Article

Cover

Title

Designing, manufacturing and mechanical tests of lattice structures based on triply periodic minimal surface

Authors

¹D.V. Sorokin, ²E.V. Moskvichev

Organizations

¹Reshetnev Siberian State University of Science and Technology
Krasnoyarsk, The Russian Federation
²Federal Research Center for Information and Computational Technologies
Krasnoyarsk, The Russian Federation

Abstract

In recent decades Triply Periodic Minimal Surfaces have attracted significant research interest in many fields, such as automotive, aerospace, chemical industry, medicine, biomaterials and others. Cellular structures obtained from such surfaces have broad capabilities in tuning physical and mechanical properties to create new materials and structural elements. In this work, the authors examine the main issues of modeling cellular structures such as Gyroid, Schwarz Primitive, I-WP (I-graph-wrapped package) and Schwarz Diamond. For two selected types of cellular structures, Gyroid and I-WP, the range of parameters affecting the relative density (volume fraction) of the material in a cubic unit cell was investigated. Based on the unit cell, geometric models of specimens with a periodically repeating structure were created for mechanical testing. The specimens were manufactured on a 3D printer and tested for compression until failure while recording load diagrams and displacements of specimens points. Experimental studies led to the conclusion that the mechanical properties of the specimens significantly depend on the relative density (volume fraction) of the unit cell. Controlling the relative density can be useful for achieving the required mechanical properties of designed materials and structural elements with unique properties.

Keywords

triply periodic minimal surfaces, cells, lattice structures, 3D printing, additive technologies, mechanical tests

References

[1] Zhou X., Ren L., Song Z., Li G., Zhang J., Li B., Wu Q., Li W., Ren L., Liu Q. Advances in 3D/4D printing of mechanical metamaterials: From manufacturing to applications // Composites Part B: Engineering, 2023, vol. 254. DOI 10.1016/j.compositesb.2023.110585

[2] Miao X., Hu J., Xu Y., Su J., Jing Y. Review on mechanical properties of metal lattice structures // Composite Structures, 2024, vol. 342. DOI 10.1016/j.compstruct.2024.118267

[3] Wu Y., Fang J., Wu C., Li C., Sun G., Li Q. Additively manufactured materials and structures: A state-of-the-art review on their mechanical characteristics and energy absorption // International Journal of Mechanical Sciences, 2023, vol. 246. DOI 10.1016/j.ijmecsci.2023.108102

[4] Vyavahare S., Mahesh V., Mahesh V., Harursampath D. Additively manufactured meta-biomaterials: A state-of-the-art review // Composite Structures, 2023, vol. 305. DOI 10.1016/j.compstruct.2022.116491

[5] Li Z., Chen Z., Chen X., Zhao R. Design and evaluation of TPMS-inspired 3D-printed scaffolds for bone tissue engineering: Enabling tailored mechanical and mass transport properties // Composite Structures, 2024, vol. 327. DOI 10.1016/j.compstruct.2023.117638

[6] Xie H., Chen J., Liu F., Wang R., Tang Y., Wang Y., Luo T., Zhang K., Cao J. Ti-PEEK interpenetrating phase composites with minimal surface for property enhancement of orthopedic implants // Composite Structures, 2024, vol. 327. DOI 10.1016/j.compstruct.2023.117638

[7] Foroughi A. H., Liu D., Razavi M. Simultaneous optimization of stiffness, permeability, and surface area in metallic bone scaffolds // International Journal of Engineering Science, 2023, vol. 193. DOI 10.1016/j.ijengsci.2023.103961

[8] Li Q., Gan W., Hu L., Liu X., Mao C., Hu H., Li D. Spherical porous structures for axial compression // International Journal of Mechanical Sciences, 2024, vol. 261. DOI 10.1016/j.ijmecsci.2023.108681

[9] Maconachie T., Leary M., Lozanovski B., Zhang X., Qian M., Faruque O., Brandt M. SLM lattice structures: Properties, performance, applications and challenges // Materials & Design, 2019, vol. 183. DOI 10.1016/j.matdes.2019.108137

[10] Thompson M. K., Moroni G., Vaneker T., Fadel G., Campbel R. I., Gibson I., Bernard A., Schulz J., Graf P., Ahuja B., Martina F. Design for Additive Manufacturing: Trends, opportunities, considerations, and constraints // CIRP Annals, 2016, vol. 65, pp. 737–760. DOI 10.1016/j.cirp.2016.05.004

[11] Sorokin D. V., Babkina L. A., Brazgovka O. V. Designing various-purpose subassemblies based on topological optimization // Spacecrafts & Technologies, 2022, vol. 6, no. 2, pp. 61–82. DOI 10.26732/j.st.2022.2.01 (in Russian)

[12] Zhang Y., Wang J., Wang C., Zeng Y., Chen T. Crashworthiness of bionic fractal hierarchical structures // Materials & Design, 2018, vol. 158, pp. 147–159. DOI 10.1016/j.matdes.2018.08.028

[13] Zhou J., Liu H., Dear J. P., Falzon B. G., Kazanc Z. Comparison of different quasi-static loading conditions of additively manufactured composite hexagonal and auxetic cellular structures // International Journal of Mechanical Sciences, 2023, vol. 244. DOI 10.1016/j.ijmecsci.2022.108054

[14] Park K-M., Min K-S., Roh Y-S. Design Optimization of Lattice Structures under Compression: Study of Unit Cell Types and Cell Arrangements // Materials, 2022, vol. 15, no. 97. DOI 10.3390/ma15010097

[15] Tunay M. Bending behavior of 3D printed sandwich structures with different core geometries and thermal aging durations // Thin–Walled Structures, 2024, vol. 194. DOI 10.1016/j.tws.2023.111329

[16] Cui Z., Zhao J., Xu R., Ding Y., Sun Z. Mechanical design and energy absorption performances of novel plate-rod hybrid lattice structures // Thin–Walled Structures, 2024, vol. 194. DOI 10.1016/j.tws.2023.111349

[17] Saremian R., Badrossamay M., Foroozmehr E., Kadkhodaei M., Forooghi F. Experimental and numerical investigation on lattice structures fabricated by selective laser melting process under quasi-static and dynamic loadings // The International Journal of Advanced Manufacturing Technology, 2021, vol. 112, pp. 2815–2836. DOI 10.1007/s00170–020–06112–0

[18] Yin H., Zhang W., Zhu L., Meng F., Liu J., Wen G. Review on lattice structures for energy absorption properties // Composite Structures, 2023, vol. 1, no. 304. DOI 10.1016/j.compstruct.2022.116397

[19] Wang Z., Cao X., Yang H., Du X., Ma B., Zheng Q., Wan Z., Li Y. Additively-manufactured 3D truss-lattice materials for enhanced mechanical performance and tunable anisotropy: Simulations & experiments // Thin-Walled Structures, 2023, vol. 183. DOI 10.1016/j.tws.2022.110439

[20] Zeng C., Wang W., b K. H., Ma S. Lightweight airborne TPMS-filled reflective mirror design for low thermal deformation // Composite Structures, 2024, vol. 327. DOI 10.1016/j.compstruct.2023.117665

[21] Zhang C., Qiao H., Yang L., Ouyang W., He T., Liu B., Chen X., Wang N., Yan C. Vibration characteristics of additive manufactured IWP-type TPMS lattice structures // Composite Structures, 2024, vol. 327. DOI 10.1016/j.compstruct.2023.117642

[22] Liu X., Wang Y., Liu X., Ren Y., Jiang H. Synergetic control mechanism for enhancing energy-absorption of 3D-printed lattice structures // International Journal of Mechanical Sciences, 2024, vol. 262. DOI 10.1016/j.ijmecsci.2023.108711

[23] Zhang Q., Sun Y. Novel metamaterial structures with negative thermal expansion and tunable mechanical properties // International Journal of Mechanical Sciences, 2024, vol. 261. DOI 10.1016/j.ijmecsci.2023.108692

[24] Qureshi Z. A., Al-Omari S. A. B., Elnajjar E., Al-Ketan O., Al-Rub R. A. On the effect of porosity and functional grading of 3D printable triply periodic minimal surface (TPMS) based architected lattices embedded with a phase change material // International Journal of Heat and Mass Transfer, 2022, vol. 183. DOI 10.1016/j.ijheatmasstransfer.2021.122111

[25] Qureshi Z. A., Al-Omari S. A. B., Elnajjar E., Al-Ketan O., Al-Rub R. A. Nature-inspired triply periodic minimal surface-based structures in sheet and solid configurations for performance enhancement of a low-thermal-conductivity phase-change material for latent-heat thermal-energy-storage applications // International Journal of Heat and Mass Transfer, 2022, vol. 173. DOI 10.1016/j.ijthermalsci.2021.107361

[26] Hu B., Wang Z., Du C., Zou W., Wu W., Tang J., Ai J., Zhou H., Chen R., Shan B. Multi-objective Bayesian optimization accelerated design of TPMS structures // International Journal of Mechanical Sciences, 2023, vol. 244. DOI 10.1016/j.ijmecsci.2022.108085

[27] Wan M., Hu D., Zhang H., Pi B., Ye X. Crashworthiness study of tubular lattice structures based on triply periodic minimal surfaces under quasi-static axial crushing // Composite Structures, 2024, vol. 327. DOI 10.1016/j.compstruct.2023.117703

[28] Cheng L., Bai J., To A. C. Functionally graded lattice structure topology optimization for the design of additive manufactured components with stress constraints // Computer Methods in Applied Mechanics and Engineering, 2019, vol. 344, pp. 334–359. DOI 10.1016/j.cma.2018.10.010

[29] Chen Z., Xie Y. M., Wu X., Wang Z., Li Q., Zhou S. On hybrid cellular materials based on triply periodic minimal surfaces with extreme mechanical properties // Materials & Design, 2019, vol. 183. DOI 10.1016/j.matdes.2019.108109

[30] Zhao M., Zhang D. Z., Liu F., Li Z., Ma Z., Ren Z. Mechanical and energy absorption characteristics of additively manufactured functionally graded sheet lattice structures with minimal surfaces // International Journal of Mechanical Sciences, 2020, vol. 167. DOI 10.1016/j.ijmecsci.2019.105262

[31] Novak N., Al-Ketan O., Borovinsek M., Krstulovic-Opara L., Rowshan R., Vesenjak M., Ren Z. Development of novel hybrid TPMS cellular lattices and their mechanical characterisation // Journal of Materials Research and Technology, 2021, vol. 15, pp. 1318–1329. DOI 10.1016/j.jmrt.2021.08.092

[32] Al-Ketan O., Pelanconi M., Ortona A., Al-Rub R. K. A. Additive manufacturing of architected catalytic ceramic substrates based on triply periodic minimal surfaces // Journal of the American Ceramic Society, 2019, vol. 102, pp. 6176–6193. DOI 10.1111/jace.16474

[33] Al-Ketan O., Lee D., Rowshan R., Al-Rub R. K. A. Functionally graded and multi-morphology sheet TPMS lattices: Design, manufacturing, and mechanical properties // Journal of the Mechanical Behavior of Biomedical Materials, 2020, vol. 102. DOI 10.1016/j.jmbbm.2019.103520

[34] Triply-periodic minimal surfaces (TPMS) // Alan Schoen geometry URL: https://schoengeometry.com/e-tpms.html (accessed: 16.07.2024).

[35] Wohlgemuth M., Yufa N., Hoffman J., Thomas E. L. Triply Periodic Bicontinuous Cubic Microdomain Morphologies by Symmetries // Macromolecules, 2001, vol. 34 (17), pp. 6083–6089. DOI 10.1021/ma0019499

[36] Von Schnering H. G., Nesper R. Nodal surfaces of Fourier series: Fundamental invariants of structured matter // Zeitschrift fur Physik B Condensed Matter, 1991, vol. 83, pp. 407–412. DOI 10.1007/bf01313411

[37] Al-Ketan O., Al-Rub R. K. A. MSLattice: A free software for generating uniform and graded lattices based on triply periodic minimal surfaces // Material Design & Processing Communications, 2021, vol. 3 (6). DOI 10.1002/mdp2.205

For citing this article

Sorokin D.V., Moskvichev E.V. Designing, manufacturing and mechanical tests of lattice structures based on triply periodic minimal surface // Spacecrafts & Technologies, 2024, vol. 8, no. 3, pp. 170-184.

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