Optimization of the Internal Structure of 3d-printed Components for Architectural Restoration

Optimization of the Internal Structure of 3d-printed Components for Architectural Restoration | 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 Research Article Optimization of the Internal Structure of 3d-printed Components for Architectural Restoration Valentina Tomei, Ernesto Grande, Maura Imbimbo This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4207370/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract In recent years, 3D printing technology has assumed an important role in advanced construction processes across various engineering fields. Among these, the application to the architectural restoration of historic structures is particularly fascinating. The ability to precisely reproduce the shape and surface details of complex elements, combined with the availability of a wide range of printing materials, makes 3D printing technology competitive compared to traditional techniques. In this context, the internal volume structure of 3D printed elements represents an additional design parameter to consider for enhancing interventions in terms of reducing the required material, and thus, lowering costs and environmental impact. The paper presents the outcomes of experimental tests and numerical analyses conducted on plates, which represent portions of more complex elements produced by using Additive Manufacturing (AM) technology. These plates feature various internal configurations (such as reticular and rhomboidal patterns) derived from a mono-objective design optimization process. The experimental tests aim to analyze the influence of the configuration and the pattern on the behavior of printed samples. Additionally, the paper discusses insights derived from both theoretical models and Finite Element analyses, providing a clearer understanding of the experimental results. 3D-printing tensile tests three-point bending test design optimization process Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 1 INTRODUCTION The capacity to reproduce complex geometries in short times and the possibility of using different types of materials (among these, also, eco-sustainable ones), make 3D-printing a technology with great potential for applications in different fields, among which architecture and construction [ 1 ]. Among these, applications concerning the recovery of structural heritage are one of the most recent fields of particular interest. Indeed, in current literature are available examples proposing the use of 3D-printing for the reproduction of small museum components [ 2 ], or the reproduction of missing parts of ancient statues [ 3 ]. Other examples concern the reproduction of ornamental architectural components [ 4 ], among which the Roman cornice from the Castulo Archaeological Site [ 5 ], or the restoration of an ancient terra sigillata plate [ 6 ]. In contrast to applications for mechanical devices, which often necessitate specific strength and stiffness characteristics for 3D-printed components, the recovery of architectural/ornamental elements prioritizes refinement of the exterior surface and shape precision. Consequently, optimizing the internal structure configuration is crucial in this context. It enables, indeed, to reduce weight, fabrication costs and environmental impact, as well as to minimize the intrusiveness of connecting the 3D-printed element to the structure, a further important aspect for historical structures. The application of 3D printing for reproducing architectural/ornamental components is currently under study, with a main focus on characterizing the performance of printed materials [ 7 – 15 ]. The parameters of the printing process intrinsically affect the mechanical properties of the printed parts. Therefore, experimental characterization of samples represents a crucial preliminary phase that supports the design process of complex elements derived from 3D printing. In this study, we present both experimental and numerical investigations aimed at assessing the structural performance of 3D printed elements made of PLA material. Initially, the focus is on characterizing the printed material through tensile tests on dog-bone samples. Subsequently, bending tests were conducted on plate samples representing small portions of 3D-printed elements with different internal structure configurations derived from numerical optimization techniques. Additionally, the paper discusses results obtained from theoretical models and Finite Element analyses, providing further insights into the experimental findings. 2 MATERIAL AND METHODS The samples for the experimental tests presented in this paper were manufactured by using additive manufacturing (AM) technology based on the fused filament technique (FFT). The black RAISE3D Premium PLA material was used, with the following main printing parameters set: - filaments diameters: 1.75 mm; - minimum/maximum printing temperature of 190°C/220°C; - nozzle diameter: 0.4 mm; - layer thickness: 0.25 mm; - layer width: 0.5 mm; - infill value: 100%; - nozzle speed: 50 mm/s; - hot-end temperature: 190°C. The selection of the PLA material was primarily based on its advantages over other common 3D printing materials, such as: biodegradability, eco-sustainability, recyclability, low extrusion and bed temperatures, reduced risk of ultrafine particle emission during printing [16–18]. However, the mechanical properties of 3D-printed elements made of PLA material are strongly influenced by various printing parameters (extrusion temperature, flow rate, layer height, and direction) and by the printing process itself [17]. Then, the study presented here further contributes to the state of the art regarding this aspect. To this specific end, dog-bone samples were indeed experimentally analyzed by performing tensile tests finalized to characterize the materials in terms of Young Modulus E and strength in terms of stress s lim . Moreover, the study experimentally and numerically analyzes the influence of the configuration and the pattern of the internal structure of 3D-printed samples representative of components or parts of more complex ornamental elements. For this purpose, plate samples underwent preliminary experimental analysis through three-point bending tests. Subsequently, numerical results were derived by using simple theoretical models and Finite Element analyses. As detailed in the following section, plate samples were printed with varying internal structure configurations (reticular and rhomboidal) and patterns (determined by different inclinations of internal walls). The same printing process was applied to both dog-bone and plate samples. Specifically, for each layer composing the sample, the perimeter was initially printed by following a linear path, while the inner area was subsequently printed by following an inclined path at an angle of ±45° alternately for each successive layer (Figure 1). In the case of dog-bone samples, a temporary support was required during the printing process (Figure 1b). 3 DESIGN OF THE INTERNAL STRUCTURE OF THE PLATE SAMPLES Plate samples were designed with two distinct configurations of the internal structure: reticular and rhomboidal, labeled as PR and PT, respectively. For each configuration, two different patterns, primarily distinguished by varying the inclination θ of the walls forming the internal structure, were also taken into account. These patterns are denoted as PR_60 and PR_72 for the reticular pattern, and PT_27 and PT_45 for the rhomboidal pattern. (Figure 2). Concerning the reticular configuration, the two distinct patterns were defined by interior walls inclined at ±60° (PR_60) and interior walls inclined at ±72° (PR_72). Both configurations maintained an identical thickness for both the flanges and the walls. (Figure 2; Table 1). Regarding the rhomboidal configuration (Figure 2; Table 1), the internal walls were arranged to create a rhomboidal mesh. Specifically, the two distinct patterns considered were distinguished by walls inclined at 27° (PT_27) and, for the other type of sample, walls inclined at 45° (PT_45). For each configuration (reticular and rhomboidal), the two pattern were derived from an optimization design process relied on a parametric geometrical model (Figure 3c) created in Grasshopper [19, 20], along with a corresponding structural model developed in Karamba3D [21]. In detail, for the reticular pattern the problem was set as in the following: - constraint conditions : the structural optimization process was carried out by imposing a constraint condition on the maximum utilization ratio, denoted as U max =s VM /s lim ≤1, where s VM represents the maximum value of Von Mises stress, considering the average strength value deduced from tensile tests on dog-bone samples (s lim =44 MPa, see section 4.1); - parameters : regarding the parameters varied during the optimization process, the PR_60 solution was obtained by adjusting both the slope θ of the internal structure walls and the thickness t (with the latter assumed to be the same for both walls and flanges). On the other hand, the PR_72 solution was derived by varying only the slope θ, while setting the thickness obtained for PR_60. This choice was made to compare structural models with the same thickness. About the rhomboidal configuration, the optimization process was set as in the following: - constraint conditions : the structural optimization process was carried out by imposing as the main constraint condition the same volume of material of the pattern PR_60 of the reticular configuration, in order to compare different solutions with the same volumeFurthermore, considering the average strength value deduced from tensile tests on dog-bone samples (s lim =44 MPa, see section 4.1), an additional constraint was imposed on the maximum utilization ratio, denoted as U max =s VM /s lim ≤1, where s VM represents the maximum value of Von Mises stress; - parameters : regarding the parameters varied during the optimization process, the PT_27 solution was obtained by adjusting both the slope θ of the internal structure walls and the thickness t (with the latter assumed to be the same for both walls and flanges). On the other hand, the PT_45 solution was derived by varying only the thickness t, while setting the slope θ to 45°. Table 1. Dimensions of the samples b 1 (mm) b 2 (mm) h 1 (mm) h 2 (mm) r (mm) t (mm) θ (°) n. of samples DB 150 80 20 10 20 4 - 5 PR_60 200 - 30 100 - 4 60 5 PR_72 200 - 30 100 - 4 72 5 PT_27 200 - 30 100 - 4 27 5 PT_45 200 - 30 100 - 3.5 45 5 The numerical analyses conducted during the optimization process simulated the experimental three-point bending test described in the paper (Figure 3b), where the span was set at S=10 cm and a uniform load was distributed along the centerline of the upper flange (the resultant of this load being the total applied force F). The optimization problem was tackled by using mono-objective genetic algorithms, defining the following objective function OF to be maximized (Eq. 2): where α is a penalty factor, assumed here to be -10 5 , and β is a parameter introduced to adhere to the constraint condition of the utilization ratio (it takes a value of -10 5 when U max >1 and 0 when U max ≤1). Here, V and V* represent respectively the volume of material of the reticular solution PR_60 (taken as the reference value) and the volume obtained during the optimization process. The developed visual script is depicted in Figure 3c, outlining all the main steps. Details regarding the dimensions of the plate sample are presented in Table 1, with the symbols referring to Figure 3. 4 EXPERIMENTAL TESTS 4.1 Dog-bone samples: material characterization The initial phase of the experimental work aimed to explore the behavior of the printed material. For this purpose, tensile tests were conducted on five samples, each featuring a common dog-bone shape (DB, see Figure 4 and Table 1). Tensile tests on DB samples were performed at the University of Cassino and Southern Lazio by using a universal testing machine Gabaldini (Figure 5). The results derived from the tensile tests on DB samples are depicted in Figure 6 in terms of stress-strain curves. Here, the stress was calculated by dividing the applied force by the cross-sectional area of the sample, while the strain was determined by dividing the displacement by the length of the sample. From the plots, it is evident that all the samples exhibit an initial linear phase followed by a post-peak behavior characterized by a softening branch. An average elastic modulus value E=1250 MPa (evaluated at 40% of the peak stress) and an average peak stress value σ lim =44 MPa were deduced from the tensile tests. Despite the similar overall force-displacement response of the samples, it is noticeable from the plots that one of the samples exhibits lower strength and stiffness values, along with greater ductility. This divergent behavior of the sample may be attributed to potential and inevitable misalignments during the test and, moreover, to geometric imperfections arising during the printing process [22, 23]. Figure 7 shows pictures of the DB samples at the conclusion of the tests. From the figure, it is evident that all the samples exhibit a characteristic fracture near the center of the sample. 4.2 Plate samples: structural characterization Regarding the plate samples, three-point bending tests were performed at the laboratory of Pa.L.Mer. in Ferentino (FR), Italy. The results obtained from the three-point bending tests on plates are illustrated in Figure 8, in terms of Force-Displacement curves. Specifically, Figure 8a compares the two patterns of the reticular configuration, while Figure 8b contrasts the two patterns of the rhomboidal configuration. Regarding the reticular configuration, Figure 8a shows that the PR_72 samples exhibit higher peak force and corresponding displacement values compared to the PR_60 samples. However, the differences are relatively small, approximately 10% in terms of peak force and 20% in terms of corresponding displacement (evaluated based on the average values). Conversely, both types of samples demonstrate similar initial stiffness values. On the other hand, concerning the plates with the rhomboidal configuration, it is noticeable that the PT_27 samples demonstrate higher values of both stiffness and strength compared to the samples with the PT_45 pattern. Conversely, the two patterns yield similar values of the displacement at the peak. Comparing the two configurations (reticular and rhomboidal), it is evident that both patterns of the rhomboidal configuration (PT_27 and PT_45) exhibit higher values of both peak force and corresponding displacement compared to the two patterns of the reticular configuration (PR_60 and PR_72). Given that the samples PR_60, PT_27, and PT_45 have the same weight, these results clearly highlight the influence of the pattern on the structural performance of the samples. Examining the failure modes of the reticular plates depicted in Figure 9, similar failure modes are evident for the PR_60 and PR_72 patterns, where cracks occurred in both flanges without affecting the internal walls. In contrast, for plates with the rhomboidal pattern, cracks involved both flanges and walls. The inclusion of internal walls in the failure of the rhomboidal plates likely contributes to the higher load attained compared to reticular plates. 5 NUMERICAL F.E. ANALYSES Numerical analyses replicating the experimental bending tests were conducted using the computer code Abaqus [24]. A 3D model was carried out by employing thin shell elements for both flanges and internal walls. Regarding the constitutive law, unlike the linear static analyses utilized in the optimization design, nonlinear static incremental analyses were performed. For this purpose, a constitutive material law was adopted, based on the findings from the tensile tests on dog-bone samples. This law featured an initial linear-elastic branch with a Young’s modulus E of 1250 MPa until reaching the peak stress (σ lim = 44 Mpa), followed by a softening branch with a slope determined by considering an ultimate strength value of 40 Mpa and a corresponding strain value of 0.055 was implemented. The developed structural model was employed for analyzing the influence of the internal pattern on the attainment of the material normal stress limit. The results of the numerical analyses are presented below in terms of force-displacement curves, with a circular symbol denoting the point at which the material yields. The comparison between experimental and numerical curves (Figure 10) underlines: a good agreement in terms of initial bending stiffness for both configurations, indicating the appropriateness of assuming an isotropic material model and the value of the Young’s modulus derived from tensile tests on dog-bone samples; for the reticular configuration, an overestimation of the plate’s performance in terms of peak load is evident from Figure 10a and b, indicating that the failure is not governed by the attainment of the maximum axial stress σ lim for the rhomboidal configuration, in both patterns PT_27 (Figure 10c) and PT_45 (Figure 10d) the numerical attainment of the material's yield strain occurs at similar values of loads and displacement, with the latter approaching the peak value of the experimental load (Figure 10c). In Figure 11 and Figure 12 are presented the minimum and maximum stresses of samples at the attainment of yielding. From the figures, as expected, is evident the concentration of normal stresses at the middle of flanges, where the failure was experimentally observed. 6 CONSIDERATIONS The results obtained from the experimental tests presented above have highlighted the influence of both configuration and pattern on the flexural response of samples. However, the F.E. numerical analyses have indicated that, in some cases, reaching the limit normal stress corresponds to significantly higher levels of load than those determined experimentally. To deepen these aspects, considerations carried out through simple models, mainly based on equilibrium considerations and assumptions concerning the failure mode, are reported in the following. Beginning with the assumption of a pure shear failure mode involving only the flanges in the case of the reticular configuration, the average value of shear stress τ p corresponding to reaching the experimental peak load F max is determined by dividing the shear action S p,PR (assumed to be half of the peak load due to the static three-point bending scheme depicted in Figure 13) by the cross-sectional area of both flanges (the depicted cross-section is shown in Figure 13b). The obtained average shear stress value (6.9 MPa) is then utilized to evaluate the force corresponding to the shear failure of samples with a rhomboidal configuration. In this regard, as the failure modes of rhomboidal samples involve both flanges and internal walls, the shear stress value obtained for reticular samples is multiplied by the cross-sectional area of both flanges and internal walls to obtain the shear force (the depicted cross-section is shown in Figure 13c). Consequently, while still considering the three-point static test scheme, the corresponding force is determined by simply doubling the shear force, resulting in a value of 22.5 kN. This obtained value closely aligns with the experimental average peak force of rhomboidal samples (approximately 21 kN), thereby confirming an ultimate behavior for these samples likely governed by a shear failure mode, rather than the attainment of the limit normal stress. Indeed, supposing, on the contrary, a bending failure mode for both reticular and rhomboidal samples (Figure 13b-c), resulting in the attainment of the limit normal stress σ lim at both exterior edges of the flanges, and assuming a linear material behavior, the corresponding forces are calculated to be 18.6 kN and 23.5 kN for reticular and rhomboidal samples, respectively. The obtained value for reticular plates exceeds the corresponding experimental average values, whereas for rhomboidal plates it approaches the experimental results. This confirms the occurrence of a shear failure mode for reticular plates and a possible balanced shear/bending failure mode for rhomboidal plates. To further emphasize that shear failure, rather than bending, governs the behavior of plates with a reticular configuration, a simplified evaluation of normal stress in the lower and upper flanges was conducted, considering a pure 2D truss behavior (Figure 14): Then, by utilizing equation (13) and the experimentally derived values of force F for reticular plates, the curves in terms of normal stress σ – displacement Δ shown in the plot of Figure 14 were obtained. In the same plots, the range of peak normal stress values obtained from tensile tests conducted on DB samples was also included. From the figure, it is evident that the peaks of the σ-Δ curves are significantly lower than the range of peak stress observed in the DB samples, thereby confirming that bending did not govern the failure for this plate configuration. 7 CONCLUSIONS 3D-printing technology is increasingly appealing for architectural and ornamental restoration projects involving historical structures. This technology enables the accurate reproduction of both the exterior surface details and the intricate shapes of the elements to be replicated. It is evident that for such applications, the shape and volume of the 3D-printed element are fixed parameters closely related to the element being restored. However, the amount of material composing the internal volume of the 3D-printed element could be considered the primary parameter to be optimized in a design optimization process. This optimization aims to achieve an internal structure with configurations and patterns that reduce the material usage (thus, fabrication costs and weight), and consequently, minimize the invasiveness of the intervention required to connect the restored element to the structure. The paper presented here has focused attention on this aspect by experimentally and numerically analyzing the influence of the configuration and pattern of the internal structure of 3D-printed plate elements, which are representative of more complex elements, on their flexural behavior. Regarding the experimental tests, before presenting the results deduced from the bending tests on the plates, a preliminary material characterization was conducted by performing simple tensile tests on samples with a typical dog-bone shape. The results obtained from these preliminary tests provided valuable information regarding the parameters governing the tensile response (Young’s modulus, tensile strength, displacement at the peak) and the tensile behavior of the printed material, characterized by an initial linear phase followed by a softening post-peak phase. The bending tests conducted on the plates generally exhibited a flexural behavior in terms of applied force-displacement (or stress-displacement) similar to that deduced from the tensile tests on dog-bone samples: an initial linear behavior followed by a nonlinear one with softening before failure, which was particularly evident for the rhomboidal configuration. In this case, the obtained results also emphasized the influence of the configuration/pattern of the internal structure. Particularly for the reticular samples, it was observed that the PR_72 samples, characterized by a greater slope and number of diagonal walls (and consequently a greater weight), exhibited slightly higher values of strength (peak force) compared to the PR_60 samples. Conversely, for the samples with a rhomboidal configuration of the internal structure, greater strength in terms of force was observed for the samples with the PT_27 pattern, i.e., the one with a lower number of internal walls. This difference was closely related to the fact that the rhomboidal samples were designed to have the same weight, with the PT_27 samples characterized by a greater thickness compared to the PT_45 samples. Another distinction with respect to the reticular configuration concerned the displacement at the peak, which, in the case of the rhomboidal configuration, was similar for both patterns, while slightly different for the reticular ones. The numerical F.E. analyses, conducted by setting constitutive laws based on those derived from the tensile tests, highlighted a good agreement in terms of both stiffness and strength for the rhomboidal configuration. On the other hand, they exhibited a good agreement in terms of stiffness only for the reticular configuration. Indeed, for the latter, the experimental tests showed a strength lower than the numerical one, indicating that the failure was not due to reaching the limit normal stress. The analyses presented in the paper, derived from simple theoretical models, confirmed this outcome by further emphasizing the influence of the configuration/pattern on the experimental response of printed samples. The paper contributes to a significant topic within the application of 3D-printing technology for architectural and ornamental restoration, forming part of a broader research effort. Future studies will delve deeper into understanding the role of internal structure configurations of printed elements. This exploration will involve considering the complex shape of the element to be reproduced as an additional parameter to be included in the optimization process. Declarations ACKNOWLEDGEMENTS The research was funded by the Lazio Region as part of the Call “DTC TE1 - Fase II - Progetti RSI”, Det. N. G07413 of 16.06.2021, public notice of LAZIO INNOVA, research project “H-S3D – Stampa 3D per Beni Culturali. Applicazioni di Recupero Strutturale e Monitoraggio di Elementi Architettonici e di Decoro”. The Araknia Labs Srl is gratefully acknowledged for the 3D-printing of the samples within the aforementioned research project. The Group of Metallurgy at the University of Cassino is gratefully acknowledged for their support in conducting some of the experimental tests discussed in the paper. 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Procedia Struct Integr 33:498–508 Mourad AHI, Idrisi AH, Christy JV et al (2019) Mechanical Performance Assessment of Internally-Defected Materials Manufactured Using Additive Manufacturing Technology. J Manuf Mater Process 2019 3:74. https://doi.org/10.3390/JMMP3030074 Michael Smith (2023) ABAQUS/Standard User’s Manual, Version 2023 Cite Share Download PDF Status: Posted Version 1 posted 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. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-4207370","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":290958762,"identity":"348ed341-0a5c-41f7-a886-6613fe4bd038","order_by":0,"name":"Valentina Tomei","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAu0lEQVRIiWNgGAWjYPACCTkGBsYGEIuHCNXMYC3GcC1E6AFrYUhsgPEJajE4wH/w0Y0Ki/QNt5sbP/z4wyBjT1gLM7NxzhmJ3A13DjZL9rYR4TDJBmY26dw2oJYbiW0MvA1Ea/knkW4A1ML45w8RWvgZQFoaJBJAWph52IjRAvSKcc4xCcOZNxKbpWXbJHh4DhDQwsbe+PBxTk2dPN+N9Icf3/yxsWdvIGQNMypXgpD6UTAKRsEoGAXEAACf4TOM285giwAAAABJRU5ErkJggg==","orcid":"https://orcid.org/0000-0002-3063-7702","institution":"University of Cassino and Southern Lazio Department of Civil and Mechanic Engineering: Universita degli Studi di Cassino e del Lazio Meridionale Dipartimento di Ingegneria Civile e Meccanica","correspondingAuthor":true,"prefix":"","firstName":"Valentina","middleName":"","lastName":"Tomei","suffix":""},{"id":290958763,"identity":"14bf3d10-2f35-49b7-a15d-ce80b920fa61","order_by":1,"name":"Ernesto Grande","email":"","orcid":"","institution":"University of Cassino and Southern Lazio Department of Civil and Mechanic Engineering: Universita degli Studi di Cassino e del Lazio Meridionale Dipartimento di Ingegneria Civile e Meccanica","correspondingAuthor":false,"prefix":"","firstName":"Ernesto","middleName":"","lastName":"Grande","suffix":""},{"id":290958764,"identity":"90228532-4406-4f57-afdb-460e2e4fb6c9","order_by":2,"name":"Maura Imbimbo","email":"","orcid":"","institution":"University of Cassino and Southern Lazio Department of Civil and Mechanic Engineering: Universita degli Studi di Cassino e del Lazio Meridionale Dipartimento di Ingegneria Civile e Meccanica","correspondingAuthor":false,"prefix":"","firstName":"Maura","middleName":"","lastName":"Imbimbo","suffix":""}],"badges":[],"createdAt":"2024-04-02 14:26:16","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4207370/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4207370/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":54812112,"identity":"beb11e89-9069-49e7-81e0-293ea3d62c83","added_by":"auto","created_at":"2024-04-17 06:30:10","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":576971,"visible":true,"origin":"","legend":"\u003cp\u003e3D-printing process: (a) disposition of layers; (b) dog-bone sample; (c) plate samples.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-4207370/v1/f78cfada06971746916aa669.png"},{"id":54812113,"identity":"d5b45549-00cd-4d00-bb66-093fd0e2a397","added_by":"auto","created_at":"2024-04-17 06:30:10","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":84726,"visible":true,"origin":"","legend":"\u003cp\u003eGeometry of the reticular samples (a) PR_60 and (b)72, and the rhomboidal samples (c) PT_27 and (d) PT_45.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-4207370/v1/fdcd54fa660e792185b71044.png"},{"id":54812120,"identity":"6790f1da-7f41-4caf-ab89-f2d0997a0dab","added_by":"auto","created_at":"2024-04-17 06:30:11","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":424224,"visible":true,"origin":"","legend":"\u003cp\u003e(a) parametric model of the rhomboidal pattern (PT); (b) structural model employed for optimization ; (c) visual script developed in Grasshopper Environment.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-4207370/v1/1e69239c8b0490d1011a9e2e.png"},{"id":54812114,"identity":"1d6ad8f8-ce60-4e92-b2b4-4b802450fc8a","added_by":"auto","created_at":"2024-04-17 06:30:10","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":5557,"visible":true,"origin":"","legend":"\u003cp\u003eGeometry of the dog-bone samples.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-4207370/v1/e28c203f9fbf5ea0235dae37.png"},{"id":54812117,"identity":"097172a8-a9b9-4838-b7c0-85ee2880c42e","added_by":"auto","created_at":"2024-04-17 06:30:11","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":275531,"visible":true,"origin":"","legend":"\u003cp\u003eTensile tests on reticular beams: picture of the testing machine.\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-4207370/v1/5e6114b6669bb67d004c3533.png"},{"id":54812115,"identity":"bfd4f8a9-23ab-48b7-adf7-d070e01bd215","added_by":"auto","created_at":"2024-04-17 06:30:10","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":29784,"visible":true,"origin":"","legend":"\u003cp\u003eTensile tests on dog-bone samples: stress-strain curves.\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-4207370/v1/d2387bcf5be0cac1ba56719a.png"},{"id":54812116,"identity":"5743c667-59cb-4652-8c7b-46a08a07b961","added_by":"auto","created_at":"2024-04-17 06:30:11","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":330636,"visible":true,"origin":"","legend":"\u003cp\u003eTensile tests on dog-bone samples: failure modes.\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-4207370/v1/7868cffeb1a60f7dc8cc5021.png"},{"id":54812124,"identity":"19396d39-0290-4a33-8396-e9cdc04ec58d","added_by":"auto","created_at":"2024-04-17 06:30:11","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":357085,"visible":true,"origin":"","legend":"\u003cp\u003eThree-point bending on reticular plates: Force-Displacement curves for plates PR (a); plates PT (b); picture of the testing machine (c).\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-4207370/v1/77d5267bb64288cd1eb34813.png"},{"id":54812121,"identity":"f0c87412-02aa-4c22-8aac-068dd5e3ee61","added_by":"auto","created_at":"2024-04-17 06:30:11","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":646148,"visible":true,"origin":"","legend":"\u003cp\u003eThree-point bending on reticular plates: failure modes.\u003c/p\u003e","description":"","filename":"9.png","url":"https://assets-eu.researchsquare.com/files/rs-4207370/v1/3630d6e297e7d0a5d4d3275e.png"},{"id":54812118,"identity":"3242267f-0fa5-4f02-8d6c-dafe9621ae3c","added_by":"auto","created_at":"2024-04-17 06:30:11","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":55242,"visible":true,"origin":"","legend":"\u003cp\u003eResults of numerical analyses: applied force vs. displacement curves.\u003c/p\u003e","description":"","filename":"10.png","url":"https://assets-eu.researchsquare.com/files/rs-4207370/v1/ad851f28e7e54b2866e0824d.png"},{"id":54812125,"identity":"28e50aa3-c7c5-417d-b5ab-c7e9f40b5452","added_by":"auto","created_at":"2024-04-17 06:30:11","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":331079,"visible":true,"origin":"","legend":"\u003cp\u003eNon-linear numerical model: minimum (a, c) and maximum (b, d) stresses for PR_60 (a, b) and PR_72 (b) at yielding.\u003c/p\u003e","description":"","filename":"11.png","url":"https://assets-eu.researchsquare.com/files/rs-4207370/v1/bf10e60f39cac12b38993942.png"},{"id":54812122,"identity":"d0434777-26dd-4a24-bd17-57f022af2863","added_by":"auto","created_at":"2024-04-17 06:30:11","extension":"png","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":560025,"visible":true,"origin":"","legend":"\u003cp\u003eNon-linear numerical model: minimum (a, c) and maximum (b, d) stresses for PT_27 (a, b) and PT_45 (c, d) at yielding.\u003c/p\u003e","description":"","filename":"12.png","url":"https://assets-eu.researchsquare.com/files/rs-4207370/v1/ff2494fa0c5bd5eb828f5f13.png"},{"id":54812119,"identity":"dd5a8ce5-b7b8-49a3-8ec7-7bca65c8a485","added_by":"auto","created_at":"2024-04-17 06:30:11","extension":"png","order_by":13,"title":"Figure 13","display":"","copyAsset":false,"role":"figure","size":31687,"visible":true,"origin":"","legend":"\u003cp\u003eStructural scheme of the samples (a), cross-sectional analysis of reticular samples (b) and rhomboidal samples (c).\u003c/p\u003e","description":"","filename":"13.png","url":"https://assets-eu.researchsquare.com/files/rs-4207370/v1/86a09008102726f3494c559e.png"},{"id":54812127,"identity":"b7682a23-0786-41ad-9c25-75bbab5df14c","added_by":"auto","created_at":"2024-04-17 06:30:12","extension":"png","order_by":14,"title":"Figure 14","display":"","copyAsset":false,"role":"figure","size":28184,"visible":true,"origin":"","legend":"\u003cp\u003eNormal stress-displacement curves for reticular plates PR.\u003c/p\u003e","description":"","filename":"14.png","url":"https://assets-eu.researchsquare.com/files/rs-4207370/v1/a9633768c701440dd585328f.png"},{"id":58818238,"identity":"c73b7943-cbc8-4401-bb0d-3029b38aa20b","added_by":"auto","created_at":"2024-06-21 13:55:27","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3823258,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4207370/v1/95d8780c-6e08-4f5c-9310-8f28eda2d97b.pdf"}],"financialInterests":"","formattedTitle":"\u003cp\u003eOptimization of the Internal Structure of 3d-printed Components for Architectural Restoration\u003c/p\u003e","fulltext":[{"header":"1 INTRODUCTION","content":"\u003cp\u003eThe capacity to reproduce complex geometries in short times and the possibility of using different types of materials (among these, also, eco-sustainable ones), make 3D-printing a technology with great potential for applications in different fields, among which architecture and construction [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. Among these, applications concerning the recovery of structural heritage are one of the most recent fields of particular interest. Indeed, in current literature are available examples proposing the use of 3D-printing for the reproduction of small museum components [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e], or the reproduction of missing parts of ancient statues [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. Other examples concern the reproduction of ornamental architectural components [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e], among which the Roman cornice from the Castulo Archaeological Site [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e], or the restoration of an ancient terra sigillata plate [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eIn contrast to applications for mechanical devices, which often necessitate specific strength and stiffness characteristics for 3D-printed components, the recovery of architectural/ornamental elements prioritizes refinement of the exterior surface and shape precision. Consequently, optimizing the internal structure configuration is crucial in this context. It enables, indeed, to reduce weight, fabrication costs and environmental impact, as well as to minimize the intrusiveness of connecting the 3D-printed element to the structure, a further important aspect for historical structures.\u003c/p\u003e \u003cp\u003eThe application of 3D printing for reproducing architectural/ornamental components is currently under study, with a main focus on characterizing the performance of printed materials [\u003cspan additionalcitationids=\"CR8 CR9 CR10 CR11 CR12 CR13 CR14\" citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. The parameters of the printing process intrinsically affect the mechanical properties of the printed parts. Therefore, experimental characterization of samples represents a crucial preliminary phase that supports the design process of complex elements derived from 3D printing.\u003c/p\u003e \u003cp\u003eIn this study, we present both experimental and numerical investigations aimed at assessing the structural performance of 3D printed elements made of PLA material. Initially, the focus is on characterizing the printed material through tensile tests on dog-bone samples. Subsequently, bending tests were conducted on plate samples representing small portions of 3D-printed elements with different internal structure configurations derived from numerical optimization techniques. Additionally, the paper discusses results obtained from theoretical models and Finite Element analyses, providing further insights into the experimental findings.\u003c/p\u003e"},{"header":"2 MATERIAL AND METHODS","content":"\u003cp\u003eThe samples for the experimental tests presented in this paper were manufactured by using additive manufacturing (AM) technology based on the fused filament technique (FFT). The black RAISE3D Premium PLA material was used, with the following main printing parameters set:\u003c/p\u003e\n\u003cp\u003e- filaments diameters: 1.75 mm;\u003c/p\u003e\n\u003cp\u003e- minimum/maximum printing temperature of 190\u0026deg;C/220\u0026deg;C;\u003c/p\u003e\n\u003cp\u003e- nozzle diameter: 0.4 mm;\u003c/p\u003e\n\u003cp\u003e- layer thickness: 0.25 mm;\u003c/p\u003e\n\u003cp\u003e- layer width: 0.5 mm;\u003c/p\u003e\n\u003cp\u003e- infill value: 100%;\u003c/p\u003e\n\u003cp\u003e- nozzle speed: 50 mm/s;\u003c/p\u003e\n\u003cp\u003e- hot-end temperature: 190\u0026deg;C.\u003c/p\u003e\n\u003cp\u003eThe selection of the PLA material was primarily based on its advantages over other common 3D printing materials, such as: biodegradability, eco-sustainability, recyclability, low extrusion and bed temperatures, reduced risk of ultrafine particle emission during printing\u0026nbsp;[16\u0026ndash;18]. However, the mechanical properties of 3D-printed elements made of PLA material are strongly influenced by various printing parameters (extrusion temperature, flow rate, layer height, and direction) and by the printing process itself\u0026nbsp;[17]. Then, the study presented here further contributes to the state of the art regarding this aspect. To this specific end, dog-bone samples were indeed experimentally analyzed by performing tensile tests finalized to characterize the materials in terms of Young Modulus \u003cem\u003eE\u0026nbsp;\u003c/em\u003eand strength in terms of stress\u0026nbsp;s\u003cem\u003e\u003csub\u003elim\u003c/sub\u003e\u003c/em\u003e.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eMoreover, the study experimentally and numerically analyzes the influence of the configuration and the pattern of the internal structure of 3D-printed samples representative of components or parts of more complex ornamental elements. For this purpose, plate samples underwent preliminary experimental analysis through three-point bending tests. Subsequently, numerical results were derived by using simple theoretical models and Finite Element analyses. As detailed in the following section, plate samples were printed with varying internal structure configurations (reticular and rhomboidal) and patterns (determined by different inclinations of internal walls).\u003c/p\u003e\n\u003cp\u003eThe same printing process was applied to both dog-bone and plate samples. Specifically, for each layer composing the sample, the perimeter was initially printed by following a linear path, while the inner area was subsequently printed by following an inclined path at an angle of \u0026plusmn;45\u0026deg; alternately for each successive layer (Figure 1). In the case of dog-bone samples, a temporary support was required during the printing process (Figure 1b).\u0026nbsp;\u003c/p\u003e"},{"header":"3 DESIGN OF THE INTERNAL STRUCTURE OF THE PLATE SAMPLES","content":"\u003cp\u003ePlate samples were designed with two distinct configurations of the internal structure: reticular and rhomboidal, labeled as PR and PT, respectively. For each configuration, two different patterns, primarily distinguished by varying the inclination \u0026theta; of the walls forming the internal structure, were also taken into account. These patterns are denoted as PR_60 and PR_72 for the reticular pattern, and PT_27 and PT_45 for the rhomboidal pattern. (Figure 2).\u003c/p\u003e\n\u003cp\u003eConcerning the reticular configuration, the two distinct patterns were defined by interior walls inclined at \u0026plusmn;60\u0026deg; (PR_60) and interior walls inclined at \u0026plusmn;72\u0026deg; (PR_72). Both configurations maintained an identical thickness for both the flanges and the walls. (Figure 2;\u0026nbsp;Table 1).\u003c/p\u003e\n\u003cp\u003eRegarding the rhomboidal configuration (Figure 2;\u0026nbsp;Table 1), the internal walls were arranged to create a rhomboidal mesh. Specifically, the two distinct patterns considered were distinguished by walls inclined at 27\u0026deg; (PT_27) and, for the other type of sample, walls inclined at 45\u0026deg; (PT_45).\u003c/p\u003e\n\u003cp\u003eFor each configuration (reticular and rhomboidal), the two pattern were derived from an optimization design process relied on a parametric geometrical model\u0026nbsp;(Figure 3c) created in Grasshopper\u0026nbsp;[19, 20], along with a corresponding structural model developed in Karamba3D\u0026nbsp;[21].\u003c/p\u003e\n\u003cp\u003eIn detail, for the reticular pattern the problem was set as in the following:\u003c/p\u003e\n\u003cp\u003e-\u003cu\u003econstraint conditions\u003c/u\u003e: the structural optimization process was carried out by imposing a constraint condition on the maximum utilization ratio, denoted as U\u003csub\u003emax\u003c/sub\u003e=s\u003csub\u003eVM\u003c/sub\u003e/s\u003csub\u003elim\u003c/sub\u003e\u0026le;1, where\u0026nbsp;s\u003csub\u003eVM\u003c/sub\u003e represents the maximum value of Von Mises stress, considering the average strength value deduced from tensile tests on dog-bone samples (s\u003csub\u003elim\u003c/sub\u003e=44 MPa, see section\u0026nbsp;4.1);\u003c/p\u003e\n\u003cp\u003e-\u003cu\u003eparameters\u003c/u\u003e: regarding the parameters varied during the optimization process, the PR_60 solution was obtained by adjusting both the slope \u0026theta; of the internal structure walls and the thickness t (with the latter assumed to be the same for both walls and flanges). On the other hand, the PR_72 solution was derived by varying only the slope \u0026theta;, while setting the thickness obtained for PR_60. This choice was made to compare structural models with the same thickness.\u003c/p\u003e\n\u003cp\u003eAbout the rhomboidal configuration, the optimization process was set as in the following:\u003c/p\u003e\n\u003cp\u003e-\u003cu\u003econstraint conditions\u003c/u\u003e: the structural optimization process was carried out by imposing as the main constraint condition the same volume of material of the pattern PR_60 of the reticular configuration, in order to compare different solutions with the same volumeFurthermore, considering the average strength value deduced from tensile tests on dog-bone samples (s\u003csub\u003elim\u003c/sub\u003e=44 MPa, see section\u0026nbsp;4.1), an additional constraint was imposed on the maximum utilization ratio, denoted as U\u003csub\u003emax\u003c/sub\u003e=s\u003csub\u003eVM\u003c/sub\u003e/s\u003csub\u003elim\u003c/sub\u003e\u0026le;1, where\u0026nbsp;s\u003csub\u003eVM\u003c/sub\u003e represents the maximum value of Von Mises stress;\u003c/p\u003e\n\u003cp\u003e-\u003cu\u003eparameters\u003c/u\u003e: regarding the parameters varied during the optimization process, the PT_27 solution was obtained by adjusting both the slope \u0026theta; of the internal structure walls and the thickness t (with the latter assumed to be the same for both walls and flanges). On the other hand, the PT_45 solution was derived by varying only the thickness t, while setting the slope \u0026theta; to 45\u0026deg;.\u003c/p\u003e\n\u003cp\u003eTable\u0026nbsp;1. Dimensions of the samples\u003c/p\u003e\n\u003cdiv align=\"\"\u003e\n \u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\" width=\"501\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd width=\"26.640159045725646%\" valign=\"bottom\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.145129224652088%\" valign=\"bottom\"\u003e\n \u003cp\u003eb\u003csub\u003e1\u003c/sub\u003e (mm)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.145129224652088%\" valign=\"bottom\"\u003e\n \u003cp\u003eb\u003csub\u003e2\u003c/sub\u003e (mm)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.145129224652088%\" valign=\"bottom\"\u003e\n \u003cp\u003eh\u003csub\u003e1\u003c/sub\u003e (mm)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.145129224652088%\" valign=\"bottom\"\u003e\n \u003cp\u003eh\u003csub\u003e2\u003c/sub\u003e (mm)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.145129224652088%\" valign=\"bottom\"\u003e\n \u003cp\u003er\u003c/p\u003e\n \u003cp\u003e(mm)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.145129224652088%\" valign=\"bottom\"\u003e\n \u003cp\u003et (mm)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"5.7654075546719685%\" valign=\"bottom\"\u003e\n \u003cp\u003e\u0026theta; (\u0026deg;)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.723658051689862%\" valign=\"bottom\"\u003e\n \u003cp\u003en. of\u003c/p\u003e\n \u003cp\u003esamples\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"26.640159045725646%\" valign=\"bottom\"\u003e\n \u003cp\u003eDB\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.145129224652088%\" valign=\"bottom\"\u003e\n \u003cp\u003e150\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.145129224652088%\" valign=\"bottom\"\u003e\n \u003cp\u003e80\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.145129224652088%\" valign=\"bottom\"\u003e\n \u003cp\u003e20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.145129224652088%\" valign=\"bottom\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.145129224652088%\" valign=\"bottom\"\u003e\n \u003cp\u003e20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.145129224652088%\" valign=\"bottom\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"5.7654075546719685%\" valign=\"bottom\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.723658051689862%\" valign=\"bottom\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"26.640159045725646%\" valign=\"bottom\"\u003e\n \u003cp\u003ePR_60\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.145129224652088%\" valign=\"bottom\"\u003e\n \u003cp\u003e200\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.145129224652088%\" valign=\"bottom\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.145129224652088%\" valign=\"bottom\"\u003e\n \u003cp\u003e30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.145129224652088%\" valign=\"bottom\"\u003e\n \u003cp\u003e100\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.145129224652088%\" valign=\"bottom\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.145129224652088%\" valign=\"bottom\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"5.7654075546719685%\" valign=\"bottom\"\u003e\n \u003cp\u003e60\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.723658051689862%\" valign=\"bottom\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"26.640159045725646%\" valign=\"bottom\"\u003e\n \u003cp\u003ePR_72\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.145129224652088%\" valign=\"bottom\"\u003e\n \u003cp\u003e200\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.145129224652088%\" valign=\"bottom\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.145129224652088%\" valign=\"bottom\"\u003e\n \u003cp\u003e30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.145129224652088%\" valign=\"bottom\"\u003e\n \u003cp\u003e100\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.145129224652088%\" valign=\"bottom\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.145129224652088%\" valign=\"bottom\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"5.7654075546719685%\" valign=\"bottom\"\u003e\n \u003cp\u003e72\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.723658051689862%\" valign=\"bottom\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"26.640159045725646%\" valign=\"bottom\"\u003e\n \u003cp\u003ePT_27\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.145129224652088%\" valign=\"bottom\"\u003e\n \u003cp\u003e200\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.145129224652088%\" valign=\"bottom\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.145129224652088%\" valign=\"bottom\"\u003e\n \u003cp\u003e30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.145129224652088%\" valign=\"bottom\"\u003e\n \u003cp\u003e100\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.145129224652088%\" valign=\"bottom\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.145129224652088%\" valign=\"bottom\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"5.7654075546719685%\" valign=\"bottom\"\u003e\n \u003cp\u003e27\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.723658051689862%\" valign=\"bottom\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"26.640159045725646%\" valign=\"bottom\"\u003e\n \u003cp\u003ePT_45\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.145129224652088%\" valign=\"bottom\"\u003e\n \u003cp\u003e200\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.145129224652088%\" valign=\"bottom\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.145129224652088%\" valign=\"bottom\"\u003e\n \u003cp\u003e30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.145129224652088%\" valign=\"bottom\"\u003e\n \u003cp\u003e100\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.145129224652088%\" valign=\"bottom\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.145129224652088%\" valign=\"bottom\"\u003e\n \u003cp\u003e3.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"5.7654075546719685%\" valign=\"bottom\"\u003e\n \u003cp\u003e45\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.723658051689862%\" valign=\"bottom\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003e\u003cbr\u003e\u003c/p\u003e\n\u003cp\u003eThe numerical analyses conducted during the optimization process simulated \u0026nbsp;the experimental three-point bending test described in the paper (Figure 3b), where the span was set at S=10 cm and a uniform load was distributed along the centerline of the upper flange (the resultant of this load being the total applied force F).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe optimization problem was tackled by using mono-objective genetic algorithms, defining the following objective function OF to be maximized (Eq. 2):\u003c/p\u003e\n\u003cp\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"309\" height=\"42\"\u003e\u003c/p\u003e\n\u003cp\u003ewhere \u0026alpha; is a penalty factor, assumed here to be -10\u003csup\u003e5\u003c/sup\u003e, and \u0026beta; is a parameter introduced to adhere to the constraint condition of the utilization ratio (it takes a value of -10\u003csup\u003e5\u003c/sup\u003e when U\u003csub\u003emax\u003c/sub\u003e\u0026gt;1 and 0 when U\u003csub\u003emax\u003c/sub\u003e\u0026le;1). Here, V and V* represent respectively the volume of material of the reticular solution PR_60 (taken as the reference value) and the volume obtained during the optimization process. The developed visual script is depicted in\u0026nbsp;Figure 3c, outlining all the main steps.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eDetails regarding the dimensions of the plate sample are presented in Table 1, with the symbols referring to \u0026nbsp;Figure 3.\u003c/p\u003e"},{"header":"4\tEXPERIMENTAL TESTS","content":"\u003ch2\u003e4.1 Dog-bone samples: material characterization\u003c/h2\u003e\n\u003cp\u003eThe initial phase of the experimental work aimed to explore the behavior of the printed material. For this purpose, tensile tests were conducted on five samples, each featuring a common dog-bone shape (DB, see Figure 4 and Table 1). \u0026nbsp;\u003c/p\u003e\n\u003cp\u003eTensile tests on DB samples were performed at the University of Cassino and Southern Lazio\u0026nbsp;by using a universal testing machine Gabaldini (Figure 5).\u003c/p\u003e\n\u003cp\u003eThe results derived from the tensile tests on DB samples are depicted in\u0026nbsp;Figure 6\u0026nbsp;in terms of stress-strain curves. Here, the stress was calculated by dividing the applied force by the cross-sectional area of the sample, while the strain was determined by dividing the displacement by the length of the sample. From the plots, it is evident that all the samples exhibit an initial linear phase followed by a post-peak behavior characterized by a softening branch. An average elastic modulus value E=1250 MPa (evaluated at 40% of the peak stress) and an average peak stress value \u0026sigma;\u003csub\u003elim\u003c/sub\u003e=44 MPa were deduced from the tensile tests. Despite the similar overall force-displacement response of the samples, it is noticeable from the plots that one of the samples exhibits lower strength and stiffness values, along with greater ductility. This divergent behavior of the sample may be attributed to potential and inevitable misalignments during the test and, moreover, to geometric imperfections arising during the printing process [22, 23].\u003c/p\u003e\n\u003cp\u003eFigure 7 shows pictures of the DB samples at the conclusion of the tests. From the figure, it is evident that all the samples exhibit a characteristic fracture near the center of the sample.\u003c/p\u003e\n\u003ch2\u003e4.2 Plate samples: structural characterization\u003c/h2\u003e\n\u003cp\u003eRegarding the plate samples, three-point bending tests were performed at the laboratory of Pa.L.Mer. in Ferentino (FR), Italy.\u003c/p\u003e\n\u003cp\u003eThe results obtained from the three-point bending tests on plates are illustrated in\u0026nbsp;Figure 8, in terms of Force-Displacement curves. Specifically,\u0026nbsp;Figure 8a compares the two patterns of the reticular configuration, while\u0026nbsp;Figure 8b contrasts the two patterns of the rhomboidal configuration. \u0026nbsp;\u003c/p\u003e\n\u003cp\u003eRegarding the reticular configuration,\u0026nbsp;Figure 8a shows that the PR_72 samples exhibit higher peak force and corresponding displacement values compared to the PR_60 samples. However, the differences are relatively small, approximately 10% in terms of peak force and 20% in terms of corresponding displacement (evaluated based on the average values). Conversely, both types of samples demonstrate similar initial stiffness values.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eOn the other hand, concerning the plates with the rhomboidal configuration, it is noticeable that the PT_27 samples demonstrate higher values of both stiffness and strength compared to the samples with the PT_45 pattern. Conversely, the two patterns yield similar values of the displacement at the peak.\u003c/p\u003e\n\u003cp\u003eComparing the two configurations (reticular and rhomboidal), it is evident that both patterns of the rhomboidal configuration (PT_27 and PT_45) exhibit higher values of both peak force and corresponding displacement compared to the two patterns of the reticular configuration (PR_60 and PR_72). Given that the samples PR_60, PT_27, and PT_45 have the same weight, these results clearly highlight the influence of the pattern on the structural performance of the samples.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eExamining the failure modes of the reticular plates depicted in Figure 9, similar failure modes are evident for the PR_60 and PR_72 patterns, where cracks occurred in both flanges without affecting the internal walls. In contrast, for plates with the rhomboidal pattern, cracks involved both flanges and walls. The inclusion of internal walls in the failure of the rhomboidal plates likely contributes to the higher load attained compared to reticular plates.\u003c/p\u003e"},{"header":"5 NUMERICAL F.E. ANALYSES","content":"\u003cp\u003eNumerical analyses replicating the experimental bending tests were conducted using the computer code Abaqus\u0026nbsp;[24]. A 3D model was carried out by employing thin shell elements for both flanges and internal walls. Regarding the constitutive law, unlike the linear static analyses utilized in the optimization design, nonlinear static incremental analyses were performed. For this purpose, a constitutive material law was adopted, based on the findings from the tensile tests on dog-bone samples. This law featured an initial linear-elastic branch with a Young\u0026rsquo;s modulus E of 1250 MPa until reaching the peak stress (\u0026sigma;\u003csub\u003elim\u003c/sub\u003e = 44 Mpa), followed by a softening branch with a slope determined by considering an ultimate strength value of 40 Mpa and a corresponding strain value of 0.055 was implemented.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe developed structural model was employed for analyzing the influence of the internal pattern on the attainment of the material normal stress limit. The results of the numerical analyses are presented below in terms of force-displacement curves, with a circular symbol denoting the point at which the material yields.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe comparison between experimental and numerical curves (Figure 10) underlines:\u003c/p\u003e\n\u003cul\u003e\n \u003cli\u003ea good agreement in terms of initial bending stiffness for both configurations, indicating the appropriateness of assuming an isotropic material model and the value of the Young\u0026rsquo;s modulus derived from tensile tests on dog-bone samples;\u003c/li\u003e\n \u003cli\u003efor the reticular configuration, an overestimation of the plate\u0026rsquo;s performance in terms of peak load is evident from\u0026nbsp;Figure 10a and b, indicating that the failure is not governed by the attainment of the maximum axial stress\u0026nbsp;\u0026sigma;\u003cem\u003e\u003csub\u003elim\u003c/sub\u003e\u003c/em\u003e\u003c/li\u003e\n \u003cli\u003efor the rhomboidal configuration, in both patterns PT_27 (Figure 10c) and PT_45 (Figure 10d) the numerical attainment of the material\u0026apos;s yield strain occurs at similar values of loads and displacement, with the latter approaching the peak value of the experimental load (Figure 10c).\u0026nbsp;\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eIn Figure 11 and Figure 12 are presented the minimum and maximum stresses of samples at the attainment of yielding. From the figures, as expected, is evident the concentration of normal stresses at the middle of flanges, where the failure was experimentally observed.\u003c/p\u003e"},{"header":"6\tCONSIDERATIONS","content":"\u003cp\u003eThe results obtained from the experimental tests presented above have highlighted the influence of both configuration and pattern on the flexural response of samples.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eHowever, the F.E. numerical analyses have indicated that, in some cases, reaching the limit normal stress corresponds to significantly higher levels of load than those determined experimentally.\u003c/p\u003e\n\u003cp\u003eTo deepen these aspects, considerations carried out through simple models, mainly based on equilibrium considerations and assumptions concerning the failure mode, are reported in the following.\u003c/p\u003e\n\u003cp\u003eBeginning with the assumption of a pure shear failure mode involving only the flanges in the case of the reticular configuration, the average value of shear stress \u0026tau;\u003csub\u003ep\u003c/sub\u003e corresponding to reaching the experimental peak load F\u003csub\u003emax\u003c/sub\u003e is determined by dividing the shear action S\u003csub\u003ep,PR\u003c/sub\u003e (assumed to be half of the peak load due to the static three-point bending scheme depicted in Figure 13) by the cross-sectional area of both flanges (the depicted cross-section is shown in Figure 13b). The obtained average shear stress value (6.9 MPa) is then utilized to evaluate the force corresponding to the shear failure of samples with a rhomboidal configuration. In this regard, as the failure modes of rhomboidal samples involve both flanges and internal walls, the shear stress value obtained for reticular samples is multiplied by the cross-sectional area of both flanges and internal walls to obtain the shear force (the depicted cross-section is shown in Figure 13c). Consequently, while still considering the three-point static test scheme, the corresponding force is determined by simply doubling the shear force, resulting in a value of 22.5 kN. This obtained value closely aligns with the experimental average peak force of rhomboidal samples (approximately 21 kN), thereby confirming an ultimate behavior for these samples likely governed by a shear failure mode, rather than the attainment of the limit normal stress.\u003c/p\u003e\n\u003cp\u003eIndeed, supposing, on the contrary, a bending failure mode for both reticular and rhomboidal samples (Figure 13b-c), resulting in the attainment of the limit normal stress \u0026sigma;\u003csub\u003elim\u003c/sub\u003e at both exterior edges of the flanges, and assuming a linear material behavior, the corresponding forces are calculated to be 18.6 kN and 23.5 kN for reticular and rhomboidal samples, respectively. The obtained value for reticular plates exceeds the corresponding experimental average values, whereas for rhomboidal plates it approaches the experimental results. This confirms the occurrence of a shear failure mode for reticular plates and a possible balanced shear/bending failure mode for rhomboidal plates.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eTo further emphasize that shear failure, rather than bending, governs the behavior of plates with a reticular configuration, a simplified evaluation of normal stress in the lower and upper flanges was conducted, considering a pure 2D truss behavior (Figure 14):\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"324\" height=\"63\"\u003e\u003c/p\u003e\n\u003cp\u003eThen, by utilizing equation (13) and the experimentally derived values of force F for reticular plates, the curves in terms of normal stress \u0026sigma; \u0026ndash; displacement \u0026Delta; shown in the plot of\u0026nbsp;Figure 14\u0026nbsp;were obtained. In the same plots, the range of peak normal stress values obtained from tensile tests conducted on DB samples was also included.\u003c/p\u003e\n\u003cp\u003eFrom the figure, it is evident that the peaks of the \u0026sigma;-\u0026Delta; curves are significantly lower than the range of peak stress observed in the DB samples, thereby confirming that bending did not govern the failure for this plate configuration.\u003c/p\u003e"},{"header":"7 CONCLUSIONS","content":"\u003cp\u003e3D-printing technology is increasingly appealing for architectural and ornamental restoration projects involving historical structures. This technology enables the accurate reproduction of both the exterior surface details and the intricate shapes of the elements to be replicated. It is evident that for such applications, the shape and volume of the 3D-printed element are fixed parameters closely related to the element being restored. However, the amount of material composing the internal volume of the 3D-printed element could be considered the primary parameter to be optimized in a design optimization process. This optimization aims to achieve an internal structure with configurations and patterns that reduce the material usage (thus, fabrication costs and weight), and consequently, minimize the invasiveness of the intervention required to connect the restored element to the structure.\u003c/p\u003e \u003cp\u003eThe paper presented here has focused attention on this aspect by experimentally and numerically analyzing the influence of the configuration and pattern of the internal structure of 3D-printed plate elements, which are representative of more complex elements, on their flexural behavior.\u003c/p\u003e \u003cp\u003eRegarding the experimental tests, before presenting the results deduced from the bending tests on the plates, a preliminary material characterization was conducted by performing simple tensile tests on samples with a typical dog-bone shape. The results obtained from these preliminary tests provided valuable information regarding the parameters governing the tensile response (Young\u0026rsquo;s modulus, tensile strength, displacement at the peak) and the tensile behavior of the printed material, characterized by an initial linear phase followed by a softening post-peak phase.\u003c/p\u003e \u003cp\u003eThe bending tests conducted on the plates generally exhibited a flexural behavior in terms of applied force-displacement (or stress-displacement) similar to that deduced from the tensile tests on dog-bone samples: an initial linear behavior followed by a nonlinear one with softening before failure, which was particularly evident for the rhomboidal configuration. In this case, the obtained results also emphasized the influence of the configuration/pattern of the internal structure. Particularly for the reticular samples, it was observed that the PR_72 samples, characterized by a greater slope and number of diagonal walls (and consequently a greater weight), exhibited slightly higher values of strength (peak force) compared to the PR_60 samples. Conversely, for the samples with a rhomboidal configuration of the internal structure, greater strength in terms of force was observed for the samples with the PT_27 pattern, i.e., the one with a lower number of internal walls. This difference was closely related to the fact that the rhomboidal samples were designed to have the same weight, with the PT_27 samples characterized by a greater thickness compared to the PT_45 samples. Another distinction with respect to the reticular configuration concerned the displacement at the peak, which, in the case of the rhomboidal configuration, was similar for both patterns, while slightly different for the reticular ones.\u003c/p\u003e \u003cp\u003eThe numerical F.E. analyses, conducted by setting constitutive laws based on those derived from the tensile tests, highlighted a good agreement in terms of both stiffness and strength for the rhomboidal configuration. On the other hand, they exhibited a good agreement in terms of stiffness only for the reticular configuration. Indeed, for the latter, the experimental tests showed a strength lower than the numerical one, indicating that the failure was not due to reaching the limit normal stress. The analyses presented in the paper, derived from simple theoretical models, confirmed this outcome by further emphasizing the influence of the configuration/pattern on the experimental response of printed samples.\u003c/p\u003e \u003cp\u003eThe paper contributes to a significant topic within the application of 3D-printing technology for architectural and ornamental restoration, forming part of a broader research effort. Future studies will delve deeper into understanding the role of internal structure configurations of printed elements. This exploration will involve considering the complex shape of the element to be reproduced as an additional parameter to be included in the optimization process.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eACKNOWLEDGEMENTS\u003c/h2\u003e \u003cp\u003eThe research was funded by the Lazio Region as part of the Call \u0026ldquo;DTC TE1 - Fase II - Progetti RSI\u0026rdquo;, Det. N. G07413 of 16.06.2021, public notice of LAZIO INNOVA, research project \u0026ldquo;H-S3D \u0026ndash; Stampa\u0026nbsp;3D per Beni Culturali.\u0026nbsp;Applicazioni di Recupero Strutturale e Monitoraggio di Elementi Architettonici e di Decoro\u0026rdquo;.\u003c/p\u003e\n\u003cp\u003eThe\u0026nbsp;Araknia Labs Srl is gratefully acknowledged for the 3D-printing of the samples within the aforementioned research project.\u003c/p\u003e\n\u003cp\u003eThe Group of Metallurgy at the University of Cassino is gratefully acknowledged for their support in conducting some of the experimental tests discussed in the paper.\u0026nbsp;\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003ePajonk A, Prieto A, Blum U, Knaack U (2022) Multi-material additive manufacturing in architecture and construction: A review. 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J Manuf Mater Process 2019 3:74. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.3390/JMMP3030074\u003c/span\u003e\u003cspan address=\"10.3390/JMMP3030074\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMichael Smith (2023) ABAQUS/Standard User\u0026rsquo;s Manual, Version 2023\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"3D-printing, tensile tests, three-point bending test, design optimization process","lastPublishedDoi":"10.21203/rs.3.rs-4207370/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4207370/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn recent years, 3D printing technology has assumed an important role in advanced construction processes across various engineering fields. Among these, the application to the architectural restoration of historic structures is particularly fascinating. The ability to precisely reproduce the shape and surface details of complex elements, combined with the availability of a wide range of printing materials, makes 3D printing technology competitive compared to traditional techniques. In this context, the internal volume structure of 3D printed elements represents an additional design parameter to consider for enhancing interventions in terms of reducing the required material, and thus, lowering costs and environmental impact. The paper presents the outcomes of experimental tests and numerical analyses conducted on plates, which represent portions of more complex elements produced by using Additive Manufacturing (AM) technology. These plates feature various internal configurations (such as reticular and rhomboidal patterns) derived from a mono-objective design optimization process. The experimental tests aim to analyze the influence of the configuration and the pattern on the behavior of printed samples. Additionally, the paper discusses insights derived from both theoretical models and Finite Element analyses, providing a clearer understanding of the experimental results.\u003c/p\u003e","manuscriptTitle":"Optimization of the Internal Structure of 3d-printed Components for Architectural Restoration","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-04-17 06:30:04","doi":"10.21203/rs.3.rs-4207370/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"0b7bd935-94ca-471d-8db7-eaf838e783e5","owner":[],"postedDate":"April 17th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2024-06-21T13:47:15+00:00","versionOfRecord":[],"versionCreatedAt":"2024-04-17 06:30:04","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-4207370","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4207370","identity":"rs-4207370","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}