Phase-field modeling of fracture via homogenization

Phase-field modeling of fracture via homogenization | 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 Phase-field modeling of fracture via homogenization Gerard Villalta, Alex Ferrer, Fermin Otero This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5737707/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 17 Jun, 2025 Read the published version in International Journal of Fracture → Version 1 posted 2 You are reading this latest preprint version Abstract This study presents a novel phase-field modeling approach for brittle fracture that incorporates computational homogenization techniques to characterize the microstructural degradation of the material. Traditional phase-field models often implement degradation and dissipation functions in terms of the phase-field variable that, despite offering satisfactory results, their physical interpretation and their extension to anisotropic fracture behavior is not always clear. To address this challenge, we develop a framework inspired by the nucleation, growth, and coalescence of microstructural voids to model macroscopic fracture. The proposed approach employs homogenization techniques to calculate the effective material properties when introducing voids of varying sizes and shapes. By solving the homogenization problem for different void geometries, we obtain degradation functions that relate the size of microstructural voids to the homogenized constitutive tensor. These degradation functions provide a direct link between microscale damage mechanisms and macroscale fracture behavior. Comparative analyses with conventional AT1 and AT2 models reveal strong correlations between their response and those obtained via homogenization techniques. This relationship highlights the ability of homogenized models to not only replicate established results but also provide a new understanding of the phase-field variable. Phase-field Homogenization Fracture Multi-scale Brittle materials Damage Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 17 Jun, 2025 Read the published version in International Journal of Fracture → Version 1 posted Submission checks completed at journal 18 Apr, 2025 First submitted to journal 16 Apr, 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. 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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-5737707","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":444704878,"identity":"6b702fcb-f760-4331-a2e2-461e7ac0a877","order_by":0,"name":"Gerard Villalta","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA+0lEQVRIiWNgGAWjYFACxsYDDxgsGBjYGxgOIETZ8GppOJDAICHBwHOAaC0MDBAtEgnIYni0yEckA22pkajjn/n44aGbO2wYDG43P2D4UHYYpxbDG4lALcckJCRupxkczj2TxmBw55gB44xzeLT0HARqYQM67HYOw+HctsMMBjdyGJh52whp+SchIX/zDEjLf4iWv3i0yLM3NhxIbJOQMLjBA9JyAKKFEY8WA7CWPgnJjWdAfmlL5pEE+uVgz7l03LY0sz988OGbDb/c8cOPP+e22cnx3W5++OBHmTVuWw6gCfAwSDAwoAui2tKAISSBT/0oGAWjYBSMRAAAjK1eQNsH42sAAAAASUVORK5CYII=","orcid":"","institution":"International Center for Numerical Methods in Engineering","correspondingAuthor":true,"prefix":"","firstName":"Gerard","middleName":"","lastName":"Villalta","suffix":""},{"id":444704879,"identity":"5d4e9560-ce63-4bca-97b8-711e522f343b","order_by":1,"name":"Alex Ferrer","email":"","orcid":"","institution":"International Center for Numerical Methods in Engineering","correspondingAuthor":false,"prefix":"","firstName":"Alex","middleName":"","lastName":"Ferrer","suffix":""},{"id":444704880,"identity":"4251c5a1-1c6f-410b-b5aa-63a47d885049","order_by":2,"name":"Fermin Otero","email":"","orcid":"","institution":"International Center for Numerical Methods in Engineering","correspondingAuthor":false,"prefix":"","firstName":"Fermin","middleName":"","lastName":"Otero","suffix":""}],"badges":[],"createdAt":"2024-12-30 20:08:09","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5737707/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5737707/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s10704-025-00861-3","type":"published","date":"2025-06-18T00:00:00+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":85088177,"identity":"78917839-b95d-49d7-99a5-13df94a4b77c","added_by":"auto","created_at":"2025-06-20 20:52:37","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1821409,"visible":true,"origin":"","legend":"","description":"","filename":"PhasefieldmodelingoffractureviahomogenizationREVIEWED.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5737707/v1_covered_e581a559-c877-45f6-979a-9a0c5ae23b9c.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Phase-field modeling of fracture via homogenization","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"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":"international-journal-of-fracture","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"frac","sideBox":"Learn more about [International Journal of Fracture](http://link.springer.com/journal/10704)","snPcode":"10704","submissionUrl":"https://submission.nature.com/new-submission/10704/3","title":"International Journal of Fracture","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Phase-field, Homogenization, Fracture, Multi-scale, Brittle materials, Damage","lastPublishedDoi":"10.21203/rs.3.rs-5737707/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5737707/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"This study presents a novel phase-field modeling approach for brittle fracture that incorporates computational homogenization techniques to characterize the microstructural degradation of the material. 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