Finite volume simulations of dynamic brittle fracture using an exponential-based hyperbolic formulation of gradient damage models

Finite volume simulations of dynamic brittle fracture using an exponential-based hyperbolic formulation of gradient damage models | 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 Finite volume simulations of dynamic brittle fracture using an exponential-based hyperbolic formulation of gradient damage models Adrien Renaud, Thomas Heuzé, Nicolas Favrie This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9009636/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 6 You are reading this latest preprint version Abstract This study provides a multidimensional extension of the hyperbolic formulation of gradient damage models introduced by Favrie et al. in one space dimension, and which allows an efficient explicit numerical solutionof dynamics problems. The proposed methodology is based on an “extended Lagrangian approach” developed by one of the authors for the nondissipative and dispersive shallow water equation. By using this strategy, the global minimization problem commonly derived for gradient damage models is recast as a hyperbolic one with purely local source terms. The numerical solution of the governing system of equations is then based on a fractional-step method consisting of a classical Godunov-type finite volume scheme to solve the homogeneous part of the system, followed by an implicit Ordinary Differential Equation solver for the local source terms. Stored-energy functions corresponding to well-known damage models (i.e. Ambrosio & Tortorelli or AT models) are used with, however, the introduction of a new relaxed damage variable to easily handle damage boundedness. The proposed model is illustrated on two-dimensional test cases: the Kalthoff-Winkler experiment and a crack branching test. Brittle fracture Dynamic fracture Gradient damage Hyperbolic models Finite volumes Kalthoff-Winkler test Crack branching Full Text Additional Declarations No competing interests reported. Supplementary Files code1Dmultifragmentation.zip Cite Share Download PDF Status: Under Review Version 1 posted Reviewers agreed at journal 10 May, 2026 Reviewers agreed at journal 04 Mar, 2026 Reviewers invited by journal 04 Mar, 2026 Editor assigned by journal 04 Mar, 2026 Submission checks completed at journal 03 Mar, 2026 First submitted to journal 02 Mar, 2026 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-9009636","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":601328071,"identity":"fc9e703f-9708-49c2-b47b-7bc4ab505017","order_by":0,"name":"Adrien Renaud","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA+klEQVRIiWNgGAWjYFCCBIYDcDZPBQMDG5TNT6SWMwgtkg14tCAAbxuCjVMLf3vuwwMfdzDk80s3P5N4O+9wHp9EAuOnm20MEuY49EiceW5wcOYZBsuZc46ZSc7ddriYTSKBWToXqEXmAHYtDDfSGA4D3WNgcCPBTJp32+HENp7zH0Ba6iRw6JAHafkL1GJ/I/2bNO8ckJYDzL9BtuDSYgDSwgiyRSIHaEsDUAt7A5s0Pi2GZ54xHOxtkzCQuJFTbDnnWDpYi3XOOQmcWuSOpzF/+NlmY8A/I33jjTc11onzmxmYb+eU2eDUAgWY0gQ0jIJRMApGwSjACwATMlOEF6whkgAAAABJRU5ErkJggg==","orcid":"","institution":"Institut Universitaire des Systèmes Thermiques Industriels","correspondingAuthor":true,"prefix":"","firstName":"Adrien","middleName":"","lastName":"Renaud","suffix":""},{"id":601328073,"identity":"1633b3dd-1188-4b32-898a-371287d4954e","order_by":1,"name":"Thomas Heuzé","email":"","orcid":"","institution":"Institut de Recherche Dupuy de Lôme","correspondingAuthor":false,"prefix":"","firstName":"Thomas","middleName":"","lastName":"Heuzé","suffix":""},{"id":601328078,"identity":"25e037df-36ad-47ab-b629-b4d694ef1af6","order_by":2,"name":"Nicolas Favrie","email":"","orcid":"","institution":"Institut Universitaire des Systèmes Thermiques Industriels","correspondingAuthor":false,"prefix":"","firstName":"Nicolas","middleName":"","lastName":"Favrie","suffix":""}],"badges":[],"createdAt":"2026-03-02 11:38:37","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9009636/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9009636/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":104405020,"identity":"4283b814-328d-4130-a247-31db8fc4b4c2","added_by":"auto","created_at":"2026-03-11 12:21:36","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":4373316,"visible":true,"origin":"","legend":"","description":"","filename":"submissionIJF.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9009636/v1_covered_042f3071-a0a1-46cd-a932-f2413656a4ea.pdf"},{"id":104268727,"identity":"e17d64b2-33bd-434a-b71f-70b6bbdef705","added_by":"auto","created_at":"2026-03-09 21:21:06","extension":"zip","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":1363424,"visible":true,"origin":"","legend":"","description":"","filename":"code1Dmultifragmentation.zip","url":"https://assets-eu.researchsquare.com/files/rs-9009636/v1/d09ead4ec6e7c98b992211fe.zip"}],"financialInterests":"No competing interests reported.","formattedTitle":"\u003cp\u003eFinite volume simulations of dynamic brittle fracture using an exponential-based hyperbolic formulation of gradient damage models\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"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":"Brittle fracture, Dynamic fracture, Gradient damage, Hyperbolic models, Finite volumes, Kalthoff-Winkler test, Crack branching","lastPublishedDoi":"10.21203/rs.3.rs-9009636/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9009636/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"This study provides a multidimensional extension of the hyperbolic formulation of gradient damage models introduced by Favrie et al. in one space dimension, and which allows an efficient explicit numerical solutionof dynamics problems. 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