Steady-state mode I crack propagation in a brittle solid

Steady-state mode I crack propagation in a brittle solid | 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PDF Research Article Steady-state mode I crack propagation in a brittle solid Martin Kroon This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8286016/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 04 Apr, 2026 Read the published version in International Journal of Fracture → Version 1 posted 8 You are reading this latest preprint version Abstract A steady-state, finite element analysis of brittle, dynamic crack propagation in PMMA is presented. The steady-state assumption means that all time derivatives are translated into a spatial derivative instead. The bulk PMMA is modelled as a linear elastic, isotropic material. The crack is modelled by use of a non-standard cohesive zone model that ensures that material stability is maintained. The cohesive zone contains two lengths, which allows for a regularisation of the crack problem. The boundary conditions were adjusted so that the results could be compared to experimental studies. The stress and strain fields at the crack tip resulting from the numerical analysis were shown, and the possible implications for damage evolution and crack branching were discussed. The study supports the idea that microcracks are initiated at some distance from the crack plane and then grow and join the main crack. The study suggests that the propagating crack goes from a 'simple crack' to an unstable crack when the peak in the maximum principal strain -- which appears at some distance from the crack plane -- exceeds the dynamic fracture strain of the material. steady-state dynamic crack cohesive zone instability Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 04 Apr, 2026 Read the published version in International Journal of Fracture → Version 1 posted Editorial decision: Revision requested 06 Mar, 2026 Reviews received at journal 01 Feb, 2026 Reviewers agreed at journal 01 Feb, 2026 Reviewers agreed at journal 08 Dec, 2025 Reviewers invited by journal 06 Dec, 2025 Editor assigned by journal 06 Dec, 2025 Submission checks completed at journal 05 Dec, 2025 First submitted to journal 05 Dec, 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. 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-8286016","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":557697781,"identity":"edcf796b-aa51-4e63-80bb-b173c7d7f736","order_by":0,"name":"Martin Kroon","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAzklEQVRIiWNgGAWjYLCCBAYGAzDjQwFxGhgbYFoYZxgQq4UBqoWZhxgtuu1nnz94uIPB2Ly9+dhjG4M7iQ38hw/g1WJ2Jt2wIfEMg5nMmWPpxjkGzxIbJNIS8Gs5kMbYkNjGYCMhkWMmnWNwGKiFgPPMzj9D0mIB0sJ//gN+LTcgtpiBtTCAtDDk4NUB1PKMcUZim4SxBM+xNMkeg8PGbRJphByWxvDxZ5uN4Qz25mMSPyoOy/bzH36A3xoIkEAw2YhRPwpGwSgYBaMAPwAAw/pBldgvMY8AAAAASUVORK5CYII=","orcid":"","institution":"Linnaeus University","correspondingAuthor":true,"prefix":"","firstName":"Martin","middleName":"","lastName":"Kroon","suffix":""}],"badges":[],"createdAt":"2025-12-05 09:23:32","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8286016/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8286016/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s10704-026-00919-w","type":"published","date":"2026-04-04T15:58:35+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":98046670,"identity":"c632bec5-9740-49eb-afbe-599ff83a77d5","added_by":"auto","created_at":"2025-12-12 08:19:49","extension":"json","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":2889,"visible":true,"origin":"","legend":"","description":"","filename":"00d5eca5d1654c148215edc707051431.json","url":"https://assets-eu.researchsquare.com/files/rs-8286016/v1/0fa46db7dec1358430107318.json"},{"id":106343402,"identity":"359ec7bc-f672-4dc2-b4ae-1de205f4de99","added_by":"auto","created_at":"2026-04-07 16:05:21","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":498168,"visible":true,"origin":"","legend":"","description":"","filename":"SteadybrittledamageSpringer5.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8286016/v1_covered_25219bb2-31c2-4f02-9a2a-e3f417a3d74b.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Steady-state mode I crack propagation in a brittle solid","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":"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":"steady-state, dynamic, crack, cohesive zone, instability","lastPublishedDoi":"10.21203/rs.3.rs-8286016/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8286016/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"A steady-state, finite element analysis of brittle, dynamic crack propagation in PMMA is presented. 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