A Peridynamic Model for Anisotropic Heat Conduction and Its Extension to Phase-Change Problems

A Peridynamic Model for Anisotropic Heat Conduction and Its Extension to Phase-Change Problems | 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 A Peridynamic Model for Anisotropic Heat Conduction and Its Extension to Phase-Change Problems Qi-Qing Liu, Francesco Scabbia, Ugo Galvanetto, Mirco Zaccariotto This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9052760/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract An anisotropic heat conduction model and its corresponding phase change extension based on the Bond-Based Peridynamic (BB-PD) framework are proposed in this paper. A novel micro‑conductivity formulation is introduced that enforces positive definiteness of the conductivity tensor, thereby preventing material instabilities while remaining fully compatible with isotropic behavior. Based on the anisotropic heat conduction model, a phase change PD formulation for anisotropic materials is developed for the first time, incorporating direction-dependent thermal conductivities and latent heat effects. A series of numerical examples are presented to validate the accuracy and applicability of the two PD models in continuous and discontinuous media. The results demonstrate that the proposed anisotropic heat conduction PD model shows excellent agreement with Finite Element Method solutions and accurately captures the thermal behavior in highly anisotropic materials. Furthermore, the anisotropic phase change PD model can effectively track the solid-liquid interface and handle complex solidification processes even in the presence of crack propagation and intersection, thereby providing a rigorous foundation for the development of thermally coupled multiphysics simulation frameworks. Anisotropic material Heat conduction Peridynamics Phase change Crack propagation Full Text Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 1 posted 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-9052760","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":602033108,"identity":"49bffc33-9e5d-4ca7-b562-658ed47a6eee","order_by":0,"name":"Qi-Qing Liu","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAyElEQVRIiWNgGAWjYDACZgaGA0BKho2BGUgbMDA2MBOphYeNgS0BqoWgHgjgASIDEIOxgYGAFr7jzBsPF/xi4OGTyPkmXVBwR7aBnf8AXi2Sh9kKDs/sAzpMIneb9AyDZ8YEHWZwmMfgMG8PVAuQnUiKlpxnJGjh+QHWwkacFrBfeBskeNh4nhlb8wD90sbMbIBXC9/5w5s/8/yxkZNvT354m+fPHdl+/oMP8FtzABR9bRIILht+9VAtDH+QuKNgFIyCUTAK0AEAAmg9GbPk+RgAAAAASUVORK5CYII=","orcid":"https://orcid.org/0009-0007-7448-3710","institution":"University of Padova","correspondingAuthor":true,"prefix":"","firstName":"Qi-Qing","middleName":"","lastName":"Liu","suffix":""},{"id":602033109,"identity":"b8048eef-acf7-4abb-9288-98b58f7304bf","order_by":1,"name":"Francesco Scabbia","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Francesco","middleName":"","lastName":"Scabbia","suffix":""},{"id":602033110,"identity":"6cc8da62-ab11-4f16-8b9b-6066abbc2979","order_by":2,"name":"Ugo Galvanetto","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Ugo","middleName":"","lastName":"Galvanetto","suffix":""},{"id":602033111,"identity":"4e6929b3-8c36-4161-b885-2fee7dfa27e8","order_by":3,"name":"Mirco Zaccariotto","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Mirco","middleName":"","lastName":"Zaccariotto","suffix":""}],"badges":[],"createdAt":"2026-03-06 17:03:24","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-9052760/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9052760/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":104279415,"identity":"472136b1-2f2b-4e1a-ae70-dd3af26dc2a1","added_by":"auto","created_at":"2026-03-10 02:41:02","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2154956,"visible":true,"origin":"","legend":"","description":"","filename":"ManuscriptEWC.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9052760/v1_covered_42f01572-f655-4224-be56-2026d4c789dc.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003e\u003cstrong\u003eA Peridynamic Model for Anisotropic Heat Conduction and Its Extension to Phase-Change Problems\u003c/strong\u003e\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"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":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Anisotropic material, Heat conduction, Peridynamics, Phase change, Crack propagation","lastPublishedDoi":"10.21203/rs.3.rs-9052760/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9052760/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eAn anisotropic heat conduction model and its corresponding phase change extension based on the Bond-Based Peridynamic (BB-PD) framework are proposed in this paper. 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