Triply periodic minimal surface (TPMS) porous structures: from multi-scale design, precise additive manufacturing to multidisciplinary applications
Source abstract
Abstract
Abstract Inspired by natural porous architectures, numerous attempts have been made to generate porous structures. Owing to the smooth surfaces, highly interconnected porous architectures, and mathematical controllable geometry features, triply periodic minimal surface (TPMS) is emerging as an outstanding solution to constructing porous structures in recent years. However, many advantages of TPMS are not fully utilized in current research. Critical problems of the process from design, manufacturing to applications need further systematic and integrated discussions. In this work, a comprehensive overview of TPMS porous structures is provided. In order to generate the digital models of TPMS, the geometry design algorithms and performance control strategies are introduced according to diverse requirements. Based on that, precise additive manufacturing methods are summarized for fabricating physical TPMS products. Furthermore, actual multidisciplinary applications are presented to clarify the advantages and further potential of TPMS porous structures. Eventually, the existing problems and further research outlooks are discussed.
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Research context
OpenAlex topics: Additive Manufacturing and 3D Printing Technologies · Cellular and Composite Structures · Advanced Materials and Mechanics
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (100+)
Show source-provided references
1. Recent progress in biomimetic additive manufacturing technology: from materials to functional structures10.1002/adma.201706539 ↗
2. Structurally controlled cellular architectures for high-performance ultra-lightweight materials10.1002/adma.201803670 ↗
3. Topological design and additive manufacturing of porous metals for bone scaffolds and orthopaedic implants: a review10.1016/j.biomaterials.2016.01.012 ↗
4. Design for additive manufacturing: trends, opportunities, considerations, and constraints10.1016/j.cirp.2016.05.004 ↗
5. Investigation of strain-rate effect on the compressive behaviour of closed-cell aluminium foam by 3D image-based modelling10.1016/j.matdes.2015.09.109 ↗
6. An ultralight graphene honeycomb sandwich for stretchable light-emitting displays10.1002/adfm.201707043 ↗
7. Mechanical properties of additively manufactured metal lattice structures: data review and design interface10.1016/j.addma.2020.101301 ↗
8. Schwarz meets Schwann: design and fabrication of biomorphic and durataxic tissue engineering scaffolds10.1016/j.media.2006.06.001 ↗
9. Porous scaffold design by solid T-splines and triply periodic minimal surfaces10.1016/j.cma.2018.03.007 ↗
10. New paradigms in internal architecture design and freeform fabrication of tissue engineering porous scaffolds10.1016/j.medengphy.2012.05.008 ↗
11. Recent trends and challenges in computer-aided design of additive manufacturing-based biomimetic scaffolds and bioartificial organs10.1007/s12541-014-0583-7 ↗
12. Periodic surface modeling for computer aided nano design10.1016/j.cad.2006.09.005 ↗
13. Mathematically defined gradient porous materials10.1016/j.matlet.2016.03.021 ↗
14. Functionally graded scaffolds with programmable pore size distribution based on triply periodic minimal surface fabricated by selective laser melting10.3390/ma13215046 ↗
15. Multi-morphology transition hybridization CAD design of minimal surface porous structures for use in tissue engineering10.1016/j.cad.2014.06.006 ↗
16. Novel real function based method to construct heterogeneous porous scaffolds and additive manufacturing for use in medical engineering10.1016/j.medengphy.2015.08.006 ↗
17. Biological and mechanical property analysis for designed heterogeneous porous scaffolds based on the refined TPMS10.1016/j.jmbbm.2020.103727 ↗
18. Heterogeneous porous scaffold design for tissue engineering using triply periodic minimal surfaces10.1007/s12541-012-0068-5 ↗
19. New paradigms in hierarchical porous scaffold design for tissue engineering10.1016/j.msec.2012.12.092 ↗
20. STL-free design and manufacturing paradigm for high-precision powder bed fusion10.1016/j.cirp.2021.03.012 ↗
21. Simple and efficient volume merging method for triply periodic minimal structures10.1016/j.cpc.2021.107956 ↗
22. Efficient generation strategy of hierarchical porous scaffolds with freeform external geometries10.1016/j.addma.2019.100943 ↗
23. Heterogeneous porous scaffold generation using trivariate B-spline solids and triply periodic minimal surfaces10.1016/j.gmod.2021.101105 ↗
24. Porous scaffold design using the distance field and triply periodic minimal surface models10.1016/j.biomaterials.2011.07.019 ↗
25. Anisotropic Ti-6Al-4V gyroid scaffolds manufactured by electron beam melting (EBM) for bone implant applications10.1016/j.matdes.2017.10.040 ↗
26. Theoretical prediction and experimental validation of the digital light processing (DLP) working curve for photocurable materials10.1016/j.addma.2020.101716 ↗
27. Energy absorption and deformation behavior of 3D printed triply periodic minimal surface stainless steel cellular structures under compression10.1002/srin.202000411 ↗
28. Effect of surface geometry on laser powder bed fusion defects10.1016/j.jmatprotec.2021.117179 ↗
29. Tunable auxeticity and elastomechanical symmetry in a class of very low density core-shell cubic crystals10.1016/j.actamat.2019.07.015 ↗
30. A mathematically defined 3D auxetic metamaterial with tunable mechanical and conduction properties10.1016/j.matdes.2020.109313 ↗
31. Poisson’s ratio and modulus of gyroid lattices10.1002/pssb.202100081 ↗
32. The anisotropic elastic behavior of the widely-used triply-periodic minimal surface based scaffolds10.1016/j.jmbbm.2019.07.012 ↗
33. Mechanical performance of additively-manufactured anisotropic and isotropic smooth shell-lattice materials: simulations & experiments10.1016/j.jmps.2018.08.022 ↗
34. Compressive anisotropy of sheet and strut based porous Ti–6Al–4V scaffolds10.1016/j.jmbbm.2020.104243 ↗
35. Mechanical properties of 3D printed polymeric cellular materials with triply periodic minimal surface architectures10.1016/j.matdes.2017.03.018 ↗
36. Insights into the mechanical properties of several triply periodic minimal surface lattice structures made by polymer additive manufacturing10.1016/j.polymer.2017.11.049 ↗
37. Topology-mechanical property relationship of 3D printed strut, skeletal, and sheet based periodic metallic cellular materials10.1016/j.addma.2017.12.006 ↗
38. Stiffness and yield strength of architectured foams based on the Schwarz primitive triply periodic minimal surface10.1016/j.ijplas.2017.03.005 ↗
39. Fatigue behaviour of NiTi shape memory alloy scaffolds produced by SLM, a unit cell design comparison10.1016/j.jmbbm.2017.01.016 ↗
40. Fatigue behavior of As-built selective laser melted titanium scaffolds with sheet-based gyroid microarchitecture for bone tissue engineering10.1016/j.actbio.2019.05.046 ↗
41. Mechanical vibration bandgaps in surface-based lattices10.1016/j.addma.2018.11.011 ↗
42. Free vibration and buckling characteristics of functionally graded beams with triply periodic minimal surface architecture10.1016/j.compstruct.2021.114342 ↗
43. Compressive failure modes and energy absorption in additively manufactured double gyroid lattices10.1016/j.addma.2017.04.003 ↗
44. Energy absorption characteristics of metallic triply periodic minimal surface sheet structures under compressive loading10.1016/j.addma.2018.08.007 ↗
45. Compressive behaviour of Neovius triply periodic minimal surface cellular structure manufactured by fused deposition modelling10.1080/17452759.2019.1615750 ↗
46. Compression and energy absorption of maraging steel primitive scaffolds produced by powder bed fusion10.1007/s00170-021-07514-4 ↗
47. Additively manufactured and surface biofunctionalized porous nitinol10.1021/acsami.6b14026 ↗
48. Effect of scaffold architecture on cell seeding efficiency: a discrete phase model CFD analysis10.1016/j.compbiomed.2019.04.025 ↗
49. Sacrificial 3D printing of shrinkable silicone elastomers for enhanced feature resolution in flexible tissue scaffolds10.1016/j.actbio.2020.10.001 ↗
50. A multiscale optimisation method for bone growth scaffolds based on triply periodic minimal surfaces10.1007/s10237-021-01496-8 ↗
51. Stereolithography printing of bone scaffolds using biofunctional calcium phosphate nanoparticles10.1016/j.jmst.2021.01.062 ↗
52. Design and biomechanical characteristics of porous meniscal implant structures using triply periodic minimal surfaces10.1186/s12967-019-1834-2 ↗
53. Design and fabrication of a customized partial hip prosthesis employing CT-scan data and lattice porous structures10.1021/acsomega.0c06144 ↗
54. Architected implant designs for long bones: advantages of minimal surface-based topologies10.1016/j.matdes.2021.109838 ↗
55. The influence of selective laser melting defects on the fatigue properties of Ti6Al4V porosity graded gyroids for bone implants10.1016/j.ijmecsci.2020.106180 ↗
56. Additively manufactured gradient porous Ti-6Al-4V hip replacement implants embedded with cell-laden gelatin methacryloyl hydrogels10.1021/acsami.0c20751 ↗
57. Heat transfer performance of a finned metal foam-phase change material (FMF-PCM) system incorporating triply periodic minimal surfaces (TPMS)10.1016/j.ijheatmasstransfer.2021.121001 ↗
58. Flow and thermal transport characteristics of triply-periodic minimal surface (TPMS)-based gyroid and Schwarz-P cellular materials10.1080/10407782.2021.1872260 ↗
59. Forced convection computational fluid dynamics analysis of architected and three-dimensional printable heat sinks based on triply periodic minimal surfaces10.1115/1.4047385 ↗
60. Feasibility of preparing additive manufactured porous stainless steel felts with mathematical micro pore structure as novel catalyst support for hydrogen production via methanol steam reforming10.1016/j.ijhydene.2019.07.187 ↗
61. Stepping toward efficient microreactors for CO2 methanation: 3D-printed gyroid geometry10.1021/acssuschemeng.1c01980 ↗
62. Estimation of the structure dependent performance of 3D rapid prototyped membranes10.1016/j.cej.2015.03.029 ↗
63. Structure-dependent gas transfer performance of 3D-membranes for artificial membrane lungs10.1016/j.memsci.2021.119371 ↗
64. Exploring periodic bicontinuous cubic network structures with complete phononic bandgaps10.1021/acs.jpcc.7b07267 ↗
65. Acoustic absorptions of multifunctional polymeric cellular structures based on triply periodic minimal surfaces fabricated by stereolithography10.1080/17452759.2020.1740747 ↗
66. Enhanced electromagnetic microwave absorption of SiOC ceramics targeting the integration of structure and function10.1016/j.jeurceramsoc.2021.06.007 ↗
67. Characterization of a mechanically tunable gyroid photonic crystal inspired by the butterfly Parides sesostris10.1002/adom.201500436 ↗
68. Optimal grading of TPMS-based lattice structures with transversely isotropic elastic bulk properties10.1080/0305215X.2020.1837790 ↗
69. Efficient representation and optimization for TPMS-based porous structures10.1109/TVCG.2020.3037697 ↗
70. Bioinspired heat exchangers based on triply periodic minimal surfaces for supercritical CO2 cycles10.1016/j.applthermaleng.2020.115686 ↗
71. Design analysis of the ‘Schwartz D’ based heat exchanger: a numerical study10.1016/j.ijheatmasstransfer.2021.121415 ↗
72. Gyroid structured aqua-sheets with sub-nanometer thickness enabling 3D fast proton relay conduction10.1039/C9SC00131J ↗
73. Design and fabrication of a non-clogging scaffold composed of semi-permeable membrane10.1016/j.matdes.2018.01.033 ↗
74. Another stretching-dominated micro-architectured material, shellular10.1016/j.mattod.2019.05.018 ↗
75. Block copolymer derived 3D interpenetrating multifunctional gyroidal nanohybrids for electrical energy storage10.1039/C7EE03571C ↗
76. Synthetic bone: design by additive manufacturing10.1016/j.actbio.2019.07.049 ↗
77. Custom-made macroporous bioceramic implants based on triply-periodic minimal surfaces for bone defects in load-bearing sites10.1016/j.actbio.2020.03.016 ↗
78. Multifunctional mechanical metamaterials based on triply periodic minimal surface lattices10.1002/adem.201900524 ↗
79. Biomimetic gyroid nanostructures exceeding their natural origins10.1126/sciadv.1600084 ↗
80. An overview of materials with triply reriodic minimal surfaces and related geometry: from biological structures to self-assembled systems10.1002/adma.201705708 ↗
81. Computer-aided porous scaffold design for tissue engineering using triply periodic minimal surfaces10.1007/s12541-011-0008-9 ↗
82. Marching cubes: a high resolution 3D surface construction algorithm10.1145/37402.37422 ↗
83. Functionally graded porous scaffolds in multiple patterns: new design method, physical and mechanical properties10.1016/j.matdes.2018.09.053 ↗
84. The design of Ti6Al4V primitive surface structure with symmetrical gradient of pore size in biomimetic bone scaffold10.1016/j.matdes.2020.108830 ↗
85. Combinational design of heterogeneous lattices with hybrid region stiffness tuning for additive manufacturing10.1016/j.matdes.2021.109955 ↗
86. Effective design and simulation of surface-based lattice structures featuring volume fraction and cell type grading10.1016/j.matdes.2018.05.058 ↗
87. An advanced multi-morphology porous scaffold design method using volumetric distance field and beta growth function10.1007/s12541-015-0263-2 ↗
88. Triply periodic minimal surfaces sheet scaffolds for tissue engineering applications: an optimization approach toward biomimetic scaffold design10.1021/acsabm.8b00052 ↗
89. Design and mechanical characterization of solid and highly porous 3D printed poly(propylene fumarate) scaffolds10.1007/s40964-017-0021-3 ↗
90. Decoupling minimal surface metamaterial properties through multi-material hyperbolic tilings10.1002/adfm.202101373 ↗
91. Nature-inspired lightweight cellular co-continuous composites with architected periodic gyroidal structures10.1002/adem.201700549 ↗
92. Isotropic porous structure design methods based on triply periodic minimal surfaces10.1016/j.matdes.2021.110050 ↗
93. Soap film inspired mechanical metamaterials approaching theoretical bound of stiffness across full density range10.1039/D0MH01408G ↗
94. On hybrid cellular materials based on triply periodic minimal surfaces with extreme mechanical properties10.1016/j.matdes.2019.108109 ↗
95. Design, mechanical properties and energy absorption capability of graded-thickness triply periodic minimal surface structures fabricated by selective laser melting10.1016/j.ijmecsci.2021.106586 ↗
96. Compressive characteristics of radially graded porosity scaffolds architectured with minimal surfaces10.1016/j.msec.2018.06.051 ↗
97. Mechanical behavior and deformation mechanism of triply periodic minimal surface sheet under compressive loading10.1080/15376494.2020.1829756 ↗
98. Compression and buckling of microarchitectured Neovius-lattice10.1016/j.eml.2020.100688 ↗
99. Compression–compression fatigue behaviour of gyroid-type triply periodic minimal surface porous structures fabricated by selective laser melting10.1016/j.actamat.2019.09.042 ↗
100. Investigation on the failure mechanism of triply periodic minimal surface cellular structures fabricated by vat photopolymerization additive manufacturing under compressive loadings10.1016/j.mechmat.2019.103150 ↗