Closed-Form Magnetoelastic Stiffness and Coupling Moduli for Helically Anisotropic Thin Tubes

Closed-Form Magnetoelastic Stiffness and Coupling Moduli for Helically Anisotropic Thin Tubes | 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 Closed-Form Magnetoelastic Stiffness and Coupling Moduli for Helically Anisotropic Thin Tubes Darius Diogo Barreto This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9447788/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 6 You are reading this latest preprint version Abstract Helically poled magnetoelastic tubes enable programmable extension, torsion, and inflation under magnetic loading, making them attractive for soft robotic and tubular actuation systems. Building on our previous variational formulation, we derive explicit closed-form expressions for the effective axial, torsional, inflation, and magnetoelastic coupling stiffnesses in the thin-tube limit. A consistent asymptotic reduction transforms the three-dimensional nonlinear magnetoelastic problem into a compact Cosserat-type model with analytically identifiable moduli that depend explicitly on the poling angle, elastic anisotropy, and magnetoelastic parameters. Unlike classical piezomagnetic formulations, the present approach captures geometry-induced coupling arising from helical magnetization and establishes a direct link between three-dimensional field equations and reduced-order structural behavior. The resulting expressions clarify how helicity governs chiral and non-chiral actuation pathways: azimuthal magnetic fields activate extension and inflation only in the presence of helicity, whereas axial magnetic loading induces deformation even for purely axial poling, with the torsional response depending on field orientation. The formulation recovers known limiting cases and yields physically consistent predictions across a range of material and geometric parameters. Order-of-magnitude estimates based on experimentally reported properties of magnetoactive elastomers further indicate that the predicted responses lie within realistic deformation regimes. The closed-form stiffness relations provide a rigorous and computationally efficient framework for rapid parametric analysis and support the systematic design of magnetically actuated soft tubular devices. Nonlinear magnetoelasticity Helical anisotropy Thin-walled tubes Magnetoelastic coupling moduli Reduced-order modeling Cosserat rods Asymptotic analysis Chiral actuation Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviewers agreed at journal 21 Apr, 2026 Reviewers agreed at journal 21 Apr, 2026 Reviewers invited by journal 21 Apr, 2026 Editor assigned by journal 21 Apr, 2026 Submission checks completed at journal 20 Apr, 2026 First submitted to journal 17 Apr, 2026 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-9447788","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":627539346,"identity":"cf8d4a63-2d24-4460-bcc6-3e63d93019c7","order_by":0,"name":"Darius Diogo Barreto","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA8klEQVRIiWNgGAWjYDCCA2DEwNgG4nwAYjZ2UrQwzgBpYSZCCwgwNgAJZh4Qk5AWvuNnHx7m+cMg28fefvGxza9t8nzMDIwfPubg1iJ5Jt3gMG8bg3Ebz5li49y+24ZtzAzMkjO34dZicCCN4TBvA0Nim0ROmnRuz21GoBY2Zl58Ws4/YwA5DKLFsue2PWEtN4C28LCBtKQfk2b4cTuRoBbJG88YDs5tkwD5hdmwt+F2chszYzNev/CdT2P+8OaPjez89vaHD378uW07v7354IePeLRAgQQQ8xhA0wA4jogC7A8YGP4Qq3gUjIJRMApGEgAAWo5R0g0D7vwAAAAASUVORK5CYII=","orcid":"","institution":"National Institute of Technology Goa","correspondingAuthor":true,"prefix":"","firstName":"Darius","middleName":"Diogo","lastName":"Barreto","suffix":""}],"badges":[],"createdAt":"2026-04-17 10:23:45","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9447788/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9447788/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":107707436,"identity":"8b8b943e-c2b8-4593-afc0-c902b0b3182b","added_by":"auto","created_at":"2026-04-24 09:20:18","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":821712,"visible":true,"origin":"","legend":"","description":"","filename":"ModulliMagnetoelasticSubmitted.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9447788/v1_covered_aeab266c-ca4e-46e6-b807-b2301d351b1b.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Closed-Form Magnetoelastic Stiffness and Coupling Moduli for Helically Anisotropic Thin Tubes","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"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":"journal-of-elasticity","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"elas","sideBox":"Learn more about [Journal of Elasticity](http://link.springer.com/journal/10659)","snPcode":"10659","submissionUrl":"https://submission.nature.com/new-submission/10659/3","title":"Journal of Elasticity","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Nonlinear magnetoelasticity, Helical anisotropy, Thin-walled tubes, Magnetoelastic coupling moduli, Reduced-order modeling, Cosserat rods, Asymptotic analysis, Chiral actuation","lastPublishedDoi":"10.21203/rs.3.rs-9447788/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9447788/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Helically poled magnetoelastic tubes enable programmable extension, torsion, and inflation under magnetic loading, making them attractive for soft robotic and tubular actuation systems. Building on our previous variational formulation, we derive explicit closed-form expressions for the effective axial, torsional, inflation, and magnetoelastic coupling stiffnesses in the thin-tube limit. A consistent asymptotic reduction transforms the three-dimensional nonlinear magnetoelastic problem into a compact Cosserat-type model with analytically identifiable moduli that depend explicitly on the poling angle, elastic anisotropy, and magnetoelastic parameters. Unlike classical piezomagnetic formulations, the present approach captures geometry-induced coupling arising from helical magnetization and establishes a direct link between three-dimensional field equations and reduced-order structural behavior. The resulting expressions clarify how helicity governs chiral and non-chiral actuation pathways: azimuthal magnetic fields activate extension and inflation only in the presence of helicity, whereas axial magnetic loading induces deformation even for purely axial poling, with the torsional response depending on field orientation. The formulation recovers known limiting cases and yields physically consistent predictions across a range of material and geometric parameters. Order-of-magnitude estimates based on experimentally reported properties of magnetoactive elastomers further indicate that the predicted responses lie within realistic deformation regimes. The closed-form stiffness relations provide a rigorous and computationally efficient framework for rapid parametric analysis and support the systematic design of magnetically actuated soft tubular devices.","manuscriptTitle":"Closed-Form Magnetoelastic Stiffness and Coupling Moduli for Helically Anisotropic Thin Tubes","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-04-23 12:50:50","doi":"10.21203/rs.3.rs-9447788/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"reviewerAgreed","content":"235144780512220889500075395508482165379","date":"2026-04-22T01:37:35+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"26493153542968015091373614561299790723","date":"2026-04-22T01:12:16+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-04-22T01:10:06+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-04-22T00:56:12+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2026-04-21T01:38:34+00:00","index":"","fulltext":""},{"type":"submitted","content":"Journal of Elasticity","date":"2026-04-17T10:20:22+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"journal-of-elasticity","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"elas","sideBox":"Learn more about [Journal of Elasticity](http://link.springer.com/journal/10659)","snPcode":"10659","submissionUrl":"https://submission.nature.com/new-submission/10659/3","title":"Journal of Elasticity","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"79798b32-8138-431d-8657-e4348f5b7452","owner":[],"postedDate":"April 23rd, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-04-23T12:50:51+00:00","versionOfRecord":[],"versionCreatedAt":"2026-04-23 12:50:50","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9447788","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9447788","identity":"rs-9447788","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}