Study on Out-of-plane Deformation Behaviors and Flexibility-elasticity of Bionic Horseshoe-shaped Microstructures

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

Abstract

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

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

CLC Number:

TB34

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.

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.

Figures/Tables 25

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

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

Fig.2 Three three-dimensional models of lattice structures

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

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

Fig.3 Physical diagram of the printed sample

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

Fig.5 Model diagram of the steel ball method

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

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

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

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

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

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

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

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

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

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

Fig.15 Diagram of the experimental process

Fig.16 Load-displacement curves of four structures

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

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

Fig.18 Comparison chart of ultimate load simulation and test

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

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

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

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

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