在自然界中，小梁骨、木材、貝殼和海膽等介觀或微觀的蜂巢結構具有良好的荷重能力，他們具有不同形狀、形式和設計，並且可以細分為開放式和封閉式蜂巢結構；用傳統製造方法很難仿製這些存在於自然界中的複雜晶格結構，但是透過積層製造（Additive Manufacturing, AM）技術的使用，讓工程師和科學家可以達到此目的。以積層製造的蜂巢結構可用於製造需要特定機械性質的訂製品或個性化產品，因此被視為是一種具有發展性的工程設計理念。而其中的主要挑戰之一，即為在晶格中移除多餘的支撐結構；列印支撐結構時需要花費額外的材料、製造時間和能量。我們可以利用化學或機械的方式將支撐結構從晶格結構中移除，這種對列印物品進行後處理的工作，也稱為後印刷製程；但是在材料擠製成型技術中，若是使用諸如熱塑性聚氨酯（TPU）等彈性材料，則會難以移除支撐結構。
在本研究中，以海膽形態為發想，設計一種新型殼形晶格結構。在製造方面，為材料擠出製程（material extrusion processes ,MEX），使用TPU超彈性線料，以加法製造方式進行，並且無需使用支撐結構；並以相同相對密度並承受彎曲的體心立方晶格（BCC）結構和乙烯-乙酸乙烯酯（EVA）發泡體做為基準，進行機械性質分析包含剛性和能量吸收，再與本研究所提出的結構進行比較。根據壓縮試驗結果，新型殼型晶格結構的剛性幾乎高於基準結構之兩倍；在能量吸收方面，幾乎與體心立方晶格相同，並優於EVA發泡體20％。

至今普遍認為封閉式蜂巢結構在製造上具有困難，並且由於無法在封閉式晶格內以不破壞晶格的方式移除支撐結構，因此尚無關於封閉式晶格在設計以及積層製造方法的公開研究。本研究同時對於材料擠製成型製程，製造封閉式晶格結構的新方法進行評估；並以相同密度的蜂窩狀和開放式海膽（SU）晶格結構作為基準，與本研究所提出的結構所具之機械性質（包括剛性、變形方式和能量吸收）進行比較；其中海膽晶格結構和週期性排列的蜂窩晶格結構，在設計上具有不同尺寸但是形態和密度相同，並以聚乳酸材料（PLA）列印。透過有限元素分析，對它們的物理性質、變形方式和壓縮性質進行研究；並探討單位晶格尺寸對機械性質的影響，再根據其性能表現進行排名。根據壓縮試驗結果，海膽局部封閉式晶格的剛性幾乎與其整體封閉式晶格相同，但與做為基準的蜂窩狀結構和海膽開放式晶格結構相比，分別高出46％和25％。
本研究在晶格結構設計領域提出三個新術語，包含無支撐晶格結構、局部封閉式晶格以及整體封閉式晶格。其中，無支撐晶格結構在保留設計自由度的前提下，省去了在晶格內去除支撐材的後處理製程，因此具有較快的製造速度並且成本較低。

In nature, mesoscopic or microscopic cellular structures like trabecular bone, wood, shell, and sea urchin, can have high load-carrying capacity. These cellular structures with diverse shapes, forms and designs can be mainly classified into open and closed cell cellular structures. It is difficult to replicate these natural complex lattice structures with traditional manufacturing, but additive manufacturing (AM) technology development enabled engineers and scientists to mimic these natural structures. Additively-manufactured cellular structures are a promising engineering design concept for making customized and personalized products where user specific mechanical properties are required. One of the major challenges in additive manufacturing (AM) process is the removal of the unwanted support structures from the lattice. The support structure consumes extra material, printing time and energy for manufacturing. Post-printing, it needs extensive post-processing work to remove it from the lattice structure through chemically or mechanically. In the case of flexible material like thermoplastic polyurethane (TPU) removing the support structure from lattice is very difficult with the material extrusion process.
In this research, a new type of a shell-shaped open cell lattice structure inspired by sea urchin morphology is designed. This lattice can be additively manufactured by material extrusion processes (MEX) with hyper-elastic filament like TPU without the requirement of any support structures. The mechanical properties of the proposed structure, like stiffness and energy absorption are evaluated and benchmarked with bending dominated body-centered cubic (BCC) lattice structure of the same relative density and Ethylene-vinyl acetate (EVA) foam.
The compressive results indicate that the stiffness property is almost twice as high compared with the benchmarked, bending-dominated, body-centered cubic (BCC) lattice structure of the same relative density and ethylene vinyl acetate (EVA) foam. Energy absorption is almost equal to the BCC lattice and 20% better than EVA foam.

Fabricating closed cell lattice structures is still considered difficult and there is no published research on design and additive manufacturing of closed cell due to the support structure enclosed within the lattices, which cannot be removed without damaging. This research also evaluates a novel way of fabricating a closed cell lattice structure with a material extrusion process. The mechanical properties of the proposed structure, including stiffness, deformation behavior and energy absorption, were compared with those of benchmarked honeycomb and open cell sea urchin (SU) lattice structures of the same density. SU lattice structures and honeycomb periodic lattice structures with varied sizes but the same morphology and fixed density were designed and printed in polylactic acid material (PLA). Their physical characteristics, deformation behavior, and compressive properties were investigated experimentally and via finite element analysis. The effect of the unit cell size on mechanical properties was studied and discussed, and the rankings of better performances were drawn. The compressive results indicate that SU local closed cell has almost the same stiffness as SU global closed closed cell, but it was 46% higher and 25% higher compared to benchmarked honeycomb and SU open cell lattice structures, respectively.
The research has contributed the three new terms: supportless lattice structure, local closed cell and global closed cell in the design of cellular structure. Supportless lattice structure eliminates the post processing of support removal within the lattice without compromising the design requirement with high speed of fabrication and low cost.

1 S. Kalpakjian, S.R. Schmid, Manufacturing engineering and technology, 7th ed., Pearson Education India, 2001.
2 G. Seliger, ed., Enabling for Sustainability in Engineering, in: Sustain Manuf, Springer Berlin Heidelberg, Berlin, Heidelberg, 2007: pp. 343–418. doi:10.1007/978-3-540-49871-1_7.
3 H.S. Kang, J.Y. Lee, S. Choi, H. Kim, J.H. Park, J.Y. Son, B.H. Kim, S. Do Noh, Smart manufacturing: Past research, present findings, and future directions, Int J Precis Eng Manuf - Green Technol. 3 (2016) 111–128. doi:10.1007/s40684-016-0015-5.
4 J. Hagel, S.J. Brown, D. Kulasooriya, C. Giffi, M. Chen, The Future of Manufacturing: Making things in a changing world, 2015. doi:10.1049/tpe.1971.0034.
5 M. Bogers, R. Hadar, A. Bilberg, Additive manufacturing for consumer-centric business models: Implications for supply chains in consumer goods manufacturing, Technol Forecast Soc Change. 102 (2016) 225–239. doi:10.1016/j.techfore.2015.07.024.
6 M. Keller, M. Rosenberg, M. Brettel, N. Friederichsen, How Virtualization, Decentrazliation and Network Building Change the Manufacturing Landscape: An Industry 4.0 Perspective, Int J Mech Aerospace, Ind Mechatron Manuf Eng. 8 (2014) 37–44. doi:10.1016/j.procir.2015.02.213.
7 T. Stock, G. Seliger, Opportunities of Sustainable Manufacturing in Industry 4.0, Procedia CIRP. 40 (2016) 536–541. doi:10.1016/j.procir.2016.01.129.
8 S. Wang, J. Wan, D. Li, C. Zhang, Implementing Smart Factory of Industrie 4.0: An Outlook, Int J Distrib Sens Networks. 2016 (2016). doi:10.1155/2016/3159805.
9 M. Rüßmann, M. Lorenz, P. Gerbert, M. Waldner, J. Justus, P. Engel, M. Harnisch, Industry 4.0. The Future of Productivity and Growth in Manufacturing, Bost Consult. (2015) 1–5. doi:10.1007/s12599-014-0334-4.
10 U.M. Dilberoglu, B. Gharehpapagh, U. Yaman, M. Dolen, The Role of Additive Manufacturing in the Era of Industry 4.0, Procedia Manuf. 11 (2017) 545–554. doi:10.1016/j.promfg.2017.07.148.
11 T. Wester, Nature Teaching Structures, Int J Sp Struct Vol. 17(2–3) (2002) 135–147. doi:https://doi.org/10.1260/026635102320321789.
12 Y. Helfman Cohen, Y. Reich, S. Greenberg, Biomimetics: Structure–Function Patterns Approach, J Mech Des. 136 (2014) 111108. doi:10.1115/1.4028169.
13 P.-Y. Chen, A.G. Stokes, J. McKittrick, Comparison of the structure and mechanical properties of bovine femur bone and antler of the North American elk (Cervus elaphus canadensis), Acta Biomater. 5 (2009) 693–706. doi:10.1016/j.actbio.2008.09.011.
14 Q. Zhang, X. Yang, P. Li, G. Huang, S. Feng, C. Shen, B. Han, X. Zhang, F. Jin, F. Xu, T.J. Lu, Bioinspired engineering of honeycomb structure – Using nature to inspire human innovation, Prog Mater Sci. 74 (2015) 332–400. doi:10.1016/j.pmatsci.2015.05.001.
15 A. Lagorce-Tachon, T. Karbowiak, C. Loupiac, A. Gaudry, F. Ott, C. Alba-Simionesco, R.D. Gougeon, V. Alcantara, D. Mannes, A. Kaestner, E. Lehmann, J.-P. Bellat, The cork viewed from the inside, J Food Eng. 149 (2015) 214–221. doi:10.1016/j.jfoodeng.2014.10.023.
16 L.J. Gibson, M.F. Ashby, Cellular solids: structure and properties, Cambridge University Press, 1999.
17 H.J. Ensikat, P. Ditsche-Kuru, C. Neinhuis, W. Barthlott, Superhydrophobicity in perfection: the outstanding properties of the lotus leaf, Beilstein J Nanotechnol. 2 (2011) 152–161. doi:10.3762/bjnano.2.19.
18 G.N. Karam, L.J. Gibson, Biomimicking of animal quills and plant stems: natural cylindrical shells with foam cores, Mater Sci Eng C. 2 (1994) 113–132. doi:10.1016/0928-4931(94)90039-6.
19 T. WESTER, Structures of Nature in Modern Buildings, 生産研究. 41 (1989) 694–700.
20 K. Feld, A.N. Kolborg, C.M. Nyborg, M. Salewski, J.F. Steffensen, K. Berg-Sørensen, Dermal denticles of three slowly swimming shark species: Microscopy and flow visualization, Biomimetics. 4 (2019) 1–20. doi:10.3390/biomimetics4020038.
21 K. Agarwal, R. Sahay, A. Baji, A.S. Budiman, Biomimetic tough helicoidally structured material through novel electrospinning based additive manufacturing, MRS Adv. 4 (2019) 2345–2354. doi:10.1557/adv.2019.313.
22 M.S. Aziz, A.Y. El Sherif, Biomimicry as an approach for bio-inspired structure with the aid of computation, Alexandria Eng J. 55 (2016) 707–714. doi:10.1016/j.aej.2015.10.015.
23 P. Fratzl, Biomimetic materials research: What can we really learn from nature’s structural materials?, J R Soc Interface. 4 (2007) 637–642. doi:10.1098/rsif.2007.0218.
24 W. Associates, Wohlers Report 2017- 3d Printing and Additive Manufacturing state of the industry annual worldwide progress report, 2017.
25 P. Pearce, Structure in nature is a strategy for design, The MIT Press: Cambridge, MA, USA, 1990.
26 T. Wester, 3-D Form and Force Language Proposal for a Structural Basis, Int J Sp Struct. 26 (2011) 229–239. doi:10.1260/0266-3511.26.3.229.
27 T. WESTER, Structures of Nature in Modern Buildings, 生産研究. 41 (1989) 694–700.
28 L.J. Gibson, M.F. Ashby, Cellular solids: structure and properties, Cambridge University Press, 1999.
29 A. Nazir, K.M. Abate, A. Kumar, J.Y. Jeng, A state-of-the-art review on types, design, optimization, and additive manufacturing of cellular structures, Int J Adv Manuf Technol. 104 (2019) 3489–3510. doi:10.1007/s00170-019-04085-3.
30 M.M.J. Opgenoord, K.E. Willcox, Design for additive manufacturing: cellular structures in early-stage aerospace design, Struct Multidiscip Optim. 60 (2019) 411–428. doi:10.1007/s00158-019-02305-8.
31 M.F. Ashby, The properties of foams and lattices, Philos Trans R Soc A Math Phys Eng Sci. 364 (2006) 15–30. doi:10.1098/rsta.2005.1678.
32 J. Knippers, T. Speck, Design and construction principles in nature and architecture, Bioinspiration and Biomimetics. 7 (2012). doi:10.1088/1748-3182/7/1/015002.
33 C. Yan, L. Hao, A. Hussein, D. Raymont, Evaluations of cellular lattice structures manufactured using selective laser melting, Int J Mach Tools Manuf. 62 (2012) 32–38. doi:10.1016/j.ijmachtools.2012.06.002.
34 G. Maliaris, E. Sarafis, Mechanical behavior of 3D printed stochastic lattice structures, Solid State Phenom. 258 SSP (2017) 225–228. doi:10.4028/www.scientific.net/SSP.258.225.
35 H. Hasib, A. Rennie, N. Burns, L. Geekie, Non-stochastic lattice structures for novel filter applications fabricated via additive manufacturing, Filtration. 15 (2014) 174–180.
36 J. Mueller, K.H. Matlack, K. Shea, C. Daraio, Energy Absorption Properties of Periodic and Stochastic 3D Lattice Materials, Adv Theory Simulations. 2 (2019) 1900081. doi:10.1002/adts.201900081.
37 F. Xu, J.L. Tian, T. Wen, Introduction, in: Thermo-Fluid Behav Period Cell Met, 2013: pp. 1–9. doi:10.1515/9783110800487.39.
38 T. Li, Y. Chen, X. Hu, Y. Li, L. Wang, Exploiting negative Poisson’s ratio to design 3D-printed composites with enhanced mechanical properties, Mater Des. 142 (2018) 247–258. doi:10.1016/j.matdes.2018.01.034.
39 L. Zhang, S. Feih, S. Daynes, S. Chang, M.Y. Wang, J. Wei, W.F. Lu, Energy absorption characteristics of metallic triply periodic minimal surface sheet structures under compressive loading, Addit Manuf. 23 (2018) 505–515. doi:10.1016/j.addma.2018.08.007.
40 C. Beyer, D. Figueroa, Design and Analysis of Lattice Structures for Additive Manufacturing, J Manuf Sci Eng Trans ASME. 138 (2016) 1–15. doi:10.1115/1.4033957.
41 T. Tancogne-Dejean, M. Diamantopoulou, M.B. Gorji, C. Bonatti, D. Mohr, 3D Plate-Lattices: An Emerging Class of Low-Density Metamaterial Exhibiting Optimal Isotropic Stiffness, Adv Mater. 30 (2018) 1–6. doi:10.1002/adma.201803334.
42 S.C. Han, J.W. Lee, K. Kang, A New Type of Low Density Material: Shellular, Adv Mater. 27 (2015) 5506–5511. doi:10.1002/adma.201501546.
43 D.W. Abueidda, M. Elhebeary, C.-S. (Andrew) Shiang, R.K. Abu Al-Rub, I.M. Jasiuk, Compression and buckling of microarchitectured Neovius-lattice, Extrem Mech Lett. 37 (2020) 100688. doi:10.1016/j.eml.2020.100688.
44 S. Amin Yavari, S.M. Ahmadi, R. Wauthle, B. Pouran, J. Schrooten, H. Weinans, A.A. Zadpoor, Relationship between unit cell type and porosity and the fatigue behavior of selective laser melted meta-biomaterials, J Mech Behav Biomed Mater. 43 (2015) 91–100. doi:10.1016/j.jmbbm.2014.12.015.
45 T. Maconachie, M. Leary, B. Lozanovski, X. Zhang, M. Qian, O. Faruque, M. Brandt, SLM lattice structures: Properties, performance, applications and challenges, Mater Des. 183 (2019). doi:10.1016/j.matdes.2019.108137.
46 V.S. Deshpande, M.F. Ashby, N.A. Fleck, Foam topology: bending versus stretching dominated architectures, Acta Mater. 49 (2001) 1035–1040. doi:10.1016/S1359-6454(00)00379-7.
47 D. Bhate, C.A. Penick, L.A. Ferry, C. Lee, Classification and Selection of Cellular Materials in Mechanical Design : Engineering and Biomimetic Approaches, Designs. 3 (2019) 19. doi:10.3390/designs3010019.
48 M.F. Ashby, L.J. Gibson, Mechanical Properties of Cellular Solids., Cambridge Univ Eng Dep (Technical Report) CUED/C-MATS. 14 (1983) 1755–1769.
49 Y. Yang, X. Song, X. Li, Z. Chen, C. Zhou, Q. Zhou, Y. Chen, Recent Progress in Biomimetic Additive Manufacturing Technology: From Materials to Functional Structures, Adv Mater. 30 (2018) 1–34. doi:10.1002/adma.201706539.
50 J.P. Kruth, Material Incress Manufacturing by Rapid Prototyping Techniques, CIRP Ann. 40 (1991) 603–614. doi:10.1016/S0007-8506(07)61136-6.
51 H. Kodama, Automatic method for fabricating a three‐dimensional plastic model with photo‐hardening polymer, Rev Sci Instrum. 52 (1981) 1770–1773. doi:10.1063/1.1136492.
52 A.J. Herbert., Solid object generation. , 8, 185–188, 1982, J Appl Photogr Eng. 8 (1982) 185–188.
53 C. Hull, Apparatus for production of three dimensional objects by Stereolithography, (1986).
54 J.-C. Andre, A. Le Mehaute, O. De Witte, Fr 2567668, 1984.
55 I. Revolution, Additive Manufacturing : Looking for the magic formula, (1915).
56 W. Associates, Wohlers Report 2017- 3d Printing and Additive Manufacturing state of the industry annual worldwide progress report, 2017.
57 I. Gibson, D. Rosen, B. Stucker, Vat Photopolymerization Processes, in: Addit Manuf Technol 3D Printing, Rapid Prototyping, Direct Digit Manuf, Springer New York, New York, NY, 2015: pp. 63–106. doi:10.1007/978-1-4939-2113-3_4.
58 T. Weiß, A. Berg, S. Fiedler, G. Hildebrand, R. Schade, M. Schnabelrauch, K. Liefeith, Two-photon polymerization for microfabrication of three-dimensional scaffolds for tissue engineering application, IFMBE Proc. 25 (2009) 140–142. doi:10.1007/978-3-642-03900-3-41.
59 Manufacturing Processes Explained, (n.d.). https://www.3dhubs.com/knowledge-base/.
60 W.E. King, A.T. Anderson, R.M. Ferencz, N.E. Hodge, C. Kamath, S.A. Khairallah, A.M. Rubenchik, Laser powder bed fusion additive manufacturing of metals; physics, computational, and materials challenges, Appl Phys Rev. 2 (2015) 041304. doi:10.1063/1.4937809.
61 D. Morgan, E. Agba, C. Hill, Support Structure Development and Initial Results for Metal Powder Bed Fusion Additive Manufacturing, Procedia Manuf. 10 (2017) 819–830. doi:10.1016/j.promfg.2017.07.083.
62 O. Diegel, A. Nordin, D. Motte, Additive Manufacturing Technologies, 2019. doi:10.1007/978-981-13-8281-9_2.
63 J. Jiang, X. Xu, J. Stringer, Support Structures for Additive Manufacturing: A Review, J Manuf Mater Process. 2 (2018) 64. doi:10.3390/jmmp2040064.
64 J. Steuben, D.L. Van Bossuyt, C. Turner, Design for fused filament fabrication additive manufacturing, Proc ASME 2015. (2015) 1–14.
65 Disrupting Traditional FDM Support Removal to Enable Scalable Additive Manufacturing, 2019. https://www.postprocess.com/.
66 WHITE PAPER Transforming FDM Post-Printing Support Removal with Volumetric Velocity Dispersion, 2019. https://www.postprocess.com/.
67 Stratasys Support Center – FDM Support Materials, (n.d.). https://support.stratasys.com/en/materials/fdm-materials/fdm-support-materials.
68 J. Wu, The Chemistry Behind Soluble Support Removal in Fused Deposition Modeling, (n.d.). https://www.padtinc.com/blog/chemistry_soluble_support_removal_fdm_3d_printing/.
69 HydroFill Filament Water Soluble Support Material for ABS, PLA, Nylon and More, (n.d.). https://airwolf3d.com/shop/water-soluble-support-3d-print/.
70 J. Gonzalez-Gutierrez, S. Cano, S. Schuschnigg, C. Kukla, J. Sapkota, C. Holzer, Additive Manufacturing of Metallic and Ceramic Components by the Material Extrusion of Highly-Filled Polymers: A Review and Future Perspectives, Materials (Basel). 11 (2018) 840. doi:10.3390/ma11050840.
71 H. Choi, J.M. Byun, W. Lee, S.-R. Bang, Y. Do Kim, Research Trend of Additive Manufacturing Technology − A=B+C+D+E, add Innovative Concept to Current Additive Manufacturing Technology: Four Conceptual Factors for Building Additive Manufacturing Technology −, J Korean Powder Metall Inst. 23 (2016) 149–169. doi:10.4150/KPMI.2016.23.2.149.
72 PostProcess, Society of Manufacturing Engineers, Annual Additive Post-Printing Survey: Trends Report 2019, 2019. http://www.postprocess.com/wp-content/uploads/2019/09/Annual-Additive-Post-Printing-Survey-Trends-Report-2019.pdf.
73 S. Mellor, L. Hao, D. Zhang, Additive manufacturing: A framework for implementation, Int J Prod Econ. 149 (2014) 194–201. doi:10.1016/j.ijpe.2013.07.008.
74 T.D. Ngo, A. Kashani, G. Imbalzano, K.T.Q. Nguyen, D. Hui, Additive manufacturing (3D printing): A review of materials, methods, applications and challenges, Compos Part B Eng. 143 (2018) 172–196. doi:.1037//0033-2909.I26.1.78.
75 O. Diegel, Additive Manufacturing, in: Compr Mater Process, Elsevier, 2014: pp. 3–18. doi:10.1016/B978-0-08-096532-1.01000-1.
76 A. Gleadall, D. Visscher, J. Yang, D. Thomas, J. Segal, Review of additive manufactured tissue engineering scaffolds: relationship between geometry and performance, Burn Trauma. 6 (2018) 1–16. doi:10.1186/s41038-018-0121-4.
77 F. Calignano, D. Manfredi, E.P. Ambrosio, S. Biamino, M. Lombardi, E. Atzeni, A. Salmi, P. Minetola, L. Iuliano, P. Fino, Overview on additive manufacturing technologies, Proc IEEE. 105 (2017) 593–612. doi:10.1109/JPROC.2016.2625098.
78 J. Hiemenz, I. Stratasys, 3D PRINTING WITH FDM: How it Works, 2008.
79 J. Firth, A.W. Basit, S. Gaisford, The Role of Semi-Solid Extrusion Printing in Clinical Practice, in: AAPS Adv Pharm Sci Ser, 2018: pp. 133–151. doi:10.1007/978-3-319-90755-0_7.
80 B. N. Turner, R. Strong, S. A. Gold, A review of melt extrusion additive manufacturing processes: I. Process design and modeling, Rapid Prototyp J. 20 (2014) 192–204. doi:10.1108/RPJ-01-2013-0012.
81 C. Hohimer, J. Christ, N. Aliheidari, C. Mo, A. Ameli, 3D printed thermoplastic polyurethane with isotropic material properties, Behav Mech Multifunct Mater Compos 2017. 10165 (2017) 1016511. doi:10.1117/12.2259810.
82 The 4 Types of FFF / FDM 3D Printer Explained (Cartesian, Delta, Polar), 2017. (n.d.). https://www.3dnatives.com/en/four-types-fdm-3d-printers140620174/.
83 M. Leary, L. Merli, F. Torti, M. Mazur, M. Brandt, Optimal topology for additive manufacture: A method for enabling additive manufacture of support-free optimal structures, Mater Des. 63 (2014) 678–690. doi:10.1016/j.matdes.2014.06.015.
84 D.S. Thomas, S.W. Gilbert, Costs and Cost Effectiveness of Additive Manufacturing, Gaithersburg, MD, 2014. doi:10.6028/NIST.SP.1176.
85 FDM Support Materials, (n.d.). https://support.stratasys.com/en/materials/fdm-materials/fdm-support-materials.
86 G. Barile, A. Leoni, M. Muttillo, R. Paolucci, G. Fazzini, L. Pantoli, Fused-Deposition-Material 3D-Printing Procedure and Algorithm Avoiding Use of Any Supports, Sensors. 20 (2020) 470. doi:10.3390/s20020470.
87 J. Flynt, Just Add Water: An Overview of Water-Soluble Filaments, (n.d.). https://3dinsider.com/water-soluble-filament/.
88 3D PRINTING – TRUTHS AND MYTHS OF 3D PRINTING WITH SUPPORT MATERIAL, (n.d.). https://airwolf3d.com/3d-printing-support-material/.
89 W. Gao, Y. Zhang, D. Ramanujan, K. Ramani, Y. Chen, C.B. Williams, C.C.L. Wang, Y.C. Shin, S. Zhang, P.D. Zavattieri, The status, challenges, and future of additive manufacturing in engineering, CAD Comput Aided Des. 69 (2015) 65–89. doi:10.1016/j.cad.2015.04.001.
90 J. Steuben, D.L. Van Bossuyt, C. Turner, Design for fused filament fabrication additive manufacturing, Proc ASME 2015. (2015) 1–14.
91 G. Barile, A. Leoni, M. Muttillo, R. Paolucci, G. Fazzini, L. Pantoli, Fused-Deposition-Material 3D-Printing Procedure and Algorithm Avoiding Use of Any Supports, Sensors. 20 (2020) 470. doi:10.3390/s20020470.
92 What Does Resolution Mean in 3D Printing, (n.d.). https://formlabs.com/blog/3d-printer-resolution-meaning/.
93 R. Brockotter, Key design considerations for 3D printing, (n.d.). https://www.3dhubs.com/knowledge-base/key-design-considerations-3d-printing/.
94 R.D. Bintara, A. Aminnudin, D. Prasetiyo, F.R. Arbianto, The Characteristic of Overhang Object to Material Usage on FDM 3D Printing Technology, J Mech Eng Sci Technol. 3 (2019) 35–41. doi:10.17977/um016v3i12019p035.
95 W. Tao, International Symposium on Flexible Automation, ISFA 2016, Int Symp Flex Autom ISFA 2016. (2016) 1–3.
96 Z. Xiao, Y. Yang, R. Xiao, Y. Bai, C. Song, D. Wang, Evaluation of topology-optimized lattice structures manufactured via selective laser melting, Mater Des. 143 (2018) 27–37. doi:10.1016/j.matdes.2018.01.023.
97 D. Bhate, C.A. Penick, L.A. Ferry, C. Lee, Classification and Selection of Cellular Materials in Mechanical Design : Engineering and Biomimetic Approaches, Designs. 3 (2019) 19. doi:10.3390/designs3010019.
98 P. Pearce, Structure in nature is a strategy for design, The MIT Press: Cambridge, MA, USA, 1990.
99 T. WESTER, Structures of Nature in Modern Buildings, 生産研究. 41 (1989) 694–700.
100 T. Malcolm, Domes, arches and urchins: The skeletal architecture of echinoids (Echinodermata), Zoomorphology. 105 (1985) 114–124. doi:10.1007/BF00312146.
101 J.H. Nebelsick, J.F. Dynowski, J.N. Grossmann, C. Tötzke, Echinoderms: Hierarchically Organized Light Weight Skeletons, in: C. Hamm (Ed.), Evol Light Struct Anal Tech Appl, Springer Netherlands, Dordrecht, 2015: pp. 141–155. doi:10.1007/978-94-017-9398-8_8.
102 M. Von Scheven, M. Bischoff, J.H. Nebelsick, Structural stress response of segmented natural shells: A numerical case study on the clypeasteroid echinoid Echinocyamus pusillus, J R Soc Interface. 15 (2018) 21–28. doi:10.1098/rsif.2018.0164.
103 T. Wester, Nature Teaching Structures, Int J Sp Struct Vol. 17(2–3) (2002) 135–147. doi:https://doi.org/10.1260/026635102320321789.
104 T. Wester, A Geodesic Dome-Type Based on Pure Plate Action, Int J Sp Struct. 5 (1990) 155–167. doi:10.1177/026635119000500302.
105 A. Bagger, Plate shell structures of glass. Studies leading to Guidelines for Structural Glass: Doctoral Dissertation, Technical University of Denmark, 2010.
106 T.B. Grun, L.K.F. Dehkordi, T. Schwinn, D. Sonntag, M. von Scheven, M. Bischoff, J. Knippers, A. Menges, J.H. Nebelsick, The Skeleton of the Sand Dollar as a Biological Role Model for Segmented Shells in Building Construction: A Research Review, Springer International Publishing, Cham, 2016. doi:10.1007/978-3-319-46374-2_11.
107 T. Schwinn, O.D. Krieg, A. Menges, “Robotic Sewing” A Textile Approach Towards the Computational Design and Fabrication of Lightweight Timber Shells, ACADIA. (2016).
108 U. Philippi, W. Nachtigall, Functional morphology of regular echinoid tests (Echinodermata, Echinoida): A finite element study, Zoomorphology. 116 (1996) 35–50. doi:10.1007/BF02526927.
109 A.T. Gaynor, J.K. Guest, Topology optimization considering overhang constraints: Eliminating sacrificial support material in additive manufacturing through design, Struct Multidiscip Optim. 54 (2016) 1157–1172. doi:10.1007/s00158-016-1551-x.
110 C. Hohimer, J. Christ, N. Aliheidari, C. Mo, A. Ameli, 3D printed thermoplastic polyurethane with isotropic material properties, Behav Mech Multifunct Mater Compos 2017. 10165 (2017) 1016511. doi:10.1117/12.2259810.
111 Q. Sun, G.M. Rizvi, C.T. Bellehumeur, P. Gu, Effect of processing conditions on the bonding quality of FDM polymer filaments, Rapid Prototyp J. 14 (2008) 72–80. doi:10.1108/13552540810862028.
112 D. Thomas, The Development of Design Rules for Selective Laser Melting: Doctoral dissertation, University of Wales, 2009.
113 M. Cloots, A.B. Spierings, K. Wegener, Assessing new support minimizing strategies for the additive manufacturing technology SLM, Solid Free Fabr Symp (SFF),. (2013) 12–14.
114 C. Beyer, D. Figueroa, Design and Analysis of Lattice Structures for Additive Manufacturing, J Manuf Sci Eng. 138 (2016) 121014. doi:10.1115/1.4033957.
115 L.J. Gibson, M.F. Ashby, Cellular solids: structure and properties, Cambridge University Press, 1999.
116 A. du Plessis, C. Broeckhoven, I. Yadroitsava, I. Yadroitsev, C.H. Hands, R. Kunju, D. Bhate, Beautiful and Functional: A Review of Biomimetic Design in Additive Manufacturing, Addit Manuf. 27 (2019) 408–427. doi:10.1016/j.addma.2019.03.033.
117 A. du Plessis, C. Broeckhoven, I. Yadroitsev, I. Yadroitsava, S.G. le Roux, Analyzing nature’s protective design: The glyptodont body armor, J Mech Behav Biomed Mater. 82 (2018) 218–223. doi:10.1016/j.jmbbm.2018.03.037.
118 Q. Zhang, X. Yang, P. Li, G. Huang, S. Feng, C. Shen, B. Han, X. Zhang, F. Jin, F. Xu, T.J. Lu, Bioinspired engineering of honeycomb structure - Using nature to inspire human innovation, Prog Mater Sci. 74 (2015) 332–400. doi:10.1016/j.pmatsci.2015.05.001.
119 P. Hao, J. Du, Energy absorption characteristics of bio-inspired honeycomb column thin-walled structure under impact loading, J Mech Behav Biomed Mater. 79 (2018) 301–308. doi:10.1016/j.jmbbm.2018.01.001.
120 S.M. Sajadi, P.S. Owuor, S. Schara, C.F. Woellner, V. Rodrigues, R. Vajtai, J. Lou, D.S. Galvão, C.S. Tiwary, P.M. Ajayan, Multiscale Geometric Design Principles Applied to 3D Printed Schwarzites, Adv Mater. 30 (2018) 1704820. doi:10.1002/adma.201704820.
121 O. Ellers, A mechanical model of growth in regular sea urchins: predictions of shape and a developmental morphospace, Proc R Soc London Ser B Biol Sci. 254 (1993) 123–129. doi:10.1098/rspb.1993.0136.
122 R. Rezaie, M. Badrossamay, A. Ghaei, H.Moosavi, Topology optimization for fused deposition modeling process, Procedia CIRP. 6 (2013) 521–526. doi:10.1016/j.procir.2013.03.098.
123 G. Dong, G. Wijaya, Y. Tang, Y.F. Zhao, Optimizing process parameters of fused deposition modeling by Taguchi method for the fabrication of lattice structures, Addit Manuf. 19 (2018) 62–72. doi:10.1016/j.addma.2017.11.004.
124 J. Worobets, J.W. Wannop, E. Tomaras, D. Stefanyshyn, Softer and more resilient running shoe cushioning properties enhance running economy, Footwear Sci. 6 (2014) 147–153. doi:10.1080/19424280.2014.918184.
125 P.-C. Sun, H.-W. Wei, C.-H. Chen, C.-H. Wu, H.-C. Kao, C.-K. Cheng, Effects of varying material properties on the load deformation characteristics of heel cushions, Med Eng Phys. 30 (2008) 687–692. doi:10.1016/j.medengphy.2007.07.010.
126 M.R. Shariatmadari, R. English, G. Rothwell, Effects of temperature on the material characteristics of midsole and insole footwear foams subject to quasi-static compressive and shear force loading, Mater Des. 37 (2012) 543–559. doi:10.1016/j.matdes.2011.10.045.
127 L. Zhang, S. Feih, S. Daynes, S. Chang, M.Y. Wang, J. Wei, W.F. Lu, Energy absorption characteristics of metallic triply periodic minimal surface sheet structures under compressive loading, Addit Manuf. 23 (2018) 505–515. doi:10.1016/j.addma.2018.08.007.
128 L.J. Gibson, M.F. Ashby, Cellular solids: structure and properties, Cambridge University Press, 1999.
129 W. Tao, M.C. Leu, Design of lattice structure for additive manufacturing, 2016 Int Symp Flex Autom. (2016) 1–3.
130 A. Takezawa, K. Yonekura, Y. Koizumi, X. Zhang, M. Kitamura, Isotropic Ti–6Al–4V lattice via topology optimization and electron-beam melting, Addit Manuf. 22 (2018) 634–642. doi:10.1016/j.addma.2018.06.008.
131 Y. Zhao, Y. Chen, Y. Zhou, Novel mechanical models of tensile strength and elastic property of FDM AM PLA materials: Experimental and theoretical analyses, Mater Des. 181 (2019) 108089. doi:10.1016/j.matdes.2019.108089.
132 R. Zou, Y. Xia, S. Liu, P. Hu, W. Hou, Q. Hu, C. Shan, Isotropic and anisotropic elasticity and yielding of 3D printed material, Compos Part B Eng. 99 (2016) 506–513. doi:10.1016/j.compositesb.2016.06.009.
133 S.Y. Choy, C.N. Sun, K.F. Leong, J. Wei, Compressive properties of functionally graded lattice structures manufactured by selective laser melting, Mater Des. 131 (2017) 112–120. doi:10.1016/j.matdes.2017.06.006.
134 I. Maskery, N.T. Aboulkhair, A.O. Aremu, C.J. Tuck, I.A. Ashcroft, R.D. Wildman, R.J.M. Hague, A mechanical property evaluation of graded density Al-Si10-Mg lattice structures manufactured by selective laser melting, Mater Sci Eng A. 670 (2016) 264–274. doi:10.1016/j.msea.2016.06.013.
135 O. Al-Ketan, R. Rowshan, R.K. Abu Al-Rub, Topology-mechanical property relationship of 3D printed strut, skeletal, and sheet based periodic metallic cellular materials, Addit Manuf. 19 (2018) 167–183. doi:10.1016/j.addma.2017.12.006.
136 S.R.G. Bates, I.R. Farrow, R.S. Trask, Compressive behaviour of 3D printed thermoplastic polyurethane honeycombs with graded densities, Mater Des. 162 (2019) 130–142. doi:10.1016/j.matdes.2018.11.019.
137 P. Zhang, D.J. Arceneaux, A. Khattab, Mechanical properties of 3D printed polycaprolactone honeycomb structure, J Appl Polym Sci. 135 (2018). doi:10.1002/app.46018.
138 M. Mohsenizadeh, F. Gasbarri, M. Munther, A. Beheshti, K. Davami, Additively-manufactured lightweight Metamaterials for energy absorption, Mater Des. 139 (2018) 521–530. doi:10.1016/j.matdes.2017.11.037.
139 T. Maconachie, M. Leary, B. Lozanovski, X. Zhang, M. Qian, O. Faruque, M. Brandt, SLM lattice structures: Properties, performance, applications and challenges, Mater Des. 183 (2019). doi:10.1016/j.matdes.2019.108137.
140 M.F. Ashby, The properties of foams and lattices, Philos Trans R Soc A Math Phys Eng Sci. 364 (2006) 15–30. doi:10.1098/rsta.2005.1678.
141 I. Maskery, N.. Aboulkhair, A.. Aremu, C.. Tuck, I.. Ashcroft, Compressive failure modes and energy absorption in additively manufactured double gyroid lattices, Addit Manuf. 16 (2017) 24–29. doi:10.1016/j.addma.2017.04.003.
142 P.B. Su, B. Han, M. Yang, Z.H. Wei, Z.Y. Zhao, Q.C. Zhang, Q. Zhang, K.K. Qin, T.J. Lu, Axial compressive collapse of ultralight corrugated sandwich cylindrical shells, Mater Des. 160 (2018) 325–337. doi:10.1016/j.matdes.2018.09.034.