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A novel design method for TPMS lattice structures with complex contour based on moving elements method

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Abstract

Over the past few decades, there have been many important achievements on the design, research, and development of minimal surface lattice structures. In this work, we propose a modeling method for triply periodic minimal surfaces (TPMS) lattice structures with complex contours. This method is based on moving elements method (MEM) and mainly includes the following parts: dividing the model mesh, solving the iso-surface of the TPMS in the model, obtaining the TPMS lattice structure triangular surface of the model outline, integrating the interior of the model and the outline, and finally generating an STL file that can be used for additive manufacturing. Furthermore, the representative femur model, rabbit model, and gear model are provided as case studies to verify the validity and correctness of the proposed modeling method. Then, this approach is compared with the distance field-based method (DFBM) in terms of modeling speed and modeling accuracy. The research results show that the time required by the MEM method was reduced by 3055.56%, 2799.70% compared to the DFBM method, when filling the network primitive and network gyroid lattice structures in the femur model. Moreover, this method provides technical means and simulation data for designing TPMS lattice structures with complex contour, and offers the underlying design ideas for the development and application of the excellent physical properties of TPMS lattice structures in medicine and engineering.

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References

  1. Tancogne-Dejean T, Karathanasopoulos N, Mohr D (2019) Stiffness and strength of hexachiral honeycomb-like metamaterials. J Appl Mech 86. https://doi.org/10.1115/1.4044494

  2. Kumar A, Verma S, Jeng JY (2020) Supportless Lattice structures for energy absorption fabricated by fused deposition modeling. 3d Printing and Additive Manufacturing 7: 85–96. https://doi.org/10.1089/3dp.2019.0089

  3. Yang C, Li QM (2020) Advanced lattice material with high energy absorption based on topology optimisation. Mech Mater 148. https://doi.org/10.1016/j.mechmat.2020.103536

  4. Alberdi R, Dingreville R, Robbins J, Walsh T, White BC, Jared B, Boyce BL (2020) Multi-morphology lattices lead to improved plastic energy absorption. Mater Design 194. https://doi.org/10.1016/j.matdes.2020.108883

  5. Tran P, Peng C (2020) Triply periodic minimal surfaces sandwich structures subjected to shock impact. J Sandwich Struct Mater 109963622090555. https://doi.org/10.1177/1099636220905551

  6. Wang X, Wang C, Zhou X, Wang D, Zhang M, Gao Y, Wang L, Zhang P (2020) Evaluating lattice mechanical properties for lightweight heat-resistant load-bearing structure design. Materials 13 https://doi.org/10.3390/ma13214786

  7. Zhou H, Cao X, Li C, Zhang X, Fan H, Lei H, Fang D (2021) Design of self-supporting lattices for additive manufacturing. J Mech Phys Solids 148 https://doi.org/10.1016/j.jmps.2021.104298

  8. Wang S, Shi ZA, Liu L, Zhou X, Zhu L, Hao Y (2020) The design of Ti6Al4V primitive surface structure with symmetrical gradient of pore size in biomimetic bone scaffold. Mater Design 193:108830. https://doi.org/10.1016/j.matdes.2020.108830

  9. Vijayavenkataraman S, Kuan LY, Lu WF (2020) 3D-printed ceramic triply periodic minimal surface structures for design of functionally graded bone implants. Mater Des 191:108602. https://doi.org/10.1016/j.matdes.2020.108602

    Article  Google Scholar 

  10. Khalil A, Ahmed FE, Hilal N (2021) The emerging role of 3D printing in water desalination. Sci Total Environ 790:148238. https://doi.org/10.1016/j.scitotenv.2021.148238

    Article  Google Scholar 

  11. Ngo TD, Kashani A, Imbalzano G, Nguyen KTQ, Hui D (2018) Additive manufacturing (3D printing): a review of materials, methods, applications and challenges. Compos B Eng 143:172–196. https://doi.org/10.1016/j.compositesb.2018.02.012

    Article  Google Scholar 

  12. Attaran M (2017) The rise of 3-D printing: the advantages of additive manufacturing over traditional manufacturing. Bus Horiz 60:677–688. https://doi.org/10.1016/j.bushor.2017.05.011

    Article  Google Scholar 

  13. Song J, Cao M, Cai L, Zhou Y, Chen J, Liu S, Zhou B, Lu Y, Zhang J, Long W, Li L (2021) 3D printed polymeric formwork for lattice cementitious composites. J Build Eng 43. https://doi.org/10.1016/j.jobe.2021.103074

  14. Spadaccini CM (2019) Additive manufacturing and processing of architected materials. MRS Bull 44:782–788. https://doi.org/10.1557/mrs.2019.234

    Article  Google Scholar 

  15. Rodrigues TA, Bairrão L, Farias FWC, Shamsolhodaei A, Shen J, Zhou N, Maawad E, Schell N, Santos TG, Oliveira JP (2022) Steel-copper functionally graded material produced by twin-wire and arc additive manufacturing (T-WAAM). Mater Design 213. https://doi.org/10.1016/j.matdes.2021.110270

  16. Ke WC, Oliveira JP, Cong BQ, Ao SS, Qi ZW, Peng B, Zeng Z (2022) Multi-layer deposition mechanism in ultra high-frequency pulsed wire arc additive manufacturing (WAAM) of NiTi shape memory alloys. Addit Manuf 50. https://doi.org/10.1016/j.addma.2021.102513

  17. Zhou H, Zhang X, Zeng H, Yang H, Lei H, Li X, Wang Y (2019) Lightweight structure of a phase-change thermal controller based on lattice cells manufactured by SLM. Chin J Aeronaut 32:1727–1732. https://doi.org/10.1016/j.cja.2018.08.017

    Article  Google Scholar 

  18. Gorji NE, O’connor R, Brabazon D (2021) XPS, SEM, AFM, and nano-indentation characterization for powder recycling within additive manufacturing process. IOP Conf Series: Mater Sci Eng 1182. https://doi.org/10.1088/1757-899x/1182/1/012025

  19. Oliveira JP, LaLonde AD, Ma J (2020) Processing parameters in laser powder bed fusion metal additive manufacturing. Mater Design 193. https://doi.org/10.1016/j.matdes.2020.108762

  20. Han L, Che S (2018) An overview of materials with triply periodic minimal surfaces and related geometry: from biological structures to self-assembled systems. Adv Mater 30:e1705708. https://doi.org/10.1002/adma.201705708

    Article  Google Scholar 

  21. Ebihara R, Hashimoto H, Kano J, Fujii T, Yoshioka S (2018) Cuticle network and orientation preference of photonic crystals in the scales of the weevil Lamprocyphus augustus. J R Soc Interface 15. https://doi.org/10.1098/rsif.2018.0360

  22. Montazerian H, Mohamed MGA, Montazeri MM, Kheiri S, Milani AS, Kim K, Hoorfar M (2019) Permeability and mechanical properties of gradient porous PDMS scaffolds fabricated by 3D-printed sacrificial templates designed with minimal surfaces. Acta Biomater 96:149–160. https://doi.org/10.1016/j.actbio.2019.06.040

    Article  Google Scholar 

  23. Sreedhar N, Thomas N, Al-Ketan O, Rowshan R, Hernandez H, Abu Al-Rub RK, Arafat HA (2018) 3D printed feed spacers based on triply periodic minimal surfaces for flux enhancement and biofouling mitigation in RO and UF. Desalination 425:12–21. https://doi.org/10.1016/j.desal.2017.10.010

    Article  Google Scholar 

  24. Sathishkumar N, Vivekanandan N, Balamurugan L, Arunkumar N, Ahamed I (2020) Mechanical properties of triply periodic minimal surface based lattices made by polyjet printing. Materials Today: Proceedings 22:2934–2940. https://doi.org/10.1016/j.matpr.2020.03.427

    Article  Google Scholar 

  25. Miralbes R, Ranz D, Pascual FJ, Zouzias D, Maza M (2020) Characterization of additively manufactured triply periodic minimal surface structures under compressive loading. Mech Adv Mater Struct. https://doi.org/10.1080/15376494.2020.1842948

    Article  Google Scholar 

  26. Zhao M, Liu F, Fu G, Zhang DZ, Zhang T, Zhou H (2018) Improved mechanical properties and energy absorption of BCC lattice structures with triply periodic minimal surfaces fabricated by SLM. Materials (Basel) 11. https://doi.org/10.3390/ma11122411

  27. Ouda M, Al-Ketan O, Sreedhar N, Ali MI, Al-Rub RK, Hong S, Arafat HA (2020) Novel static mixers based on triply periodic minimal surface (TPMS) architectures. J Environ Chem Eng 8. https://doi.org/10.1016/j.jece.2020.104289

  28. Shen M, Qin W, Xing B, Zhao W, Gao S, Sun Y, Jiao T, Zhao Z (2021) Mechanical properties of 3D printed ceramic cellular materials with triply periodic minimal surface architectures. J Eur Ceram Soc 41:1481–1489. https://doi.org/10.1016/j.jeurceramsoc.2020.09.062

    Article  Google Scholar 

  29. Zhao M, Zhang DZ, Liu F, Li Z, Ma Z, Ren Z (2020) Mechanical and energy absorption characteristics of additively manufactured functionally graded sheet lattice structures with minimal surfaces. Int J Mech Sci 167:105262. https://doi.org/10.1016/j.ijmecsci.2019.105262

    Article  Google Scholar 

  30. Ma X, Zhang DZ, Zhao M, Jiang J, Luo F, Zhou H (2021) Mechanical and energy absorption properties of functionally graded lattice structures based on minimal curved surfaces. The International Journal of Advanced Manufacturing Technology 118:995–1008. https://doi.org/10.1007/s00170-021-07768-y

    Article  Google Scholar 

  31. Alhammadi A, Al-Ketan O, Khan KA, Ali M, Rowshan R, Al-Rub RK (2020) Microstructural characterization and thermomechanical behavior of additively manufactured AlSi10Mg sheet cellular materials. Mater Sci Eng A 791. https://doi.org/10.1016/j.msea.2020.139714

  32. Thomas N, Sreedhar N, Al-Ketan O, Rowshan R, Abu Al-Rub RK, Arafat H (2018) 3D printed triply periodic minimal surfaces as spacers for enhanced heat and mass transfer in membrane distillation. Desalination 443:256–271. https://doi.org/10.1016/j.desal.2018.06.009

    Article  Google Scholar 

  33. Xu H, Xie YM, Chan R, Zhou S (2020) Piezoelectric properties of triply periodic minimum surface structures. Compos Sci Technol 200:108417. https://doi.org/10.1016/j.compscitech.2020.108417

    Article  Google Scholar 

  34. Abueidda DW, Abu Al-Rub RK, Dalaq AS, Lee D-W, Khan KA, Jasiuk I (2016) Effective conductivities and elastic moduli of novel foams with triply periodic minimal surfaces. Mech Mater 95:102–115. https://doi.org/10.1016/j.mechmat.2016.01.004

    Article  Google Scholar 

  35. Qureshi ZA, Elnajjar E, Al-Ketan O, Al-Rub RA, Al-Omari SB (2021) Heat transfer performance of a finned metal foam-phase change material (FMF-PCM) system incorporating triply periodic minimal surfaces (TPMS). Int J Heat Mass Transf 170:121001. https://doi.org/10.1016/j.ijheatmasstransfer.2021.121001

    Article  Google Scholar 

  36. Li ZHJXY, Zhou X, Lu K (2020) Constrained minimal-interface structures in polycrystalline copper with extremely fine grains. Science. https://doi.org/10.1126/science.abe1267

    Article  Google Scholar 

  37. Ting Yang HC, Jia Z, Deng Z, Chen L, Peterman EM, Weaver JC, Li L (2022) A damage-tolerant, dual-scale, single-crystalline microlattice in the knobby starfish, Protoreaster nodosus. Science 375:647–652

    Article  Google Scholar 

  38. Liu F, Mao Z, Zhang P, Zhang DZ, Jiang J, Ma Z (2018) Functionally graded porous scaffolds in multiple patterns: new design method, physical and mechanical properties. Mater Des 160:849–860. https://doi.org/10.1016/j.matdes.2018.09.053

    Article  Google Scholar 

  39. Cai S, Xi J, Chua CK (2012) A novel bone scaffold design approach based on shape function and all-hexahedral mesh refinement. Methods Mol Biol 868:45–55. https://doi.org/10.1007/978-1-61779-764-4_3

    Article  Google Scholar 

  40. Yoo DJ (2011) Porous scaffold design using the distance field and triply periodic minimal surface models. Biomaterials 32:7741–7754. https://doi.org/10.1016/j.biomaterials.2011.07.019

    Article  Google Scholar 

  41. Yu X, Li L, Zhang T, Zhang Z (2021) Modeling of complex contour lattice structure based on triply periodic minimal surface and voxel distance field. J Chongqing Univ. https://doi.org/10.11835/j.issn.1000-582X.2021.115

  42. Lorensen WE (2020) History of the marching cubes algorithm. IEEE Comput Graphics Appl

  43. Chan EOPSL (1998) A new tetrahedral tesselation scheme for isosurface generation. Comput Graphics 22:83–90. https://doi.org/10.1016/S0097-8493(97)00085-X

    Article  Google Scholar 

  44. Lorensen WE, Cline HE (1987) Marching cubes: a high resolution 3D surface construction algorithm. Comput Graphics 21. https://doi.org/10.1145/37401.37422

  45. Treece RWPGM, Gee AH (1999) Technical section regularised marching tetrahedra: improved iso-surface extraction. Comput Graph 23:583–598. https://doi.org/10.1016/S0097-8493(99)00076-X

    Article  Google Scholar 

  46. Lu T, Chen F (2012) Quantitative analysis of molecular surface based on improved Marching Tetrahedra algorithm. J Mol Graph Model 38:314–323. https://doi.org/10.1016/j.jmgm.2012.07.004

    Article  Google Scholar 

  47. Chan EOPSL (1998) A new tetrahedral tesselation scheme for isosurface generation. Comput Graphics

  48. Zhuangya Z, Ke Z, Yuesong L (2020) Porous structure method of bone scaffold based on voxel and triple cycle minimal surfaces. Comput Integr Manuf Syst 26:697–706. https://doi.org/10.13196/j.cims.2020.03.013

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Funding

This work was supported by the Key projects of Natural Science Foundation of Chongqing (cstc2020jcyj-zdxmX0021) and the Natural Science Foundation of Chongqing (cstc2021jcyj-msxmX0395).

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Authors and Affiliations

  1. State Key Laboratory of Mechanical Transmissions, Chongqing University, Chongqing, 400044, China

    Xiangyu Ma, David Z. Zhang, Zhihao Ren & Shenglan Mao

  2. Chongqing Key Laboratory of Metal Additive Manufacturing (3D Printing), Chongqing University, Chongqing, 400044, China

    Xiangyu Ma, David Z. Zhang, Zhihao Ren & Shenglan Mao

  3. College of Engineering, Mathematics and Physical Sciences, University of Exeter, North Park Road, Exeter, EX4 4QF, UK

    David Z. Zhang

  4. Guangzhou Zhongwang Longteng Software Co, Ltd, Guangzhou, 510635, China

    Xuewei Yu

  5. School of Intelligent Manufacturing Engineering, Chongqing University of Arts and Sciences, Chongqing, 402160, China

    Xunjia Zheng

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  1. Xiangyu Ma
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Xiangyu Ma, David Z. Zhang, and Xuewei Yu designed the work, performed the research, and analyzed the data. Xiangyu Ma, Zhihao Ren, Shenglan Mao, and Xunjia Zheng discussed the results and wrote the manuscript. All authors contributed to drafting and revising the manuscript.

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Ma, X., Zhang, D.Z., Yu, X. et al. A novel design method for TPMS lattice structures with complex contour based on moving elements method. Int J Adv Manuf Technol 123, 21–33 (2022). https://doi.org/10.1007/s00170-022-09980-w

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