四方对称TPMS晶格结构的设计及各向异性分析

doi:10.3901/JME.260025

摘要/Abstract

摘要： 为提升生物骨支架的轴向力学性能和质量传输性能，保证承载的稳定性并促进营养输送与细胞增殖，提出了一类基于三周期极小曲面(Triply periodic minimal surface, TPMS)的新型四方对称晶格结构的设计方法。该设计方法通过控制隐函数中三角函数的组合方式来调整TPMS中值面的曲率，实现晶格拓扑构型从立方对称性向四方对称性的重构。研究结果表明，相比于立方对称晶格结构，基于该方法设计的四方对称晶格结构凭借其特殊的几何构型和各向异性，不仅能显著增强特定方向的弹性模量和抗压强度达98%和120%，还能改变晶格结构的变形主导行为及其失效机制。此外，四方对称晶格结构在该特定方向展现出更优越的内部连通性和更高的流体速度，可有效降低流体压降，并显著提升其渗透率达165%。该四方对称晶格结构的设计方法能有效提高其综合性能，为生物骨支架的多性能优化设计提供了新的参考。

关键词: 三周期极小曲面, 四方对称晶格, 力学性能, 质量传输性能, 各向异性

Abstract: To enhance the axial mechanical properties and mass-transport properties of bio-bone scaffolds, ensuring load-bearing stability and supporting nutrient delivery and cell proliferation, a novel design method for tetragonal symmetric lattice structures based on triply periodic minimal surface (TPMS) is proposed. By adjusting the iso-surface curvature of the TPMS through the controlled combination of trigonometric functions in the implicit function, this design method realizes the reconstruction of the lattice topology from cubic symmetry to tetragonal symmetry. The results show that, compared with the corresponding cubic symmetric lattice structures, the tetragonal symmetric lattice structures designed by the method, owing to their unique geometric configuration and anisotropy, not only significantly enhance the elastic modulus and compressive strength in specific direction by up to 98% and 120% respectively, but also alter the deformation-dominant behavior and failure mechanisms of the lattice structures. In addition, the tetragonal symmetric lattice structures have superior internal connectivity and higher fluid velocity in this specific direction, which can effectively reduce the pressure drop and increase the permeability by up to 165%. The design method of the tetragonal symmetric lattice structures can effectively improve the comprehensive performance, and also provide a new reference for the multi-performance optimization design of biological bone scaffolds.

Key words: triply periodic minimal surface, tetragonal symmetric lattice, mechanical property, mass-transport property, anisotropy

中图分类号:

TG665
R318

罗智超, 唐倩, 宋军, 张远航, 陈俊杰, 马帅, 冯琪翔. 四方对称TPMS晶格结构的设计及各向异性分析[J]. 机械工程学报, 2026, 62(1): 347-360.

LUO Zhichao, TANG Qian, SONG Jun, ZHANG Yuanhang, CHEN Junjie, MA Shuai, FENG Qixiang. Design and Anisotropy Analysis of Tetragonal Symmetric TPMS Lattice Structures[J]. Journal of Mechanical Engineering, 2026, 62(1): 347-360.

参考文献

[1] ZHAO Miao,LI Xinwei,ZHANG D Z,et al.Geometry effect on mechanical properties and elastic isotropy optimization of bamboo-inspired lattice structures[J].Additive Manufacturing,2023,64:103438.
[2] LI Xinwei,CHUA J W,YU X,et al.3D-Printed Lattice structures for sound absorption:Current progress,mechanisms and models,structural-property relationships,and future outlook[J].Advanced Science,2024,11(4).
[3] ZOU Bihui,LIANG Zihe,ZHONG Dijia,et al.Magneto-thermomechanically reprogrammable mechanical metamaterials[J].Advanced Materials,2023,35(8):2207349.
[4] AN Qing,LI Dawei,LIAO Wenhe,et al.A novel ultra-wideband electromagnetic-wave-absorbing metastructure inspired by bionic gyroid structures[J].Advanced Materials,2023,35(26):2300659.
[5] SMEETS B J R,FAGAN E M,MATTHEWS K,et al.Structural testing of a shear web attachment points on a composite lattice cylinder for aerospace applications[J].Composites Part B:Engineering,2021,212:108691.
[6] 郑晖,廖恕,王会东,等.航空点阵结构制造技术、测试及表征方法研究进展[J].兵器材料科学与工程,2023,46(6):113-126.ZHENG Hui,LIAO Shu,WANG Huidong,et al.Advances in manufacturing technology,testing and characterization methods of aeronautical lattice structures[J].Ordnance Material Science and Engineering, 2023,46(6):113-126.
[7] YUAN Xun,ZHU Wei,YANG Zhongyuan,et al.Recent advances in 3D printing of smart scaffolds for bone tissue engineering and regeneration[J].Advanced Materials,2024,36:2403641.
[8] ZHANG Lei,SONG Bo,CHOI S,et al.Anisotropy-inspired,simulation-guided design and 3D printing of microlattice metamaterials with tailored mechanical-transport performances[J].Composites Part B:Engineering,2022,236:109837.
[9] 梁鸿宇,刘百川,马芳武,等.多工况碰撞载荷下点阵结构填充吸能盒设计策略研究[J].汽车工程,2023,45(2):293-303.LIANG Hongyu,LIU Baichuan,MA Fangwu,et al.Research on design strategy of lattice structure filled crash box under multi-angle impact loadin[J].Automotive Engineering,2023,45(2):293-303.
[10] WANG Hui,TAN Dingwen,LIU Zhipeng,et al.On crashworthiness of novel porous structure based on composite TPMS structures[J].Engineering Structures,2022,252:113640.
[11] 汪飞雪,姚龙飞,张天翊,等.基于SLM工艺的变截面四棱锥点阵结构建模与试验研究[J].机械工程学报,2021,57(24):158-165.WANG Feixue,YAO Longfei,ZHANG Tianyi,et al.Modeling and experimental study of S-GBCC lattice structure based on SLM process[J].Journal of Mechanical Engineering,2021,57(24):158-165.
[12] 石岩,张恒.面向选区激光熔化增材制造的多孔结构设计与力学性能分析[J].机械工程学报,2023,59(18):175-185.SHI Yan,ZHANG Heng.Design and mechanical properties analysis of additive manufactured porous structures by selective laser melting[J].Journal of Mechanical Engineering,2023,59(18):175-185.
[13] 张明康,师文庆,徐梅珍,等.隐式曲面多孔结构压缩性能与流体压降性能研究[J].机械工程学报,2024,60(18):394-406.ZHANG Mingkang,SHI Wenqing,XU Meizhen,et al.Compression and fluid pressure drop properties of implicit surface cellular structures[J].Journal of Mechanical Engineering,2024,60(18):394-406.
[14] MA Shuai,TANG Qian,FENG Qixiang,et al.Mechanical behaviours and mass transport properties of bone-mimicking scaffolds consisted of gyroid structures manufactured using selective laser melting[J].Journal of the Mechanical Behavior of Biomedical Materials,2019,93:158-169.
[15] YÁNEZ A,CUADRADO A,MARTEL O,et al.Mechanical and permeability properties of skeletal and sheet triply periodic minimal surface scaffolds in bone defect reconstruction[J].Results in Engineering,2024,21:101883.
[16] ZHANG Jun,CHEN Xiaohong,SUN Yuanxi,et al.Design of a biomimetic graded TPMS scaffold with quantitatively adjustable pore size[J].Materials & Design,2022,218:110665.
[17] ZHANG Lei,SONG Bo,YANG Lei,et al.Tailored mechanical response and mass transport characteristic of selective laser melted porous metallic biomaterials for bone scaffolds[J].Acta Biomaterialia,2020,112:298-315.
[18] LUO Zhichao,TANG Qian,MA Shuai,et al.Effect of aspect ratio on mechanical anisotropy of lattice structures[J].International Journal of Mechanical Sciences,2024,270:109111.
[19] QIU Na,ZHANG Jiazhong,YUAN Feiquan,et al.Mechanical performance of triply periodic minimal surface structures with a novel hybrid gradient fabricated by selective laser melting[J].Engineering Structures,2022,263:114377.
[20] MODREK M,VISWANATH A,KHAN K A,et al.Multi-objective topology optimization of passive heat sinks including self-weight based on triply periodic minimal surface lattices[J].Case Studies in Thermal Engineering, 2023,42:102684.
[21] MA Xiaofei,GUO Ce,HU Caiji,et al.Study on the topological morphology and mechanical properties of variable-amplitude TPMS structures[J].Journal of Materials Research and Technology,2023,27:3459-3472.
[22] CAZZANI A,ROVATI M.Extrema of Young's modulus for elastic solids with tetragonal symmetry[J].International Journal of Solids and Structures,2005,42(18-19):5057-5096.
[23] CAZZANI A,ROVATI M.Extrema of Young's modulus for cubic and transversely isotropic solids[J].International Journal of Solids and Structures,2003,40(7):1713-1744.
[24] LUO Zhichao,TANG Qian,SONG Jun,et al.TPMS-based strut-shell interpenetrating lattice metamaterial with wide-range customizable mechanical properties and superior energy absorption[J].Composite Structures,2024,349-350:118555.
[25] DESHPANDE V S,ASHBY M F,FLECK N A.Foam topology:Bending versus stretching dominated architectures[J].Acta Materialia,2001,49(6):1035-1040.
[26] LUO Zhichao,TANG Qian,FENG Qixiang,et al.Finite element analysis of the mechanical properties of sheet- and skeleton-gyroid Ti6Al4V structures produced by laser powder bed fusion[J].Thin-Walled Structures,2023,192:111098.
[27] ZHAO Miao,ZHANG D Z,LIU Fei,et al.Mechanical and energy absorption characteristics of additively manufactured functionally graded sheet lattice structures with minimal surfaces[J].International Journal of Mechanical Sciences,2020,167:105262.
[28] LIU Fei,TANG Yichuan,XIE Haiqiong,et al.Strengthening mechanisms of minimal surface lattices with CT deviation[J].International Journal of Mechanical Sciences,2023,240:107932.
[29] MA Shuai,TANG Qian,HAN Xiaoxiao,et al.Manufacturability,mechanical properties,mass-transport properties and biocompatibility of triply periodic minimal surface (TPMS) porous scaffolds fabricated by selective laser melting[J].Materials & Design,2020,195:109034.
[30] PLESSIS A,YADROITSAVA I,YADROITSEV I,et al.Numerical comparison of lattice unit cell designs for medical implants by additive manufacturing[J].Virtual and Physical Prototyping,2018,13(4):266-281.