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A Study of the Mechanical Properties of Materials with the Tpmes Topology by Computer Simulation

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Abstract

In this paper, the physical and mechanical properties of products with the geometry of a triply periodic minimal energy surfaces (TPMES) are studied by computer simulation. The calculations are performed by the FEN method (hyperelastic viscoplastic fracture with a finite deformation) for typical samples of polyamide-12 material obtained by selective laser sintering (SLS). As a result of the study using the Comsol Multiphysics program, the distribution of mechanical stresses and the appearance of deformed products at various values of the applied mechanical stress, as well as the deformation curves, were obtained. The convergence of the calculations on the mesh size of the model under study is shown. The simulation results are in close agreement with the experimental data. As a result of the study, excellent physical and mechanical characteristics of the samples with the proposed geometry are found.

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REFERENCES

  1. Bieri-Gross, B. and Nesper, R., Topological modeling of reconstructive phase transitions through periodic surfaces: Tin dioxide I–A calcium chloride to palladium fluoride type transition, Z. Anorg. Allgem. Chem., 2015, vol. 641, pp. 1503–1509.

    Article  CAS  Google Scholar 

  2. Makogon A.I., Shevchenko V.Ya., and Sychov M.M., Modeling of reaction-diffusion processes of synthesis of materials with regular (periodic) microstructure, Open Ceram., 2021, in press.

  3. Bieri-Gross, B. and Nesper, R., Topological modeling of reconstructive phase periodic hyperbolic surfaces: The β-quartz to keatite type transition, Zeitschr. Kristallogr., 2011, vol. 226, pp. 670–677.

    Article  CAS  Google Scholar 

  4. Shevchenko, V.Ya., Topological forms of future of structural chemistry of new substances and materials, Tr. Kol’sk. Nauch. Tsentra RAN, 2018, vol. 9, no. 2-1, pp. 109–114.

  5. Zürn, A. and Shnering, H.G., Topological analysis of mesoporous solids and their ordered pore structures by periodic nodal surfaces, Z. Anorg. Allgem. Chem., 2008, vol. 634, pp. 2761–2764.

    Article  CAS  Google Scholar 

  6. Leoni, S. and Nesper, R., Elucidation of simple pathways for reconstructive phase transitions using periodic equi-surfaces (PES) descriptors. II. The strontium disilicide transition, Solid State Sci., 2003, vol. 5, pp. 95–107.

    Article  CAS  Google Scholar 

  7. Nesper, R. and Leoni, S., On tilings and patterns on hyperbolic surfaces and their relation to structural chemistry, ChemPhysChem, 2001, vol. 2, pp. 413–422.

    Article  CAS  Google Scholar 

  8. Shevchenko, V.Ya., Koval’chuk, M.V., Oryshchenko, A.S., and Perevislov, S.N., New chemical technologies based on reactive-diffusion turing processes, Dokl. Akad. Nauk, Khim. Nauki Mater., 2021, vol. 496, no. 1, pp. 25–29.

    Google Scholar 

  9. Shevchenko, V.Ya., What is a chemical substance and how it is formed?, Struct. Chem., 2012, vol. 23, no. 4, pp. 1089–1101.

    Article  CAS  Google Scholar 

  10. Von Shnering, H.G. and Nesper, R., How nature adapts chemical structures to curved surfaces, Angew. Chem., Int. Ed., 1987, vol. 26, no. 11, pp. 1059–1200.

    Article  Google Scholar 

  11. Andersson, S., Hyde, S.T., Larsson, K., and Lidin, S., Minimal surfaces and structures: From inorganic and metal crystals to cell membranes and biopolymers, Chem. Rev., 1988, vol. 88, no. 1, pp. 221–242.

    Article  CAS  Google Scholar 

  12. Andersson, S., Hyde, S.T., and von Schnering, H.G., The intrinsic curvature of solids, Zeitschr. Kristallogr., 1984, vol. 168, nos. 1–4, pp. 1–17.

    Article  CAS  Google Scholar 

  13. von Shnering, H.G. and Nesper, R., Nodal surfaces of Fourier series: Fundamental invariants of structured matter, Zeitschr. Phys., B, 1991, vol. 83, pp. 407–412.

  14. Mackay, A.L., Crystallographic surfaces, Proc. R. Soc. London, Ser. A, 1993, vol. 442, no. 1914, pp. 47–59.

  15. Schwarz, H.A., Gesammelte mathematische Abhandlungen, Berlin: Springer, 1933, pp. 1843–1921.

    Google Scholar 

  16. Han, L. and Che, S., An overview of materials with triply periodic minimal surfaces and related geometry: From biological structures to self-assembled systems, Adv. Mater., 2018, vol. 30, no. 17, pp. 0935–9648.

  17. Thomsen, P., Malmström, J., Emanuelsson, L., René, M., and Snis, A., Electron beam-melted, free-form-fabricated titanium alloy implants: Material surface characterization and early bone response in rabbits, J. Biomed. Mater. Res. B, 2009, vol. 90, no. 1, pp. 35–44.

    Google Scholar 

  18. Tancogne-Dejean, T., Spierings, A.B., and Mohr, D., Additively-manufactured metallic micro-lattice materials for high specific energy absorption under static and dynamic loading, Acta Mater., 2016, vol. 116, pp. 14–28.

    Article  CAS  Google Scholar 

  19. Leitlmeier, D., Degischer, H.P., and Flankl, H.J., Development of a foaming process for particulate reinforced aluminum melts, Adv. Eng. Mater., 2002, vol. 4, no. 10, pp. 735–740.

    Article  CAS  Google Scholar 

  20. Wang, Z., Jiao, X., Feng, P., Wang, X., Liu, Z., and Akhtar, F., Highly porous open cellular TiAl-based intermetallics fabricated by thermal explosion with space holder process, Intermetallics, 2016, vol. 68, pp. 95–100.

    Article  CAS  Google Scholar 

  21. Korner, C. and Singer, R.F., Processing of metal foams-challenges and opportunities, Adv. Eng. Mater., 2000, vol. 2, no. 4, pp. 159–165.

    Article  CAS  Google Scholar 

  22. Ducheyne, P. and Martens, M., Orderly oriented wire meshes as porous coatings on orthopaedic implants I: Morphology, Clin. Mater., 1986, vol. 1, no. 1, pp. 59–67.

    Article  Google Scholar 

  23. Tancogne-Dejean, T., Spierings, A.B., and Mohr, D., Additively-manufactured metallic micro-lattice materials for high specific energy absorption under static and dynamic loading, Acta Mater., 2016, vol. 116, pp. 14–28.

    Article  CAS  Google Scholar 

  24. Yang, L., Harrysson, O., West, H., and Cormier, D., Compressive properties of Ti6Al4V auxetic mesh structures made by electron beam melting, Acta Mater., 2012, vol. 60, no. 8, pp. 3370–3379.

    Article  CAS  Google Scholar 

  25. Van Bael, S., Chai, Y.C., Truscello, S., Moesen, M., Kerckhofs, G., van Oosterwyck, H., Kruth, J.-P., and Schrooten, J., The effect of pore geometry on the in vitro biological behavior of human periosteum-derived cells seeded on selective laser-melted Ti6Al4V bone scaffolds, Acta Biomater., 2012, vol. 8, no. 7, pp. 2824–2834.

    Article  CAS  Google Scholar 

  26. Bartolo, P., Kruth, J.-P., Silva, J., Levy, G., Malshe, A., Rajurkar, K., Mitsuishi, M., Ciurana, J., and Leu, M., Biomedical production of implants by additive electro-chemical and physical processes, Cirp Ann.-Manuf. Technol., 2012, vol. 61, no. 2, pp. 635–655.

    Article  Google Scholar 

  27. McKown, S., Shen, Y., Brookes, W.K., Sutcliffe, C.J., Cantwell, W.J., Langdon, G.S., Nurick, G.N., and Theobald, M.D., The quasi-static and blast loading response of lattice structures, Int. J. Impact Eng., 2008, vol. 35, no. 8, pp. 795–810.

    Article  Google Scholar 

  28. Yan, C., Hao, L., Hussein, A., Wei, Q., and Shi, Y., Microstructural and surface modifications and hydroxyapatite coating of Ti6Al4V triply periodic minimal surface lattices fabricated by selective laser melting, Mater. Sci. Eng. C, 2017, vol. 75, pp. 1515–1524.

    Article  CAS  Google Scholar 

  29. Olakanmi, E.O., Cochrane, R.F., and Dalgarno, K.W., A review on selective laser sintering/melting (SLS/SLM) of aluminium alloy powders: Processing, microstructure, and properties, Prog. Mater. Sci., 2015, vol. 74, pp. 401–477.

    Article  CAS  Google Scholar 

  30. Bergstrom, J.S., Mechanics of Solid Polymers: Theory and Computational Modeling, Amsterdam: William Andrew, Elsevier, 2015, p. 520.

  31. Abueidda, D.W., Bakir, M., Abu Al-Rub, R.K.B., Jörgen, S., Sobh, N.A., and Jasiuk, I., Mechanical properties of 3D printed polymeric cellular materials with triply periodic minimal surface architectures, Mater.Des., 2017, vol. 122, pp. 255–267.

    Article  CAS  Google Scholar 

  32. Bergström, J., PolyUMod User’s Manual, Needham, MA: Veryst Engineering, 2009, p. 7.

    Google Scholar 

  33. Abou-Ali, A.M., Al-Ketan, O., Lee, D.-W., Rowshan, R., and Abu Al-Rub, R.K., Mechanical behavior of polymeric selective laser sintered ligament and sheet based lattices of triply periodic minimal surface architectures, Mater. Des., 2020, vol. 196, p. 109100.

    Article  CAS  Google Scholar 

  34. Montazerian, H., Davoodi, E., Asadi-Eydivand, M., Kadkhodapour, J., and Solati-Hashjin, M., Porous scaffold internal architecture design based on minimal surfaces: A compromise between permeability and elastic properties, Mater. Des., 2017, vol. 126, pp. 98–114.

    Article  CAS  Google Scholar 

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Funding

The study of the mechanical properties of structures and the development of topologies were financially supported by the Russian Science Foundation (project no. 20-73-10171). The development of a technique for modeling mechanical properties was carried out as part of a state assignment of the Institute of Chemistry of the Russian Academy of Sciences (state registration number of the topic, AAAA-A19-119022290092-5).

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  1. Grebenshchikov Institute of Silicate Chemistry, Russian Academy of Sciences, 199034, St. Petersburg, Russia

    M. Yu. Arsentiev, E. I. Sysoev & S. V. Balabanov

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  1. M. Yu. Arsentiev
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  2. E. I. Sysoev
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  3. S. V. Balabanov
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Correspondence to M. Yu. Arsentiev.

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Arsentiev, M.Y., Sysoev, E.I. & Balabanov, S.V. A Study of the Mechanical Properties of Materials with the Tpmes Topology by Computer Simulation. Glass Phys Chem 47, 496–501 (2021). https://doi.org/10.1134/S1087659621050047

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  • DOI: https://doi.org/10.1134/S1087659621050047

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