Fully Coupled Multiphysics Modelling of Fracture Behaviour in Silicon Particles during Lithiation–Delithiation Using the Phase-Field Method

Fully Coupled Multiphysics Modelling of Fracture Behaviour in Silicon Particles during Lithiation–Delithiation Using the Phase-Field Method | 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 Fully Coupled Multiphysics Modelling of Fracture Behaviour in Silicon Particles during Lithiation–Delithiation Using the Phase-Field Method Jie Yang, Wei Tan This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6572406/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 08 Jan, 2026 Read the published version in Engineering with Computers → Version 1 posted 10 You are reading this latest preprint version Abstract In this study, a multiphysics model fully coupling mass transport, deformation, phase field, and fatigue damage was developed to investigate the cracking and fracturing behaviours of Si particles during the single lithiation-delithiation cycle and fatigue damage during multiple cycles. The effects of particle diameter, charge rate, and pre-existing notches on the failure behaviour of Si particles were systematically analysed. The results showed that the increase in charge rate, particle diameter, and pre-existing notch length leads to larger cracking rates and faster fracturing of the particle. Then, a validated contour map of Si particle’s fracture behaviours was developed. Additionally, the influence of pre-existing notch length and charge rate on fatigue damage was examined, and it was found that longer pre-existing notch length and larger charge rate can shorten the particle's cyclic life. Finally, to alleviate the particle fracture, nanopores were introduced in the particle, and the influence of porosity on the fracture behaviours was investigated. The results showed that nanopores can reduce expansion, dissipate global tensile stresses and elongate the crack propagation path, and an optimal porosity was found to be 40%. The developed computational framework established a predictive relationship between stress-diffusion coupling theory and particle-level degradation, providing guidance for future design and manufacturing of failure-resistant Si-based anodes for lithium-ion batteries. Multiphysics modelling Fracture behaviours Si particle Phase field method Lithiation-delithiation Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 08 Jan, 2026 Read the published version in Engineering with Computers → Version 1 posted Editorial decision: Revision requested 05 Sep, 2025 Reviews received at journal 21 Aug, 2025 Reviews received at journal 13 Aug, 2025 Reviewers agreed at journal 20 Jul, 2025 Reviewers agreed at journal 17 Jul, 2025 Reviewers agreed at journal 17 Jul, 2025 Reviewers invited by journal 01 Jul, 2025 Editor assigned by journal 02 May, 2025 Submission checks completed at journal 02 May, 2025 First submitted to journal 01 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-6572406","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":478949080,"identity":"4a752a41-48d6-477d-bc3c-b3c5cc25184e","order_by":0,"name":"Jie Yang","email":"","orcid":"","institution":"Queen Mary University of London","correspondingAuthor":false,"prefix":"","firstName":"Jie","middleName":"","lastName":"Yang","suffix":""},{"id":478949081,"identity":"252e3aec-a0fc-4374-9ea7-998f052ac265","order_by":1,"name":"Wei Tan","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAzUlEQVRIiWNgGAWjYFACxgYQKQdiHQAL8BCjBajUGMQkVgtEaWID0VoMjjc3MH+ouZPed+2MwQGGGjsGgzMHCGg5cxDosGPPcmfezgFqOZbMYHC2Ab8WsxtAJx1gO5y7AayF7QCDwXkCDjO7/xCo5d/hdAOwln/EaLkBDLGDbYcTwFoY2w4Qdpj9mcSGA2f7DhvOvJ1WcCCxL5lHkpD3JduPP3xQ8e2wPN/t5I0PPnyzk+M7k0DAZQyw6ACRCURGJIrGUTAKRsEoGAWYAADoe1Ckf8utkQAAAABJRU5ErkJggg==","orcid":"","institution":"Queen Mary University of London","correspondingAuthor":true,"prefix":"","firstName":"Wei","middleName":"","lastName":"Tan","suffix":""}],"badges":[],"createdAt":"2025-05-01 14:08:15","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6572406/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6572406/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s00366-025-02233-w","type":"published","date":"2026-01-08T15:59:19+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":100069460,"identity":"5aaf1c45-051b-4b8d-85d4-a44649eff080","added_by":"auto","created_at":"2026-01-12 16:14:22","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":6441291,"visible":true,"origin":"","legend":"","description":"","filename":"hfddyzcgjyzgkxmpwjyjrywcpvfjvdgg.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6572406/v1_covered_f31032ff-ee00-4e5a-8558-a013fcf0df57.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Fully Coupled Multiphysics Modelling of Fracture Behaviour in Silicon Particles during Lithiation–Delithiation Using the Phase-Field Method","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":"Multiphysics modelling, Fracture behaviours, Si particle, Phase field method, Lithiation-delithiation","lastPublishedDoi":"10.21203/rs.3.rs-6572406/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6572406/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"In this study, a multiphysics model fully coupling mass transport, deformation, phase field, and fatigue damage was developed to investigate the cracking and fracturing behaviours of Si particles during the single lithiation-delithiation cycle and fatigue damage during multiple cycles. The effects of particle diameter, charge rate, and pre-existing notches on the failure behaviour of Si particles were systematically analysed. The results showed that the increase in charge rate, particle diameter, and pre-existing notch length leads to larger cracking rates and faster fracturing of the particle. Then, a validated contour map of Si particle’s fracture behaviours was developed. Additionally, the influence of pre-existing notch length and charge rate on fatigue damage was examined, and it was found that longer pre-existing notch length and larger charge rate can shorten the particle's cyclic life. Finally, to alleviate the particle fracture, nanopores were introduced in the particle, and the influence of porosity on the fracture behaviours was investigated. The results showed that nanopores can reduce expansion, dissipate global tensile stresses and elongate the crack propagation path, and an optimal porosity was found to be 40\\%. The developed computational framework established a predictive relationship between stress-diffusion coupling theory and particle-level degradation, providing guidance for future design and manufacturing of failure-resistant Si-based anodes for lithium-ion batteries.","manuscriptTitle":"Fully Coupled Multiphysics Modelling of Fracture Behaviour in Silicon Particles during Lithiation–Delithiation Using the Phase-Field Method","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-07-03 15:43:00","doi":"10.21203/rs.3.rs-6572406/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-09-05T21:08:09+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-08-21T16:55:53+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-08-13T15:41:59+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"22710580694878453914281721180976356026","date":"2025-07-20T22:44:44+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"34625103065470819279194663887165413387","date":"2025-07-17T14:18:06+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"228641884529316849402257671738922287960","date":"2025-07-17T08:10:39+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-07-01T07:00:17+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-05-02T13:58:37+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-05-02T13:31:57+00:00","index":"","fulltext":""},{"type":"submitted","content":"Engineering with Computers","date":"2025-05-01T13:58:50+00:00","index":"","fulltext":""}],"status":"published","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}}],"origin":"","ownerIdentity":"13caec42-c468-423e-8dd4-fb5cd01640a0","owner":[],"postedDate":"July 3rd, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2026-01-12T16:06:48+00:00","versionOfRecord":{"articleIdentity":"rs-6572406","link":"https://doi.org/10.1007/s00366-025-02233-w","journal":{"identity":"engineering-with-computers","isVorOnly":false,"title":"Engineering with Computers"},"publishedOn":"2026-01-08 15:59:19","publishedOnDateReadable":"January 8th, 2026"},"versionCreatedAt":"2025-07-03 15:43:00","video":"","vorDoi":"10.1007/s00366-025-02233-w","vorDoiUrl":"https://doi.org/10.1007/s00366-025-02233-w","workflowStages":[]},"version":"v1","identity":"rs-6572406","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6572406","identity":"rs-6572406","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}