Adaptive enhancement design of triply periodic minimal surface lattice structure based on non-uniform stress distribution

doi:10.1007/s10483-023-3013-9

Abstract

Abstract: The Schwarz primitive triply periodic minimal surface (P-type TPMS) lattice structures are widely used. However, these lattice structures have weak load-bearing capacity compared with other cellular structures. In this paper, an adaptive enhancement design method based on the non-uniform stress distribution in structures with uniform thickness is proposed to design the P-type TPMS lattice structures with higher mechanical properties. Two types of structures are designed by adjusting the adaptive thickness distribution in the TPMS. One keeps the same relative density, and the other keeps the same of non-enhanced region thickness. Compared with the uniform lattice structure, the elastic modulus for the structure with the same relative density increases by more than 17%, and the yield strength increases by more than 10.2%. Three kinds of TPMS lattice structures are fabricated by laser powder bed fusion (L-PBF) with 316L stainless steel to verify the proposed enhanced design. The manufacture-induced geometric deviation between the as-design and as-printed models is measured by micro X-ray computed tomography (μ-CT) scans. The quasi-static compression experimental results of P-type TPMS lattice structures show that the reinforced structures have stronger elastic moduli, ultimate strengths, and energy absorption capabilities than the homogeneous P-TPMS lattice structure.

Key words: additive manufacturing(AM), triply periodic minimal surface(TPMS), enhanced design model, mechanical property, micro X-ray computed tomography(μ-CT)

2010 MSC Number:

74Q05

Yijin ZHANG, Bin LIU, Fei PENG, Heran JIA, Zeang ZHAO, Shengyu DUAN, Panding WANG, Hongshuai LEI. Adaptive enhancement design of triply periodic minimal surface lattice structure based on non-uniform stress distribution. Applied Mathematics and Mechanics (English Edition), 2023, 44(8): 1317-1330.

TrendMD

References

[1] ZHAO, C. Y. Review on thermal transport in high porosity cellular metal foams with open cells. International Journal of Heat and Mass Transfer, 55(13-14), 3618-3632(2012)
[2] WANG, Y., LIU, F., ZHANG, X. Y., ZHANG, K. F., WANG, X., GAN, D. Q., and YANG, B. Y. Cell-size graded sandwich enhances additive manufacturing fidelity and energy absorption. International Journal of Mechanical Sciences, 211, 106798(2021)
[3] FENG, J. W., FU, J. Z., YAO, X. H., and HE, Y. Triply periodic minimal surface (TPMS) porous structures:from multi-scale design, precise additive manufacturing to multidisciplinary applications. International Journal of Extreme Manufacturing, 4(2), 1-31(2022)
[4] AL-KETAN, O., ABU AL-RUB, R. K., and ROWSHAN, R. The effect of architecture on the mechanical properties of cellular structures based on the IWP minimal surface. Journal of Materials Research, 33(3), 343-359(2018)
[5] YANG, F., MA, Z. Y., and GUO, X. M. Bandgap characteristics of the two-dimensional missing rib lattice structure. Applied Mathematics and Mechanics (English Edition), 43(11), 1631-1640(2022) https://doi.org/10.1007/s10483-022-2923-6
[6] FENG, J., FU, J., SHANG, C., LIN, Z., and LI, B. Porous scaffold design by solid T-splines and triply periodic minimal surfaces. Computer Methods in Applied Mechanics and Engineering, 336, 333-352(2018)
[7] ZHOU, H. L., ZHAO, M., MA, Z. B., ZHANG, D. Z., and FU, G. Sheet and network based functionally graded lattice structures manufactured by selective laser melting:design, mechanical properties, and simulation. International Journal of Mechanical Sciences, 175, 105480(2020)
[8] ZHENG, X. Y., GUO, X. F., and WATANABE, I. A mathematically defined 3D auxetic metamaterial with tunable mechanical and conduction properties. Materials & Design, 198, 109313(2021)
[9] DEVALK, T. and LAKES, R. Poisson's ratio and modulus of gyroid lattices. Physica Status Solidi-Rapid Research Letters, 258(12), 2100081(2021)
[10] LU, Y., ZHAO, W., CUI, Z., ZHU, H., and WU, C. The anisotropic elastic behavior of the widely-used triply-periodic minimal surface based scaffolds. Journal of the Mechanical Behavior of Biomedical Materials, 99, 56-65(2019)
[11] BONATTI, C. and MOHR, D. Mechanical performance of additively-manufactured anisotropic and isotropic smooth shell-lattice materials:simulations & experiments. Journal of the Mechanics and Physics of Solids, 122, 1-26(2019)
[12] BARBER, H., KELLY, C. N., NELSON, K., and GALL, K. Compressive anisotropy of sheet and strut based porous Ti-6Al-4V scaffolds. Journal of the Mechanical Behavior of Biomedical Materials, 115, 104243(2021)
[13] KELLY, C. N., FRANCOVICH, J., JULMI, S., SAFRANSKI, D., GULDBERG, R. E., MAIER, H. J., and GALL, K. Fatigue behavior of as-built selective laser melted titanium scaffolds with sheet-based gyroid microarchitecture for bone tissue engineering. Acta Biomaterialia, 94, 610-626(2019)
[14] VIET, N. V. and ZAKI, W. Free vibration and buckling characteristics of functionally graded beams with triply periodic minimal surface architecture. Composite Structures, 274, 114342(2021)
[15] EJEH, C. J., BARSOUM, I., and ABU AL-RUB, R. K. Flexural properties of functionally graded additively manufactured AlSi10Mg TPMS latticed-beams. International Journal of Mechanical Sciences, 223, 107293(2022)
[16] FAN, X. J., TANG, Q., FENG, Q. X., MA, S., SONG, J., JIN, M. X., GUO, F. Y., and JIN, P. Design, mechanical properties and energy absorption capability of graded-thickness triply periodic minimal surface structures fabricated by selective laser melting. International Journal of Mechanical Sciences, 204, 106586(2021)
[17] WANG, Z., WANG, X., GAO, T., and SHI, C. Mechanical behavior and deformation mechanism of triply periodic minimal surface sheet under compressive loading. Mechanics of Advanced Materials and Structures, 28(19), 2057-2069(2020)
[18] ABUEIDDA, D. W., ELHEBEARY, M., SHIANG, C. S., ABU AL-RUB, R. K., and JASIUK, I. M. Compression and buckling of microarchitectured Neovius-lattice. Extreme Mechanics Letters, 37, 100688(2020)
[19] KESHAVARZAN, M., KADKHODAEI, M., BADROSSAMAY, M., and KARAMOOZ RAVARI, M. R. Investigation on the failure mechanism of triply periodic minimal surface cellular structures fabricated by Vat photopolymerization additive manufacturing under compressive loadings. Mechanics of Materials, 140, 103150(2020)
[20] ZHAO, M., ZHANG, D. Z., LIU, F., LI, Z. H., MA, Z. B., and REN, Z. H. Mechanical and energy absorption characteristics of additively manufactured functionally graded sheet lattice structures with minimal surfaces. International Journal of Mechanical Sciences, 167, 105262(2020)
[21] FU, H. and KAEWUNRUEN, S. Experimental and DEM investigation of axially-loaded behaviours of IWP-based structures. International Journal of Mechanical Sciences, 235, 107738(2022)
[22] ATTARZADEH, R., ROVIRA, M., and DUWIG, C. Design analysis of the "Schwartz D" based heat exchanger:a numerical study. International Journal of Heat and Mass Transfer, 177, 121415(2021)
[23] YIN, H. F., LIU, Z. P., DAI, J. L., WEN, G. L., and ZHANG, C. Crushing behavior and optimization of sheet-based 3D periodic cellular structures. Composites Part B:Engineering, 182, 107565(2020)
[24] FAN, Z. H., FU, Y. J., GAO, R. J., and LIU, S. T. Investigation on heat transfer enhancement of phase change material for battery thermal energy storage system based on composite triply periodic minimal surface. Journal of Energy Storage, 57, 106222(2023)
[25] BELDA, R., MEGIAS, R., MARCO, M., VERCHER-MARTINEZ, A., and GINER, E. Numerical analysis of the influence of triply periodic minimal surface structures morphometry on the mechanical response. Computer Methods and Programs in Biomedicine, 230, 107342(2023)
[26] MASKERY, I., STURM, L., AREMU, A. O., PANESAR, A., WILLIAMS, C. B., TUCK, C. J., WILDMAN, R. D., ASHCROFT, I. A., and HAGUE, R. J. M. Insights into the mechanical properties of several triply periodic minimal surface lattice structures made by polymer additive manufacturing. Polymer, 152, 62-71(2018)
[27] PRÉVE, D., LENARDA, P., MASKERY, I., and PAGGI, M. A comprehensive characterization of fracture in unit cell open foams generated from triply periodic minimal surfaces. Engineering Fracture Mechanics, 277, 108949(2023)
[28] LEE, D. W., KHAN, K. A., and ABU AL-RUB, R. K. Stiffness and yield strength of architectured foams based on the Schwarz primitive triply periodic minimal surface. International Journal of Plasticity, 95, 1-20(2017)
[29] BIAN, Y. J., LI, P. H., YANG, F., WANG, P., LI, W. W., and FAN, H. L. Deformation mode and energy absorption of polycrystal-inspired square-cell lattice structures. Applied Mathematics and Mechanics (English Edition), 41(10), 1561-1582(2020) https://doi.org/10.1007/s10483-020-2648-8
[30] LIU, F., MAO, Z., ZHANG, P., ZHANG, D. Z., JIANG, J., and MA, Z. Functionally graded porous scaffolds in multiple patterns:new design method, physical and mechanical properties. Materials & Design, 160, 849-860(2018)
[31] WANG, S., SHI, Z. A., LIU, L. L., ZHOU, X., ZHU, L. C., and HAO, Y. Q. The design of Ti6Al4V primitive surface structure with symmetrical gradient of pore size in biomimetic bone scaffold. Materials & Design, 193, 108830(2020)
[32] PENG, C. X., MARZOCCA, P., and TRAN, P. Triply periodic minimal surfaces based honeycomb structures with tuneable mechanical responses. Virtual and Physical Prototyping, 18(1), e2125879(2022)
[33] CALLENS, S. J. P., ARNS, C. H., KULIESH, A., and ZADPOOR, A. A. Decoupling minimal surface metamaterial properties through multi-material hyperbolic tilings. Advanced Functional Materials, 31(30), 2101373(2021)
[34] MA, Q., ZHANG, L., DING, J., QU, S., FU, J., ZHOU, M., FU, M. W., SONG, X., and WANG, M. Y. Elastically-isotropic open-cell minimal surface shell lattices with superior stiffness via variable thickness design. Additive Manufacturing, 47, 102293(2021)
[35] ZHANG, L., MA, Q. P., DING, J. H., QU, S., FU, J., FU, M. W., SONG, X., and WANG, M. Y. Design of elastically isotropic shell lattices from anisotropic constitutive materials for additive manufacturing. Additive Manufacturing, 59, 103185(2022)
[36] YANG, W. J., AN, J., CHUA, C. K., and ZHOU, K. Acoustic absorptions of multifunctional polymeric cellular structures based on triply periodic minimal surfaces fabricated by stereolithography. Virtual and Physical Prototyping, 15(2), 242-249(2020)
[37] HERDERING, A., ABENDROTH, M., GEHRE, P., HUBÁKOVÁ, J., and ANEZIRIS, C. G. Additive manufactured polyamide foams with periodic grid as templates for the production of functional coated carbon-bonded alumina foam filters. Ceramics International, 45(1), 153-159(2019)
[38] YUAN, L., DING, S. L., and WEN, C. Additive manufacturing technology for porous metal implant applications and triple minimal surface structures:a review. Bioactive Materials, 4(1), 56-70(2019)
[39] MA, S., TANG, Q., HAN, X. X., FENG, Q. X., SONG, J., SETCHI, R., LIU, Y., LIU, Y., GOULAS, A., ENGSTRØM, D. S., TSE, Y. Y., and ZHEN, N. Manufacturability, mechanical properties, mass-transport properties and biocompatibility of triply periodic minimal surface (TPMS) porous scaffolds fabricated by selective laser melting. Materials & Design, 195, 109034(2020)
[40] SHARMA, D. and HIREMATH, S. S. Additively manufactured mechanical metamaterials based on triply periodic minimal surfaces:performance, challenges, and application. Mechanics of Advanced Materials and Structures, 29(26), 5077-5107(2022)
[41] YIN, H. F., ZHOU, J., WEN, G. L., and WU, Z. T. Crushing analysis and optimization for bio-inspired hierarchical 3D cellular structure. Composite Structures, 286, 115333(2022)
[42] YANG, L., FERRUCCI, M., MERTENS, R., DEWULF, W., YAN, C., SHI, Y. S., and YANG, S. F. An investigation into the effect of gradients on the manufacturing fidelity of triply periodic minimal surface structures with graded density fabricated by selective laser melting. Journal of Materials Processing Technology, 275, 116367(2020)
[43] STRÖMBERG, N. Optimal grading of TPMS-based lattice structures with transversely isotropic elastic bulk properties. Engineering Optimization, 53(11), 1871-1883(2020)
[44] JIA, H. R., LEI, H. S., WANG, P. D., MENG, J. X., LI, C. L., ZHOU, H., ZHANG, X. Y., and FANG, D. N. An experimental and numerical investigation of compressive response of designed Schwarz primitive triply periodic minimal surface with non-uniform shell thickness. Extreme Mechanics Letters, 37, 100671(2020)
[45] LETHBRIDGE, Z. A. D., WALTON, R. I., MARMIER, A. S. H., SMITH, C. W., and EVANS, K. E. Elastic anisotropy and extreme Poisson's ratios in single crystals. Acta Materialia, 58(19), 6444-6451(2010)