>B>G>H；比吸收能方面，C>B>D>H>E>G>F>A. 可以看出，5种基础点阵结构单元试样的力学性能差异较大，且各项优势与劣势分明；而3种组合单元试样的力学性能则较为接近，且整体处于中等水平.
依据本研究的具体需求，同时考虑整体结构的连接性与可制造性，从众多试样中挑选出了4种具有代表性的结构，分别为ALL-A、ALL-B、ALL-E以及ALL-F. 其中，ALL-A与ALL-E在比模量和屈服应力方面存在显著差异，而ALL-B和ALL-F在这两项性能指标上则较为相近. 这4种结构的综合性能对比情况已清晰呈现于图5之中. 将这4种结构对应的单元组成EA、FB、AE、BF这4种组合，开展后续的研究工作.
2.3　混杂点阵夹芯结构的力学性能响应
2.3.1　弱单元置换强基体方式下混杂结构的力学性能
对选取的EA组合和FB组合的各10种混杂结构进行压缩试验，后处理得到最终的应力-应变曲线. 根据选取的基体单元与置换单元的差异将结果分别呈现，同时各图中均保留了对应基体的曲线，以便对照，如图6所示.
从图6可以看出，当芯层的置换单元占比相同，不同排布方式所对应的曲线表现出较高的重叠程度. 这一现象表明，这些结构在性能方面具有较强的相似性. 为更精确、更直观地对各结构性能进行比较，本研究对图6中的曲线进行了定量分析.
图7详细计算了各组合在不同置换单元占比下的比模量和屈服应力的平均值与标准差. 为便于统一标准下的对比分析，还进一步计算了各结构在同占比下比模量、屈服应力与平均值之间的偏差，并通过求取偏差绝对值的均值得到平均偏差. 计算结果表明，比模量方面的最大偏差约为10.21%，平均偏差小于3.6%；屈服应力方面的最大偏差为18.38%，平均偏差小于5.2%.
综合上述分析结果，在相同置换单元占比的条件下，各结构的性能表现相似，能够根据实际结构需求相互替换，为点阵结构的优化设计与工程应用提供了更多的选择和灵活性.
从图6中还可以看到，2种组合的曲线随着置换单元占比的变化趋势一致，且所有混杂结构的曲线与其对应基体的曲线存在较大差异. 性能上，相较于基体，2种组合的比模量分别降低至少41.78%和25.58%，屈服应力分别降低45.19%和26.07%，随着置换单元占比的增加，曲线会进一步下移.
2.3.2　强单元置换弱基体方式下混杂结构的力学性能
对单元选择相反的AE和BF两种组合的各10种混杂结构进行压缩试验，得到对应的应力-应变曲线. 根据选取的基体单元与置换单元的差异将结果分别呈现，各图中均保留了对应基体的曲线，如图8所示.
如图8所示，这2种组合的曲线与先前的两种组合存在明显差异，并且这2种组合之间各曲线的相对位置关系也有显著不同. 具体而言，AE组合的性能表现更趋近于基体的性能水平，而BF组合的性能与基体性能相比仍存在较大差距.
从置换单元占比与曲线的关系来看，AE组合的曲线随着置换单元占比的增加而上移，表明其性能有所提升；BF组合的曲线变化趋势则相反，随着占比增加而下降. 值得关注的是，在曲线的致密化阶段，如图8中圆圈处的放大图所示，大部分混杂结构的承载能力将超过基体结构.
更值得一提的是，无论置换单元的占比如何变化，或是其在结构中的排布方式怎样调整，各混杂结构的曲线始终保持着较高的相似度. 经计算，与各组比模量和屈服应力的平均值相比，所有混杂结构中比模量的最大偏差约为10.50%，平均偏差小于4.2%；屈服应力的最大偏差约为13.98%，平均偏差小于6.6%.
2.4　混杂结构性能差异及其变形机制
为深入探究结构变形模式与性能变化之间的内在关联，本研究从每个组合的每种占比中各选取了一种典型的排布，与其对应的基体一起进行了有限元模拟. 通过分析，得到了ε=0.15时各结构的全局应力分布及变形模式，并与试验结果进行了对照，如图9所示.
结果表明，有限元分析结果与试验结果具有较高的吻合度，结构各层所呈现的变形模式在二者之间实现了一一对应. 这充分说明，本研究所建立的有限元分析方法以及构建的分析模型，能够较为精准地对夹芯板的变形模式进行预测，为深入理解夹芯板的力学行为和性能优化提供了可靠的分析手段和理论依据.
如图9所示，各基体在受压的过程中表现出了相似的变形模式，各层均有相应的变形，其中上下两层的变形量略大于芯层，而在置换各组合对应的单元后，各混杂结构的变形模式发生了不同方向的变化.
对EA组合和FB组合的研究表明，其基体与混杂结构的变形模式存在显著差异. 具体表现为，混杂结构的变形几乎集中于芯层，而上下两层的变形量相对较小. 这一现象可以解释为：在低应变状态下，基体中几乎所有单元均参与了承载过程；然而，对于混杂结构而言，主要是由芯层的单元率先承担载荷，直至芯层发生致密化并得到强化后，上下两层才开始参与承载. 上述显著差异可归因于在芯层所置换的单元比基体单元的承载能力更弱. 无论置换单元的占比如何，这种情况都会导致芯层成为整个结构中的薄弱层，从而使得芯层与上下两层在承载能力上出现差异. 这就致使芯层率先发生屈服，造成整体结构受力不均，最终导致基体与混杂结构在性能上产生巨大鸿沟. 此外，随着置换单元占比的增加，这一现象愈发明显. 此时，整体结构的性能在很大程度上依赖于芯层的性能. 由于置换的弱单元占比增加，整体结构的性能会进一步下降.
对AE组合和BF组合而言，其不同之处在于此时芯层得到了强化. 从变形模式的角度分析，这种强化表现为在基体原先变形的基础上，进一步促使上下两层产生更显著的变形. 这一现象能够很好地阐释为何这两种组合的混杂结构性能趋于一致. 在低应变状态下，芯层基本不参与承担载荷，整体结构的性能主要由上下两层主导. 直到致密化阶段，芯层的潜在性能才得以激发，这使得各混杂结构的应力-应变曲线相对于基体呈现出前期降低、后期升高的变化态势.
综合上述分析，这两类组合分别对应着基体变形模式诱导机制的两个不同作用方向. 在承载过程中，整体结构会优先由力学性能较弱的各层承担载荷，直至其达到屈服状态. 值得注意的是，该诱导机制的具体表现与基体单元及置换单元其本身的变形模式密切相关. 具体表现为，相较于EA组合，FB组合呈现出更为显著的芯层率先屈服现象；而对比AE组合，BF组合的下层与上层则表现出交替屈服的特征，致使整体结构的力学性能显著下降.
3　结论
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本文结合压缩试验与有限元数值模拟，研究了混杂芯层的置换方式对点阵夹芯结构力学性能和变形机制的影响规律，所得主要结论如下：
（1）置换式混杂芯层设计主要通过改变混杂结构的变形模式来调控其力学性能，总体上对变形模式有两种诱导方向，芯层优先变形和上下两层优先变形，同时这种诱导变形机制也与基体单元和置换单元其本身的变形模式密切相关.
（2）弱单元置换强基体会使得结构变形模式发生突变，低应变状态下芯层单独承载，使得两组混杂结构的比模量分别降低至少41.78%和25.58%，屈服应力则为45.19%和26.07%. 此时，芯层各单元的排布在相同置换单元占比下对整体结构的性能影响较小，比模量的最大偏差在10.21%左右，平均偏差小于3.6%，屈服应力则为18.38%和5.2%. 这表明，相同置换单元占比下的各种混杂结构性能相似，可根据实际结构需求相互替换.
（3）强单元置换弱基体则是使得结构在基体的变形模式下，加剧上下两层的承载负担，由于芯层在低应变状态下几乎不参与承载过程，各混杂结构表现出极为相似的力学性能特征，比模量的最大偏差和平均偏差仅有不到10.5%和4.2%，屈服应力则为14.0%和6.6%. 芯层的承载潜力延后到致密化阶段，此时大部分混杂结构的承载能力将超过基体.
（4）在工程实际应用中，应避免在结构芯层与性能弱于基体单元的点阵单元进行置换，这会导致结构提前屈服，难以发挥其整体性能；相反，与性能强于基体单元的点阵单元进行置换能够显著增强结构在高应变下的承载能力. 这一特性随着置换单元占比的增加而更加突出，在大变形工况下展现出显著优势.
基金
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  • 国家自然科学基金项目(U21A20132)
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2025年第46卷第5期
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doi: 10.19636/j.cnki.cjsm42-1250/o3.2025.028
  • 接收时间：2025-09-18
  • 首发时间：2026-03-20
  • 出版时间：2025-10-27
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  • 收稿日期：2025-09-18
基金
国家自然科学基金项目(U21A20132)
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    1中南大学轻合金研究院，长沙，410083
    2极端服役性能精准制造全国重点实验室，长沙，410083

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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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