EI、Scopus 收录
Volume 54 Issue 5
May  2022
Turn off MathJax
Article Contents
Wang Shuheng, Dai Shi, Wu Xinwei, Ma Yongbin, Deng Zichen. Design of elastically isotropic PLA lattice strucrure in fused filament fabrication considering material anisotropy. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(5): 1291-1302 doi: 10.6052/0459-1879-22-031
Citation: Wang Shuheng, Dai Shi, Wu Xinwei, Ma Yongbin, Deng Zichen. Design of elastically isotropic PLA lattice strucrure in fused filament fabrication considering material anisotropy. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(5): 1291-1302 doi: 10.6052/0459-1879-22-031


doi: 10.6052/0459-1879-22-031
  • Received Date: 2022-01-16
  • Accepted Date: 2022-04-02
  • Available Online: 2022-04-03
  • Publish Date: 2022-05-01
  • The rise of additive manufacturing technology stimulates researchers' enthusiasm for structural innovative design. However, the anisotropy of additive manufactured materials poses certain difficulties for the prediction and design of structural mechanical properties. To accurately predict the elastic properties of polylactic acid (PLA) materials and lattice structures made in fused filament fabrication and realize the elastically isotropic design of lattice structures, firstly, this paper adopts an orthogonal anisotropic elastic model to describe the elastic behavior of the PLA materials, and obtains the nine independent elastic constants needed for the orthogonal anisotropic model through experiments and calculations. Then, a 2D compound truss lattice structure with tunable mechanical properties is designed, and its analytical expressions for the in-plane effective elastic properties and elastic isotropy condition are derived based on the representative volume element (RVE) method without considering the material anisotropy. Finally, the elastic modulus and thickness of the struts in the lattice structure are adjusted according to the anisotropy of the PLA material, and the analytical expressions of the in-plane elastic properties and elastic isotropy condition of the lattice structur are derived based on the RVE method. The results show that the orthogonal anisotropic elastic model is suitable for describing the elastic behavior of fused filament fabricated PLA materials, and the elastic modulus of PLA materials in arbitrary direction can be accurately predicted based on this model. The anisotropy of the material needs to be fully considered when predicting and designing the mechanical properties of the fused filament fabricated lattice structures. After considering the material anisotropy, the elastic isotropy design of part of lattice structures can be realized by adjusting their geometric sizes based on the RVE method.


  • loading
  • [1]
    卢秉恒, 李涤尘. 增材制造 (3D 打印) 技术发展. 机械制造与自动化, 2013, 42(4): 1-4 (Lu Bingheng, Li Dichen. Development of the additive manufacturing (3D printing) technology. Machine Building & Automation, 2013, 42(4): 1-4 (in Chinese) doi: 10.3969/j.issn.1671-5276.2013.04.001
    吴斌, 王向明, 玄明昊等. 基于增材制造的新型战机结构创新. 航空材料学报, 2021, 41(6): 1-12 (Wu Bin, Wang Xiangming, Xuan Minghao. Structural innovation of new fighter based on additive manufacturing. Journal of Aeronautical Materials, 2021, 41(6): 1-12 (in Chinese) doi: 10.11868/j.issn.1005-5053.2021.000094
    Zhu JH, Zhou H, Wang C, et al. A review of topology optimization for additive manufacturing: Status and challenges. Chinese Journal of Aeronautics, 2021, 34(1): 91-110 doi: 10.1016/j.cja.2020.09.020
    Gu DD, Shi XY, Poprawe R, et al. Material-structure-performance integrated laser-metal additive manufacturing. Science, 2021, 372: eabg1487 doi: 10.1126/science.abg1487
    卢天健, 何德, 陈常青等. 超轻多孔金属材料的多功能特性及应用. 力学进展, 2006, 36(4): 517-535 (Lu Tianjian, He Deping, Chen Changqing, et al. The multi-functionality of ultra-light porous metals and their applications. Advances in Mechanics, 2006, 36(4): 517-535 (in Chinese) doi: 10.3321/j.issn:1000-0992.2006.04.004
    熊健, 杜昀桐, 杨雯等. 轻质复合材料夹芯结构设计及力学性能最新进展. 宇航学报, 2020, 41(6): 749-760 (Xiong Jian, Du Yuntong, Yang Wen, et al. Research progress on design and mechanical properties of lightweight composite sandwich structures. Journal of Astronautics, 2020, 41(6): 749-760 (in Chinese)
    雷红帅, 赵则昂, 郭晓岗等. 航天器轻量化多功能结构设计与制造技术研究进展. 宇航材料工艺, 2021, 51(4): 10-22 (Lei Hongshuai, Zhao Zeang, Guo Xiaogang, et al. Research progress on the design and manufacture technology of lightweight multifunctional spacecraft structures. Aerospace Materials &Technology, 2021, 51(4): 10-22 (in Chinese)
    Latture RM, Begley MR, Zok FW. Design and mechanical properties of elastically isotropic trusses. Journal of Materials Research, 2018, 33(3): 249-263 doi: 10.1557/jmr.2018.2
    Xu S, Shen J, Zhou S, et al. Design of lattice structures with controlled anisotropy. Materials & Design, 2016, 93: 443-447
    Wang SH, Ma YB, Deng ZC, et al. Two elastically equivalent compound truss lattice materials with controllable anisotropic mechanical properties. International Journal of Mechanical Sciences, 2022, 213: 106879 doi: 10.1016/j.ijmecsci.2021.106879
    陈泽坤, 蒋佳希, 王宇嘉等. 金属增材制造中的缺陷、组织形貌和成形材料力学性能. 力学学报, 2021, 53(12): 3190-3205 (Chen Zekun, Jiang Jiaxi, Wang Yujia, et al. Defects, microstructures and mechanical properties of materials fabricated by metal additive manufacturing. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(12): 3190-3205 (in Chinese) doi: 10.6052/0459-1879-21-472
    张江涛, 谭援强, 纪财源等. 增材制造中滚筒铺粉工艺参数对尼龙粉体铺展性的影响研究. 力学学报, 2021, 53(9): 2416-2426 (Zhang Jiangtao, Tan Yuanqiang, Ji Caiyuan, et al. Research on the effects of roller-spreading parameters for nylon powder spreadability in additive manufacturing. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(9): 2416-2426 (in Chinese) doi: 10.6052/0459-1879-21-240
    朱继宏, 曹吟锋, 翟星玥等. 增材制造316钢高周疲劳性能的微观力学研究. 力学学报, 2021, 53(12): 3181-3189 (Zhu Jihong, Cao Yinfeng, Zhai Xingyue, et al. Micromechanical study of the high cycle fatigue property of additive-manufactured 316 steel. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(12): 3181-3189 (in Chinese) doi: 10.6052/0459-1879-21-396
    廉艳平, 王潘丁, 高洁等. 金属增材制造若干关键力学问题研究进展. 力学进展, 2021, 51(3): 648-701 (Yan Yanping, Wang Panding, Gao Jie, et al. Fundamental mechanics problems in metal additive manufacturing: A state-of-art review. Advances in Mechanics, 2021, 51(3): 648-701 (in Chinese) doi: 10.6052/1000-0992-21-037
    Wang SH, Ma YB, Deng ZC, et al. Implementation of an elastoplastic constitutive model for 3D-printed materials fabricated by stereolithography. Additive Manufacturing, 2020, 33: 101104 doi: 10.1016/j.addma.2020.101104
    Wang SH, Ma YB, Deng ZC, et al. Effects of fused deposition modeling process parameters on tensile, dynamic mechanical properties of 3 D printed polylactic acid materials. Polymer Testing, 2020, 86: 106483 doi: 10.1016/j.polymertesting.2020.106483
    张登辉. 3D打印纤维增强高分子复合材料的各向异性研究. [硕士论文]. 南京: 南京航空航天大学, 2019

    Xu Ke. Constitutive modeling of acrylonitrile butadiene styrene material in fused deposition modeling and the application. [Master's Thesis]. Nanjing: Nanjing University of Aeronautics and Astronautics, 2019 (in Chinese))
    Zou R, Xia Y, Liu S, et al. Isotropic and anisotropic elasticity and yielding of 3 D printed material. Composites Part B: Engineering, 2016, 99: 506-513 doi: 10.1016/j.compositesb.2016.06.009
    Xia Y, Xu K, Zheng G, et al. Investigation on the elasto-plastic constitutive equation of parts fabricated by fused deposition modeling. Rapid Prototyping Journal, 2019, 25(3): 592-601 doi: 10.1108/RPJ-06-2018-0147
    徐可. 熔融沉积增材制造ABS材料本构模型研究及其应用. [硕士论文]. 大连: 大连理工大学, 2018

    Xu Ke. Constitutive modeling of acrylonitrile butadiene styrene material in fused deposition modeling and the application. [Master's Thesis]. Dalian: Dalian University of Technology, 2018 (in Chinese))
    Casavola C, Cazzato A, Moramarco V, et al. Orthotropic mechanical properties of fused deposition modelling parts described by classical laminate theory. Materials & Design, 2016, 90: 453-459
    Dai S, Deng ZC, Yu YJ, et al. Orthotropic elastic behaviors and yield strength of fused deposition modeling materials: Theory and experiments. Polymer Testing, 2020, 87: 106520 doi: 10.1016/j.polymertesting.2020.106520
    Biswas P, Guessasma S, Li J. Numerical prediction of orthotropic elastic properties of 3D-printed materials using micro-CT and representative volume element. Acta Mechanica, 2020, 231: 503-516 doi: 10.1007/s00707-019-02544-2
    张志威. 熔融沉积打印试样各向同性和力学承载的研究和优化. [硕士论文]. 天津: 天津大学, 2018

    Zhang Zhiwei. Research and optimization of isotropic and load-bearing properties of fused deposition modeling parts. [Master's Thesis]. Tianjin: Tianjin University, 2018 (in Chinese))
    Guth DC, Luersen MA, Muñoz-Rojas PA. Optimization of three-dimensional truss-like periodic materials considering isotropy constraints. Structural and Multidisciplinary Optimization, 2015, 52: 889-901 doi: 10.1007/s00158-015-1282-4
    Chen W, Watts S, Jackson JA. Stiff isotropic lattices beyond the Maxwell criterion. Science Advance, 2019, 5: eaaw1937
    Wang Y, Groen JP, Sigmund O. Simple optimal lattice structures for arbitrary loadings. Extreme Mechanics Letters, 2019, 29: 100447 doi: 10.1016/j.eml.2019.03.004
    Berger JB, Wadley HNG, McMeeking RM. Mechanical metamaterials at the theoretical limit of isotropic elastic stiffness. Nature, 2017, 543: 533-537 doi: 10.1038/nature21075
    Feng J, Liu B, Lin Z, et al. Isotropic octet-truss lattice structure design and anisotropy control strategies for implant application. Materials & Design, 2021, 203: 109595
    Tancogne-Dejean T, Mohr D. Elastically-isotropic elementary cubic lattices composed of tailored hollow beams. Extreme Mechanics Letters, 2018, 22: 13-18 doi: 10.1016/j.eml.2018.04.005
    Mukhopadhyay T, Naskar S, Adhikari S. Anisotropy tailoring in geometrically isotropic multi-material lattices. Extreme Mechanics Letters, 2020, 40: 100934 doi: 10.1016/j.eml.2020.100934
    Kulagin R, Beygelzimer Y, Estrin Y, et al. Architectured lattice materials with tunable anisotropy: design and analysis of the material property space with the aid of machine learning. Advanced Engineering Materials, 2020, 22: 2001069 doi: 10.1002/adem.202001069
    王飞, 庄守兵, 虞吉林. 用均匀化理论分析蜂窝结构的等效弹性参数. 力学学报, 2002, 34(6): 914-923 (Wang Fei, Zhuang Shoubing, Yu Jilin. Application of homogenization FEM to the equivalent elastic constants of honeycomb structures. Chinese Journal of Theoretical and Applied Mechanics, 2002, 34(6): 914-923 (in Chinese) doi: 10.3321/j.issn:0459-1879.2002.06.009
    阎军, 程耿东, 刘书田等. 周期性点阵类桁架材料等效弹性性能预测及尺寸效应. 固体力学学报, 2005, 26(4): 421-428 (Yan Jun, Cheng Gengdong, Liu Shutian, et al. Perdition of equivalent elastic properties of truss materials with periodic microstructure and the scale effects. Chinese Journal of Solid Mechanics, 2005, 26(4): 421-428 (in Chinese) doi: 10.3969/j.issn.0254-7805.2005.04.007
    Wang SH, Ma YB, Deng ZC. Two-node method for the effective elastic properties of periodic cellular truss materials and experiment verification via stereolithography. European Journal of Mechanics A/Solids, 2021, 86: 104201
    Auld BA. Acoustic Field and Waves in Solids. New York: John Wiley and Sons. Inc., 1973
    沈观林, 胡更开, 刘彬. 复合材料力学 (第二版). 北京: 清华大学出版社, 2013

    Shen Guanlin, Hu Gengkai, Liu Bin. Mechanics of Composite Materials (Second Edition). Beijing: Tsinghua University Press, 2013 (in Chinese)
    桂俊川, 陈平, 马天寿. 正交各向异性岩石弹性参数的空间展布. 西南石油大学学报(自然科学版), 2019, 41(3): 13-28 (Gui Junchuan, Chen Ping, Ma Tianshou. The spatial distribution of elastic parameters of orthotropic rocks. Journal of Southwest Petroleum University (Science &Technology Edition), 2019, 41(3): 13-28 (in Chinese)
    Deshpande VS, Ashby MF, Fleck NA. Foam topology: bending versus stretching dominated architectures. Acta Materialia, 2001, 49: 1035-1040 doi: 10.1016/S1359-6454(00)00379-7
    Nye JF. Physical Properties of Crystals. Oxford: Clarendon Press, 1985
  • 加载中


    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Figures(12)  / Tables(7)

    Article Metrics

    Article views (704) PDF downloads(108) Cited by()
    Proportional views


    DownLoad:  Full-Size Img  PowerPoint