新型余弦函数基点阵材料变形吸能特性及结构梯度化设计

吕若萱; 任浩乾; 梅轩; 牛心想; 曹悉奥; 王振; 朱国华

新型余弦函数基点阵材料变形吸能特性及结构梯度化设计

长安大学　汽车学院, 西安 710064

基金项目: 国家重点研发计划 (2021YFB2501705)；陕西省重点研发计划(2021LLRH-04-02-01)；陕西省自然科学基金 (2023-JC-QN-0430, 2024JC-YBMS-267)；陕西省博士后科研项目(2023BSHYDZZ124); 中国博士后科学基金(2023M740358); 长安大学研究生科研创新实践项目(300103723029)

详细信息

通讯作者:
王振，博士，讲师，研究方向为汽车轻量化　E-mail: zhenwang_chd@chd.edu.cn

中图分类号: TB383
计量
- 文章访问数: 65
- HTML全文浏览量: 35
- 被引次数: 0
出版历程
- 收稿日期: 2023-12-29
- 修回日期: 2024-02-04
- 录用日期: 2024-02-28
- 网络出版日期: 2024-03-29

Deformation energy absorption characteristics and structure gradient design of novel cosine function-based lattice materials

School of Automobile, Chang’an University, Xi’an 710064, China

Funds: National Key R&D Program of China (2021YFB2501705); Shaanxi Province Key R&D Program (2021LLRH-04-02-01)；Natural Science Foundation of Shaanxi Province (2023-JC-QN-0430, 2024JC-YBMS-267); Shaanxi Province Postdoctoral Research Project Funding (2023BSHYDZZ124); China Postdoctoral Science Foundation(2023M740358); Scientific Innovation Practice Project of Postgraduates of Chang’an University(300103723029)

摘要

摘要: 提出了一种新型的余弦函数胞元基(Cosine function cell-based，CFCB)点阵材料，并对其面外压缩载荷下的力学性能开展试验及仿真研究，试验结果表明新型CFCB点阵材料在准静态面外压缩载荷下的能量吸收较相同质量的(Body centered cubic，BCC)点阵材料提升了134.4%；此外，通过有限元仿真发现CFCB点阵材料的能量吸收随胞元单杆直径增加而增加。为了进一步改善均匀型CFCB点阵材料的面外压缩变形模式并提高其承载性能，设计了一种层间梯度CFCB点阵构型，并结合试验与仿真手段探究了梯度CFCB点阵材料在准静态面外压缩载荷下的能量吸收特性及关键参数对其吸能特性的影响规律。结果表明，与均匀CFCB点阵材料相比，梯度CFCB点阵材料在吸能方面具有更强的优势，且增大梯度系数可以提高层间梯度点阵材料的承载能力与能量吸收能力。最后采用离散变量多目标优化方法对层间梯度CFCB点阵材料进行了优化设计，优化后的梯度CFCB梯度点阵材料质量减少20.9%，能量吸收增加7.1%。研究能够对新型CFCB点阵材料及其梯度构型设计提供可靠的试验结果、准确的数值模型以及高效的优化方法。
- 点阵材料 /
- 能量吸收 /
- 数值模拟 /
- 梯度结构 /
- 优化设计
Abstract: This study proposes a new type of cosine function cell-based (CFCB) lattice materials and conducts experimental and simulation studies on the mechanical properties of such materials under quasi-static out-of-plane compressive load. The experimental results show that the energy absorption of the CFCB lattice material is improved by 134.4% compared with that of the body centered cubic (BCC) lattice material. Besides, Through numerical simulation, it is found that the energy absorption of CFCB lattice materials increases with the increase of the diameter of the single-cell diameter. In order to further improve the out-of-plane compression deformation mode and improve the bearing performance of uniform CFCB lattice materials, an interlayer gradient CFCB lattice material was designed, and energy absorption capacity of these gradient lattice materials and their key affecting factors are experimentally and numerically investigated. The results show that the gradient CFCB lattice materials have superior advantages in energy absorption compared with uniform CFCB lattice materials, and it is also found that increasing gradient coefficients can improve their load-bearing capacity and energy absorption capacity. Finally, the multi-objective discrete optimization method was used to optimize the design of the interlayer gradient CFCB lattice material, and the mass of the optimized gradient CFCB gradient lattice material was reduced by 20.9%, and the energy absorption was increased by 7.1%. This study can provide reliable experimental results, accurate numerical models and efficient optimization methods for the design of novel CFCB lattice materials and their gradient configurations.
- lattice material /
- energy absorption /
- numerical simulation /
- gradient structure /
- optimization design

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图 1 不同点阵材料构型

Figure 1. Different lattice material conformation

BCC—Body centered cubic lattice materials; CFCB—Cosine function cell-based lattice materials; l₁, l—Length; w₁，w—Width; h₁，t—Height; d，d₁—Diameter; a and h—Amplitude and period length of CFCB lattice material

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图 2 点阵材料的制备

Figure 2. Preparation of the lattice materials

L₁,L—Length; W₁,W—Width; H₁, H—Height

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图 3 准静态压缩试验设置

Figure 3. Setup of quasi-static compression tests

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图 4 两种点阵材料在面外压缩载荷下的载荷-位移曲线

Figure 4. Force-displacement curves of two lattice materials under out-of-plane compressive loading

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图 5 两种点阵材料面外压缩过程

Figure 5. Out-of-plane compression process for two types of lattice materials

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图 6 余弦函数胞元基点阵材料面外压缩试验有限元模型

Figure 6. Finite element model for the out-plane compression test of Cosine function cell-based lattice material

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图 7 网格收敛性分析

Figure 7. Analysis of mesh convergence

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图 8 316L不锈钢单轴拉伸试验

Figure 8. Uniaxial tensile tests for 316L stainless steel

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图 9 CFCB点阵材料压缩过程以及载荷-位移曲线的试验与仿真对比

Figure 9. Experimental and simulation comparison of compression process and force-displacement curve of CFCB lattice material

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图 10 s=4 mm时两点阵材料的应力云图

Figure 10. Stress cloud of two lattice materials at s=4 mm

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图 11 余弦函数胞元基点阵材料两种典型的变形模式

Figure 11. Two typical deformation patterns of cosine function cell-based lattice materials

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图 12 余弦函数胞元基点阵材料的不同杆直径和周期长度组合的分布模式

Figure 12. Distribution patterns of different combinations of rod diameters and cycle lengths for cosine function cell-based lattice materials

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图 13 不同杆件直径的CFCB点阵材料性能指标变化规律

Figure 13. Variation rule of the performance indicators for CFCB lattice materials with different rod diameters

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图 14 不同周期长度的CFCB点阵材料性能指标变化规律

Figure 14. Variation rule of the performance indicators for CFCB lattice materials with different period lengths

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图 15 层间梯度点阵材料

Figure 15. Interlayer gradient lattice material

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图 16 不同梯度点阵材料及其对应均匀点阵材料载荷-位移曲线对比

Figure 16. Comparison of force-displacement curves of different gradient lattice materials and their corresponding uniform lattice materials

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图 17 不同梯度点阵材料及其对应均匀点阵材料变形模式对比

Figure 17. Comparison of deformation patterns of different gradient lattice materials and their corresponding uniform lattice materials

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图 18 层间梯度点阵材料(m=1.5)试验与仿真载荷-位移曲线及压缩过程对比

Figure 18. Comparison of the force-displacement curve and compression process between the experimental and the simulation for gradient lattice material (m=1.5)

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图 19 不同梯度系数的层间梯度点阵材料载荷-位移曲线及性能指标对比

Figure 19. Comparison of force-displacement curves and performance indicators of interlayer gradient lattice materials with different gradient coefficients

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图 20 不同单胞幅值的层间梯度点阵材料载荷-位移曲线及性能指标对比

Figure 20. Comparison of force-displacement curves and performance indicators of interlayer gradient lattice materials with different cell amplitudes

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图 21 多目标离散优化流程图

Figure 21. Multi-objective discrete optimization flowchart

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图 22 层间梯度点阵材料离散优化迭代曲线

Figure 22. Iterative curves for discrete optimization of interlayer gradient lattice materials

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表 1 单胞结构几何参数

Table 1. Geometric parameters of single cell structures

Type	Length/ mm	Width/ mm	Height/ mm	d/ mm	a/ mm	h/ mm
BCC	9	9	9	1.12	-	9
CFCB	8.95	8.95	10	1.24	2.15	10

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表 2 点阵材料实际样件几何参数

Table 2. Geometric parameters of the actual prototype of the lattice material

Type	Length/ mm	Width/ mm	Height/ mm	d/ mm	a/ mm	Mass/ g
BCC	45.20	45.19	44.97	1.12	-	46.66
CFCB	44.42	44.47	50.29	1.24	2.15	45.86

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表 3 两种点阵材料在面外压缩载荷下的性能指标对比

Table 3. Performance indicators of two lattice materials under out-of-plane compression load

Type	s/mm	E_a/J	E_s/(J·g⁻¹)	F_m/kN	C_e
BCC	31.01	122.50	2.63	3.95	0.75
CFCB	30.57	287.09	6.26	9.39	0.74
Notes: s—compressive displacement; E_a—Engergy absorption; E_s—Specific energy absorption; F_m—Mean crushing force; C_e—Crushing force efficiency.

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表 4 316L不锈钢的材料参数

Table 4. Material properties of 316L stainless steel

Density/ (g·cm⁻³)	Poisson’s ratio	Young’s modulus/GPa	Yield stress/MPa
7.5	0.287	165.35	439

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表 5 CFCB点阵材料试验和数值结果之间的性能指标对比

Table 5. Comparison of performance indicators of CFCB lattice material between experimental and numerical results

Specimen	Type	E_a/J	E_s/(J·g⁻¹)	F_m/kN	C_e
CFCB	Experiment	287.09	6.26	9.39	0.74
CFCB	Simulation	286.23	6.15	9.12	0.62

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表 6 层间梯度点阵材料不同梯度参数的直径

Table 6. Diameter of interlayer gradient lattice material with different gradient parameters

m	d_n−1/mm
m=1.4	1;1.1;1.2;1.31;1.43
m=1.5	1;1.125;1.25;1.39;1.55
m=1.6	1;1.15;1.3;1.47;1.67
Notes: m—Gradient coefficient; d_n−1—Diameters of different layers in CFCB lattice materials.

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表 7 层间梯度点阵材料与CFCB型均匀点阵材料的几何设计尺寸及样件实际质量

Table 7. Geometric design dimensions and actual quality of samples of interlayer gradient lattice material and CFCB type uniform lattice material

Material type	Length×Width/mm	Height/ mm	d/ mm	Mass/g
m1.4-TD	45.17×45.17	45.8	-	47.31
m1.4-JY	44.76×44.76	45.8	1.216	47.76
m1.5-TD	45.29×45.29	45.8	-	52.01
m1.5-JY	44.82×44.82	45.8	1.276	51.31
m1.6-TD	45.41×45.17	45.8	-	55.50
Notes: TD—Gradient lattice materials; JY—Uniform lattice materials.

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表 8 层间梯度点阵材料与CFCB均匀点阵材料性能指标对比

Table 8. Performance indexes of interlayer gradient lattice material and CFCB-type uniform lattice material

Material type	E_a/J	E_s/(J·g^-1)	F_m/kN	C_e
m1.4-TD	287.70	6.08	11.04	0.57
m1.4-JY	259.92	5.44	10.00	0.78
m1.5-TD	331.23	6.37	12.78	0.53
m1.5-JY	318.49	6.21	12.17	0.79
m1.6-TD	356.55	6.42	14.47	0.46
m1.6-JY	345.01	6.13	13.83	0.72

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表 9 层间梯度点阵材料第一次迭代设计变量水平及数值

Table 9. Levels and values of design variables for the first iteration of interlayer gradient lattice materials

Design variable	Level
Design variable	1	2	3
m	1.2	1.5	1.7
a	2.00	2.15	2.30

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表 10 层间梯度点阵材料正交实验表

Table 10. Table of orthogonal experiments of interlayer gradient lattice materials

NO.	Design variable		Objective function
NO.	m	a	E_a	Mass
1	1.2	2.00	420.14	34.20
2	1.2	2.15	437.51	34.80
3	1.2	2.30	391.77	36.20
4	1.5	2.00	419.02	48.40
5	1.5	2.15	644.70	46.80
6	1.5	2.30	652.80	49.80
7	1.7	2.00	869.94	56.80
8	1.7	2.15	751.88	58.80
9	1.7	2.30	798.56	60.10

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表 11 层间梯度点阵材料第一次迭代的指标响应与惩罚函数计算结果

Table 11. Indicator Response and Penalty Function Calculations for the First Iteration of interlayer gradient lattice materials

No.	Respense		Penalty
No.	E_a	Mass	E_a	Mass
1	420.14	34.20	413.83	37.36
2	437.51	34.80	430.88	38.12
3	391.77	36.20	383.47	40.35
4	419.02	48.40	414.99	50.42
5	644.70	46.80	644.70	46.80
6	652.80	49.80	652.58	49.91
7	869.94	56.80	869.94	56.80
8	751.88	58.80	751.88	58.80
9	798.56	60.10	798.56	60.10

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表 12 层间梯度点阵材料第一次迭代的灰色关联度分析计算结果

Table 12. Calculated grey relational grades analysis for the first iteration of interlayer gradient lattice materials

No.	Normalisation		Grey correlation analysis		GRD	Order
No.	E_a	Mass	E_a	Mass	GRD	Order
1	0.0624	0.0000	0.3478	0.3333	0.3406	9
2	0.0975	0.0334	0.3565	0.3409	0.3487	8
3	0.0000	0.1315	0.3333	0.3654	0.3493	7
4	0.0648	0.5743	0.3484	0.5401	0.4443	6
5	0.5370	0.4151	0.5192	0.4609	0.4900	5
6	0.5532	0.5519	0.5281	0.5274	0.5277	4
7	1.0000	0.8549	1.0000	0.7751	0.8875	1
8	0.7573	0.9428	0.6732	0.8974	0.7853	3
9	0.8533	1.0000	0.7731	1.0000	0.8866	2
Note: GRD—Grey relational grades.

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表 13 层间梯度点阵材料第一次迭代的均值计算结果

Table 13. Results of ANOM calculations for the first iteration of interlayer gradient lattice materials

Design variable	Level
Design variable	1	2	3
m	0.3462	0.4873	0.8531
a	0.5575	0.5414	0.5879

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表 14 层间梯度点阵材料迭代过程中最优设计变量取值

Table 14. The optimal design variables take values during the iterative process of interlayer gradient lattice materials

Number of iterations	Variable Values	Number of iterations	Variable Values	Number of iterations	Variable Values	Number of iterations	Variable Values
0	m=1.5	1	m=1.7	2	m=1.5	3	m=1.3
0	a=2.15	1	a=2.00	2	a=1.85	3	a=1.85
4	m=1.3	5	m=1.3	6	m=1.3	7	m=1.3
4	a=1.85	5	a=1.85	6	a=1.85	7	a=1.85

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表 15 层间梯度点阵材料初始与优化设计对比

Table 15. Comparison of initial and optimised designs of interlayer gradient lattice materials

	Variable values	E_a/J	E_s/(J·g^-1)
Initial	m=1.5 a=2.15	644.70	13.78
Optimal	m=1.3 a=1.85	690.17	18.65
Increasing ratio	-	+7.1%	+35.3%

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