Dynamic propagation of a Dugdale-model interfacial crack in two dissimilar one-dimensional hexagonal piezoelectric quasicrystals

Dynamic propagation of a Dugdale-model interfacial crack in two dissimilar one-dimensional hexagonal piezoelectric quasicrystals | 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 Dynamic propagation of a Dugdale-model interfacial crack in two dissimilar one-dimensional hexagonal piezoelectric quasicrystals Jia-Yi Zhao, Yan-Bin Zhou This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8808177/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 13 Apr, 2026 Read the published version in Zeitschrift für angewandte Mathematik und Physik → Version 1 posted 9 You are reading this latest preprint version Abstract A moving Dugdale-type interfacial crack between two dissimilar\one-dimensional (1D) hexagonal piezoelectric quasicrystals (PQCs) is considered. By considering the coupling effects of the phonon field, phason field, and electric field, the dynamic behavior of the interfacial crack under anti-plane mechanical loading and in-plane electrical loading is investigated. The mixed boundary value problem is transformed into dual integral equations by using the Fourier transform. The explicit expressions for the yield zone sizes and the crack sliding displacement are derived separately for both the phonon field and phason field. The results show that the electric field load exerts a significant regulatory effect on the interfacial cracks in 1D hexagonal PQCs. Both the yield zone sizes and crack sliding displacement have a functional correlation with external loads and are strongly regulated by the electric field. An increase in the Mach number exacerbates the material mismatch effect, resulting in different amplitudes of crack sliding displacement on the upper and lower crack surfaces. \noindent\textbf{Key words:} 1D hexagonal PQCs; Moving Dugdale interfacial crack; Dual integral equations; The yield zone; Crack sliding displacement. 1D hexagonal PQCs Moving Dugdale interfacial crack Dual integral equations The yield zone Crack sliding displacement Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 13 Apr, 2026 Read the published version in Zeitschrift für angewandte Mathematik und Physik → Version 1 posted Editorial decision: Accepted 30 Mar, 2026 Reviews received at journal 29 Mar, 2026 Reviews received at journal 01 Mar, 2026 Reviewers agreed at journal 11 Feb, 2026 Reviewers agreed at journal 10 Feb, 2026 Reviewers invited by journal 09 Feb, 2026 Editor assigned by journal 09 Feb, 2026 Submission checks completed at journal 09 Feb, 2026 First submitted to journal 06 Feb, 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-8808177","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":588768446,"identity":"6806c67b-1b24-4e21-9453-fe0d41889a47","order_by":0,"name":"Jia-Yi Zhao","email":"","orcid":"","institution":"Inner Mongolia Normal University","correspondingAuthor":false,"prefix":"","firstName":"Jia-Yi","middleName":"","lastName":"Zhao","suffix":""},{"id":588768447,"identity":"0326d331-dce1-4501-80e6-2c2512824126","order_by":1,"name":"Yan-Bin Zhou","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA4UlEQVRIie3NoQ7CMBCA4SMkm1mY7QzwCKdAIHiVNQhMR0jwBFUMCxbeAtzkYAmYktnhtpCgZghqDsoUiDIcon+aimu/HIBO958Z4II89TAsB25lYrg/kPKbhVCJ4PF0SLNgOrIJu+3PQQS2yRCKQEHEaIhUGBNn5W0iT0TgLHKs+UJBQtYhlFt0k0jCI8CEYb3GFSTOJSFPwtIX6X8lyWsLSgLlFvKFOEneRcpdul5c8UmGFhHX8c5XkEbMOlnBp3RpDi53j/ea9nywTQsFaYcfA0ten8O3WjPVq06n0+lkD58TWECxMLj7AAAAAElFTkSuQmCC","orcid":"","institution":"Inner Mongolia Normal University","correspondingAuthor":true,"prefix":"","firstName":"Yan-Bin","middleName":"","lastName":"Zhou","suffix":""}],"badges":[],"createdAt":"2026-02-06 14:25:24","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8808177/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8808177/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s00033-026-02786-w","type":"published","date":"2026-04-13T15:58:19+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":107352316,"identity":"bb6ae0f3-8e6b-4a59-b88d-1758dc767364","added_by":"auto","created_at":"2026-04-20 16:13:43","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2160201,"visible":true,"origin":"","legend":"","description":"","filename":"DynamicPropagationofaDugdalemodelInterfacialCrackin1D.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8808177/v1_covered_9cee27bb-d695-4e55-8256-5b4dee106535.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Dynamic propagation of a Dugdale-model interfacial crack in two dissimilar\none-dimensional hexagonal piezoelectric quasicrystals","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":"zeitschrift-fur-angewandte-mathematik-und-physik","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"zamp","sideBox":"Learn more about [Zeitschrift für angewandte Mathematik und Physik](http://link.springer.com/journal/33)","snPcode":"33","submissionUrl":"https://submission.nature.com/new-submission/33/3","title":"Zeitschrift für angewandte Mathematik und Physik","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"1D hexagonal PQCs, Moving Dugdale interfacial crack, Dual integral equations, The yield zone, Crack sliding displacement","lastPublishedDoi":"10.21203/rs.3.rs-8808177/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8808177/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"A moving Dugdale-type interfacial crack between two\ndissimilar\\one-dimensional (1D) hexagonal piezoelectric quasicrystals (PQCs)\nis considered. By considering the coupling effects of the phonon field, phason\nfield, and electric field, the dynamic behavior of the interfacial crack under\nanti-plane mechanical loading and in-plane electrical loading is investigated.\nThe mixed boundary value problem is transformed into dual integral equations\nby using the Fourier transform. The explicit expressions for the yield zone\nsizes and the crack sliding displacement are derived separately for both the\nphonon field and phason field. The results show that the electric field load\nexerts a significant regulatory effect on the interfacial cracks in 1D\nhexagonal PQCs. Both the yield zone sizes and crack sliding displacement have\na functional correlation with external loads and are strongly regulated by the\nelectric field. An increase in the Mach number exacerbates the material\nmismatch effect, resulting in different amplitudes of crack sliding\ndisplacement on the upper and lower crack surfaces.\n\\noindent\\textbf{Key words:} 1D hexagonal PQCs; Moving Dugdale interfacial\ncrack; Dual integral equations; The yield zone; Crack sliding displacement.","manuscriptTitle":"Dynamic propagation of a Dugdale-model interfacial crack in two dissimilar\none-dimensional hexagonal piezoelectric quasicrystals","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-02-12 14:26:48","doi":"10.21203/rs.3.rs-8808177/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Accepted","date":"2026-03-30T15:21:55+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-03-30T03:22:02+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-03-01T15:20:10+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"182181653318195491420181014218406314861","date":"2026-02-12T01:00:59+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"179928165532150572363307347880017544420","date":"2026-02-10T07:14:38+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-02-09T16:25:51+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-02-09T16:07:52+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2026-02-09T07:18:53+00:00","index":"","fulltext":""},{"type":"submitted","content":"Zeitschrift für angewandte Mathematik und Physik","date":"2026-02-06T14:12:21+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"zeitschrift-fur-angewandte-mathematik-und-physik","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"zamp","sideBox":"Learn more about [Zeitschrift für angewandte Mathematik und Physik](http://link.springer.com/journal/33)","snPcode":"33","submissionUrl":"https://submission.nature.com/new-submission/33/3","title":"Zeitschrift für angewandte Mathematik und Physik","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"2df4dd01-6281-421b-bdc3-e56eea5950b3","owner":[],"postedDate":"February 12th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2026-04-20T16:11:23+00:00","versionOfRecord":{"articleIdentity":"rs-8808177","link":"https://doi.org/10.1007/s00033-026-02786-w","journal":{"identity":"zeitschrift-fur-angewandte-mathematik-und-physik","isVorOnly":false,"title":"Zeitschrift für angewandte Mathematik und Physik"},"publishedOn":"2026-04-13 15:58:19","publishedOnDateReadable":"April 13th, 2026"},"versionCreatedAt":"2026-02-12 14:26:48","video":"","vorDoi":"10.1007/s00033-026-02786-w","vorDoiUrl":"https://doi.org/10.1007/s00033-026-02786-w","workflowStages":[]},"version":"v1","identity":"rs-8808177","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8808177","identity":"rs-8808177","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}