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Additive manufacturing has made it possible to create complicated geometries and lattice structures, and it is also the greatest approach for producing nature-inspired cellular structures. Triply periodic minimal surface (TPMS) cellular structure, which is additively built, has a high strength-to-weight ratio, making it useful in various applications, including structural weight reduction, biomedical, aerospace, and impact absorption. TPMS is a natural-inspired surface with zero mean curvature and a local minimal area. The type of structure, loading mechanism, unit cell characteristics, and relative density significantly affect the structure’s strength and stiffness. As a result, this article will cover the history, classification, characteristics, manufacturing processes, failure mechanism, and applications of the TPMS.

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TPMS, Cellular Structures, Gyroid, Primitive, Additive Manufacturing.

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Abou-Ali, A. M., Al-Ketan, O., Lee, D. W., Rowshan, R., & Abu Al-Rub, R. K. (2020). Mechanical behaviour of polymeric selective laser sintered ligament and sheet based lattices of triply periodic minimal surface architectures. Materials & Design, 196, 109100. https:/ /doi.org/10.1016/J.MATDES.2020.109100

Abueidda, D. W., Bakir, M., Abu Al-Rub, R. K., Bergström, J. S., Sobh, N. A., & Jasiuk, I. (2017). Mechanical properties of 3D printed polymeric cellular materials with triply periodic minimal surface architectures. Materials and Design, 122, 255–267. https://doi.org/10.1016/J.MATDES.2017.03.018

Abueidda, D. W., Elhebeary, M., Shiang, C. S. (Andrew), Pang, S., Abu Al-Rub, R. K., & Jasiuk, I. M. (2019). Mechanical properties of 3D printed polymeric Gyroid cellular structures: Experimental and finite element study. Materials & Design,165, 107597. https://doi.org/10.1016/J.MATDES.2019.107597

Al-Ketan, O., & Abu Al-Rub, R. K. (2019). Multifunctional Mechanical Metamaterials Based on Triply Periodic Minimal Surface Lattices. Advanced Engineering Materials, 21(10), 1900524. https:// doi.org/10.1002/ADEM.201900524

Al-Ketan, O., Rowshan, R., & Abu Al-Rub, R. K. (2018). Topology-mechanical property relationship of 3D printed strut, skeletal, and sheet based periodic metallic cellular materials. Additive Manufacturing, 19, 167–183. https://doi.org/10.1016/J.ADDMA. 2017.12.006

Ashby, M. F. (2000). Metal foams/ : a design guide. 251.

Ashby, M. F. (2005a). The properties of foams and lattices. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences,364(1838), 15–30. https://doi.org/10.1098/ RSTA.2005.1678

Ashby, M. F. (2005b). The properties of foams and lattices. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 364(1838), 15–30. https://doi.org/10.1098/ RSTA.2005.1678

Barba, D., Alabort, E., & Reed, R. C. (2019). Synthetic bone: Design by additive manufacturing. Acta Biomaterialia, 97, 637–656. https://doi.org/10.1016/ J.ACTBIO.2019.07.049

Benedetti, M., du Plessis, A., Ritchie, R. O., Dallago, M., Razavi, S. M. J., & Berto, F. (2021). Architected cellular materials: A review on their mechanical properties towards fatigue-tolerant design and fabrication. Materials Science and Engineering: R: Reports, 144, 100606. https://doi.org/10.1016/J. MSER. 2021.100606

Bobbert, F. S. L., Lietaert, K., Eftekhari, A. A., Pouran, B., Ahmadi, S. M., Weinans, H., & Zadpoor, A. A. (2017a). Additively manufactured metallic porous biomaterials based on minimal surfaces: A unique combination of topological, mechanical, and mass transport properties. Acta Biomaterialia, 53, 572–584. https://doi.org/10.1016/J.ACTBIO.2017.02.024

Bobbert, F. S. L., Lietaert, K., Eftekhari, A. A., Pouran, B., Ahmadi, S. M., Weinans, H., & Zadpoor, A. A. (2017b). Additively manufactured metallic porous biomaterials based on minimal surfaces: A unique combination of topological, mechanical, and mass transport properties. Acta Biomaterialia, 53, 572–584. https://doi.org/10.1016/J.ACTBIO.2017.02.024

Brennan-Craddock, J., Brackett, D., Wildman, R., & Hague, R. (2012). The design of impact absorbing structures for additive manufacture. Journal of Physics: Conference Series,382(1). https://doi.org/ 10.1088/1742-6596/382/1/012042

Burton, H. E., Eisenstein, N. M., Lawless, B. M., Jamshidi, P., Segarra, M. A., Addison, O., Shepherd, D. E. T., Attallah, M. M., Grover, L. M., & Cox, S. C. (2019). The design of additively manufactured lattices to increase the functionality of medical implants. Materials Science & Engineering. C, Materials for Biological Applications, 94, 901–908. https://doi.org/ 10.1016/J.MSEC.2018.10.052

Chen, H., Han, Q., Wang, C., Liu, Y., Chen, B., & Wang, J. (2020). Porous Scaffold Design for Additive Manufacturing in Orthopedics: A Review. Frontiers in Bioengineering and Biotechnology, 8, 609. https:// doi.org/10.3389/FBIOE.2020.00609/BIBTEX

Chen, H. Y., Kwon, Y., & Thornton, K. (2009). Multifunctionality of three-dimensional self-assembled composite structure. Scripta Materialia, 1(61), 52–55. https://doi.org/10.1016/J.SCRIPTAMAT.2009.03.006

du Plessis, A., Razavi, S. M. J., Benedetti, M., Murchio, S., Leary, M., Watson, M., Bhate, D., & Berto, F. (2022a). Properties and applications of additively manufactured metallic cellular materials: A review. Progress in Materials Science,125, 100918. https:// doi.org/10.1016/J.PMATSCI.2021.100918

du Plessis, A., Razavi, S. M. J., Benedetti, M., Murchio, S., Leary, M., Watson, M., Bhate, D., & Berto, F. (2022b). Properties and applications of additively manufactured metallic cellular materials: A review. Progress in Materials Science, 125, 100918. https:// doi.org/10.1016/J.PMATSCI.2021.100918

Echeta, I., Feng, X., Dutton, B., Leach, R., & Piano, S. (2019). Review of defects in lattice structures manufactured by powder bed fusion. The International Journal of Advanced Manufacturing Technology 2019 106:5, 106(5), 2649–2668. https://doi.org/10.1007/ S00170-019-04753-4

Feng Lu, W., Zhang, L., Feih, S., Daynes, S., Chang, S., Yu Wang, M., & Wei, J. (2018). Energy absorption characteristics of metallic triply periodic minimal surface sheet structures under compressive loading. 23, 505–515.

Frazier, W. E. (2014). Metal additive manufacturing: A review. Journal of Materials Engineering and Performance, 23(6), 1917–1928. https://doi.org/10.1007/ S11665-014-0958-Z/FIGURES/9

Gandy, P. J. F., & Klinowski, J. (2002). Nodal Surface Approximations to the Zero Equipotential Surfaces for Cubic Lattices. Journal of Mathematical Chemistry 200231:1, 31(1), 1–16. https://doi.org/10.1023/ A:1015444012997

Grasso, M., & Colosimo, B. M. (n.d.). Process defects and in situ monitoring methods in metal powder bed fusion: A review Grasso, MARCO LUIGI; Colosimo, BIANCA MARIA Process Defects and In-situ Monitoring Methods in Metal Powder Bed Fusion: a Review. https://doi.org/10.1088/1361-6501/aa5c4f

Guo, N., & Leu, M. C. (2013a). Additive manufacturing: Technology, applications and research needs. Frontiers of Mechanical Engineering, 8(3), 215–243. https://doi.org/10.1007/S11465-013-0248-8

Guo, N., & Leu, M. C. (2013b). Additive manufacturing: Technology, applications and research needs. Frontiers of Mechanical Engineering, 8(3), 215–243. https://doi.org/10.1007/S11465-013-0248-8

Han, S. C., Lee, J. W., & Kang, K. (2015). A New Type of Low Density Material: Shellular. Advanced Materials, 27(37), 5506–5511. https://doi.org/10.1002/ ADMA.201501546

Infinite periodic minimal surfaces without self-intersections - NASA Technical Reports Server (NTRS). (n.d.-a). Retrieved May 10, 2022, from https:/ /ntrs.nasa.gov/citations/19700020472

Infinite periodic minimal surfaces without self-intersections - NASA Technical Reports Server (NTRS). (n.d.-b). Retrieved May 10, 2022, from https:/ /ntrs.nasa.gov/citations/19700020472

ISO - ISO 13314:2011 - Mechanical testing of metals – Ductility testing – Compression test for porous and cellular metals. (n.d.). Retrieved May 10, 2022, from https://www.iso.org/standard/53669.html

Khan, S. Z., Masood, S. H., Ibrahim, E., & Ahmad, Z. (2019). Compressive behaviour of Neovius Triply Periodic Minimal Surface cellular structure manufactured by fused deposition modelling. Https:// Doi.Org/10.1080/17452759.2019.1615750, 14(4), 360– 370. https://doi.org/10.1080/17452759.2019.1615750

Lai, M., Kulak, A. N., Law, D., Zhang, Z., Meldrum, F. C., & Riley, D. J. (2007). Profiting from nature: macroporous copper with superior mechanical properties. Chemical Communications, 34, 3547–3549. https://doi.org/10.1039/B707469G

Leary, M., Mazur, M., Williams, H., Yang, E., Alghamdi, A., Lozanovski, B., Zhang, X., Shidid, D., Farahbod-Sternahl, L., Witt, G., Kelbassa, I., Choong, P., Qian, M., & Brandt, M. (2018). Inconel 625 lattice structures manufactured by selective laser melting (SLM): Mechanical properties, deformation and failure modes. Materials and Design, 157, 179–199. https://doi.org/ 10.1016/J.MATDES.2018.06.010

Medical Implants Market Size | Industry Forecast by 2027. (n.d.). Retrieved May 10, 2022, from https:// www.alliedmarketresearch.com/medical-implants-market

Miralbes, R., Ranz, D., Pascual, F. J., Zouzias, D., & Maza, M. (2020). Characterization of additively manufactured triply periodic minimal surface structures under compressive loading. Https://Doi.Org/10.1080/ 15376494.2020.1842948. https://doi.org/10.1080/ 15376494.2020.1842948

Mohamed, O. A., Masood, S. H., & Bhowmik, J. L. (2017). Experimental investigation of time-dependent mechanical properties of PC-ABS prototypes processed by FDM additive manufacturing process. Materials Letters, C(193), 58–62. https://doi.org/ 10.1016/J.MATLET.2017.01.104

Multi-Jet Fluid Deposition In 3D Printing: A Review. (n.d.). Retrieved May 10, 2022, from https:// www.jetir.org/view?paper=JETIRA006021

Park, S. Y., Kim, K. S., AlMangour, B., Grzesiak, D., & Lee, K. A. (2021). Effect of unit cell topology on the tensile loading responses of additive manufactured CoCrMo triply periodic minimal surface sheet lattices. Materials & Design, 206, 109778. https://doi.org/ 10.1016/J.MATDES.2021.109778

Paufler, P. (1990). L. L. Gibson, M. F. Ashby. Cellular solids. Structure & properties. Pergamon Press, Oxford 1988. IX + 357 p. Preis $ 40.00. ISBN 0-08-036607-4. Crystal Research and Technology, 25(9), 1038–1038. https://doi.org/10.1002/CRAT.2170250912

Pham, D. T., & Dimov, S. S. (2001). Rapid Manufacturing. https://doi.org/10.1007/978-1-4471-0703-3

Poladian, L., Wickham, S., Lee, K., & Large, M. C. J. (2008). Iridescence from photonic crystals and its suppression in butterfly scales. Journal of The Royal Society Interface, 6(SUPPL. 2). https://doi.org/10.1098/ RSIF.2008.0353.FOCUS

Rapid Prototyping - Selective Laser Sintering (SLS). (n.d.). Retrieved May 10, 2022, from https:// www.custompartnet.com/wu/selective-laser-sintering

Rashed, M. G., Ashraf, M., Mines, R. A. W., & Hazell, P. J. (2016). Metallic microlattice materials: A current state of the art on manufacturing, mechanical properties and applications. Materials and Design, 95, 518–533. https://doi.org/10.1016/J.MATDES. 2016.01.146

Riemer, A., Leuders, S., Thöne, M., Richard, H. A., Tröster, T., & Niendorf, T. (2014). On the fatigue crack growth behaviour in 316L stainless steel manufactured by selective laser melting. Engineering Fracture Mechanics,120, 15–25. https://doi.org/10.1016/ J.ENGFRACMECH.2014.03.008

Schmidt, M., Merklein, M., Bourell, D., Dimitrov, D., Hausotte, T., Wegener, K., Overmeyer, L., Vollertsen, F., & Levy, G. N. (2017). Laser based additive manufacturing in industry and academia. CIRP Annals - Manufacturing Technology,2(66), 561–583. https:// doi.org/10.1016/J.CIRP.2017.05.011

Schwarz, H. A. 1843-1921. (2005). Gesammelte mathematische Abhandlungen, von H. A. Schwarz. http://name.umdl.umich.edu/AAT0607.0001.001

Sharma, D., & Hiremath, S. S. (2021). Additively manufactured mechanical metamaterials based on triply periodic minimal surfaces: Performance, challenges, and application. Https://Doi.Org/10.1080/ 15376494.2021.1948151. https://doi.org/10.1080/ 15376494.2021.1948151

Standard Terminology for Additive Manufacturing Technologies,. (n.d.). Retrieved May 10, 2022, from https://www.astm.org/f2792-12.html

Tafazoli, M., & Nouri, M. D. (2020). Investigation of the experimental, statistical and optimisation of 3D printed lattice core sandwich panel energy absorber with novel configuration using response surface method. Https://Doi.Org/10.1080/ 13588265.2020.1786913, 1–12. https://doi.org/10.1080/ 13588265.2020.1786913

Torquato, S., & Donev, A. (2004). Minimal surfaces and multifunctionality. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 460(2047), 1849–1856. https://doi.org/10.1098/ RSPA.2003.1269

Travitzky, N., Bonet, A., Dermeik, B., Fey, T., Filbert-Demut, I., Schlier, L., Schlordt, T., & Greil, P. (2014). Additive Manufacturing of Ceramic-Based Materials. Advanced Engineering Materials,16(6), 729–754. https://doi.org/10.1002/ADEM.201400097

Utela, B., Storti, D., Anderson, R., & Ganter, M. (2008). A review of process development steps for new material systems in three dimensional printing (3DP). Journal of Manufacturing Processes, 10, 96–104. https://doi.org/10.1016/j.jmapro.2009.03.002

Wang, L., Lau, J., Thomas, E. L., & Boyce, M. C. (2011). Co-Continuous Composite Materials for Stiffness, Strength, and Energy Dissipation. Advanced Materials, 23(13), 1524–1529. https://doi.org/10.1002/ ADMA.201003956

Wang, X., Wang, C., Zhou, X., Zhang, M., Zhang, P., & Wang, L. (2020). Innovative design and additive manufacturing of regenerative cooling thermal protection system based on the triply periodic minimal surface porous structure. CMES - Computer Modeling in Engineering and Sciences, 123(2), 495–508. https:// doi.org/10.32604/CMES.2020.09778

Yan, C., Hao, L., Hussein, A., Young, P., & Raymont, D. (2014). Advanced lightweight 316L stainless steel cellular lattice structures fabricated via selective laser melting. Materials and Design, 55, 533–541. https:// doi.org/10.1016/J.MATDES.2013.10.027

Zhou, J., Shrotriya, P., & Soboyejo, W. O. (2004). On the deformation of aluminum lattice block structures: from struts to structures. Mechanics of Materials, 36(8), 723–737. https://doi.org/10.1016/ J.MECHMAT.2003.08.007

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Gupta, Arpit

Triply Periodic Minimal Surfaces: An Overview of Their Features, Failure Mechanisms, and Applications

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