Design and fabrication of carbon fiber lattices using 3D weaving

Design and fabrication of carbon fiber lattices using 3D weaving | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Design and fabrication of carbon fiber lattices using 3D weaving Hayley McClintock, Hod Lipson, Zechen Xiong, Bruno Rergis This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-2762108/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 10 Sep, 2023 Read the published version in Scientific Reports → Version 1 posted 9 You are reading this latest preprint version Abstract We present a method of designing and fabricating 3D carbon fiber lattices. The lattice design and fabrication is based on crocheting and sewing techniques, where carbon fiber tow is woven through two parallel carbon fiber grids and reinforced with vertical carbon fiber tubes. This process allows for more design flexibility than other current methods. For example, within a single lattice, different density weave patterns can be used to address specific load requirements. Though fabricated manually here, this process can also be automated for large scale production. With this design flexibility, simplified fabrication, and high strength, the lattices proposed here offer an advantage as compared to similar existing structures. Physical sciences/Engineering/Mechanical engineering Physical sciences/Materials science/Structural materials Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Introduction When designing structures for aerospace applications, it is critical to reduce mass as much as possible while maintaining strength. To achieve this objective, lattice structures are often used as a way to engineer a low density material that maintains the desired mechanical properties. Lattice geometry has long been the subject of scientific study. There are a number of geometries that yield high performance lattices, such as octet-truss 1 , tetrahedral 2 , 3 , pyramidal 4 , 5 , and 3D Kagome lattices 6 , 7 . Traditionally, these lattices were made from metal, and were fabricated using traditional manufacturing methods such as investment casting 8 and sheet folding 9 – 11 . Recently, carbon fiber has emerged as a superior alternative to metal for constructing lattices. With a higher strength to weight ratio, carbon fiber performs better than other previously used metals. Carbon fiber lattices can be fabricated using some of the same methods used for metallic lattices. Common techniques are usually cutting and folding 12 , 13 , snap fitting 5 , 14 , hot press molding 10 , 11 , 15 , or using mechanical fasteners 16 , 17 . One drawback with almost all of these fabrication methods is that they require manual assembly. This is time consuming and unwieldy, and is not practical for fabricating structures at larger scales. One possible avenue to circumvent this issue is to use additive manufacturing methods, such as 3D printing. By em- ploying digital manufacturing processes, not only is fabrication time reduced, but errors introduced by manual assembly are eliminated as well. Moreover, the programability of digital manufacturing processes allows for customization and optimization not afforded using bulk production processes. Currently, there are a number of carbon fiber 3D printers commercially available. Many use chopped carbon fiber particles mixed with thermosets 18 , but some also use continuous carbon fibers 19 , 20 , though these fibers do not usually span across multiple layers. For example, Liu et. al 21 demonstrated a free-hanging 3D printing technique that allows for the truss orientation to follow the axis of the slant of the struts. Similarly, Eichenhofer et. al 22 presented a pultrusion/extrusion method to additively manufacture lattices in a continuous manner with directed orientation of the fibers. However, the 3D printing process can still be quite time consuming. However, additive manufacturing frequently these methods would not allow for a robust connection between layers if a lattice was made with more than one unit cell in height. In this research, we explore an alternative method to designing and fabricating carbon fiber lattices. Drawing inspiration from crocheting and sewing processes, the carbon fiber is woven through a diagonal carbon fiber grid held tightly in a jig. These taught threads are equivalent to the warp threads in a loom, except that they are criscrossed into a lattice instead of being parallel. We then join lattice by weaving thread vertically, equivalent o the Weft threads in a loom. The resulting 3D lattices then contain both diagonal and rectangular struts. Though previous work has demonstrated the effectiveness of woven lattices 23 , 24 , the method here offers the advantage of not needing a faceplate during fabrication. Without the restriction of the faceplate, more advanced designs can be created. For example, the warp planes do not need to be parallel to each other or even planar or uniform. Similarly, the weft threads can be non-uniform, optimizing strength to weight performance. Methods Carbon fiber tow is used as the main lattice material, as it is high strength and low weight, and is commercially available. The carbon fiber tow (HMT301-34/700 Tow Preg, Northern Composites) is pre-impregnanted with resin, meaning that the tow can be directly cured without having to apply resin after shaping the material. The method described here is based on crocheting and sewing principles. First, an aluminum jig is fabricated that contains holes along each wall. Carbon fiber tow can then be woven through these holes to form a diagonal grid. Two layers of these grids are woven onto the jig to use as a substrate for the weaving process. Additionally, if desired, vertical carbon fiber tubes can be added at each node of the grid by placing unidirectional carbon fiber tubes (McMaster-Carr) at the nodes and curing them in place with a small amount of epoxy. Here, two different tubes are studied; one with an outer diameter of 3mm and an inner diameter of 2mm, and another with an outer diameter of 8mm and an inner diameter of 6mm. Once the tubes are cured in place (or after the grid is woven if tubes are not being used), a latch hook is used to loop and knot carbon fiber tow around the grid. The latch hook is first lowered through both grid layers with the latch open. Then, the carbon fiber tow is wrapped around the hook, and the hook is pulled back up and the latch is closed. Once pulled through, the latch hook is then moved above the next location and the process is repeated. An overview of this process can be found in Figure . Once the grid is in place, the lattices are cured at 450°F for 20 minutes. After curing, the lattice is removed by cutting the connections to the jig. Both the weaving process and the removal process can be automated in future iterations of this project. A final step of dipping the entire structure in epoxy is also added to increase the strength of the lattice. An overview of this process is shown in Figure 2. Results Three different lattice designs were tested in this study. These include two lattices made with different diameter tubes and a lattice woven without tubes. Examples of these structures, as well as other lattice designs, are shown in Figure 3. The variety of fabricated structures demonstrates the versatility of the design approach. Compression testing To characterize the strength of the lattice, compression tests were performed on three different designs to determine their respective compressive strengths. Samples were placed in a universal testing machine (Instron) and compressed at a rate of 5 mm/min. This gave a maximum force, which was then converted to compressive strength by dividing by the cross sectional area of the lattice. Relative density was computed by normalizing the density of the lattices by the density of the constituent carbon fiber, coated in epoxy. This value was computed experimentally, and was found to be 1100 kg/ m 3 . The results of the compression tests are shown in Figure 4, where the data is also plotted with reported values from similar lattice structures found in the literature. Stress-strain curves were also computed for each sample type, and are shown in Figure 5. Compared to similar lattices, the lattices with the added carbon fiber tubes show a comparable performance to similar designs. However, many other similar designs utilize a faceplate when testing their lattices. This adds a significant amount of structural support. The lattice presented here was specifically designed without a faceplate so as to provide maximum flexibility with the weaving design. During compression tests of the lattice designs, videos were captured to examine the main failure modes of the structures (movies S1, S2, S3). For the lattice made without tubes, the main failure mode was the buckling of the diagonal struts, but there was also some delamination of the struts from the horizontal, diagonal grids, which caused the internal structure to slide. As shown in Figure 3, there are two failure modes for the woven lattice with the vertical tubes; buckling of the carbon fiber tubes and buckling of the diagonal struts. In compression, the tubes are the main supporting feature, but in bending or in out-of-plane compression, a different failure mode is expected and the supporting woven structure should provide the needed support. Table 1. List of comparable carbon fiber lattices. Source Method Density (kg/m 3 ) Relative Density Compressive strength (MPa) Faceplate? Liu, et. al 21 3D Printing 29.56 0.056 1.24 Yes Xu, et. al 17 Mechanical fasteners 28.78 0.03 0.1198 No Schneider, et. al 12 Hot press molding and cut 60 0.037 2 Yes Yin, et. al 25 Hot press molding 0.16 0.00585 0.447 Yes 2.28 0.0645 1.35 Yes 2.28 0.0645 1.21 Yes 0.43 0.0123 1.31 Yes 0.27 0.0103 0.66 Yes Wang, et. al 15 Hot press molding 12.78 0.012 0.84 Yes Dong, et. al 13 Snap fit 24.48 0.017 0.073 No 77.76 0.054 4.39 No 135.36 0.094 7.98 No 187.2 0.13 9.9 No 228.96 0.159 11.39 No Wu, et. al 11 Hot press molding and cut 79.70 0.0547 12.44 Yes Eichenhofer, et. al 22 Pultrusion/extrusion 9.22 0.0066 0.2 Yes 8.67 0.0062 0.18 Yes 8.63 0.0061 0.23 Yes Xiong, et. al 26 Hot press molding and cut 52.86 0.0341 0.32 No 77.35 0.0499 0.91 No 122.61 0.0791 1.78 No 52.86 0.0341 0.21 No 77.35 0.0499 0.54 No 122.61 0.0791 1.01 No 50.53 0.0326 0.5 No 73.94 0.0477 1.03 No 117.03 0.0755 1.92 No Sun, et. al 10 Hot press molding 42.16 0.0272 4.83 Yes Che, et. al 23 Stitching 7.17 0.0075 0.33 Yes 22.27 0.0141 1.14 Yes 35.71 0.0226 2.57 Yes Fan, et. al 24 Weaving 0.028 0.77 Yes Snap fit 0.086 1.31 Yes Liu, et. al 16 Mechanical fasteners 0.0085 0.48 Yes 0.0133 1.2 Yes 0.0168 1.63 Yes 0.0217 1.97 Yes 0.0289 2.46 Yes 0.0435 3.32 Yes Finnegan, et. al 5 Snap fit 0.01 1 Yes 0.02 3 Yes 0.035 5 Yes 0.05 9.5 Yes This work Weaving 89.68 0.0813 1.01 No 88.66 0.0804 2.80 No 144.86 0.1314 6.79 No Finite Element Analysis (FEA) To validate the findings from the compression testing, finite element (FE) simulations were also conducted. Correspond- ing FE simulations were performed with the commercial finite element package ABAQUS/Explicit (2020, Dassault Systèmes Simulia Corp., USA) to obtain more insight into the compressive behaviors of the carbon fiber/epoxy lattice structures. Three different FE models are built to match the geometries of the fabricated samples in Fig. 3. In each of these models, a total of 4 x 5 repeating units were used and the cured carbon fiber strand is approximated to be a uniform beam with a sectional size of 2.2 mm by 0.5 mm (Figure 6). Overlapped areas (knots) of different carbon fiber ribbons in the lattices are assumed to be non-destructible since they are much stiffer, and are simulated with the isotropic carbon fiber/epoxy model. ABAQUS/Explicit was found to be a better tool than ABAQUS/Standard to simulate complicated nonlinear and failure problems in terms of convergence and computational cost 27 , and that Hashin’s damage theory is suitable for fiber-reinforced composite materials 16 . To ensure a quasi-static condition, all compressions are carried out in 90 seconds with a loading rate of 5 mm/min. Additionally, the kinetic energy of all simulations is guaranteed to be a small fraction (less than 5%) of their respective internal energies. A mass scaling factor of 1e7 and total numbers of 13032, 42088, and 35240 S4R elements with 5 integration points are used to address the trade-off between accuracy and economy. While material and geometric imperfections of the specimens due to fabrication processes can not be included in the simulations, a Hashin damage model is defined in Table 2 to reproduce the failure of the experiments. Table 2. Mechanical property of the carbon fiber/epoxy composite material. Variable ρ is mass density, E i , ν i j , G i j , and τ i j are Young’s modulus, Poisson’s ratio, shear modulus, and shear strength in corresponding directions; σ i ,T /C and U i ,T /C are tensile/compressive strengths in the corresponding directions 28 In the simulated model without supporting tubes (Model 1 in Figure 6), the compressive loading leads to Euler buckling of the struts and causes cracking and lattice failure (highlighted with red squares in Fig. 6, movie S1). Since all repeating units in a FE lattice are perfectly aligned in the loading direction, the same buckling and cracking patterns appear in different spots almost at the same time. Therefore, the peak and the dropping of its stress-strain curve appear much earlier than that of experimental plots (Figure 5). However, together with the supporting videos, simulation models with tubes reveal two other interesting failure modes. Before the buckling failure of the diagonal struts, the compressive load leads to transverse or matrix tensile failure at the top and bottom of the tubes (Figure 6), i.e., carbon fibers would delaminate in the 90 degree direction due to a much lower transverse strength (movie S2 and movie S3). For the tubes with a higher slenderness ratio in model 2, compressive column buckling takes place in the tubes after a certain level of material degradation, denoting the total failure of the lattice. On the other hand, tubes in model 3 do not buckle due to a larger radius and wall thickness, consistent with the experiments. Discussion Here, a novel carbon fiber lattice was developed using crocheting and sewing techniques. Using a jig with two parallel carbon fiber grids as a scaffold, prepreg carbon fiber tow was woven through the grid in a rectangular pattern using a latch hook. Additional structures with vertical carbon fiber tubes were also studied. This process yields a cellular lattice with a relatively high compressive strength to density ratio and demonstrates a comparable performance to other similar lattice structures found in the literature. However, while other approaches require the presence of a face plate, the absence of a face plate here allows for a more free-form fabrication approach. Additionally, the weaving process in this approach allows for the possibility of automation. While the weaving could be easily automated, the additional steps of adding in vertical tubes and removing excess carbon fiber from the edges will be more difficult to automate. Declarations Acknowledgements This research was supported in part by NASA NSTRF grant 80NSSC20K0587, and by the US National Science Foundation (NSF) AI Institute for Dynamical Systems, grant 2112085. Author contributions statement H.M. and H.L. conceived the experiment(s). H.M., Z.X., B.R. conducted the experiment(s), and H.M. and Z.X. analyzed the results. All authors reviewed the manuscript. Competing interests statement The authors declare no competing interests. Data Availability The datasets used and/or analysed during the current study available from the corresponding author on reasonable request. References Deshpande, V. S., Fleck, N. A. & Ashby, M. F. Effective properties of the octet-truss lattice material. J. Mech. Phys. Solids 49 , 1747–1769 (2001). Deshpande, V. S. & Fleck, N. Collapse of truss core sandwich beams in 3-point bending. Int. J. Solids Struct. 38 , 6275–6305 (2001). Sugimura, Y. Mechanical response of single-layer tetrahedral trusses under shear loading. Mech. materials 36 , 715–721 (2004). Hyun, S., Karlsson, A. M., Torquato, S. & Evans, A. Simulated properties of kagomé and tetragonal truss core panels. Int. J. Solids Struct. 40 , 6989–6998 (2003). Finnegan, K., Kooistra, G., Wadley, H. N. & Deshpande, V. The compressive response of carbon fiber composite pyramidal truss sandwich cores. Int. J. Mater. Res. 98 , 1264–1272 (2007). Wallach, J. & Gibson, L. Mechanical behavior of a three-dimensional truss material. Int. J. Solids Struct. 38 , 7181–7196 (2001). Wang, J., Evans, A. G., Dharmasena, K. & Wadley, H. G. On the performance of truss panels with kagome cores. Int. J. Solids Struct. 40 , 6981–6988 (2003). Kooistra, G. W., Deshpande, V. S. & Wadley, H. N. Compressive behavior of age hardenable tetrahedral lattice truss structures made from aluminium. Acta Materialia 52 , 4229–4237 (2004). Wadley, H. N., Fleck, N. A. & Evans, A. G. Fabrication and structural performance of periodic cellular metal sandwich structures. Compos. science technology 63 , 2331–2343 (2003). Sun, Y., Guo, L.-c., Wang, T.-s., Yao, L.-j. & Sun, X.-y. Bending strength and failure of single-layer and double-layer sandwich structure with graded truss core. Compos. Struct. 226 , 111204 (2019). Wu, Q., Ma, L., Wu, L. & Xiong, J. A novel strengthening method for carbon fiber composite lattice truss structures. Compos. Struct. 153 , 585–592 (2016). Schneider, C., Velea, M. N., Kazemahvazi, S. & Zenkert, D. Compression properties of novel thermoplastic carbon fibre and poly-ethylene terephthalate fibre composite lattice structures. Mater. & Des. (1980-2015) 65 , 1110–1120 (2015). Dong, L. & Wadley, H. Mechanical properties of carbon fiber composite octet-truss lattice structures. Compos. Sci. Technol. 119 , 26–33 (2015). Wang, X.-T., Li, X.-W. & Ma, L. Interlocking assembled 3d auxetic cellular structures. Mater. & Des. 99 , 467–476 (2016). Wang, B., Wu, L., Ma, L., Sun, Y. & Du, S. Mechanical behavior of the sandwich structures with carbon fiber-reinforced pyramidal lattice truss core. Mater. & Des. (1980-2015) 31 , 2659–2663 (2010). Liu, X., Alizadeh, V. & Hansen, C. J. The compressive response of octet lattice structures with carbon fiber composite hollow struts. Compos. Struct. 239 , 111999 (2020). Xu, B. et al. Long-fiber reinforced thermoplastic composite lattice structures: fabrication and compressive properties. Compos. Part A: Appl. Sci. Manuf. 97 , 41–50 (2017). Markforged. Metal x system. . Zok, F. W. et al. A protocol for characterizing the structural performance of metallic sandwich panels: application to pyramidal truss cores. Int. J. Solids Struct. 41 , 6249–6271 (2004). Makerbot. Method carbon fiber. . Liu, S., Li, Y. & Li, N. A novel free-hanging 3d printing method for continuous carbon fiber reinforced thermoplastic lattice truss core structures. Mater. & Des. 137 , 235–244 (2018). Eichenhofer, M., Wong, J. C. & Ermanni, P. Continuous lattice fabrication of ultra-lightweight composite structures. Addit. Manuf. 18 , 48–57 (2017). Che, L. et al. Compressive and shear characteristics of an octahedral stitched sandwich composite. Compos. Struct. 112 , 179–187 (2014). Fan, H., Meng, F. & Yang, W. Mechanical behaviors and bending effects of carbon fiber reinforced lattice materials. Arch. Appl. Mech. 75 , 635–647 (2006). Yin, S., Wu, L., Ma, L. & Nutt, S. Hybrid truss concepts for carbon fiber composite pyramidal lattice structures. Compos. Part B: Eng. 43 , 1749–1755 (2012). Xiong, J., Ma, L., Vaziri, A., Yang, J. & Wu, L. Mechanical behavior of carbon fiber composite lattice core sandwich panels fabricated by laser cutting. Acta Materialia 60 , 5322–5334 (2012). Pederson, J. Finite element analysis of carbon fiber composite ripping using ABAQUS . Ph.D. thesis, Clemson University (2008). Liu, P., Xing, L. & Zheng, J. Failure analysis of carbon fiber/epoxy composite cylindrical laminates using explicit finite element method. Compos. Part B: Eng. 56 , 54–61 (2014). Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 10 Sep, 2023 Read the published version in Scientific Reports → Version 1 posted Editorial decision: Major revision 17 May, 2023 Reviews received at journal 10 May, 2023 Reviewers agreed at journal 04 May, 2023 Reviewers agreed at journal 04 May, 2023 Reviewers invited by journal 13 Apr, 2023 Editor assigned by journal 13 Apr, 2023 Editor invited by journal 06 Apr, 2023 Submission checks completed at journal 06 Apr, 2023 First submitted to journal 31 Mar, 2023 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-2762108","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":189696776,"identity":"690126ff-ddd0-4dda-8450-9eee0c5b3e21","order_by":0,"name":"Hayley McClintock","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA2klEQVRIiWNgGAWjYBACAwbmgw8+VNgwMLAzMDADuUCQQEgLW7LhjDNpIPVEa+Exk+ZtOwzVwkCEFnOxA8YGvG3n5fmZeUw3FxTYMfCz5xjg1WI5OyHxgcS524Yzm3nMbs8wSGaQ7HmDX4vB7YTDBgZltxMMDgO18BgAvXODgC0GtxPbJBLYzsG01DPYE9aSzCZxoO0ATMthBgMJglrSmA0bziQD/cJWBvTLcR6JM88KCGjJ//j4T4WdPD9787bbBX+q5fjbkzfg1YIBeEhTPgpGwSgYBaMAKwAADRZF3MaV5OIAAAAASUVORK5CYII=","orcid":"","institution":"Columbia University","correspondingAuthor":true,"prefix":"","firstName":"Hayley","middleName":"","lastName":"McClintock","suffix":""},{"id":189696777,"identity":"b421d4c9-94cc-46d3-8124-c26ac1366531","order_by":1,"name":"Hod Lipson","email":"","orcid":"","institution":"Columbia University","correspondingAuthor":false,"prefix":"","firstName":"Hod","middleName":"","lastName":"Lipson","suffix":""},{"id":189696778,"identity":"73cab095-4404-4f54-9ca9-aa719284e423","order_by":2,"name":"Zechen Xiong","email":"","orcid":"","institution":"Columbia University","correspondingAuthor":false,"prefix":"","firstName":"Zechen","middleName":"","lastName":"Xiong","suffix":""},{"id":189696779,"identity":"ad4877b3-ffa4-46c5-9ed4-f909861b6452","order_by":3,"name":"Bruno Rergis","email":"","orcid":"","institution":"Columbia University","correspondingAuthor":false,"prefix":"","firstName":"Bruno","middleName":"","lastName":"Rergis","suffix":""}],"badges":[],"createdAt":"2023-03-31 15:44:13","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-2762108/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-2762108/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41598-023-40962-4","type":"published","date":"2023-09-10T15:01:55+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":35525205,"identity":"d43ba419-051c-4c96-9633-09bde3577734","added_by":"auto","created_at":"2023-04-10 14:11:02","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":1628905,"visible":true,"origin":"","legend":"\u003cp\u003eWoven carbon fiber lattices. a) Lattice woven without supporting carbon fiber tubes. b) Lattice woven with supporting carbon fiber tubes with a 3mm outer diameter. c) Lattice woven with supporting carbon fiber tubes with a 8mm outer diameter. d) Lattice with an alternative weave pattern. e) Lattice with a differing density weave pattern. f) Lattice woven with a height gradation.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-2762108/v1/2907aecb1325036d08b4e9ff.png"},{"id":35523897,"identity":"69ecc9b4-ee08-47d7-afd8-ad14d809df50","added_by":"auto","created_at":"2023-04-10 14:03:02","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":1075426,"visible":true,"origin":"","legend":"\u003cp\u003eLattice fabrication. a) Side cross-section schematic of weaving process. b) Top view schematic of weaving process. The blue and purple arrows denote the direction of the weaving. c) Images of the weaving fabrication process.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-2762108/v1/c0951bb31d7e5e67e797839f.png"},{"id":35523900,"identity":"255f8956-7661-410f-a526-1d8752151e51","added_by":"auto","created_at":"2023-04-10 14:03:02","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":1572543,"visible":true,"origin":"","legend":"\u003cp\u003eFailure modes. a) Failure mode of a lattice made without tubes. b) Failure mode of a lattice made with tubes with an outer diameter of 3mm. Failure occurs at both the tube and the diagonal truss. c) Failure mode of lattice made with tubes with an outer diameter of 8mm. Failure occurs at both the tube and the diagonal truss.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-2762108/v1/d8e75d76136521f5d961bdc0.png"},{"id":35523898,"identity":"80421c12-eecb-49a6-bbd0-00f2bbe1778a","added_by":"auto","created_at":"2023-04-10 14:03:02","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":224532,"visible":true,"origin":"","legend":"\u003cp\u003eCompression strength comparison. Comparison of the compressive strengths as a function of relative density for similar lattice structures. Specific values for compression strength and relative density are given in Table 1.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-2762108/v1/f50fc4d7a4d3e6bbc4e99dbe.png"},{"id":35523901,"identity":"0751eb2f-fd10-4a70-8f77-ca81f064d7f0","added_by":"auto","created_at":"2023-04-10 14:03:02","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":142308,"visible":true,"origin":"","legend":"\u003cp\u003eCompression test results. A total of five samples were tested for each lattice geometry. FE model results are shown in blue. a) Stress-strain curves for lattices made without tubes. b) Stress-strain curves for lattices made with tubes with an outer diameter of 3mm. c) Stress-strain curves for lattices made with tubes with an outer diameter of 8mm.\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-2762108/v1/a0f763772fb1b504fa2a5850.png"},{"id":35523902,"identity":"dad3ffbd-3d62-4fd3-a629-b05d4e4ec4e6","added_by":"auto","created_at":"2023-04-10 14:03:03","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":1352420,"visible":true,"origin":"","legend":"\u003cp\u003eFinite-element (FE) modeling of the carbon fiber/epoxy lattice structures. Hashin damage variables HSNFCCRT (fiber direction compression criterion value), HSNMTCRT (transverse direction tensile damage criterium value), and DMICRTMAXVAL (maximum damage initiation value) are contoured respectively in models 1-3 due to their different failure modes. Red squares denote compressive buckling and cracking in the diagonal struts, yellow squares mean tube transverse tensile failure, and purple squares indicate tube buckling. The bottom row shows the corresponding failure observed in the experimental samples.\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-2762108/v1/9a9ff167ff48b9517dd7b72a.png"},{"id":42947375,"identity":"f9081f2f-055d-4c9d-874a-f0350634c588","added_by":"auto","created_at":"2023-09-11 15:08:51","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":5287390,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-2762108/v1/47cf59ef-1cfb-459f-a9a1-da556179a13e.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Design and fabrication of carbon fiber lattices using 3D weaving","fulltext":[{"header":"Introduction","content":"\u003cp\u003eWhen designing structures for aerospace applications, it is critical to reduce mass as much as possible while maintaining strength. To achieve this objective, lattice structures are often used as a way to engineer a low density material that maintains the desired mechanical properties. Lattice geometry has long been the subject of scientific study. There are a number of geometries that yield high performance lattices, such as octet-truss\u003csup\u003e1\u003c/sup\u003e, tetrahedral\u003csup\u003e2\u003c/sup\u003e\u003csup\u003e,\u003c/sup\u003e\u003csup\u003e3\u003c/sup\u003e, pyramidal\u003csup\u003e4\u003c/sup\u003e\u003csup\u003e,\u003c/sup\u003e\u003csup\u003e5\u003c/sup\u003e, and 3D Kagome lattices\u003csup\u003e6\u003c/sup\u003e\u003csup\u003e,\u003c/sup\u003e\u003csup\u003e7\u003c/sup\u003e. Traditionally, these lattices were made from metal, and were fabricated using traditional manufacturing methods such as investment casting\u003csup\u003e8\u003c/sup\u003e and sheet folding\u003csup\u003e9\u003c/sup\u003e\u003csup\u003e\u0026ndash;\u003c/sup\u003e\u003csup\u003e11\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eRecently, carbon fiber has emerged as a superior alternative to metal for constructing lattices. With a higher strength to weight ratio, carbon fiber performs better than other previously used metals. Carbon fiber lattices can be fabricated using some of the same methods used for metallic lattices. Common techniques are usually cutting and folding\u003csup\u003e12\u003c/sup\u003e\u003csup\u003e,\u003c/sup\u003e\u003csup\u003e13\u003c/sup\u003e, snap fitting\u003csup\u003e5\u003c/sup\u003e\u003csup\u003e,\u003c/sup\u003e\u003csup\u003e14\u003c/sup\u003e, hot press molding\u003csup\u003e10\u003c/sup\u003e\u003csup\u003e,\u003c/sup\u003e\u003csup\u003e11\u003c/sup\u003e\u003csup\u003e,\u003c/sup\u003e\u003csup\u003e15\u003c/sup\u003e, or using mechanical fasteners\u003csup\u003e16\u003c/sup\u003e\u003csup\u003e,\u003c/sup\u003e\u003csup\u003e17\u003c/sup\u003e. One drawback with almost all of these fabrication methods is that they require manual assembly. This is time consuming and unwieldy, and is not practical for fabricating structures at larger scales.\u003c/p\u003e\n\u003cp\u003eOne possible avenue to circumvent this issue is to use additive manufacturing methods, such as 3D printing. By em- ploying digital manufacturing processes, not only is fabrication time reduced, but errors introduced by manual assembly are eliminated as well. Moreover, the programability of digital manufacturing processes allows for customization and optimization not afforded using bulk production processes.\u003c/p\u003e\n\u003cp\u003eCurrently, there are a number of carbon fiber 3D printers commercially available. Many use chopped carbon fiber particles mixed with thermosets\u003csup\u003e18\u003c/sup\u003e, but some also use continuous carbon fibers\u003csup\u003e19\u003c/sup\u003e\u003csup\u003e,\u003c/sup\u003e\u003csup\u003e20\u003c/sup\u003e, though these fibers do not usually span across multiple layers. For example, Liu et. al\u003csup\u003e21\u003c/sup\u003e demonstrated a free-hanging 3D printing technique that allows for the truss orientation to follow the axis of the slant of the struts. Similarly, Eichenhofer et. al\u003csup\u003e22\u003c/sup\u003e presented a pultrusion/extrusion method to additively manufacture lattices in a continuous manner with directed orientation of the fibers. However, the 3D printing process can still be quite time consuming. However, additive manufacturing frequently these methods would not allow for a robust connection between layers if a lattice was made with more than one unit cell in height.\u003c/p\u003e\n\u003cp\u003eIn this research, we explore an alternative method to designing and fabricating carbon fiber lattices. Drawing inspiration from crocheting and sewing processes, the carbon fiber is woven through a diagonal carbon fiber grid held tightly in a jig. These taught threads are equivalent to the \u003cem\u003ewarp \u003c/em\u003ethreads in a loom, except that they are criscrossed into a lattice instead of being parallel. We then join lattice by weaving thread vertically, equivalent o the \u003cem\u003eWeft \u003c/em\u003ethreads in a loom. \u003c/p\u003e\n\u003cp\u003eThe resulting 3D lattices then contain both diagonal and rectangular struts. Though previous work has demonstrated the effectiveness of woven lattices\u003csup\u003e23\u003c/sup\u003e\u003csup\u003e,\u003c/sup\u003e\u003csup\u003e24\u003c/sup\u003e, the method here offers the advantage of not needing a faceplate during fabrication. Without the restriction of the faceplate, more advanced designs can be created. For example, the warp planes do not need to be parallel to each other or even planar or uniform. Similarly, the weft threads can be non-uniform, optimizing strength to weight performance.\u003c/p\u003e"},{"header":"Methods","content":"\u003cp\u003eCarbon fiber tow is used as the main lattice material, as it is high strength and low weight, and is commercially available. The carbon fiber tow (HMT301-34/700 Tow Preg, Northern Composites) is pre-impregnanted with resin, meaning that the tow can be directly cured without having to apply resin after shaping the material. The method described here is based on crocheting and sewing principles. First, an aluminum jig is fabricated that contains holes along each wall. Carbon fiber tow can then be woven through these holes to form a diagonal grid. Two layers of these grids are woven onto the jig to use as a substrate for the weaving process. Additionally, if desired, vertical carbon fiber tubes can be added at each node of the grid by placing unidirectional carbon fiber tubes (McMaster-Carr) at the nodes and curing them in place with a small amount of epoxy. Here, two different tubes are studied; one with an outer diameter of 3mm and an inner diameter of 2mm, and another with an outer diameter of 8mm and an inner diameter of 6mm. Once the tubes are cured in place (or after the grid is woven if tubes are not being used), a latch hook is used to loop and knot carbon fiber tow around the grid. The latch hook is first lowered through both grid layers with the latch open. Then, the carbon fiber tow is wrapped around the hook, and the hook is pulled back up and the latch is closed. Once pulled through, the latch hook is then moved above the next location and the process is repeated. An overview of this process can be found in Figure . Once the grid is in place, the lattices are cured at 450\u0026deg;F for 20 minutes. After curing, the lattice is removed by cutting the connections to the jig. Both the weaving process and the removal process can be automated in future iterations of this project. A final step of dipping the entire structure in epoxy is also added to increase the strength of the lattice. An overview of this process is shown in Figure 2.\u003c/p\u003e"},{"header":"Results","content":"\u003cp\u003eThree different lattice designs were tested in this study. These include two lattices made with different diameter tubes and a lattice woven without tubes. Examples of these structures, as well as other lattice designs, are shown in Figure 3. The variety of fabricated structures demonstrates the versatility of the design approach.\u003c/p\u003e\n\u003ch3\u003eCompression testing\u003c/h3\u003e\n\u003cp\u003eTo characterize the strength of the lattice, compression tests were performed on three different designs to determine their respective compressive strengths. Samples were placed in a universal testing machine (Instron) and compressed at a rate of 5 mm/min. This gave a maximum force, which was then converted to compressive strength by dividing by the cross sectional area of the lattice. Relative density was computed by normalizing the density of the lattices by the density of the constituent carbon fiber, coated in epoxy. This value was computed experimentally, and was found to be 1100 kg/\u003cem\u003em\u003c/em\u003e\u003csup\u003e3\u003c/sup\u003e. The results of the compression tests are shown in Figure 4, where the data is also plotted with reported values from similar lattice structures found in the literature. Stress-strain curves were also computed for each sample type, and are shown in Figure 5.\u003c/p\u003e\n\u003cp\u003eCompared to similar lattices, the lattices with the added carbon fiber tubes show a comparable performance to similar designs. However, many other similar designs utilize a faceplate when testing their lattices. This adds a significant amount of structural support. The lattice presented here was specifically designed without a faceplate so as to provide maximum flexibility with the weaving design. During compression tests of the lattice designs, videos were captured to examine the main failure modes of the structures (movies S1, S2, S3). For the lattice made without tubes, the main failure mode was the buckling of the diagonal struts, but there was also some delamination of the struts from the horizontal, diagonal grids, which caused the internal structure to slide. As shown in Figure 3, there are two failure modes for the woven lattice with the vertical tubes; buckling of the carbon fiber tubes and buckling of the diagonal struts. In compression, the tubes are the main supporting feature, but in bending or in out-of-plane compression, a different failure mode is expected and the supporting woven structure should provide the needed support.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTable 1.\u0026nbsp;\u003c/strong\u003eList of comparable carbon fiber lattices.\u003c/p\u003e\n\u003ctable border=\"1\" cellpadding=\"0\" cellspacing=\"0\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"18.452380952380953%\"\u003e\n \u003cp\u003e\u003cstrong\u003eSource\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"23.214285714285715%\"\u003e\n \u003cp\u003e\u003cstrong\u003eMethod\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.625%\"\u003e\n \u003cp\u003e\u003cstrong\u003eDensity\u0026nbsp;(kg/m\u003c/strong\u003e\u003cstrong\u003e3\u003c/strong\u003e\u003cstrong\u003e)\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"16.071428571428573%\"\u003e\n \u003cp\u003e\u003cstrong\u003eRelative\u0026nbsp;Density\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.178571428571429%\"\u003e\n \u003cp\u003e\u003cstrong\u003eCompressive\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003estrength\u0026nbsp;(MPa)\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"11.458333333333334%\"\u003e\n \u003cp\u003e\u003cstrong\u003eFaceplate?\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"18.452380952380953%\"\u003e\n \u003cp\u003eLiu,\u0026nbsp;et.\u0026nbsp;al\u003ca href=\"#_bookmark25\"\u003e\u003csup\u003e21\u003c/sup\u003e\u003c/a\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"23.214285714285715%\"\u003e\n \u003cp\u003e3D\u0026nbsp;Printing\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.625%\"\u003e\n \u003cp\u003e29.56\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"16.071428571428573%\"\u003e\n \u003cp\u003e0.056\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.178571428571429%\"\u003e\n \u003cp\u003e1.24\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"11.458333333333334%\"\u003e\n \u003cp\u003eYes\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"18.452380952380953%\"\u003e\n \u003cp\u003eXu,\u0026nbsp;et.\u0026nbsp;al\u003ca href=\"#_bookmark21\"\u003e\u003csup\u003e17\u003c/sup\u003e\u003c/a\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"23.214285714285715%\"\u003e\n \u003cp\u003eMechanical\u0026nbsp;fasteners\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.625%\"\u003e\n \u003cp\u003e28.78\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"16.071428571428573%\"\u003e\n \u003cp\u003e0.03\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.178571428571429%\"\u003e\n \u003cp\u003e0.1198\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"11.458333333333334%\"\u003e\n \u003cp\u003eNo\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"18.452380952380953%\"\u003e\n \u003cp\u003eSchneider,\u0026nbsp;et.\u0026nbsp;al\u003ca href=\"#_bookmark16\"\u003e\u003csup\u003e12\u003c/sup\u003e\u003c/a\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"23.214285714285715%\"\u003e\n \u003cp\u003eHot\u0026nbsp;press\u0026nbsp;molding\u0026nbsp;and\u0026nbsp;cut\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.625%\"\u003e\n \u003cp\u003e60\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"16.071428571428573%\"\u003e\n \u003cp\u003e0.037\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.178571428571429%\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"11.458333333333334%\"\u003e\n \u003cp\u003eYes\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"18.452380952380953%\"\u003e\n \u003cp\u003eYin,\u0026nbsp;et.\u0026nbsp;al\u003ca href=\"#_bookmark29\"\u003e\u003csup\u003e25\u003c/sup\u003e\u003c/a\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"23.214285714285715%\"\u003e\n \u003cp\u003eHot\u0026nbsp;press\u0026nbsp;molding\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.625%\"\u003e\n \u003cp\u003e0.16\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"16.071428571428573%\"\u003e\n \u003cp\u003e0.00585\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.178571428571429%\"\u003e\n \u003cp\u003e0.447\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"11.458333333333334%\"\u003e\n \u003cp\u003eYes\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"18.452380952380953%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"23.214285714285715%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.625%\"\u003e\n \u003cp\u003e2.28\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"16.071428571428573%\"\u003e\n \u003cp\u003e0.0645\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.178571428571429%\"\u003e\n \u003cp\u003e1.35\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"11.458333333333334%\"\u003e\n \u003cp\u003eYes\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"18.452380952380953%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"23.214285714285715%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.625%\"\u003e\n \u003cp\u003e2.28\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"16.071428571428573%\"\u003e\n \u003cp\u003e0.0645\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.178571428571429%\"\u003e\n \u003cp\u003e1.21\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"11.458333333333334%\"\u003e\n \u003cp\u003eYes\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"18.452380952380953%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"23.214285714285715%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.625%\"\u003e\n \u003cp\u003e0.43\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"16.071428571428573%\"\u003e\n \u003cp\u003e0.0123\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.178571428571429%\"\u003e\n \u003cp\u003e1.31\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"11.458333333333334%\"\u003e\n \u003cp\u003eYes\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"18.452380952380953%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"23.214285714285715%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.625%\"\u003e\n \u003cp\u003e0.27\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"16.071428571428573%\"\u003e\n \u003cp\u003e0.0103\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.178571428571429%\"\u003e\n \u003cp\u003e0.66\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"11.458333333333334%\"\u003e\n \u003cp\u003eYes\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"18.452380952380953%\"\u003e\n \u003cp\u003eWang,\u0026nbsp;et.\u0026nbsp;al\u003ca href=\"#_bookmark19\"\u003e\u003csup\u003e15\u003c/sup\u003e\u003c/a\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"23.214285714285715%\"\u003e\n \u003cp\u003eHot\u0026nbsp;press\u0026nbsp;molding\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.625%\"\u003e\n \u003cp\u003e12.78\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"16.071428571428573%\"\u003e\n \u003cp\u003e0.012\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.178571428571429%\"\u003e\n \u003cp\u003e0.84\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"11.458333333333334%\"\u003e\n \u003cp\u003eYes\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"18.452380952380953%\"\u003e\n \u003cp\u003eDong,\u0026nbsp;et.\u0026nbsp;al\u003ca href=\"#_bookmark17\"\u003e\u003csup\u003e13\u003c/sup\u003e\u003c/a\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"23.214285714285715%\"\u003e\n \u003cp\u003eSnap\u0026nbsp;fit\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.625%\"\u003e\n \u003cp\u003e24.48\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"16.071428571428573%\"\u003e\n \u003cp\u003e0.017\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.178571428571429%\"\u003e\n \u003cp\u003e0.073\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"11.458333333333334%\"\u003e\n \u003cp\u003eNo\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"18.452380952380953%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"23.214285714285715%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.625%\"\u003e\n \u003cp\u003e77.76\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"16.071428571428573%\"\u003e\n \u003cp\u003e0.054\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.178571428571429%\"\u003e\n \u003cp\u003e4.39\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"11.458333333333334%\"\u003e\n \u003cp\u003eNo\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"18.452380952380953%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"23.214285714285715%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.625%\"\u003e\n \u003cp\u003e135.36\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"16.071428571428573%\"\u003e\n \u003cp\u003e0.094\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.178571428571429%\"\u003e\n \u003cp\u003e7.98\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"11.458333333333334%\"\u003e\n \u003cp\u003eNo\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"18.452380952380953%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"23.214285714285715%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.625%\"\u003e\n \u003cp\u003e187.2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"16.071428571428573%\"\u003e\n \u003cp\u003e0.13\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.178571428571429%\"\u003e\n \u003cp\u003e9.9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"11.458333333333334%\"\u003e\n \u003cp\u003eNo\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"18.452380952380953%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"23.214285714285715%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.625%\"\u003e\n \u003cp\u003e228.96\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"16.071428571428573%\"\u003e\n \u003cp\u003e0.159\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.178571428571429%\"\u003e\n \u003cp\u003e11.39\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"11.458333333333334%\"\u003e\n \u003cp\u003eNo\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"18.452380952380953%\"\u003e\n \u003cp\u003eWu,\u0026nbsp;et.\u0026nbsp;al\u003ca href=\"#_bookmark15\"\u003e\u003csup\u003e11\u003c/sup\u003e\u003c/a\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"23.214285714285715%\"\u003e\n \u003cp\u003eHot\u0026nbsp;press\u0026nbsp;molding\u0026nbsp;and\u0026nbsp;cut\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.625%\"\u003e\n \u003cp\u003e79.70\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"16.071428571428573%\"\u003e\n \u003cp\u003e0.0547\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.178571428571429%\"\u003e\n \u003cp\u003e12.44\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"11.458333333333334%\"\u003e\n \u003cp\u003eYes\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"18.452380952380953%\"\u003e\n \u003cp\u003eEichenhofer,\u0026nbsp;et.\u0026nbsp;al\u003ca href=\"#_bookmark26\"\u003e\u003csup\u003e22\u003c/sup\u003e\u003c/a\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"23.214285714285715%\"\u003e\n \u003cp\u003ePultrusion/extrusion\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.625%\"\u003e\n \u003cp\u003e9.22\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"16.071428571428573%\"\u003e\n \u003cp\u003e0.0066\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.178571428571429%\"\u003e\n \u003cp\u003e0.2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"11.458333333333334%\"\u003e\n \u003cp\u003eYes\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"18.452380952380953%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"23.214285714285715%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.625%\"\u003e\n \u003cp\u003e8.67\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"16.071428571428573%\"\u003e\n \u003cp\u003e0.0062\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.178571428571429%\"\u003e\n \u003cp\u003e0.18\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"11.458333333333334%\"\u003e\n \u003cp\u003eYes\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"18.452380952380953%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"23.214285714285715%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.625%\"\u003e\n \u003cp\u003e8.63\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"16.071428571428573%\"\u003e\n \u003cp\u003e0.0061\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.178571428571429%\"\u003e\n \u003cp\u003e0.23\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"11.458333333333334%\"\u003e\n \u003cp\u003eYes\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"18.452380952380953%\"\u003e\n \u003cp\u003eXiong,\u0026nbsp;et.\u0026nbsp;al\u003ca href=\"#_bookmark30\"\u003e\u003csup\u003e26\u003c/sup\u003e\u003c/a\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"23.214285714285715%\"\u003e\n \u003cp\u003eHot\u0026nbsp;press\u0026nbsp;molding\u0026nbsp;and\u0026nbsp;cut\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.625%\"\u003e\n \u003cp\u003e52.86\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"16.071428571428573%\"\u003e\n \u003cp\u003e0.0341\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.178571428571429%\"\u003e\n \u003cp\u003e0.32\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"11.458333333333334%\"\u003e\n \u003cp\u003eNo\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"18.452380952380953%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"23.214285714285715%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.625%\"\u003e\n \u003cp\u003e77.35\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"16.071428571428573%\"\u003e\n \u003cp\u003e0.0499\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.178571428571429%\"\u003e\n \u003cp\u003e0.91\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"11.458333333333334%\"\u003e\n \u003cp\u003eNo\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"18.452380952380953%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"23.214285714285715%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.625%\"\u003e\n \u003cp\u003e122.61\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"16.071428571428573%\"\u003e\n \u003cp\u003e0.0791\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.178571428571429%\"\u003e\n \u003cp\u003e1.78\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"11.458333333333334%\"\u003e\n \u003cp\u003eNo\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"18.452380952380953%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"23.214285714285715%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.625%\"\u003e\n \u003cp\u003e52.86\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"16.071428571428573%\"\u003e\n \u003cp\u003e0.0341\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.178571428571429%\"\u003e\n \u003cp\u003e0.21\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"11.458333333333334%\"\u003e\n \u003cp\u003eNo\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"18.452380952380953%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"23.214285714285715%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.625%\"\u003e\n \u003cp\u003e77.35\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"16.071428571428573%\"\u003e\n \u003cp\u003e0.0499\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.178571428571429%\"\u003e\n \u003cp\u003e0.54\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"11.458333333333334%\"\u003e\n \u003cp\u003eNo\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"18.452380952380953%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"23.214285714285715%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.625%\"\u003e\n \u003cp\u003e122.61\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"16.071428571428573%\"\u003e\n \u003cp\u003e0.0791\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.178571428571429%\"\u003e\n \u003cp\u003e1.01\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"11.458333333333334%\"\u003e\n \u003cp\u003eNo\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"18.452380952380953%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"23.214285714285715%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.625%\"\u003e\n \u003cp\u003e50.53\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"16.071428571428573%\"\u003e\n \u003cp\u003e0.0326\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.178571428571429%\"\u003e\n \u003cp\u003e0.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"11.458333333333334%\"\u003e\n \u003cp\u003eNo\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"18.452380952380953%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"23.214285714285715%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.625%\"\u003e\n \u003cp\u003e73.94\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"16.071428571428573%\"\u003e\n \u003cp\u003e0.0477\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.178571428571429%\"\u003e\n \u003cp\u003e1.03\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"11.458333333333334%\"\u003e\n \u003cp\u003eNo\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"18.452380952380953%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"23.214285714285715%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.625%\"\u003e\n \u003cp\u003e117.03\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"16.071428571428573%\"\u003e\n \u003cp\u003e0.0755\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.178571428571429%\"\u003e\n \u003cp\u003e1.92\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"11.458333333333334%\"\u003e\n \u003cp\u003eNo\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"18.452380952380953%\"\u003e\n \u003cp\u003eSun,\u0026nbsp;et.\u0026nbsp;al\u003ca href=\"#_bookmark14\"\u003e\u003csup\u003e10\u003c/sup\u003e\u003c/a\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"23.214285714285715%\"\u003e\n \u003cp\u003eHot\u0026nbsp;press\u0026nbsp;molding\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.625%\"\u003e\n \u003cp\u003e42.16\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"16.071428571428573%\"\u003e\n \u003cp\u003e0.0272\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.178571428571429%\"\u003e\n \u003cp\u003e4.83\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"11.458333333333334%\"\u003e\n \u003cp\u003eYes\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"18.452380952380953%\"\u003e\n \u003cp\u003eChe,\u0026nbsp;et.\u0026nbsp;al\u003ca href=\"#_bookmark27\"\u003e\u003csup\u003e23\u003c/sup\u003e\u003c/a\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"23.214285714285715%\"\u003e\n \u003cp\u003eStitching\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.625%\"\u003e\n \u003cp\u003e7.17\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"16.071428571428573%\"\u003e\n \u003cp\u003e0.0075\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.178571428571429%\"\u003e\n \u003cp\u003e0.33\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"11.458333333333334%\"\u003e\n \u003cp\u003eYes\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"18.452380952380953%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"23.214285714285715%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.625%\"\u003e\n \u003cp\u003e22.27\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"16.071428571428573%\"\u003e\n \u003cp\u003e0.0141\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.178571428571429%\"\u003e\n \u003cp\u003e1.14\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"11.458333333333334%\"\u003e\n \u003cp\u003eYes\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"18.452380952380953%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"23.214285714285715%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.625%\"\u003e\n \u003cp\u003e35.71\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"16.071428571428573%\"\u003e\n \u003cp\u003e0.0226\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.178571428571429%\"\u003e\n \u003cp\u003e2.57\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"11.458333333333334%\"\u003e\n \u003cp\u003eYes\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"18.452380952380953%\"\u003e\n \u003cp\u003eFan,\u0026nbsp;et.\u0026nbsp;al\u003ca href=\"#_bookmark28\"\u003e\u003csup\u003e24\u003c/sup\u003e\u003c/a\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"23.214285714285715%\"\u003e\n \u003cp\u003eWeaving\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.625%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"16.071428571428573%\"\u003e\n \u003cp\u003e0.028\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.178571428571429%\"\u003e\n \u003cp\u003e0.77\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"11.458333333333334%\"\u003e\n \u003cp\u003eYes\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"18.452380952380953%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"23.214285714285715%\"\u003e\n \u003cp\u003eSnap\u0026nbsp;fit\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.625%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"16.071428571428573%\"\u003e\n \u003cp\u003e0.086\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.178571428571429%\"\u003e\n \u003cp\u003e1.31\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"11.458333333333334%\"\u003e\n \u003cp\u003eYes\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"18.452380952380953%\"\u003e\n \u003cp\u003eLiu,\u0026nbsp;et.\u0026nbsp;al\u003ca href=\"#_bookmark20\"\u003e\u003csup\u003e16\u003c/sup\u003e\u003c/a\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"23.214285714285715%\"\u003e\n \u003cp\u003eMechanical\u0026nbsp;fasteners\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.625%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"16.071428571428573%\"\u003e\n \u003cp\u003e0.0085\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.178571428571429%\"\u003e\n \u003cp\u003e0.48\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"11.458333333333334%\"\u003e\n \u003cp\u003eYes\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"18.452380952380953%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"23.214285714285715%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.625%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"16.071428571428573%\"\u003e\n \u003cp\u003e0.0133\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.178571428571429%\"\u003e\n \u003cp\u003e1.2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"11.458333333333334%\"\u003e\n \u003cp\u003eYes\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"18.452380952380953%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"23.214285714285715%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.625%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"16.071428571428573%\"\u003e\n \u003cp\u003e0.0168\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.178571428571429%\"\u003e\n \u003cp\u003e1.63\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"11.458333333333334%\"\u003e\n \u003cp\u003eYes\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"18.452380952380953%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"23.214285714285715%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.625%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"16.071428571428573%\"\u003e\n \u003cp\u003e0.0217\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.178571428571429%\"\u003e\n \u003cp\u003e1.97\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"11.458333333333334%\"\u003e\n \u003cp\u003eYes\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"18.452380952380953%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"23.214285714285715%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.625%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"16.071428571428573%\"\u003e\n \u003cp\u003e0.0289\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.178571428571429%\"\u003e\n \u003cp\u003e2.46\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"11.458333333333334%\"\u003e\n \u003cp\u003eYes\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"18.452380952380953%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"23.214285714285715%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.625%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"16.071428571428573%\"\u003e\n \u003cp\u003e0.0435\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.178571428571429%\"\u003e\n \u003cp\u003e3.32\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"11.458333333333334%\"\u003e\n \u003cp\u003eYes\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"18.452380952380953%\"\u003e\n \u003cp\u003eFinnegan,\u0026nbsp;et.\u0026nbsp;al\u003ca href=\"#_bookmark9\"\u003e\u003csup\u003e5\u003c/sup\u003e\u003c/a\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"23.214285714285715%\"\u003e\n \u003cp\u003eSnap\u0026nbsp;fit\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.625%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"16.071428571428573%\"\u003e\n \u003cp\u003e0.01\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.178571428571429%\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"11.458333333333334%\"\u003e\n \u003cp\u003eYes\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"18.452380952380953%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"23.214285714285715%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.625%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"16.071428571428573%\"\u003e\n \u003cp\u003e0.02\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.178571428571429%\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"11.458333333333334%\"\u003e\n \u003cp\u003eYes\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"18.452380952380953%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"23.214285714285715%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.625%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"16.071428571428573%\"\u003e\n \u003cp\u003e0.035\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.178571428571429%\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"11.458333333333334%\"\u003e\n \u003cp\u003eYes\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"18.452380952380953%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"23.214285714285715%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.625%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"16.071428571428573%\"\u003e\n \u003cp\u003e0.05\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.178571428571429%\"\u003e\n \u003cp\u003e9.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"11.458333333333334%\"\u003e\n \u003cp\u003eYes\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"18.452380952380953%\"\u003e\n \u003cp\u003eThis\u0026nbsp;work\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"23.214285714285715%\"\u003e\n \u003cp\u003eWeaving\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.625%\"\u003e\n \u003cp\u003e89.68\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"16.071428571428573%\"\u003e\n \u003cp\u003e0.0813\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.178571428571429%\"\u003e\n \u003cp\u003e1.01\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"11.458333333333334%\"\u003e\n \u003cp\u003eNo\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"18.452380952380953%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"23.214285714285715%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.625%\"\u003e\n \u003cp\u003e88.66\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"16.071428571428573%\"\u003e\n \u003cp\u003e0.0804\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.178571428571429%\"\u003e\n \u003cp\u003e2.80\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"11.458333333333334%\"\u003e\n \u003cp\u003eNo\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"18.452380952380953%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"23.214285714285715%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.625%\"\u003e\n \u003cp\u003e144.86\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"16.071428571428573%\"\u003e\n \u003cp\u003e0.1314\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.178571428571429%\"\u003e\n \u003cp\u003e6.79\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"11.458333333333334%\"\u003e\n \u003cp\u003eNo\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003e\u003cbr\u003e\u003c/p\u003e\n\u003ch3\u003eFinite Element Analysis (FEA)\u003c/h3\u003e\n\u003cp\u003eTo validate the findings from the compression testing, finite element (FE) simulations were also conducted. Correspond- ing FE simulations were performed with the commercial finite element package ABAQUS/Explicit (2020, Dassault Syst\u0026egrave;mes Simulia Corp., USA) to obtain more insight into the compressive behaviors of the carbon fiber/epoxy lattice structures. Three different FE models are built to match the geometries of the fabricated samples in Fig. 3. In each of these models, a total of 4 x 5 repeating units were used and the cured carbon fiber strand is approximated to be a uniform beam with a sectional size of 2.2 mm by 0.5 mm (Figure 6). Overlapped areas (knots) of different carbon fiber ribbons in the lattices are assumed to be non-destructible since they are much stiffer, and are simulated with the isotropic carbon fiber/epoxy model. ABAQUS/Explicit was found to be a better tool than ABAQUS/Standard to simulate complicated nonlinear and failure problems in terms of convergence and computational cost\u003csup\u003e27\u003c/sup\u003e, and that Hashin\u0026rsquo;s damage theory is suitable for fiber-reinforced composite materials\u003csup\u003e16\u003c/sup\u003e. To ensure a quasi-static condition, all compressions are carried out in 90 seconds with a loading rate of 5 mm/min. Additionally, the kinetic energy of all simulations is guaranteed to be a small fraction (less than 5%) of their respective internal energies. A mass scaling factor of 1e7 and total numbers of 13032, 42088, and 35240 S4R elements with 5 integration points are used to address the trade-off between accuracy and economy. While material and geometric imperfections of the specimens due to fabrication processes can not be included in the simulations, a Hashin damage model is defined in Table 2 to reproduce the failure of the experiments.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTable 2.\u0026nbsp;\u003c/strong\u003eMechanical property of the carbon fiber/epoxy composite material. Variable \u003cem\u003e\u0026rho;\u0026nbsp;\u003c/em\u003eis mass density, \u003cem\u003eE\u003csub\u003ei\u003c/sub\u003e\u003c/em\u003e, \u003cem\u003e\u0026nu;\u003csub\u003ei\u003c/sub\u003e \u003csub\u003ej\u003c/sub\u003e\u003c/em\u003e, \u003cem\u003eG\u003csub\u003ei\u003c/sub\u003e \u003csub\u003ej\u003c/sub\u003e\u003c/em\u003e, and \u003cem\u003e\u0026tau;\u003csub\u003ei\u003c/sub\u003e \u003csub\u003ej\u003c/sub\u003e\u0026nbsp;\u003c/em\u003eare Young\u0026rsquo;s modulus, Poisson\u0026rsquo;s ratio, shear modulus, and shear strength in corresponding directions; \u003cem\u003e\u0026sigma;\u003csub\u003ei\u003c/sub\u003e\u003c/em\u003e\u003cem\u003e\u003csub\u003e,T\u003c/sub\u003e\u003c/em\u003e\u003cem\u003e\u003csub\u003e/C\u003c/sub\u003e\u0026nbsp;\u003c/em\u003eand \u003cem\u003eU\u003csub\u003ei\u003c/sub\u003e\u003c/em\u003e\u003cem\u003e\u003csub\u003e,T\u003c/sub\u003e\u003c/em\u003e\u003cem\u003e\u003csub\u003e/C\u003c/sub\u003e\u0026nbsp;\u003c/em\u003eare tensile/compressive strengths in the corresponding directions\u003csup\u003e28\u003c/sup\u003e\u003c/p\u003e\n\u003cp\u003e\u003cimg 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\" width=\"1016\" height=\"92\"\u003e\u003cbr\u003e\u003c/p\u003e\n\u003cp\u003eIn the simulated model without supporting tubes (Model 1 in Figure 6), the compressive loading leads to Euler buckling of the struts and causes cracking and lattice failure (highlighted with red squares in Fig. 6, movie S1). Since all repeating units in a FE lattice are perfectly aligned in the loading direction, the same buckling and cracking patterns appear in different spots almost at the same time. Therefore, the peak and the dropping of its stress-strain curve appear much earlier than that of experimental plots (Figure 5). However, together with the supporting videos, simulation models with tubes reveal two other interesting failure modes. Before the buckling failure of the diagonal struts, the compressive load leads to transverse or matrix tensile failure at the top and bottom of the tubes (Figure 6), i.e., carbon fibers would delaminate in the 90 degree direction due to a much lower transverse strength (movie S2 and movie S3). For the tubes with a higher slenderness ratio in model 2, compressive column buckling takes place in the tubes after a certain level of material degradation, denoting the total failure of the lattice. On the other hand, tubes in model 3 do not buckle due to a larger radius and wall thickness, consistent with the experiments.\u003c/p\u003e"},{"header":"Discussion","content":"\u003cp\u003eHere, a novel carbon fiber lattice was developed using crocheting and sewing techniques. Using a jig with two parallel carbon fiber grids as a scaffold, prepreg carbon fiber tow was woven through the grid in a rectangular pattern using a latch hook. Additional structures with vertical carbon fiber tubes were also studied. This process yields a cellular lattice with a relatively high compressive strength to density ratio and demonstrates a comparable performance to other similar lattice structures found in the literature. However, while other approaches require the presence of a face plate,\u003c/p\u003e\n\n\u003cp\u003ethe absence of a face plate here allows for a more free-form fabrication approach. Additionally, the weaving process in this approach allows for the possibility of automation. While the weaving could be easily automated, the additional steps of adding in vertical tubes and removing excess carbon fiber from the edges will be more difficult to automate.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAcknowledgements\u003c/h2\u003e\n\u003cp\u003eThis research was supported in part by NASA NSTRF grant 80NSSC20K0587, and by the US National Science Foundation (NSF) AI Institute for Dynamical Systems, grant 2112085.\u0026nbsp;\u003c/p\u003e\n\u003ch2\u003eAuthor contributions statement\u003c/h2\u003e\n\u003cp\u003eH.M. and H.L. conceived the experiment(s). H.M., Z.X., B.R. conducted the experiment(s), and H.M. and Z.X. analyzed the results. All authors reviewed the manuscript.\u0026nbsp;\u003c/p\u003e\n\u003ch2\u003eCompeting interests statement\u003c/h2\u003e\n\u003cp\u003eThe authors declare no competing interests.\u0026nbsp;\u003c/p\u003e\n\u003ch2\u003eData Availability\u003c/h2\u003e\n\u003cp\u003eThe datasets used and/or analysed during the current study available from the corresponding author on reasonable request.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eDeshpande, V. S., Fleck, N. A. \u0026amp; Ashby, M. F. Effective properties of the octet-truss lattice material. \u003cem\u003eJ. Mech. Phys. Solids \u003c/em\u003e\u003cstrong\u003e49\u003c/strong\u003e, 1747\u0026ndash;1769 (2001).\u003c/li\u003e\n\u003cli\u003eDeshpande, V. S. \u0026amp; Fleck, N. Collapse of truss core sandwich beams in 3-point bending. \u003cem\u003eInt. J. Solids Struct. \u003c/em\u003e\u003cstrong\u003e38\u003c/strong\u003e, 6275\u0026ndash;6305 (2001).\u003c/li\u003e\n\u003cli\u003eSugimura, Y. Mechanical response of single-layer tetrahedral trusses under shear loading. \u003cem\u003eMech. materials \u003c/em\u003e\u003cstrong\u003e36\u003c/strong\u003e, 715\u0026ndash;721 (2004).\u003c/li\u003e\n\u003cli\u003eHyun, S., Karlsson, A. M., Torquato, S. \u0026amp; Evans, A. Simulated properties of kagom\u0026eacute; and tetragonal truss core panels. \u003cem\u003eInt. J. Solids Struct. \u003c/em\u003e\u003cstrong\u003e40\u003c/strong\u003e, 6989\u0026ndash;6998 (2003).\u003c/li\u003e\n\u003cli\u003eFinnegan, K., Kooistra, G., Wadley, H. N. \u0026amp; Deshpande, V. The compressive response of carbon fiber composite pyramidal truss sandwich cores. \u003cem\u003eInt. J. Mater. Res. \u003c/em\u003e\u003cstrong\u003e98\u003c/strong\u003e, 1264\u0026ndash;1272 (2007).\u003c/li\u003e\n\u003cli\u003eWallach, J. \u0026amp; Gibson, L. Mechanical behavior of a three-dimensional truss material. \u003cem\u003eInt. J. Solids Struct. \u003c/em\u003e\u003cstrong\u003e38\u003c/strong\u003e, 7181\u0026ndash;7196 (2001).\u003c/li\u003e\n\u003cli\u003eWang, J., Evans, A. G., Dharmasena, K. \u0026amp; Wadley, H. G. On the performance of truss panels with kagome cores. \u003cem\u003eInt. J. Solids Struct. \u003c/em\u003e\u003cstrong\u003e40\u003c/strong\u003e, 6981\u0026ndash;6988 (2003).\u003c/li\u003e\n\u003cli\u003eKooistra, G. W., Deshpande, V. S. \u0026amp; Wadley, H. N. Compressive behavior of age hardenable tetrahedral lattice truss structures made from aluminium. \u003cem\u003eActa Materialia \u003c/em\u003e\u003cstrong\u003e52\u003c/strong\u003e, 4229\u0026ndash;4237 (2004).\u003c/li\u003e\n\u003cli\u003eWadley, H. N., Fleck, N. A. \u0026amp; Evans, A. G. Fabrication and structural performance of periodic cellular metal sandwich structures. \u003cem\u003eCompos. science technology \u003c/em\u003e\u003cstrong\u003e63\u003c/strong\u003e, 2331\u0026ndash;2343 (2003).\u003c/li\u003e\n\u003cli\u003eSun, Y., Guo, L.-c., Wang, T.-s., Yao, L.-j. \u0026amp; Sun, X.-y. Bending strength and failure of single-layer and double-layer sandwich structure with graded truss core. \u003cem\u003eCompos. Struct. \u003c/em\u003e\u003cstrong\u003e226\u003c/strong\u003e, 111204 (2019).\u003c/li\u003e\n\u003cli\u003eWu, Q., Ma, L., Wu, L. \u0026amp; Xiong, J. A novel strengthening method for carbon fiber composite lattice truss structures. \u003cem\u003eCompos. Struct. \u003c/em\u003e\u003cstrong\u003e153\u003c/strong\u003e, 585\u0026ndash;592 (2016).\u003c/li\u003e\n\u003cli\u003eSchneider, C., Velea, M. N., Kazemahvazi, S. \u0026amp; Zenkert, D. Compression properties of novel thermoplastic carbon fibre and poly-ethylene terephthalate fibre composite lattice structures. \u003cem\u003eMater. \u0026amp; Des. (1980-2015) \u003c/em\u003e\u003cstrong\u003e65\u003c/strong\u003e, 1110\u0026ndash;1120 (2015).\u003c/li\u003e\n\u003cli\u003eDong, L. \u0026amp; Wadley, H. Mechanical properties of carbon fiber composite octet-truss lattice structures. \u003cem\u003eCompos. Sci. Technol. \u003c/em\u003e\u003cstrong\u003e119\u003c/strong\u003e, 26\u0026ndash;33 (2015).\u003c/li\u003e\n\u003cli\u003eWang, X.-T., Li, X.-W. \u0026amp; Ma, L. Interlocking assembled 3d auxetic cellular structures. \u003cem\u003eMater.\u003c/em\u003e\u003cem\u003e \u003c/em\u003e\u003cem\u003e\u0026amp;\u003c/em\u003e\u003cem\u003e \u003c/em\u003e\u003cem\u003eDes.\u003c/em\u003e\u003cem\u003e \u003c/em\u003e\u003cstrong\u003e99\u003c/strong\u003e, 467\u0026ndash;476 (2016).\u003c/li\u003e\n\u003cli\u003eWang, B., Wu, L., Ma, L., Sun, Y. \u0026amp; Du, S. Mechanical behavior of the sandwich structures with carbon fiber-reinforced pyramidal lattice truss core. \u003cem\u003eMater. \u0026amp; Des. (1980-2015) \u003c/em\u003e\u003cstrong\u003e31\u003c/strong\u003e, 2659\u0026ndash;2663 (2010).\u003c/li\u003e\n\u003cli\u003eLiu, X., Alizadeh, V. \u0026amp; Hansen, C. J. The compressive response of octet lattice structures with carbon fiber composite hollow struts. \u003cem\u003eCompos. Struct. \u003c/em\u003e\u003cstrong\u003e239\u003c/strong\u003e, 111999 (2020).\u003c/li\u003e\n\u003cli\u003eXu, B. \u003cem\u003eet al. \u003c/em\u003eLong-fiber reinforced thermoplastic composite lattice structures: fabrication and compressive properties. \u003cem\u003eCompos. Part A: Appl. Sci. Manuf. \u003c/em\u003e\u003cstrong\u003e97\u003c/strong\u003e, 41\u0026ndash;50 (2017).\u003c/li\u003e\n\u003cli\u003eMarkforged. Metal x system. .\u003c/li\u003e\n\u003cli\u003eZok, F. W. \u003cem\u003eet al. \u003c/em\u003eA protocol for characterizing the structural performance of metallic sandwich panels: application to pyramidal truss cores. \u003cem\u003eInt. J. Solids Struct. \u003c/em\u003e\u003cstrong\u003e41\u003c/strong\u003e, 6249\u0026ndash;6271 (2004).\u003c/li\u003e\n\u003cli\u003eMakerbot. Method carbon fiber. . \u003c/li\u003e\n\u003cli\u003eLiu, S., Li, Y. \u0026amp; Li, N. A novel free-hanging 3d printing method for continuous carbon fiber reinforced thermoplastic lattice truss core structures. \u003cem\u003eMater. \u0026amp; Des. \u003c/em\u003e\u003cstrong\u003e137\u003c/strong\u003e, 235\u0026ndash;244 (2018).\u003c/li\u003e\n\u003cli\u003eEichenhofer, M., Wong, J. C. \u0026amp; Ermanni, P. Continuous lattice fabrication of ultra-lightweight composite structures.\u003cem\u003eAddit. Manuf. \u003c/em\u003e\u003cstrong\u003e18\u003c/strong\u003e, 48\u0026ndash;57 (2017).\u003c/li\u003e\n\u003cli\u003eChe, L. \u003cem\u003eet\u003c/em\u003e\u003cem\u003e \u003c/em\u003e\u003cem\u003eal.\u003c/em\u003e\u003cem\u003e \u003c/em\u003eCompressive and shear characteristics of an octahedral stitched sandwich composite. \u003cem\u003eCompos.\u003c/em\u003e\u003cem\u003e \u003c/em\u003e\u003cem\u003eStruct.\u003c/em\u003e\u003cstrong\u003e112\u003c/strong\u003e, 179\u0026ndash;187 (2014).\u003c/li\u003e\n\u003cli\u003eFan, H., Meng, F. \u0026amp; Yang, W. Mechanical behaviors and bending effects of carbon fiber reinforced lattice materials.\u003cem\u003eArch. Appl. Mech. \u003c/em\u003e\u003cstrong\u003e75\u003c/strong\u003e, 635\u0026ndash;647 (2006).\u003c/li\u003e\n\u003cli\u003eYin, S., Wu, L., Ma, L. \u0026amp; Nutt, S. Hybrid truss concepts for carbon fiber composite pyramidal lattice structures.\u003cem\u003eCompos. Part B: Eng. \u003c/em\u003e\u003cstrong\u003e43\u003c/strong\u003e, 1749\u0026ndash;1755 (2012).\u003c/li\u003e\n\u003cli\u003eXiong, J., Ma, L., Vaziri, A., Yang, J. \u0026amp; Wu, L. Mechanical behavior of carbon fiber composite lattice core sandwich panels fabricated by laser cutting. \u003cem\u003eActa Materialia \u003c/em\u003e\u003cstrong\u003e60\u003c/strong\u003e, 5322\u0026ndash;5334 (2012).\u003c/li\u003e\n\u003cli\u003ePederson, J. \u003cem\u003eFinite element analysis of carbon fiber composite ripping using ABAQUS\u003c/em\u003e. Ph.D. thesis, Clemson University (2008).\u003c/li\u003e\n\u003cli\u003eLiu, P., Xing, L. \u0026amp; Zheng, J. Failure analysis of carbon fiber/epoxy composite cylindrical laminates using explicit finite element method. \u003cem\u003eCompos. Part B: Eng. \u003c/em\u003e\u003cstrong\u003e56\u003c/strong\u003e, 54\u0026ndash;61 (2014).\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-2762108/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-2762108/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"We present a method of designing and fabricating 3D carbon fiber lattices. The lattice design and fabrication is based on crocheting and sewing techniques, where carbon fiber tow is woven through two parallel carbon fiber grids and reinforced with vertical carbon fiber tubes. This process allows for more design flexibility than other current methods. For example, within a single lattice, different density weave patterns can be used to address specific load requirements. Though fabricated manually here, this process can also be automated for large scale production. With this design flexibility, simplified fabrication, and high strength, the lattices proposed here offer an advantage as compared to similar existing structures.","manuscriptTitle":"Design and fabrication of carbon fiber lattices using 3D weaving","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2023-04-10 14:02:57","doi":"10.21203/rs.3.rs-2762108/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Major revision","date":"2023-05-17T06:46:18+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2023-05-10T19:37:15+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"c6da4058-59f6-4ef6-947e-4abb56d35691","date":"2023-05-04T14:27:23+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"e0e30aca-526e-4680-996a-3bbf5e1a80ff","date":"2023-05-04T14:23:06+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2023-04-13T17:02:22+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2023-04-13T16:04:56+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2023-04-06T10:50:41+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2023-04-06T10:44:38+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2023-03-31T15:29:56+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"0c38dfa5-2f92-4c26-b5c0-6510c314895e","owner":[],"postedDate":"April 10th, 2023","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":20511382,"name":"Physical sciences/Engineering/Mechanical engineering"},{"id":20511383,"name":"Physical sciences/Materials science/Structural materials"}],"tags":[],"updatedAt":"2023-09-11T15:06:52+00:00","versionOfRecord":{"articleIdentity":"rs-2762108","link":"https://doi.org/10.1038/s41598-023-40962-4","journal":{"identity":"scientific-reports","isVorOnly":false,"title":"Scientific Reports"},"publishedOn":"2023-09-10 15:01:55","publishedOnDateReadable":"September 10th, 2023"},"versionCreatedAt":"2023-04-10 14:02:57","video":"","vorDoi":"10.1038/s41598-023-40962-4","vorDoiUrl":"https://doi.org/10.1038/s41598-023-40962-4","workflowStages":[]},"version":"v1","identity":"rs-2762108","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-2762108","identity":"rs-2762108","version":["v1"]},"buildId":"_2-kVJe1T_tPrBINL-cwx","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}