Asymptotically correct dimensional reduction of Fung orthotropic model using VAM

Asymptotically correct dimensional reduction of Fung orthotropic model using VAM | 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 Asymptotically correct dimensional reduction of Fung orthotropic model using VAM Shravan Kumar Bhadoria, Ramesh Gupta Burela This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6637938/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 This study aims to derive an asymptotically accurate 2D non-linear constitutive law for the compressible orthotropic Fung model. This is achieved using the Variational Asymptotic Method (VAM). The model accounts for geometric nonlinearity due to finite displacements and rotations and material nonlinearity due to the hyperelastic material model. VAM splits the analysis into 2 parts using the inherent small parameters (geometric and physical small parameters). The first part involves analyzing through the thickness (1D analysis), while the second focuses on mid-surface analysis (2D). The 1D analysis derives analytical expressions for the 3D warping functions, 2D non-linear constitutive law, and 3D recovery relations. For the mid-surface analysis, a 2D non-linear finite element method is employed. This method uses the derived 2D non-linear constitutive law to find the 2D displacements and strains. After that, the 3D displacements are derived using recovery relations. The method’s accuracy and reliability is verified by applying it to standard test cases and comparing the results with those obtained from the FEA software. Orthotropic Fung model Dimensional reduction Asymptotics Geometric and material nonlinearity Constitutive law VAM Nonlinear FEA 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. 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-6637938","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":456104213,"identity":"780fa2a5-0c8b-45ac-bd07-e039aa70347d","order_by":0,"name":"Shravan Kumar Bhadoria","email":"","orcid":"","institution":"Shiv Nadar University Institution of Eminence","correspondingAuthor":false,"prefix":"","firstName":"Shravan","middleName":"Kumar","lastName":"Bhadoria","suffix":""},{"id":456104214,"identity":"5e6253b4-af8d-47c0-8c42-cf8e1d6b58bb","order_by":1,"name":"Ramesh Gupta Burela","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA+ElEQVRIiWNgGAWjYFACHhBhwcDPwNgAYiUwsIOFJQhpkWCQbGBsbDiQANTCTKwWgwNAa5C04Abm/WuPSVdUSMgb325uf/zxx708c2YGxg8/GCzycGmRufEuTfLMGQnDbXcOghxWXGzZzMAs2cMgUYxLi4TEGTPJxjYJxm03EkFaEhI3HGZgkAZKJDbg1fJPwn7zDIQW5t94tfD3ALU0SCRukEBoYSNgC1+yZcMxieQZQIfNOJOWAPQLY5tljwE+W84evNlQY2PbPyP9wYcKm4Q8c/bmwzd+VNTh1MIgkYAmYABOBga41AMB/wEMLaNgFIyCUTAKUAEAccRY1gjgi4AAAAAASUVORK5CYII=","orcid":"","institution":"NITTTR","correspondingAuthor":true,"prefix":"","firstName":"Ramesh","middleName":"Gupta","lastName":"Burela","suffix":""}],"badges":[],"createdAt":"2025-05-11 06:23:14","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6637938/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6637938/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":84683340,"identity":"7b0972d7-c068-4e0d-96cd-295a34195a5c","added_by":"auto","created_at":"2025-06-16 08:38:57","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":692329,"visible":true,"origin":"","legend":"","description":"","filename":"AsymptoticallycorrectdimensionalreductionofFungorthotropicmodelusingVAM.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6637938/v1_covered_5090d927-af57-4951-a4c9-0aeb68ecee50.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Asymptotically correct dimensional reduction of Fung orthotropic model using VAM","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":"Orthotropic Fung model, Dimensional reduction, Asymptotics, Geometric and material nonlinearity Constitutive law, VAM, Nonlinear FEA","lastPublishedDoi":"10.21203/rs.3.rs-6637938/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6637938/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis study aims to derive an asymptotically accurate 2D non-linear constitutive law for the compressible orthotropic Fung model. 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