مجله مهندسی مکانیک

مجله مهندسی مکانیک

مروری بر مشخصات مکانیکی و کاربردهای سازه ‌های طراحی شده بر مبنای سطوح مینیمال تکرار شونده و نحوه مدل سازی آن ‌ها

نوع مقاله : مقاله مروری

نویسندگان
1 دانشجوی کارشناسی ارشد، دانشکده مهندسی، گروه مهندسی مکانیک، دانشگاه بیرجند، بیرجند
2 استادیار، دانشکده مهندسی، گروه مهندسی مکانیک، دانشگاه بیرجند، بیرجند
چکیده
سطوح مینیمال، نوعی خاصی از سطوح هندسی هستند که مجموع انحناهای اصلی آن‌ ها در دو راستا در هر نقطه روی سطح، برابر با صفر است. از مهم ‌ترین انواع این سطوح می ‌توان به سطوح مینیمال شوارز پی، الماسی، ژیروید و I-WP اشاره کر­­د. از کاربردهای برجسته این سطوح می ‌توان به طراحی و ساخت سازه‌ های سبک، فیلتراسیون، عایق ‌ها، کاتالیزورها، جاذب ‌ها و همچنین کاربردهای پزشکی نظیر تولید استخوان‌ های مصنوعی و ایمپلنت ‌ها اشاره نمود. در این پژوهش خواص مکانیکی ساختارهای سه ‌بعدی که در اثر تکرار سلولهای واحد مینیمال ایجاد می ‌شوند نظیر استحکام و سفتی، همچنین قابلیت جذب انرژی، خستگی و دوام آن ها مورد بررسی قرار گرفته است. همچنین کاربردهای این سطوح در حوزه ‌های مهندسی پزشکی، سازه ‌ای، سیالات و انتقال حرارت و خودروسازی بررسی شده است. در ادامه روش ‌های شبیه ‌سازی و مدل سازی این سطوح که در المان محدود و پرینت سه ‌بعدی مورد نیاز است ارائه می ‌شود. سطوح مینیمال تکرار شونده به دلیل ویژگی‌ های منحصر به فرد خود از جمله فراهم نمودن نسبت سطح به حجم بالا و نسبت سفتی به وزن و استحکام به وزن بالا پتانسیل بالایی برای استفاده در حوزه‌ های مختلف صنعتی و پزشکی دارند و قابلیت این را دارند که در چارت ‌های انتخاب مواد، گزینه‌ های جدیدی را فرا روی پژوهشگران و مهندسان قرار دهند.
کلیدواژه‌ها

موضوعات


[1] W. Chen, L. Gan, and J. Huang, "Design, Manufacturing and Functions of Pore-Structured Materials: From Biomimetics to Artificial," Biomimetics (Basel), vol. 8, no. 2, Mar 29 2023, doi: https://doi.org/10.3390/biomimetics8020140.
 
[2] Z. Chen et al., "Understanding porous materials with pair distribution functions," Cell Reports Physical Science, vol. 4, no. 12, 2023, doi: https://doi.org/10.1016/j.xcrp.2023.101681.
 
[3] K. Yeranee and Y. Rao, "Triply Periodic Minimal Surfaces Thermal HydraulicEffects," encyclopedia.pub, 2022, doi: 10.3390/en15238994            https://encyclopedia.pub/entry/3918.
 
[4] S. Zou et al., "Mechanical and biological properties of enhanced porous scaffolds based on triply periodic minimal surfaces," Materials & Design, vol. 219, p. 110803, 2022, doi: https://doi.org/10.1016/j.matdes.2022.110803.
 
[5] M. Zhang, J. Li, C. Liu, M. Deng, X. Liao, and D. Wang, "Study on the Anisotropy of Triply Periodic Minimal Surface Porous Structures," Coatings, vol. 13, no. 7, p. 1206, 2023, doi: https://doi.org/10.3390/coatings13071206.
 
[6] H. Zhou, M. Zhao, Z. Ma, D. Z. Zhang, and G. Fu, "Sheet and network based functionally graded lattice structures manufactured by selective laser melting: Design, mechanical properties, and simulation," International Journal of Mechanical Sciences, vol. 175, p. 105480, 2020, doi: https://doi.org/10.1016/j.ijmecsci.2020.105480.
 
[7] C. Yan et al., "Design of TPMS structures," triply period. Minimal Surf Lattices Addit Manuf by Sel Laser Melting, Elsevier, pp. 27-38, 2021, doi: https://doi.org/10.1016/B978-0-12-824438-8.00002-9.
 
[8] M. Shen et al., "Mechanical properties of 3D printed ceramic cellular materials with triply periodic minimal surface architectures," Journal of the European Ceramic Society, vol. 41, no. 2, pp. 1481-1489, 2021, doi: https://doi.org/10.1016/j.jeurceramsoc.2020.09.062.
 
[9] O. Al-Ketan, R. K. A. Al-Rub, and R. Rowshan, "The effect of architecture on the mechanical properties of cellular structures based on the IWP minimal surface," Journal of Materials Research, vol. 33, no. 3, pp. 343-359, 2018, doi: https://doi.org/10.1557/jmr.2018.1.
 
[10]         A. Dadashi and G. Rahimi, "A comprehensive investigation of the lattice structure mechanical properties based on Schwarz Primitive triply periodic minimal surface: Elastic modulus, yield strength, and maximum bearing force in the elastic region," International Journal of Solids and Structures, vol. 295, p. 112776, 2024, doi: https://doi.org/10.1016/j.ijsolstr.2024.112776.
 
 
[11]         M. Teimouri, M. Mahbod, and M. Asgari, "Topology-optimized hybrid solid-lattice structures for efficient mechanical performance," in Structures, 2021, vol. 29: Elsevier, pp. 549-560, doi: https://doi.org/10.1016/j.istruc.2020.11.055.
 
[12]         K. A. Khan and R. K. Abu Al-Rub, "Viscoelastic properties of architected foams based on the Schoen IWP triply periodic minimal surface," Mechanics of advanced materials and structures, vol. 27, no. 10, pp. 775-788, 2020, doi: https://doi.org/10.1080/15376494.2018.1538470.
 
[13]         Y. Cui, A. K. Gain, L. Zhang, and Z. Li, "Manufacture and property characterization of interconnected pore-gradient TPMS materials," Materials Science and Engineering: A, vol. 892, p. 146100, 2024, doi: https://doi.org/10.1016/j.msea.2024.146100.
 
[14]         S. Hussain, A. Nazir, S. Waqar, U. Ali, and O. Gokcekaya, "Effect of additive manufactured hybrid and functionally graded novel designed cellular lattice structures on mechanical and failure properties," The International Journal of Advanced Manufacturing Technology, vol. 128, no. 11-12, pp. 4873-4891, 2023, doi: https://doi.org/10.1007/s00170-023-12201-7.
 
[15]         B. Sokollu, O. Gulcan, and E. I. Konukseven, "Mechanical properties comparison of strut-based and triply periodic minimal surface lattice structures produced by electron beam melting," Additive Manufacturing, vol. 60, p. 103199, 2022, doi: https://doi.org/10.1016/j.addma.2022.103199.
 
[16]         K. M. Gide and S. Bagheri, "Mechanical Behavior and Material Modeling of Fused Filament Fabricated PEEK based on TPMS Lattices: A Comparative Study," 2024, doi: https://doi.org/10.21203/rs.3.rs-4320202/v1.
 
[17]         X. Ma, C. Guo, C. Hu, Z. Zhang, and J. Shen, "Study on the topological morphology and mechanical properties of variable-amplitude TPMS structures," Journal of Materials Research and Technology, vol. 27, pp. 3459-3472, 2023, doi: https://doi.org/10.1016/j.jmrt.2023.10.164.
 
[18]         N. Novak et al., "High strain rate mechanical behaviour of uniform and hybrid metallic TPMS cellular structures," Thin-Walled Structures, vol. 191, p. 111109, 2023, doi: https://doi.org/10.1016/j.tws.2023.111109.
 
[19]         H. Nguyen-Xuan, K. Q. Tran, C. H. Thai, and J. Lee, "Modelling of functionally graded triply periodic minimal surface (FG-TPMS) plates," Composite Structures, vol. 315, p. 116981, 2023, doi: https://doi.org/10.1016/j.compstruct.2023.116981.
 
[20]         C. Iandiorio, G. Mattei, E. Marotta, G. Costanza, M. E. Tata, and P. Salvini, "The Beneficial Effect of a TPMS-Based Fillet Shape on the Mechanical Strength of Metal Cubic Lattice Structures," Materials, vol. 17, no. 7, p. 1553, 2024, doi: https://doi.org/10.3390/ma17071553.
 
[21]         M. Zhao, X. Li, D. Z. Zhang, and W. Zhai, "TPMS-based interpenetrating lattice structures: design, mechanical properties and multiscale optimization," International Journal of Mechanical Sciences, vol. 244, p. 108092, 2023, doi: https://doi.org/10.1016/j.ijmecsci.2022.108092.
 
[22]         M. Zhao, D. Z. Zhang, F. Liu, Z. Li, Z. Ma, and Z. Ren, "Mechanical and energy absorption characteristics of additively manufactured functionally graded sheet lattice structures with minimal surfaces," International Journal of Mechanical Sciences, vol. 167, p. 105262, 2020, doi: https://doi.org/10.1016/j.ijmecsci.2019.105262.
 
[23]         O. Al-Ketan, D.-W. Lee, R. Rowshan, and R. K. A. Al-Rub, "Functionally graded and multi-morphology sheet TPMS lattices: Design, manufacturing, and mechanical properties," Journal of the mechanical behavior of biomedical materials, vol. 102, p. 103520, 2020, doi: https://doi.org/10.1016/j.jmbbm.2019.103520.
 
[24]         A. I. Ansari, N. A. Sheikh, and N. Kumar, "Evaluation of the energy absorbing capacity of the two combinations of TPMS structure subjected to different compressive strain rates," Journal of the Brazilian Society of Mechanical Sciences and Engineering, vol. 46, no. 6, p. 334, 2024, doi: https://doi.org/10.1007/s40430-024-04925-8.
 
[25]         L. Bai et al., "Mechanical properties and energy absorption capabilities of functionally graded lattice structures: Experiments and simulations," International Journal of Mechanical Sciences, vol. 182, p. 105735, 2020, doi: https://doi.org/10.1016/j.ijmecsci.2020.105735.
 
 [26]        H. Zhou, M. Zhao, N. He, T. Zhang, X. Ma, and D. Z. Zhang, "Compressive response and energy absorption of additive manufactured Ti-6Al-4V triply periodic minimal surface honeycomb structure," Journal of Alloys and Compounds, p. 173744, 2024, doi: https://doi.org/10.1016/j.jallcom.2024.173744.
 
[27]         C. Zhang et al., "Mechanical responses of sheet-based gyroid-type triply periodic minimal surface lattice structures fabricated using selective laser melting," Materials & Design, vol. 214, p. 110407, 2022, doi: https://doi.org/10.1016/j.matdes.2022.110407.
 
 [28]        X. Ma, D. Z. Zhang, M. Zhao, J. Jiang, F. Luo, and H. Zhou, "Mechanical and energy absorption properties of functionally graded lattice structures based on minimal curved surfaces," The International Journal of Advanced Manufacturing Technology, pp. 1-14, 2022, doi: https://doi.org/10.1007/s00170-021-07768-y.
 
[29]         D. B. Alemayehu and M. Todoh, "Enhanced Energy Absorption in Bioinspired Combined TPMS-Gyroid and Walled TPMS-Gyroid Lattice Structure Manufactured via Fused Filament Fabrication (FFF)," 2024, doi: https://doi.org/10.20944/preprints202403.1003.v1.
 
[30]         Z. Fulong, P. Mingbo, L. Yanzhou, S. Liu, and W. Xi, "Parametric design and mechanical properties of TPMS porous structure," 2024, doi: https://doi.org/10.21203/rs.3.rs-3848979/v1.
 
[31]         P. Bunsri, S. Lophisarn, P. Jongpradist, S. Kongwat, and D. Watanabe, "Design parameter effects on crashworthiness of IWP and FRD in TPMS cellular structures," Journal of the Brazilian Society of Mechanical Sciences and Engineering, vol. 46, no. 2, p. 87, 2024, doi: https://doi.org/10.1007/s40430-023-04667-z.
 
[32]         L. Xiao, G. Shi, G. Feng, S. Li, S. Liu, and W. Song, "Large deformation response of a novel triply periodic minimal surface skeletal-based lattice metamaterial with high stiffness and energy absorption," International Journal of Solids and Structures, vol. 296, p. 112830, 2024, doi: https://doi.org/10.1016/j.ijsolstr.2024.112830.
 
[33]         H. Gharehbaghi, A. Farrokhabadi, and Z. Noroozi, "Introducing a new hybrid surface strut-based lattice structure with enhanced energy absorption capacity," Mechanics of Advanced Materials and Structures, vol. 31, no. 14, pp. 2955-2964, 2024, doi: https://doi.org/10.1080/15376494.2023.2167246.
 
[34]         A. R. Bernard and M. S. ElSayed, "Design, Manufacturing, and Analysis of Periodic Three-Dimensional Cellular Materials for Energy Absorption Applications: A Critical Review," Materials, vol. 17, no. 10, p. 2181, 2024, doi: https://doi.org/10.3390/ma17102181.
 
[35]         L. Yang et al., "Compression–compression fatigue behaviour of gyroid-type triply periodic minimal surface porous structures fabricated by selective laser melting," Acta Materialia, vol. 181, pp. 49-66, 2019, doi: https://doi.org/10.1016/j.actamat.2019.09.042.
 
[36]         G. Schultheiß, B. Heine, and M. Merkel, "Characterization of flexural fatigue behaviour of additively manufactured (PBF–LB) gyroid structures," Progress in Additive Manufacturing, pp. 1-10, 2024, doi: https://doi.org/10.1007/s40964-024-00607-y.
 
[37]         Y. Song et al., "Systematic study of the thermal and hydraulic characteristics of a heat exchanger based on the Schwartz-D structure for aviation application," International Communications in Heat and Mass Transfer, vol. 156, p. 107611, 2024, doi: https://doi.org/10.1016/j.icheatmasstransfer.2024.107611.
 
[38]         S. K. Sahoo, N. Saintier, and Y. Chemisky, "Exploration of the orientational-dependent fatigue response of triply periodic minimal surface cellular structures: A numerical study," Procedia Structural Integrity, vol. 57, pp. 375-385, 2024, doi: https://doi.org/10.1016/j.prostr.2024.03.040.
 
[39]         S. Seehanam, W. Chanchareon, and P. Promoppatum, "Assessing the effect of manufacturing defects and non-Newtonian blood model on flow behaviors of additively manufactured Gyroid TPMS structures," Heliyon, vol. 9, no. 5, 2023, doi: https://doi.org/10.1016/j.heliyon.2023.e15711.
 
[40]         L. Dong et al., "3D printing Al porous metamaterials with triply periodic minimal surfaces (TPMS) for hydrogen generation from Al-water reaction," International Journal of Hydrogen Energy, vol. 49, pp. 1426-1435, 2024, doi: https://doi.org/10.1016/j.ijhydene.2023.10.047.
 
[41]         E. H. Khogalia, H. L. Choo, and W. H. Yap, "Performance of triply periodic minimal surface lattice structures under compressive loading for tissue engineering applications," in AIP conference proceedings, 2020, vol. 2233, no. 1: AIP Publishing, doi: https://doi.org/10.1063/5.0001631.
 
[42]         S. Ibrahimi, L. D’Andrea, D. Gastaldi, M. W. Rivolta, and P. Vena, "Machine Learning approaches for the design of biomechanically compatible bone tissue engineering scaffolds," Computer Methods in Applied Mechanics and Engineering, vol. 423, p. 116842, 2024, doi: https://doi.org/10.1016/j.cma.2024.116842.
 
[43]         F. Günther et al., "Characterization of additively manufactured lumbar interbody fusion cages based on triply periodic minimal surfaces," Materials Today Communications, vol. 39, p. 108634, 2024, doi: https://doi.org/10.1016/j.mtcomm.2024.108634.
 
[44]         S. Seehanam, S. Khrueaduangkham, C. Sinthuvanich, U. Sae-Ueng, V. Srimaneepong, and P. Promoppatum, "Evaluating the effect of pore size for 3d-printed bone scaffolds," Heliyon, 2024, doi: https://doi.org/10.1016/j.heliyon.2024.e26005.
 
[45]         A. Dehaghani, Z. Javanbakht, M. Barzan, D. Lloyd, and S. Feih, "Multi‐Functional Design of TPMS‐Structures for Temporary Paediatric Fixation Devices," Advanced Engineering Materials, doi: https://doi.org/10.1002/adem.202400518.
 
[46]         Y.-Z. Chen, C.-H. Wang, T.-Y. Hsieh, C.-C. Tung, P.-Y. Chen, and T.-H. Huang, "An Efficient Parameterized Neural Network Enhanced Multiscale Finite Element Modeling for Triply Periodic Minimal Surface Meta-Structures and its Applications for Femur," Journal of Materials Research and Technology, 2024, doi: https://doi.org/10.1016/j.jmrt.2024.05.023.
 
[47]         M. Mamuti, L. Chao, and Z. Tian, "Analysis of mechanical characteristics and permeability of TPMS and Voronoi porous structure for bone scaffold," Computer Methods in Biomechanics and Biomedical Engineering, pp. 1-14, 2024, doi: https://doi.org/10.1080/10255842.2024.2358378.
 
[48]         N. Novak et al., "Compression behaviour of TPMS-filled stainless steel tubes," Materials Science and Engineering: A, vol. 852, p. 143680, 2022, doi: https://doi.org/10.1016/j.msea.2022.143680.
 
[49]         D. Lohuis, H. Traub, and C. Hühne, "Mechanical testing of threaded inserts for additively manufactured sandwich panels with Gyroid core structures," Results in Materials, p. 100543, 2024, doi: https://doi.org/10.1016/j.rinma.2024.100543.
 
[50]         Mirafazli, Seyed Mohammad Baqer, and Hassan Abadi, "Investigation of the energy absorption of the porous Schwarz Pi structure made by 3D printing method," Iran Construction and Production Engineering, vol. 9, no. 11, pp. 13-20, 2023, [In Persian] doi: https://doi.org/10.22034/IJME.2023.383269.1744.
 
[51]         M. Wan, D. Hu, H. Zhang, and Z. Zhang, "Energy absorption characteristics of TPMS-filled square tubes under quasi-static axial crushing," Thin-Walled Structures, vol. 199, p. 111811, 2024, doi: https://doi.org/10.1016/j.tws.2024.111811.
 
[52]         S.-H. Oh, C.-H. An, B. Seo, J. Kim, C. Y. Park, and K. Park, "Functional morphology change of TPMS structures for design and additive manufacturing of compact heat exchangers," Additive Manufacturing, vol. 76, p. 103778, 2023, doi: https://doi.org/10.1016/j.addma.2023.103778.
 
[53]         Z. A. Qureshi, S. A. B. Al-Omari, E. Elnajjar, O. Al-Ketan, and R. A. Al-Rub, "Using triply periodic minimal surfaces (TPMS)-based metal foams structures as skeleton for metal-foam-PCM composites for thermal energy storage and energy management applications," International Communications in Heat and Mass Transfer, vol. 124, p. 105265, 2021, doi: https://doi.org/10.1016/j.icheatmasstransfer.2021.105265.
 
[54]         M. G. Gado, S. Ookawara, S. Nada, M. F. Elkady, and H. Hassan, "Adsorbent beds packed in triply periodic minimal surface-derived structures and their performance in adsorption desalination/cooling systems," International Communications in Heat and Mass Transfer, vol. 150, p. 107205, 2024, doi: https://doi.org/10.1016/j.icheatmasstransfer.2023.107205.
 
[55]         G. Brambati, M. Guilizzoni, and S. Foletti, "Convective heat transfer correlations for Triply Periodic Minimal Surfaces based heat exchangers," Applied Thermal Engineering, vol. 242, p. 122492, 2024, doi: https://doi.org/10.1016/j.applthermaleng.2024.122492.
 
[56]         W. Huang et al., "Thermal-hydraulic performance of TPMS-based regenerators in combined cycle aero-engine," Applied Thermal Engineering, p. 123510, 2024, doi: https://doi.org/10.1016/j.applthermaleng.2024.123510.
 
[57]         G. Yan et al., "Thermal-hydraulic performance of modified Schwartz-Diamond solid-networks triply periodic minimal surface structures," Applied Thermal Engineering, p. 123384, 2024, doi: https://doi.org/10.1016/j.applthermaleng.2024.123384.
 
[58]         I. El Khadiri, M. Abouelmajd, M. Zemzami, N. Hmina, M. Lagache, and S. Belhouideg, "Comprehensive analysis of flow and heat transfer performance in triply periodic minimal surface (TPMS) heat exchangers based on Fischer-Koch S, PMY, FRD, and Gyroid structures," International Communications in Heat and Mass Transfer, vol. 156, p. 107617, 2024, doi: https://doi.org/10.1016/j.icheatmasstransfer.2024.107617.
 
[59]         S. Ormiston and S. Srinivas Sundarram, "Fiberglass‐reinforced triply periodic minimal surfaces (TPMS) lattice structures for energy absorption applications," Polymer Composites, vol. 45, no. 1, pp. 523-534, 2024, doi: https://doi.org/10.1002/pc.27795.
 
[60]         X. Zhao, Z. Li, Y. Zou, and X. Zhao, "Compressive Characteristics and Energy Absorption Capacity of Automobile Energy-Absorbing Box with Filled Porous TPMS Structures," Applied Sciences, vol. 14, no. 9, p. 3790, 2024, doi: https://doi.org/10.3390/app14093790.
 
[61]         D.-Y. Kim, H.-S. Kim, S. S. Kamath, X. Hou, J.-W. Choi, and S.-H. Park, "TPMS-based auxetic structure for high-performance airless tires with variable stiffness depending on deformation," Scientific Reports, vol. 14, no. 1, p. 11419, 2024, doi: https://doi.org/10.1038/s41598-024-62101-3.
 
[62]         Z. Hooshmand-Ahoor, H. Luo, and K. Danas, "M-Voronoi and other random open and closed-cell elasto-plastic cellular materials: Geometry generation and numerical study at small and large strains," International Journal of Solids and Structures, vol. 290, p. 112680, 2024, doi: https://doi.org/10.1016/j.ijsolstr.2024.112680.
 
[63]         M.-T. Hsieh and L. Valdevit, "Minisurf–A minimal surface generator for finite element modeling and additive manufacturing," Software Impacts, vol. 6, p. 100026, 2020, doi: https://doi.org/10.1016/j.simpa.2020.100026.
 
 [64]        G. Chouhan and B. Gunji, "Additive manufacturing TPMS lattice structures: Experimental study on airflow resistivity," Results in Materials, vol. 20, p. 100478, 2023, doi: https://doi.org/10.1016/j.rinma.2023.100478.
 
[65]         C. Lu, L. A. Lesmana, F. Chen, and M. Aziz, "MD-TPMS: Multi-dimensional gradient minimal surface generator," Software Impacts, vol. 17, p. 100527, 2023, doi: https://doi.org/10.1016/j.simpa.2023.100527.
 
[66]         A. Hassan Abadi, "Designing the microstructure of heterogeneous materials using polygonal callus," 1400. [Online]. Available: [In Persian] https://www.iranjme.ir/article_131941.html.
 
[67]         K. Q. Tran, T.-D. Hoang, J. Lee, and H. Nguyen-Xuan, "Three novel computational modeling frameworks of 3D-printed graphene platelets reinforced functionally graded triply periodic minimal surface (GPLR-FG-TPMS) plates," Applied Mathematical Modelling, vol. 126, pp. 667-697, 2024, doi: https://doi.org/10.1016/j.apm.2023.10.043.
 
[68]         M. Afshar, A. P. Anaraki, and H. Montazerian, "Compressive characteristics of radially graded porosity scaffolds architectured with minimal surfaces," Materials Science and Engineering: C, vol. 92, pp. 254-267, 2018, doi: https://doi.org/10.1016/j.msec.2018.06.051.
 
[69]         A. Hasanabadi, "Construction of Porous Multiscale Heterogeneous Microstructures using Statistical Correlation Functions and Minimal Surfaces," Journal of Solid Mechanics, vol. 14, no. 4, pp. 491-498, 2022, doi: https://doi.org/10.22034/jsm.2021.1921437.1674.
 
 
 
 
 
 
 
 
 
 
 
 
 
دوره 33، شماره 3 - شماره پیاپی 156
مرداد و شهریور 1403
صفحه 58-85

  • تاریخ دریافت 27 اردیبهشت 1403
  • تاریخ بازنگری 01 تیر 1403
  • تاریخ پذیرش 16 تیر 1403