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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

吕若萱, 任浩乾, 梅轩, 等. 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[J]. 复合材料学报, 2024, 42(0): 1-17.
引用本文: 吕若萱, 任浩乾, 梅轩, 等. 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[J]. 复合材料学报, 2024, 42(0): 1-17.
LV Ruoxuan, REN Haoqian, MEI Xuan, et al. Deformation energy absorption characteristics and structure gradient design of novel cosine function-based lattice materials[J]. Acta Materiae Compositae Sinica.
Citation: LV Ruoxuan, REN Haoqian, MEI Xuan, et al. Deformation energy absorption characteristics and structure gradient design of novel cosine function-based lattice materials[J]. Acta Materiae Compositae Sinica.

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

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

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

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: 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。

     

  • 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; w1w—Width; h1t—Height; dd1—Diameter; a and h—Amplitude and period length of CFCB lattice material

    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

    图  3  准静态压缩试验设置

    Figure  3.  Setup of quasi-static compression tests

    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

    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

    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

    图  7  网格收敛性分析

    Figure  7.  Analysis of mesh convergence

    图  8  316L不锈钢单轴拉伸试验

    Figure  8.  Uniaxial tensile tests for 316L stainless steel

    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

    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

    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

    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

    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

    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

    图  15  层间梯度点阵材料

    Figure  15.  Interlayer gradient lattice material

    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

    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

    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)

    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

    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

    图  21  多目标离散优化流程图

    Figure  21.  Multi-objective discrete optimization flowchart

    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

    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
    下载: 导出CSV

    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
    下载: 导出CSV

    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 Ea/J Es/(J·g−1) Fm/kN Ce
    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; Ea—Engergy absorption; Es—Specific energy absorption; Fm—Mean crushing force; Ce—Crushing force efficiency.
    下载: 导出CSV

    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
    下载: 导出CSV

    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 Ea/J Es/(J·g−1) Fm/kN Ce
    CFCB Experiment 287.09 6.26 9.39 0.74
    Simulation 286.23 6.15 9.12 0.62
    下载: 导出CSV

    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 dn−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; dn−1—Diameters of different layers in CFCB lattice materials.
    下载: 导出CSV

    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.
    下载: 导出CSV

    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 typeEa/JEs/(J·g-1)Fm/kNCe
    m1.4-TD287.706.0811.040.57
    m1.4-JY259.925.4410.000.78
    m1.5-TD331.236.3712.780.53
    m1.5-JY318.496.2112.170.79
    m1.6-TD356.556.4214.470.46
    m1.6-JY345.016.1313.830.72
    下载: 导出CSV

    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
    1 2 3
    m 1.2 1.5 1.7
    a 2.00 2.15 2.30
    下载: 导出CSV

    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
    m a Ea 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
    下载: 导出CSV

    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
    Ea Mass Ea 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
    下载: 导出CSV

    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
    Ea Mass Ea Mass
    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.
    下载: 导出CSV

    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
    1 2 3
    m 0.3462 0.4873 0.8531
    a 0.5575 0.5414 0.5879
    下载: 导出CSV

    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
    a=2.15 a=2.00 a=1.85 a=1.85
    4 m=1.3 5 m=1.3 6 m=1.3 7 m=1.3
    a=1.85 a=1.85 a=1.85 a=1.85
    下载: 导出CSV

    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 valuesEa/JEs/(J·g-1)
    Initialm=1.5
    a=2.15
    644.7013.78
    Optimalm=1.3
    a=1.85
    690.1718.65
    Increasing ratio-+7.1%+35.3%
    下载: 导出CSV
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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

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