仿生马蹄形微结构的面外变形行为与柔弹性研究

doi:10.3969/j.issn.1004-132X.2026.06.019

摘要/Abstract

摘要：

马蹄形微结构具有强拉伸性、高透气性及拓扑可编程性等优异特性，广泛应用于生物医学设备、柔性显示器、组织工程等重要领域。基于BCT2000测试原理与GB/T 24218.5—2016钢球顶破法，构建了针对马蹄形微结构的面外变形测试方法，系统研究了三角形、Kagome形及蜂窝形三种仿生马蹄形微结构的面外变形行为。通过数值模拟和实验分析对三种马蹄形微结构的顶破载荷-位移曲线进行研究，分析了应力分布情况以及结构的面外变形情况，并以三角直线结构作为对照组。从四个方面建立了柔弹性能评价标准，分析了四种因素对柔弹性能的影响。三角形微结构展现出最优异的柔弹性综合性能，相较于传统直线型结构有明显柔弹性优势，最大面外位移增大了88.9%，低载荷承载位移增大了428.1%，面外刚度降低了59.3%，能量吸收量提高了31.5%。

关键词: 软网络材料, 马蹄形微结构, 面外变形, 顶破性能, 柔弹性

Abstract:

Horseshoe-shaped microstructures possessed excellent characteristics such as high stretchability， high air permeability， and topological programmability， and were widely used in important fields including biomedical devices， flexible displays， and tissue engineering. Based on the BCT2000 test principle and GB/T 24218.5-2016 steel ball bursting test method， a test method for out-of-plane deformations of horseshoe-shaped microstructures was established herein， and the out-of-plane deformation behaviors of three types of bionic horseshoe-shaped microstructures （triangular， Kagome， and honeycomb-shaped） were systematically studied. The bursting load-displacement curves of the three types of horseshoe-shaped microstructures were studied through numerical simulations and experimental analyses， the stress distribution and the out-of-plane deformations of the structures were analyzed， and triangular linear structures were used as the control group. Flexible-elastic performance evaluation criteria were established from four aspects， and the effects of four factors on flexible-elastic performances were initially analyzed. Triangular microstructures exhibit the most excellent comprehensive flexible-elastic performance and have obvious flexible-elastic advantages compared with traditional linear structures. Specifically， their maximum out-of-plane displacements are increased by 88.9%， the low-load bearing displacements are increased by 428.1%， the out-of-plane stiffness is reduced by 59.3%， and the energy absorption capacity is increased by 31.5%.

Key words: soft network material, horseshoe-shaped microstructure, out-of-plane deformation, burst resistance performance, flexible elasticity

中图分类号:

TB34

冯浩, 纪小刚, 牛国法, 徐新纪. 仿生马蹄形微结构的面外变形行为与柔弹性研究[J]. 中国机械工程, 2026, 37(6): 1462-1471.

FENG Hao, JI Xiaogang, NIU Guofa, XU Xinji. Study on Out-of-plane Deformation Behaviors and Flexibility-elasticity of Bionic Horseshoe-shaped Microstructures[J]. China Mechanical Engineering, 2026, 37(6): 1462-1471.

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链接本文: https://www.cmemo.org.cn/CN/10.3969/j.issn.1004-132X.2026.06.019

https://www.cmemo.org.cn/CN/Y2026/V37/I6/1462

图/表 25

图1 马蹄形微结构几何参数示意图

Fig.1 Schematic diagram of geometric parameters of horseshoe-shaped microstructures

表1 三种晶格结构尺寸

Tab.1 Three lattice - structure dimensions

晶格类型	R₀/mm	ω/mm	θ₀/（°）	ω₀	l/mm
三角形	3.0	0.75	180	0.25	12
Kagome形	1.5	0.75	180	0.50	6
蜂窝形	1.5	1.125	180	0.75	6

图2 三种晶格结构三维模型

Fig.2 Three three-dimensional models of lattice structures

表2 DLP工艺参数选择

Tab.2 Selection of DLP process parameters

工艺参数配置项	具体参数
层厚/mm	0.02
曝光时间/s	6
关灯时间/s	1
底部曝光时间/s	35
底部层数	4
抗锯齿等级	4
Z轴抬升距离/mm	5
Z轴抬升速度/（mm∙s $- 1$ ）	2
Z轴回退速度/（mm∙s $- 1$ ）	2

表2 DLP工艺参数选择

Tab.2 Selection of DLP process parameters

工艺参数配置项	具体参数
层厚/mm	0.02
曝光时间/s	6
关灯时间/s	1
底部曝光时间/s	35
底部层数	4
抗锯齿等级	4
Z轴抬升距离/mm	5
Z轴抬升速度/（mm∙s $- 1$ ）	2
Z轴回退速度/（mm∙s $- 1$ ）	2

图3 试样打印实物

Fig.3 Physical diagram of the printed sample

图4 弹性材料机械特性测试（BCT-2000）原理

Fig.4 Schematic diagram of the mechanical properties test of elastic materials（BCT-2000）

图5 钢球法模型图

Fig.5 Model diagram of the steel ball method

图6 马蹄形微结构柔弹性实验方法

Fig.6 Test method for the flexible elasticity of horseshoe-shaped microstructures

图7 三种结构及球形顶杆的网格划分

Fig.7 Mesh generation for three types of structures and the spherical ejector pin

表3 Mooney-Rivlin本构模型相关参数拟合结果

Tab.3 Fitting results of relevant parameters of the Mooney - Rivlin constitutive model

	本构系数
	C₁₀	C₀₁	D₁
数值	0.317	0.076	0.254

图8 10 mm位移载荷下四种结构的等效应力云图分布

Fig.8 Distribution of equivalent stress nephograms of four structures under 10mm displacement load

图9 15 mm位移载荷下四种结构的等效应力云图分布

Fig.9 Distribution of equivalent stress nephograms of four structures under 15mm displacement load

图10 20 mm位移载荷下四种结构的等效应力云图分布

Fig.10 Distribution of equivalent stress nephograms of four structures under 20mm displacement load

图11 25 mm位移载荷下四种结构的等效应力云图分布

Fig.11 Distribution of equivalent stress nephograms of four structures under 25mm displacement load

图12 四种结构数值模拟载荷-位移曲线

Fig.12 Numerical simulation of the load-displacement curves of four types of structures

图13 传统马蹄形微结构应力-应变曲线

Fig.13 Stress-strain curve of traditional horseshoe-shaped microstructure

图14 马蹄形微结构面外变形的理论模型

Fig.14 Theoretical model of out-of-plane deformation for horseshoe-shaped microstructure

图15 实验过程

Fig.15 Diagram of the experimental process

图16 四种结构的载荷-位移曲线

Fig.16 Load-displacement curves of four structures

表4 四种结构的面外变形实验数据

Tab.4 Out-of-plane deformation experimental data of four structures

试样	最大顶破位移S_max/mm	最大顶破载荷N_0max/N
三角直线形	19.58	5.40
三角形	36.99	5.34
Kagome形	28.45	3.58
蜂窝形	28.45	3.46

图17 马蹄形微结构顶破载荷-位移曲线

Fig.17 The bursting load-displacement curve of the horseshoe-shaped microstructures

图18 极限载荷模拟-实验对比图

Fig.18 Comparison chart of ultimate load simulation and test

表5 三种结构的柔弹性能评价指标

Tab.5 Evaluation indicators of the flexible-elastic properties of three structures

结构

类型

最大面外

位移/mm

面外刚度/

（N∙m $- 1$ ）

吸收的能量/J

低载荷承载

位移/mm

表5 三种结构的柔弹性能评价指标

Tab.5 Evaluation indicators of the flexible-elastic properties of three structures

结构

类型

最大面外

位移/mm

面外刚度/

（N∙m $- 1$ ）

吸收的能量/J

低载荷承载

位移/mm

三角形

36.99

172.41

0.075

8.99

Kagome形

28.45

175.01

0.037

7.65

蜂窝形

28.45

201.25

0.034

7.69

图19 结构最大面外位移与面外刚度对比

Fig.19 Comparison diagram of the maximum out-of-plane displacement and out-of-plane stiffness of the structure

图20 结构吸收的能量和低载荷承载位移对比

Fig.20 Comparison diagram of the structural energy absorption and the displacement under low load bearing

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