Assessment of Orientation Transitions on Stress Redistribution in Triply Periodic Minimal Surface Lattices

Assessment of Orientation Transitions on Stress Redistribution in Triply Periodic Minimal Surface Lattices | 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 Assessment of Orientation Transitions on Stress Redistribution in Triply Periodic Minimal Surface Lattices Osvaldo Iván Meza Jr. Hernández, Agustín Vidal Lesso, Héctor Plascencia Mora This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9248188/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 Triply Periodic Minimal Surface (TPMS) structures have demonstrated significant potential in several applications due to their tunable mechanical response and orientation-dependent behavior. While orientation grading enhances structural performance, the transition zones between differently oriented regions introduce geometric discontinuities that may generate stress concentrations. This numerical study evaluates the modeling parameters of the orientation transition zone in a Gyroid TPMS structure to identify configurations that minimize stress concentration. A 3³ Design of Experiments (DoE) was first implemented to assess the influence of three factors: the number of unit cells, the transition zone size, and the orientation angle change. Regression models were developed using both an Ordinary Least Squares (OLS) approach and TableCurve3D. To improve predictive capability, the dataset was further analyzed using a segmented 3² DoE approach. Results show that, although tensile- and compressive-based material models produce different absolute stress values, they follow the same trend, enabling consistent comparative evaluation. A strongly nonlinear influence of the number of unit cells was identified, explaining the limited correlation of the full 3³ regression model. The best configuration to minimize stress concentration corresponds to 2 unit cells, a 25% transition zone, and an orientation change between 5° and 8.75°. Reduced unit cell count significantly improves response stability and model predictability. Triply Periodic Minimal Surface Design of Experiments Finite Element Analysis Orientation Grading Gyroid Full Text Additional Declarations No competing interests reported. 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. 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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-9248188","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":625596190,"identity":"bb836238-8557-45d3-8404-53748923fc49","order_by":0,"name":"Osvaldo Iván Meza Jr. Hernández","email":"","orcid":"","institution":"Universidad de Guanajuato","correspondingAuthor":false,"prefix":"","firstName":"Osvaldo","middleName":"Iván Meza Jr.","lastName":"Herná","suffix":"Jr."},{"id":625596191,"identity":"47af06a4-3f1f-4443-86b6-756a40b4a8b0","order_by":1,"name":"Agustín Vidal Lesso","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA7ElEQVRIiWNgGAWjYNACAyBmBpIPKojVcQCmJeEMAwMPcVpgdiW2EaGFv3+N8ecPBXcYDI4zb/yQOO+w3X72BtbN+PRJ3HhjJnHA4BmDwWG2YonEbYeTe3gOsN2cgc+aG2fMgH45zCDZzGMA1sIjkcB24wMeHfI3zhh/gGox/pE4B6olAY8Wg/M9BhIgLfzMPGYSiQ2H7QjaYniDrUzijMFhHn5mtjKLhGPpCTxnDrbh9Yvc+cObP1T8OSzHxn94840PNdb27O3Nx27jDWkJiLPhahIbGBgb8GkARswBVL49fuWjYBSMglEwEgEAKpxQrLfyj1EAAAAASUVORK5CYII=","orcid":"","institution":"Universidad de Guanajuato","correspondingAuthor":true,"prefix":"","firstName":"Agustín","middleName":"Vidal","lastName":"Lesso","suffix":""},{"id":625596192,"identity":"46b99306-339c-4e02-b6b3-3ea62836895a","order_by":2,"name":"Héctor Plascencia Mora","email":"","orcid":"","institution":"Universidad de Guanajuato","correspondingAuthor":false,"prefix":"","firstName":"Héctor","middleName":"Plascencia","lastName":"Mora","suffix":""}],"badges":[],"createdAt":"2026-03-27 20:38:55","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9248188/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9248188/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":107423124,"identity":"bca7dd88-8363-473f-ba3b-43a3b6393bc9","added_by":"auto","created_at":"2026-04-21 10:51:51","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":305054,"visible":true,"origin":"","legend":"","description":"","filename":"AssessmentofOrientationTransitionsonStressRedistributioninTPMS.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9248188/v1_covered_3c69b597-0dd7-427b-a366-4a9302da7839.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Assessment of Orientation Transitions on Stress Redistribution in Triply Periodic Minimal Surface Lattices","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"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":"Triply Periodic Minimal Surface, Design of Experiments, Finite Element Analysis, Orientation Grading, Gyroid","lastPublishedDoi":"10.21203/rs.3.rs-9248188/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9248188/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eTriply Periodic Minimal Surface (TPMS) structures have demonstrated significant potential in several applications due to their tunable mechanical response and orientation-dependent behavior. While orientation grading enhances structural performance, the transition zones between differently oriented regions introduce geometric discontinuities that may generate stress concentrations. This numerical study evaluates the modeling parameters of the orientation transition zone in a Gyroid TPMS structure to identify configurations that minimize stress concentration. A 3\u0026sup3; Design of Experiments (DoE) was first implemented to assess the influence of three factors: the number of unit cells, the transition zone size, and the orientation angle change. Regression models were developed using both an Ordinary Least Squares (OLS) approach and TableCurve3D. To improve predictive capability, the dataset was further analyzed using a segmented 3\u0026sup2; DoE approach. Results show that, although tensile- and compressive-based material models produce different absolute stress values, they follow the same trend, enabling consistent comparative evaluation. A strongly nonlinear influence of the number of unit cells was identified, explaining the limited correlation of the full 3\u0026sup3; regression model. The best configuration to minimize stress concentration corresponds to 2 unit cells, a 25% transition zone, and an orientation change between 5\u0026deg; and 8.75\u0026deg;. 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