On the modeling of activation in biological transversely isotropic materials

On the modeling of activation in biological transversely isotropic materials | 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 On the modeling of activation in biological transversely isotropic materials Giulia Giantesio, Alessandro Musesti This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4378090/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 17 Dec, 2024 Read the published version in Journal of Elasticity → Version 1 posted 9 You are reading this latest preprint version Abstract Many biological materials exhibit the ability to activate, essentially due to the action of muscle cells. While the mathematical description of passive materials is well-established, even for large deformations, this is not the case for activation, since capturing its complexities poses significant challenges. This paper focuses on the mathematical modeling of activation of biological materials, guided by the important example of skeletal muscle tissue. We will consider an incompressible and transversely isotropic material within a hyperelastic framework. Our goal is to design constitutive relations that agree with uniaxial experimental data whenever possible. Finally, we propose a novel model based on a coercive and polyconvex elastic energy density for a fiber-reinforced material; in this model, activation occurs solely through a change in the reference configuration of the fibers, following the mixture active strain approach. This model assumes constant activation, preserving the good mathematical features of the original model while still capturing the essential aspects of activation observed in experiments. Mathematics Subject Classification (2020) 74B20 · 74L15 skeletal muscle activation hyperelasticity polyconvexity Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 17 Dec, 2024 Read the published version in Journal of Elasticity → Version 1 posted Editorial decision: Revision requested 17 Aug, 2024 Reviews received at journal 11 Aug, 2024 Reviews received at journal 03 Jun, 2024 Reviewers agreed at journal 22 May, 2024 Reviewers agreed at journal 21 May, 2024 Reviewers invited by journal 19 May, 2024 Editor assigned by journal 07 May, 2024 Submission checks completed at journal 07 May, 2024 First submitted to journal 06 May, 2024 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-4378090","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":301672996,"identity":"d50d493d-acdb-4977-8fef-90e789f85db5","order_by":0,"name":"Giulia Giantesio","email":"","orcid":"","institution":"Catholic University of the Sacred Heart","correspondingAuthor":false,"prefix":"","firstName":"Giulia","middleName":"","lastName":"Giantesio","suffix":""},{"id":301672997,"identity":"87f01cba-c03b-49b5-ba02-e57d0e3a8f68","order_by":1,"name":"Alessandro Musesti","email":"data:image/png;base64,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","orcid":"","institution":"Catholic University of the Sacred Heart","correspondingAuthor":true,"prefix":"","firstName":"Alessandro","middleName":"","lastName":"Musesti","suffix":""}],"badges":[],"createdAt":"2024-05-06 16:02:07","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4378090/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4378090/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s10659-024-10101-9","type":"published","date":"2024-12-17T15:58:25+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":72202633,"identity":"30a7d540-bdcc-4e64-a5c8-f4e539055393","added_by":"auto","created_at":"2024-12-23 16:15:12","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":383804,"visible":true,"origin":"","legend":"","description":"","filename":"SkeletalMuscle.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4378090/v1_covered_75a913d9-2650-4e4d-bea6-7877e34bb93a.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"On the modeling of activation in biological transversely isotropic materials","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"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":"skeletal muscle, activation, hyperelasticity, polyconvexity","lastPublishedDoi":"10.21203/rs.3.rs-4378090/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4378090/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eMany biological materials exhibit the ability to activate, essentially due to the action of muscle cells. 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