This study involved the fabrication and experimental testing of five distinct geometries of triply periodic minimal surface (TPMS) cellular structures characterized by uniform and relative density grading. The specific geometries examined were Schoen-Gyroid, Schwarz-Diamond, Schoen-I-WP, Schwarz-Primitive, and Fischer-Koch S. The experimental tests focused on subjecting these structures to compression loads. Samples were produced with a masked stereolithography (MSLA) printer. The samples had initial and end volume fractions (VFs) ranging from 20% to 60% in increments of 10%, with five varied relative densities. The Taguchi method is utilized to determine the optimal testing parameters, while the Analysis of Variance (ANOVA) test is employed to examine the data. The novelty of this paper is to comprehensively investigate the structural efficiency and versatility of TPMS for various applications by optimizing five different functionally graded TPMSs. The ANOVA findings highlighted the substantial impacts of Initial VF, Final VF, and TPMS type on the observed fluctuations in stress at the first peak. The Initial VF made a significant contribution, demonstrating 28.8% higher effectiveness than the Final VF. The TPMS type had a statistically significant effect on the amount of energy absorbed, revealing that different lattice types have abilities to absorb energy.
PalaniyappanSVeemanDSivakumarNK, et al.Optimization of compressive property for the development of triply periodic minimal surface lattice structure on polylactic acid polymeric material. J Reinforc Plast Compos2022; 073168442210995, DOI: 10.1177/07316844221099582
2.
WangYNiQ-QZhuY, et al.Fabrication of functionally graded nano-TiO2-reinforced epoxy matrix composites. Polym Compos2014; 35: 557–563, DOI: 10.1002/pc.22695
3.
WangYNiQ-QZhuY, et al.Development of functionally graded vapor-grown carbon-fiber/polymer materials. Polym Compos2013; 34: 1774–1781, DOI: 10.1002/pc.22581
4.
LiYFengZHaoL, et al.A review on functionally graded materials and structures via additive manufacturing: from multi-scale design to versatile functional properties. Adv Mater Technol2020; 5: 1900981, DOI: 10.1002/admt.201900981
5.
KozhevnikovAKunnenRPJvan BaarsGE, et al.Feedforward control to suppress the leading edge bulge in photopolymerization-based additive manufacturing. Rapid Prototyp J2022; 28: 1040–1059, DOI: 10.1108/RPJ-05-2021-0106
TemizA. The effects of process parameters on tensile characteristics and printing time for masked stereolithography components, analyzed using the response surface method. J Mater Eng Perform2023; 1–10, DOI: 10.1007/s11665-023-08617-7
8.
BorraNDNeigapulaVSN. Parametric optimization for dimensional correctness of 3D printed part using masked stereolithography: Taguchi method. Rapid Prototyp J2022; 29: 166–184, DOI: 10.1108/RPJ-03-2022-0080
9.
AlMahriSSantiagoRLeeD-W, et al.Evaluation of the dynamic response of triply periodic minimal surfaces subjected to high strain-rate compression. Addit Manuf2021; 46: 102220, DOI: 10.1016/j.addma.2021.102220
10.
WangYRenXChenZ, et al.Numerical and experimental studies on compressive behavior of Gyroid lattice cylindrical shells. Mater Des2020; 186: 108340, DOI: 10.1016/j.matdes.2019.108340
11.
ZhangQMaLJiX, et al.High-strength hydroxyapatite scaffolds with minimal surface macrostructures for load-bearing bone regeneration. Adv Funct Mater2022; 32: 2204182, DOI: 10.1002/adfm.202204182
12.
VelosoFGomes-FonsecaJMoraisP, et al.Overview of methods and software for the design of functionally graded lattice structures. Adv Eng Mater2022; 24: 2200483, DOI: 10.1002/adem.202200483
13.
WiesnerFLimperAMarthC, et al.Additive manufacturing of intertwined electrode pairs - guided mass transport with gyroids. Adv Eng Mater2023; 25: 2200986, DOI: 10.1002/adem.202200986
14.
TemizAAlshemaryAZAkarN, et al.Rapid casting of biodegradable porous magnesium scaffolds and electrophoretic deposition of 45S5 bioactive glass nanoparticles coatings on porous scaffolds: characterization and in vitro bioactivity analysis. Inter Metalcast2023; 17: 1871–1882, DOI: 10.1007/s40962-022-00903-9
15.
ZhangMXuMLiJ, et al.Compressive behavior of hollow triply periodic minimal surface cellular structures manufactured by selective laser melting. RPJ2023; 29: 569–581, DOI: 10.1108/RPJ-04-2022-0128
16.
YuanGZhuQLiK, et al.Manufacture and mechanical properties of batwing-type Al cellular metamaterials by selective laser melting. Adv Eng Mater2023; 25: 2201540, DOI: 10.1002/adem.202201540
17.
Torres-SanchezCBorgmanJMSargeantB, et al.Comparison of selective laser melted commercially pure titanium sheet-based triply periodic minimal surfaces and trabecular-like strut-based scaffolds for tissue engineering. Adv Eng Mater2022; 24: 2100527, DOI: 10.1002/adem.202100527
18.
ChannaSSunDStyliosGK. Impact resistance of 3D cellular structures for protective clothing. Adv Eng Mater2023; 25: 2201336, DOI: 10.1002/adem.202201336
19.
YangWAnJChuaCK, et al.Acoustic absorptions of multifunctional polymeric cellular structures based on triply periodic minimal surfaces fabricated by stereolithography. Virtual Phys Prototyp2020; 15: 242–249, DOI: 10.1080/17452759.2020.1740747
20.
DemirSTemizAPehlivanF. The investigation of printing parameters effect on tensile characteristics for triply periodic minimal surface designs by Taguchi. Polym Eng Sci2023; 64: 1209–1221, DOI: 10.1002/pen.26608
21.
TammaroDDella GattaRVilloneMM, et al.Continuous 3D printing of hierarchically structured microfoamed objects. Adv Eng Mater2022; 24: 2101226, DOI: 10.1002/adem.202101226
22.
HanLCheS. An overview of materials with triply periodic minimal surfaces and related geometry: from biological structures to self-assembled systems. Adv Mater2018; 30: 1705708, DOI: 10.1002/adma.201705708
23.
TemizAYaşarMKoçE. Fabrication of open-pore biodegradable magnesium alloy scaffold via infiltration technique. Inter Metalcast2022; 16: 317–328, DOI: 10.1007/s40962-021-00604-9
24.
ZhaoMLiuFFuG, et al.Improved mechanical properties and energy absorption of BCC lattice structures with triply periodic minimal surfaces fabricated by SLM. Materials2018; 11: 2411, DOI: 10.3390/ma11122411
25.
WallatLAltschuhPRederM, et al.Computational design and characterisation of gyroid structures with different gradient functions for porosity adjustment. Materials2022; 15: 3730, DOI: 10.3390/ma15103730
26.
WeberDSrinivas SundarramS. 3D-printed and foamed triply periodic minimal surface lattice structures for energy absorption applications. Polym Eng Sci2023; 63: 1133–1145, DOI: 10.1002/pen.26270
27.
SharpRPelletierMHWalshWR, et al.Corrosion resistance of 3D printed Ti6Al4V gyroid lattices with varying porosity. Materials2022; 15: 4805, DOI: 10.3390/ma15144805
28.
RavichanderBBJagdaleSHKumarG. Surface morphology, compressive behavior, and energy absorption of graded triply periodic minimal surface 316L steel cellular structures fabricated by laser powder bed fusion. Materials2022; 15: 8294, DOI: 10.3390/ma15238294
29.
SalehMAnwarSAl-AhmariAM, et al.Compression performance and failure analysis of 3D-printed carbon fiber/PLA composite TPMS lattice structures. Polymers2022; 14: 4595, DOI: 10.3390/polym14214595
30.
AlmesmariAAlaghaANNajiMM, et al.Recent advancements in design optimization of lattice-structured materials. Adv Eng Mater2023; 25: 2201780, DOI: 10.1002/adem.202201780
31.
TorresJColeMOwjiA, et al.An approach for mechanical property optimization of fused deposition modeling with polylactic acid via design of experiments. Rapid Prototyp J2016; 22: 387–404, DOI: 10.1108/RPJ-07-2014-0083
32.
VeemanDPalaniyappanSSurendharG, et al.Process optimization of compressive property and dimensional error on wood polylactic acid gyroid-structured polymer composite. J Reinforc Plast Compos2022; 073168442210964, DOI: 10.1177/07316844221096486
33.
UnalHFiciciFMimarogluA, et al.Prediction and optimization of tribological behavior of nylon composites using Taguchi analysis method. J Braz Soc Mech Sci Eng2016; 38: 2097–2104, DOI: 10.1007/s40430-015-0398-1
34.
AlvesFCMonticeliFMVoorwaldHJC, et al.The relation of porosity and creep behavior of glass fiber/epoxy composite: design of experiments approach. Polym Compos2021; 42: 5869–5879, DOI: 10.1002/pc.26267
35.
ZhouHZhaoMMaZ, et al.Sheet and network based functionally graded lattice structures manufactured by selective laser melting: design, mechanical properties, and simulation. Int J Mech Sci2020; 175: 105480, DOI: 10.1016/j.ijmecsci.2020.105480
36.
Al-KetanOLeeD-WRowshanR, et al.Functionally graded and multi-morphology sheet TPMS lattices: design, manufacturing, and mechanical properties. J Mech Behav Biomed Mater2020; 102: 103520, DOI: 10.1016/j.jmbbm.2019.103520
37.
LiDLiaoWDaiN, et al.Comparison of mechanical properties and energy absorption of sheet-based and strut-based gyroid cellular structures with graded densities. Materials2019; 12: 2183, DOI: 10.3390/ma12132183
38.
Al-KetanOAbu Al-RubRK. Multifunctional mechanical metamaterials based on triply periodic minimal surface lattices. Adv Eng Mater2019; 21: 1900524, DOI: 10.1002/adem.201900524
39.
Al-KetanOAbu Al-RubRK. MSLattice: a free software for generating uniform and graded lattices based on triply periodic minimal surfaces. Material Design & Processing Communications2021; 3: e205, DOI: 10.1002/mdp2.205
40.
KadkhodapourJMontazerianHRaeisiS. Investigating internal architecture effect in plastic deformation and failure for TPMS-based scaffolds using simulation methods and experimental procedure. Mater Sci Eng C2014; 43: 587–597, DOI: 10.1016/j.msec.2014.07.047
41.
Catchpole-SmithSSéloRRJDavisAW, et al.Thermal conductivity of TPMS lattice structures manufactured via laser powder bed fusion. Addit Manuf2019; 30: 100846, DOI: 10.1016/j.addma.2019.100846
42.
MaskeryISturmLAremuAO, et al.Insights into the mechanical properties of several triply periodic minimal surface lattice structures made by polymer additive manufacturing. Polymer2018; 152: 62–71, DOI: 10.1016/j.polymer.2017.11.049
ASTM D695-23. Standard test method for compressive properties of rigid plastics. West Conshohocken, PA: ASTM International, 2023.
45.
MishraAKChavanHKumarA. Effect of material variation on the uniaxial compression behavior of FDM manufactured polymeric TPMS lattice materials. Mater Today Proc2021; 46: 7752–7759, DOI: 10.1016/j.matpr.2021.02.276
46.
LiZChenZChenX, et al.Effect of unit configurations and parameters on the properties of Ti–6Al–4V unit-stacked scaffolds: a trade-off between mechanical and permeable performance. J Mech Behav Biomed Mater2021; 116: 104332, DOI: 10.1016/j.jmbbm.2021.104332
47.
YuSSunJBaiJ. Investigation of functionally graded TPMS structures fabricated by additive manufacturing. Mater Des2019; 182: 108021, DOI: 10.1016/j.matdes.2019.108021
48.
TengFSunYGuoS, et al.Topological and mechanical properties of different lattice structures based on additive manufacturing. Micromachines2022; 13: 1017, DOI: 10.3390/mi13071017
49.
KhannaPSoodSMishraP, et al.Analysis of compression and energy absorption behaviour of SLM printed AlSi10Mg triply periodic minimal surface lattice structures. Structures2024; 64: 106580, DOI: 10.1016/j.istruc.2024.106580
50.
BrennemanJLovalekarMPanatR. A semiempirical model for post-yield stress instability in the stress–strain response of 3D lattice structures under compressive loads. Adv Eng Mater2023; 25: 2201428, DOI: 10.1002/adem.202201428
51.
MaoAZhaoNLiangY, et al.Mechanically efficient cellular materials inspired by cuttlebone. Adv Mater2021; 33: 2007348, DOI: 10.1002/adma.202007348
52.
DaraAJohnney MertensARaju BahubalendruniMVA. Characterization of penetrate and interpenetrate tessellated cellular lattice structures for energy absorption. Proc Inst Mech Eng Part L2023; 237: 906–913, DOI: 10.1177/14644207221129709
53.
RahmanHYaraliEZolfagharianA, et al.Energy absorption and mechanical performance of functionally graded soft–hard lattice structures. Materials2021; 14: 1366, DOI: 10.3390/ma14061366
54.
WakjiraYLemuHGHaglandHR. Triply periodic minimal surfaces based functionally graded biomimetic scaffold fabrication via stereolithography. IOPscience2023; 1294(1): 012051. DOI: 10.1088/1757-899X/1294/1/012051
