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考虑时变刚度特性的复合材料微结构拓扑优化设计方法

徐世鹏 丁晓红 段朋云 张横

徐世鹏, 丁晓红, 段朋云, 张横. 考虑时变刚度特性的复合材料微结构拓扑优化设计方法. 力学学报, 2022, 54(1): 135-147 doi: 10.6052/0459-1879-21-395
引用本文: 徐世鹏, 丁晓红, 段朋云, 张横. 考虑时变刚度特性的复合材料微结构拓扑优化设计方法. 力学学报, 2022, 54(1): 135-147 doi: 10.6052/0459-1879-21-395
Xu Shipeng, Ding Xiaohong, Duan Pengyun, Zhang Heng. Topology optimization of composite material microstructure considering time-changeable stiffness. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(1): 135-147 doi: 10.6052/0459-1879-21-395
Citation: Xu Shipeng, Ding Xiaohong, Duan Pengyun, Zhang Heng. Topology optimization of composite material microstructure considering time-changeable stiffness. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(1): 135-147 doi: 10.6052/0459-1879-21-395

考虑时变刚度特性的复合材料微结构拓扑优化设计方法

doi: 10.6052/0459-1879-21-395
基金项目: 国家自然科学基金项目(51975380, 52005337), 中国博士后科学基金(2020 M681346)资助项目
详细信息
    作者简介:

    丁晓红, 教授, 主要研究方向: 机械系统和结构优化设计方法. E-mail: dingxhsh021@126.com

  • 中图分类号: TH122

TOPOLOGY OPTIMIZATION OF COMPOSITE MATERIAL MICROSTRUCTURE CONSIDERING TIME-CHANGEABLE STIFFNESS

  • 摘要: 理想的骨折内固定植入物在组织愈合或修复的过程中, 其结构性能需要满足不同愈合阶段对生物力学的需求. 提出一种对生物可降解复合材料微结构的时变刚度特性进行调控设计的拓扑优化方法, 以达到理想的骨折内固定植入物特殊的时变刚度特性需求. 使用具有不同降解速率和刚度的两种可降解材料, 以相对密度作为设计变量来描述不同材料的分布, 以特定降解时间步中间结构的刚度之和最大为优化目标, 对复合材料微结构的构型进行拓扑优化设计, 使其具有符合骨愈合规律的时变刚度特性. 使用均匀腐蚀方法, 利用与时间相关的材料残留率描述结构的降解过程, 建立考虑时间维度材料降解的有限元模型, 基于Heaviside函数和Kreisselmeier-Steinhauser函数建立降解更新的连续方程, 利用均匀化方法得到不同降解时间步中间结构的力学性能, 并计算优化目标对于设计变量的灵敏度. 通过与仅使用单材料的结构和无时变刚度特性调控的拓扑优化结构进行对比, 验证了所提出设计方法的有效性, 并研究了不同参数对单胞优化构型和时变刚度特性的影响.

     

  • 图  1  理想骨折内固定植入物和愈伤组织整体刚度随时间变化趋势

    Figure  1.  The change trend of stiffness of ideal fracture internal fixation implant and callus with time

    图  2  具有特定时变刚度特性的复合材料结构

    Figure  2.  Periodic composite structure with specific time-changeable characteristics

    图  3  降解过程示意图

    Figure  3.  Schematic diagram of degradation process

    图  4  单元e及其相邻单元位置标记

    Figure  4.  Location marking of element e and its neighbors

    图  5  考虑时变刚度特性的复合材料微结构拓扑优化流程

    Figure  5.  Multi material microstructure topology optimization process considering time-changeable characteristics

    图  6  单胞几何模型和两个可降解边界

    Figure  6.  Unit cell model and two degradable interface

    图  7  不同φ的设计结果: (a)初始构型, (b)优化结果, (c) 3 × 3结构

    Figure  7.  Optimal design with different φ: (a) initial configuration, (b) topology optimization result, (c) 3 × 3 structure

    图  8  不同φ的优化迭代历程

    Figure  8.  Iterative process of optimization with different φ

    图  9  φ为0.5时单胞构型和材料1体积分数随迭代历程变化趋势

    Figure  9.  The unit cell configuration and volume fraction vary with the iterative process when φ = 0.5

    图  10  不同φ的优化结果降解过程中D33变化趋势

    Figure  10.  Variation trend of D33 during degradation with different φ optimization results

    图  11  有/无时变刚度特性调控的优化结果比较: (a) 考虑时变刚度特性, (b) 无时变刚度特性调控

    Figure  11.  Optimization result: (a) considering time-changeable characteristics, (b) non-time-changeable characteristic regulation

    图  12  不同结构降解历程: (a)仅使用材料1, (b)仅使用材料2, (c)考虑时变刚度特性, (d)无时变刚度特性调控

    Figure  12.  Degradation of different structures: (a) using material 1 only, (b) using material 2 only, (c) considering time-changeable characteristics, (d) non-time-changeable characteristic regulation

    图  13  不同结构降解过程中D33变化趋势

    Figure  13.  Variation trend of D33 during degradation with different structures

    图  14  不同初始构型优化设计: (a)初始构型1, (b)初始构型2, (c)初始构型3

    Figure  14.  Optimal design of different initial configurations: (a) initial 1, (b) initial 2, (c) initial 3

    图  15  不同初始构型优化结果降解过程中D33变化趋势

    Figure  15.  Variation trend of D33 during degradation of optimization results of different initial configurations

    图  16  宏观结构几何尺寸与边界条件

    Figure  16.  Geometric dimensions and boundary conditions of macro-structure

    17  有/无时变刚度特性调控设计的宏观结构降解历程: (a) 考虑时变刚度特性, (b) 无时变刚度特性调控

    17.  Degradation of different macro-structures: (a) considering time-changeable characteristics, (b) non-time-changeable characteristic regulation

    图  17  有/无时变刚度特性调控设计的宏观结构降解历程: (a) 考虑时变刚度特性, (b) 无时变刚度特性调控 (续)

    Figure  17.  Degradation of different macro-structures: (a) considering time-changeable characteristics, (b) non-time-changeable characteristic regulation (continued)

    图  18  不同宏观结构降解过程中加载点在加载方向的位移变化趋势

    Figure  18.  Variation trend of displacement of loading point in loading direction in the degradation process of different macro-structures

    图  19  不同可降解边界条件优化结果

    Figure  19.  Optimization results of different degradable interface condition

    图  20  不同可降解边界条件优化结果降解过程中D33变化趋势

    Figure  20.  Variation trend of D33 during degradation of optimization results with different degradable interface condition

    表  1  材料属性[5]

    Table  1.   Material properties[5]

    MaterialE/GPaμd/(mm·a−1)
    material 11500.30.29
    material 2400.31.85
    下载: 导出CSV

    表  2  不同φ优化结果降解过程中D33(GPa)在不同时间段的降低量

    Table  2.   The variation of D33 (GPa) in different time periods during the degradation of different optimization results

    Time/dφ=0.4φ=0.5φ=0.6φ=0.7
    Δ1-604.964.275.106.99
    Δ60-704.032.794.263.98
    Δ60-70/Δ1-600.810.650.830.57
    下载: 导出CSV
  • [1] Han HS, Loffredo S, Jun ID, et al. Current status and outlook on the clinical translation of biodegradable metals. Materials Today, 2019, 23: 57-71 doi: 10.1016/j.mattod.2018.05.018
    [2] Zhao DW, Witte F, Lu FQ, et al. Current status on clinical applications of magnesium-based orthopedic implants: A review from clinical translational perspective. Biomaterials, 2017, 112: 287-302 doi: 10.1016/j.biomaterials.2016.10.017
    [3] Zheng YF, Gu XN, Witte F. Biodegradable metals. Materials Science and Engineering: Reports, 2014, 77: 1-34 doi: 10.1016/j.mser.2014.01.001
    [4] Yang YW, He CX, E DY, et al. Mg bone implant: Features, developments and perspectives. Materials & Design, 2020, 185: 108259
    [5] Wang JL, Xu JK, Hopkins C, et al. Biodegradable magnesium-based implants in orthopedics-a general review and perspectives. Advanced Science, 2020, 7: 1902443 doi: 10.1002/advs.201902443
    [6] Mehboob H, Chang SH. Application of composites to orthopedic prostheses for effective bone healing: A review. Composite Structures, 2014, 118: 328-341 doi: 10.1016/j.compstruct.2014.07.052
    [7] 李信卿, 赵清海, 张洪信等. 周期性功能梯度结构稳态热传导拓扑优化设计. 中国机械工程, 2021, 32(19): 2348-2356 (Li Xinqing, Zhao Qinghai, Zhang Hongxin, et al. Optimal design of steady-state heat conduction topology for periodic functionally graded structure. China Mechanical Engineering, 2021, 32(19): 2348-2356 (in Chinese) doi: 10.3969/j.issn.1004-132X.2021.19.010
    [8] 任鑫, 张相玉, 谢亿民. 负泊松比材料和结构的研究进展. 力学学报, 2019, 51(3): 656-687 (Ren Xin, Zhang Xiangyu, Xie Yimin. Research progress in auxetic materials and structures. Chinese Journal of Theoretical and Applied, 2019, 51(3): 656-687 (in Chinese) doi: 10.6052/0459-1879-18-381
    [9] 李想, 严子铭, 柳占立等. 基于仿真和数据驱动的先进结构材料设计. 力学进展, 2021, 51(1): 82-105 (Li Xiang, Yan Ziming, Liu Zhanli, et al. Advanced structural material design based on simulation and data-driven method. Advances in Mechanics, 2021, 51(1): 82-105 (in Chinese) doi: 10.6052/1000-0992-20-012
    [10] 张横, 丁晓红, 沈磊等. 考虑连接性的三明治阻尼复合结构拓扑优化设计. 中国机械工程, 2021, 32(20): 2403-2410 (Zhang Heng, Ding Xiaohong, Shen Lei, et al. Topology optimization of sandwich damping composite structure with connective stiffness phase. China Mechanical Engineering, 2021, 32(20): 2403-2410 (in Chinese) doi: 10.3969/j.issn.1004-132X.2021.20.002
    [11] 倪维宇, 张横, 姚胜卫. 双材料自由阻尼层结构拓扑优化设计方法研究. 包装工程, 2021, 42(15): 156-164 (Ni Weiyu, Zhang Heng, Yao Shengwei. Topology optimization design of bi-material free-layer damping treatments. Packing engineering, 2021, 42(15): 156-164 (in Chinese)
    [12] 倪维宇, 张横, 姚胜卫. 考虑阻尼性能的复合结构多尺度拓扑优化设计. 航空学报, 2021, 42(3): 338-348 (Ni Weiyu, Zhang Heng, Yao Shengwei. Concurrent topology optimization of composite structures for considering structural damping. Acta Aeronautica et Astronautica Sinica, 2021, 42(3): 338-348 (in Chinese)
    [13] James KA, Waisman H. Topology optimization of viscoelastic structures using a time-dependent adjoint method. Computer Methods in Applied Mechanics and Engineering, 2015, 285: 166-187 doi: 10.1016/j.cma.2014.11.012
    [14] Wang WM, Munro D, Wang C, et al. Space-time topology optimization for additive manufacturing. Structural and Multidisciplinary Optimization, 2020, 61(1): 1-18 doi: 10.1007/s00158-019-02420-6
    [15] Wu C, Zheng KK, Fang JG, et al. Time-dependent topology optimization of bone plates considering bone remodeling. Computer Methods in Applied Mechanics and Engineering, 2020, 359: 112702 doi: 10.1016/j.cma.2019.112702
    [16] Li X, Wang Y, Chu CL, et al. A study on Mg wires/poly-lactic acid composite degradation under dynamic compression and bending load for implant applications. Journal of the Mechanical Behavior of Biomedical Materials, 2020, 105: 103707 doi: 10.1016/j.jmbbm.2020.103707
    [17] Barzegari M, Mei D, Lamaka SV, et al. Computational modeling of degradation process of biodegradable magnesium biomaterials. Corrosion Science, 2021, 190: 109674 doi: 10.1016/j.corsci.2021.109674
    [18] Shi WL, Li HX, Mitchell K, et al. A multi-dimensional non-uniform corrosion model for bioabsorbable metallic vascular stents. Acta Biomaterialia, 2021, 131: 572-580 doi: 10.1016/j.actbio.2021.07.008
    [19] Grogan JA, Leen SB, Mchugh PE. A physical corrosion model for bioabsorbable metal stents. Acta biomaterialia, 2014, 10(5): 2313-2322 doi: 10.1016/j.actbio.2013.12.059
    [20] Guo C, Sheng XB, Chu CL, et al. A cellular automaton simulation of the degradation of porous polylactide scaffold: I. Effect of porosity. Materials Science & Engineering C, 2009, 29(6): 1950-1958
    [21] Grogan JA, Brien O, Leen SB, et al. A corrosion model for bioabsorbable metallic stents. Acta Biomaterialia, 2011, 7(9): 3523-3533 doi: 10.1016/j.actbio.2011.05.032
    [22] Yun KS, Youn SK. Topology optimization of viscoelastic damping layers for attenuating transient response of shell structures. Finite Elements in Analysis & Design, 2018, 141: 154-165
    [23] Wang CF, Qian XP. Heaviside projection-based aggregation in stress-constrained topology optimization. International Journal for Numerical Methods in Engineering, 2018, 115(7): 849-871 doi: 10.1002/nme.5828
    [24] Chu S, Gao L, Xiao M, et al. Stress-based multi-material topology optimization of compliant mechanisms. International Journal for Numerical Methods in Engineering, 2018, 113: 1021-1044 doi: 10.1002/nme.5697
    [25] Zhang H, Ding XH, Li H, et al. Multi-scale structural topology optimization of free-layer damping structures with damping composite materials. Composite Structures, 2019, 212: 609-624 doi: 10.1016/j.compstruct.2019.01.059
    [26] Lambe AB, Kennedy GJ, Martins JRRA. An evaluation of constraint aggregation strategies for wing box mass minimization. Structural and Multidisciplinary Optimization, 2016, 55(1): 257-277
    [27] Ferrari, F, Sigmund O. A new generation 99 line Matlab code for compliance topology optimization and its extension to 3D. Structural and Multidisciplinary Optimization, 2020, 62(4): 2211-2228 doi: 10.1007/s00158-020-02629-w
    [28] Zhou, M, Sigmund O. Complementary lecture notes for teaching the 99/88-line topology optimization codes. Structural and Multidisciplinary Optimization, 2021, 64: 3227-3231 doi: 10.1007/s00158-021-03004-z
    [29] Andreassen E, Andreasen CS. How to determine composite material properties using numerical homogenization. Computer Materials Science, 2014, 83: 488-495 doi: 10.1016/j.commatsci.2013.09.006
    [30] Liu P, Liang XX, Li ZZ, et al. Decoupled effects of bone mass, microarchitecture and tissue property on the mechanical deterioration of osteoporotic bones. Composites Part B:Engineering, 2019, 177: 107436 doi: 10.1016/j.compositesb.2019.107436
    [31] Li, ZZ, Liu P, Yuan YN, et al. Loss of longitudinal superiority marks the micoarchitecture deterioration of osteoporotic cancellous bones. Biomechanics and Modeling in Mechanobiology, 2021, 20(5): 2013-2030 doi: 10.1007/s10237-021-01491-z
    [32] Andreassen E, Clausen A, Schevenels M. Efficient topology optimization in MATLAB using 88 lines of code. Structural and Multidisciplinary Optimization, 2011, 43: 1-16 doi: 10.1007/s00158-010-0594-7
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出版历程
  • 收稿日期:  2021-08-16
  • 录用日期:  2021-11-26
  • 网络出版日期:  2021-11-27
  • 刊出日期:  2022-01-05

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