Multiscale Modeling of Interacting Fracture Networks | 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 Multiscale Modeling of Interacting Fracture Networks Maria Laura De Bellis, Giulio Alfano, Anna Pandolfi, Elio Sacco This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7992859/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 29 Jan, 2026 Read the published version in International Journal of Fracture → Version 1 posted 7 You are reading this latest preprint version Abstract This study introduces a theoretical and numerical model for the spontaneous nucleation and propagation of distributed brittle fractures in initially intact materials. The formulation adopts a kinematic description of nested discontinuities characterized by a micromechanical interface law accounting for cohesion, unilateral contact and friction. The model allows for a unified treatment of the mixed-mode frictional fracture. The implementation of the model into a finite element framework is validated against benchmark tests, exhibiting independence of the discretization. The solution of selected quasi-static boundary value problems demonstrates the predictive capabilities of the framework in capturing key features observed in laboratory tests and in field problems involving confined quasi-brittle materials. Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 29 Jan, 2026 Read the published version in International Journal of Fracture → Version 1 posted Editorial decision: Revision requested 11 Dec, 2025 Reviews received at journal 10 Dec, 2025 Reviewers agreed at journal 03 Nov, 2025 Reviewers invited by journal 03 Nov, 2025 Editor assigned by journal 03 Nov, 2025 Submission checks completed at journal 31 Oct, 2025 First submitted to journal 30 Oct, 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. 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-7992859","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":539408128,"identity":"e26b1209-23de-4553-9f7d-2eaac356259c","order_by":0,"name":"Maria Laura De Bellis","email":"","orcid":"","institution":"University of Chieti-Pescara","correspondingAuthor":false,"prefix":"","firstName":"Maria","middleName":"Laura","lastName":"De Bellis","suffix":""},{"id":539408129,"identity":"c495256b-1788-41b1-bb02-f90ad9994c23","order_by":1,"name":"Giulio Alfano","email":"","orcid":"","institution":"Brunel University London","correspondingAuthor":false,"prefix":"","firstName":"Giulio","middleName":"","lastName":"Alfano","suffix":""},{"id":539408132,"identity":"c939c028-fb2c-4213-8c57-c3af67b41e8c","order_by":2,"name":"Anna Pandolfi","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA60lEQVRIiWNgGAWjYFCDA8wNHxIqGBj4mIFsBgOitDA2zkg4w8DABtFCjB6QFsY2oBYIF7cW/tm9Bz8w7rDL4zve2NjwcN4dOTZ27sQDDAV/cGqRuHMuWYLxTHKx5JmDjQ2J254ZszHzbsDvsBs5BhKMbcyJG24ktj9I3HY4sY2QFvkbOcY/GNvqQVqAtswhQovBjRwzoC2HoVoaiNBiCNRikXjmeOJMkF8SjkH9kmBgjFOLHNBhNz7uqE7sO958sPFHzR05fv6zmz98+COH2/sgkNgAZx6AUAn4NTAwMGJoGQWjYBSMglGABAA9jV/9kHj4qQAAAABJRU5ErkJggg==","orcid":"","institution":"Politecnico di Milano","correspondingAuthor":true,"prefix":"","firstName":"Anna","middleName":"","lastName":"Pandolfi","suffix":""},{"id":539408134,"identity":"63c3aed9-92de-40a5-99f2-ceb906c8d1e2","order_by":3,"name":"Elio Sacco","email":"","orcid":"","institution":"University of Naples Federico II","correspondingAuthor":false,"prefix":"","firstName":"Elio","middleName":"","lastName":"Sacco","suffix":""}],"badges":[],"createdAt":"2025-10-30 22:23:13","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7992859/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7992859/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s10704-025-00904-9","type":"published","date":"2026-01-29T15:58:02+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":95785869,"identity":"fbac05d8-efb7-4adb-926f-b4d92f988d95","added_by":"auto","created_at":"2025-11-13 05:11:45","extension":"json","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":5036,"visible":true,"origin":"","legend":"","description":"","filename":"34f21026bcf44d7da884161d931b2dee.json","url":"https://assets-eu.researchsquare.com/files/rs-7992859/v1/544519b00f2130982d522cde.json"},{"id":101690855,"identity":"68017863-1f3c-4858-91a9-6899e688d79f","added_by":"auto","created_at":"2026-02-02 16:10:39","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1636768,"visible":true,"origin":"","legend":"","description":"","filename":"Fig.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7992859/v1_covered_d8f946b8-2579-4c96-a6b8-df0c9655aea9.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Multiscale Modeling of Interacting Fracture Networks","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":"","lastPublishedDoi":"10.21203/rs.3.rs-7992859/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7992859/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"This study introduces a theoretical and numerical model for the spontaneous nucleation and propagation of distributed brittle fractures in initially intact materials. The formulation adopts a kinematic description of nested discontinuities characterized by a micromechanical interface law accounting for cohesion, unilateral contact and friction. The model allows for a unified treatment of the mixed-mode frictional fracture. The implementation of the model into a finite element framework is validated against benchmark tests, exhibiting independence of the discretization. The solution of selected quasi-static boundary value problems demonstrates the predictive capabilities of the framework in capturing key features observed in laboratory tests and in field problems involving confined quasi-brittle materials.","manuscriptTitle":"Multiscale Modeling of Interacting Fracture Networks","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-11-13 05:11:40","doi":"10.21203/rs.3.rs-7992859/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-12-11T22:20:32+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-12-10T22:20:05+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"217900973223197238686896207160201390808","date":"2025-11-03T19:46:22+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-11-03T19:00:42+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-11-03T18:53:22+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-11-01T03:26:17+00:00","index":"","fulltext":""},{"type":"submitted","content":"International Journal of Fracture","date":"2025-10-30T22:10:19+00:00","index":"","fulltext":""}],"status":"published","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}}],"origin":"","ownerIdentity":"9ba52708-9bd4-49b2-843c-a9b0943dd4fa","owner":[],"postedDate":"November 13th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2026-02-02T16:07:23+00:00","versionOfRecord":{"articleIdentity":"rs-7992859","link":"https://doi.org/10.1007/s10704-025-00904-9","journal":{"identity":"international-journal-of-fracture","isVorOnly":false,"title":"International Journal of Fracture"},"publishedOn":"2026-01-29 15:58:02","publishedOnDateReadable":"January 29th, 2026"},"versionCreatedAt":"2025-11-13 05:11:40","video":"","vorDoi":"10.1007/s10704-025-00904-9","vorDoiUrl":"https://doi.org/10.1007/s10704-025-00904-9","workflowStages":[]},"version":"v1","identity":"rs-7992859","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7992859","identity":"rs-7992859","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}
Text is read by the "Ask this paper" AI Q&A widget below.
Extraction quality varies by source — PMC NXML preserves structure
cleanly, OA-HTML may include some navigation residue, and OA-PDF can
have broken hyphenation. The publisher copy
(via DOI)
is the canonical version.