Damage Phase-Field Model for Fractional Derivative-Based Viscoelastic Materials

Damage Phase-Field Model for Fractional Derivative-Based Viscoelastic 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 Damage Phase-Field Model for Fractional Derivative-Based Viscoelastic Materials Geovane Augusto Haveroth, Thais Clara da Costa Haveroth, Marco Lúcio Bittencourt, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6770418/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 02 Feb, 2026 Read the published version in Engineering with Computers → Version 1 posted 10 You are reading this latest preprint version Abstract This work presents a thermodynamically consistent damage phase-field model incorporating fractional derivatives for characterization of viscoelastic materials. The proposed framework addresses the complexities of hereditary behavior, finite strains, and thermal influences in materials modeled by a serial rheological arrangement based on a very consistent and general formulation. Mixed finite element approximations are used to solve the obtained differential equations. Numerical 3D simulations demonstrate the model's ability to represent a wide range of damage behaviors in both small and large strain regimes, highlighting its potential for studying failure mechanisms in viscoelastic media. Additionally, a Python-based implementation built on open-source libraries is provided to facilitate further use and development. Phase-field model Damage Viscoelastic materials Fractional derivatives Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 02 Feb, 2026 Read the published version in Engineering with Computers → Version 1 posted Editorial decision: Revision requested 29 Jul, 2025 Reviews received at journal 19 Jul, 2025 Reviewers agreed at journal 20 Jun, 2025 Reviews received at journal 19 Jun, 2025 Reviewers agreed at journal 18 Jun, 2025 Reviewers agreed at journal 18 Jun, 2025 Reviewers invited by journal 18 Jun, 2025 Editor assigned by journal 29 May, 2025 Submission checks completed at journal 29 May, 2025 First submitted to journal 28 May, 2025 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-6770418","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":473741679,"identity":"d426c8f2-4756-42c7-87c3-0e10e99dc4c8","order_by":0,"name":"Geovane Augusto Haveroth","email":"","orcid":"","institution":"Universidade de São Paulo","correspondingAuthor":false,"prefix":"","firstName":"Geovane","middleName":"Augusto","lastName":"Haveroth","suffix":""},{"id":473741680,"identity":"98365073-2fea-4e38-83d2-368f8de0be83","order_by":1,"name":"Thais Clara da Costa Haveroth","email":"","orcid":"","institution":"State University of Campinas","correspondingAuthor":false,"prefix":"","firstName":"Thais","middleName":"Clara da Costa","lastName":"Haveroth","suffix":""},{"id":473741681,"identity":"03aa867f-f677-4889-a202-74efc5c3bad7","order_by":2,"name":"Marco Lúcio Bittencourt","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAnklEQVRIiWNgGAWjYDACdh7GBwwMEmA2M3FamHmYDUjWwiYBZxOlQ7eZ91g17w4Lef5pZw8wF+4hQovZYb6027xnJAxn3M5LYJ7xjCgtPGa3edskEhhu5xgw8xwgUksxSIs8SVqYQVoMSNDClyw5t03CcCPQL4dnEKXleO/BD2/b6uTlbucefFxAjBYkwMNAogaQllEwCkbBKBgFWAEAwvIwSvw1+eAAAAAASUVORK5CYII=","orcid":"","institution":"State University of Campinas","correspondingAuthor":true,"prefix":"","firstName":"Marco","middleName":"Lúcio","lastName":"Bittencourt","suffix":""},{"id":473741682,"identity":"55b15f12-f931-4b79-afbf-bc63dcaa55a9","order_by":3,"name":"José Luiz Boldrini","email":"","orcid":"","institution":"State University of Campinas","correspondingAuthor":false,"prefix":"","firstName":"José","middleName":"Luiz","lastName":"Boldrini","suffix":""}],"badges":[],"createdAt":"2025-05-28 18:08:19","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6770418/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6770418/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s00366-025-02253-6","type":"published","date":"2026-02-02T15:57:58+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":102234171,"identity":"bee50e59-1b13-4b1a-a1d2-d9f7b051c884","added_by":"auto","created_at":"2026-02-09 16:07:05","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1549238,"visible":true,"origin":"","legend":"","description":"","filename":"paperthaissubmitted.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6770418/v1_covered_815948f0-0c49-4d63-a6fe-10fc6c29e96c.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Damage Phase-Field Model for Fractional Derivative-Based Viscoelastic 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":"engineering-with-computers","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"ewco","sideBox":"Learn more about [Engineering with Computers](http://link.springer.com/journal/366)","snPcode":"366","submissionUrl":"https://submission.nature.com/new-submission/366/3","title":"Engineering with Computers","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Phase-field model, Damage, Viscoelastic materials, Fractional derivatives","lastPublishedDoi":"10.21203/rs.3.rs-6770418/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6770418/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"This work presents a thermodynamically consistent damage phase-field model incorporating fractional derivatives for characterization of viscoelastic materials. 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