Local stress-geometry equation of 2D frictionless granular systems

Local stress-geometry equation of 2D frictionless granular systems | 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 Local stress-geometry equation of 2D frictionless granular systems Xinggang Zhang, Dan Dai, Yan Tang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5720923/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 For an isostatic granular system, the constitutive equation of stresstensor fields may be in the form of a stress-geometry equation whichis of great significance for understanding the mechanical behaviorsof static granular matter. To investigate force moment tensors andtheir stress-geometry equation of two-dimensional(2D) granular systems,we propose some algebraic theoretics of dyadic space \((\mathbb{T}^{2}(\mathbb{R}^{2}))\) such as the decomposition formula of a 2nd-order tensor and the crossproduct of two symmetric tensors. For 2D frictionless disk packings,a local stress-geometry equation for disks with four contacts is derivedbased on the analysis of mechanical equilibrium equations of contactforces. The definition of the geometry tensor in the stress-geometryequation shows complex associations between contact branch vectorsof a disk and the local Janssen coefficient is given from the eigenvaluesof this geometry tensor. Discrete element method(DEM) simulationsfor random frictionless disk packings are performed to verify thelocal stress-geometry equation and the numerical results are in goodagreement with the theoretical predictions. Granular matter Force moment tensor Constitutive equation Stress-geometry equation DEM simulation Full Text Additional Declarations No competing interests reported. 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. 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-5720923","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":396179503,"identity":"112d04f8-10dd-4e83-bf62-dc725b081d51","order_by":0,"name":"Xinggang Zhang","email":"","orcid":"","institution":"Guizhou University","correspondingAuthor":false,"prefix":"","firstName":"Xinggang","middleName":"","lastName":"Zhang","suffix":""},{"id":396179504,"identity":"02ab1f77-f772-4831-a800-090cb7543b09","order_by":1,"name":"Dan Dai","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAtklEQVRIiWNgGAWjYDCCAwkMBz5AmAbEazk4g2QtzDwkaeE7nvzwsM2vusQG9uZtEgw1dwhrkTzzzOBwbh9bYgPPsTIJhmPPCGsxuJEA1NLDk9ggkWMmwdhwmBgt6R8OW/ZIJDbIvyFaS47BYYYfBkBbeIjUInnmTcHB3oYE4zaetGKLhGNEaOE7nr75w48/dbL97Ic33vhQQ4QWMGBsY2BgAzESiNQABH+IVzoKRsEoGAUjEAAAXwA/ZspZka0AAAAASUVORK5CYII=","orcid":"","institution":"Guizhou University","correspondingAuthor":true,"prefix":"","firstName":"Dan","middleName":"","lastName":"Dai","suffix":""},{"id":396179505,"identity":"2a835488-1b17-49ba-9de1-0ae3043c37a7","order_by":2,"name":"Yan Tang","email":"","orcid":"","institution":"Guizhou University","correspondingAuthor":false,"prefix":"","firstName":"Yan","middleName":"","lastName":"Tang","suffix":""}],"badges":[],"createdAt":"2024-12-27 10:38:04","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5720923/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5720923/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":79450872,"identity":"c86fc2ef-0cca-45ab-8bc1-6dae701e2c2e","added_by":"auto","created_at":"2025-03-28 14:53:30","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1806409,"visible":true,"origin":"","legend":"","description":"","filename":"snmanuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5720923/v1_covered_e08eeca7-460e-426d-a46b-42aaff2d7078.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Local stress-geometry equation of 2D frictionless granular systems","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"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":"Granular matter, Force moment tensor, Constitutive equation, Stress-geometry equation, DEM simulation","lastPublishedDoi":"10.21203/rs.3.rs-5720923/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5720923/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eFor an isostatic granular system, the constitutive equation of stresstensor fields may be in the form of a stress-geometry equation whichis of great significance for understanding the mechanical behaviorsof static granular matter. To investigate force moment tensors andtheir stress-geometry equation of two-dimensional(2D) granular systems,we propose some algebraic theoretics of dyadic space \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\((\\mathbb{T}^{2}(\\mathbb{R}^{2}))\\)\u003c/span\u003e\u003c/span\u003esuch as the decomposition formula of a 2nd-order tensor and the crossproduct of two symmetric tensors. For 2D frictionless disk packings,a local stress-geometry equation for disks with four contacts is derivedbased on the analysis of mechanical equilibrium equations of contactforces. The definition of the geometry tensor in the stress-geometryequation shows complex associations between contact branch vectorsof a disk and the local Janssen coefficient is given from the eigenvaluesof this geometry tensor. Discrete element method(DEM) simulationsfor random frictionless disk packings are performed to verify thelocal stress-geometry equation and the numerical results are in goodagreement with the theoretical predictions.\u003c/p\u003e","manuscriptTitle":"Local stress-geometry equation of 2D frictionless granular systems","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-01-02 02:25:34","doi":"10.21203/rs.3.rs-5720923/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","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}}],"origin":"","ownerIdentity":"1763316c-fdd1-4b97-a7b4-e1611d698dea","owner":[],"postedDate":"January 2nd, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-03-28T14:53:11+00:00","versionOfRecord":[],"versionCreatedAt":"2025-01-02 02:25:34","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-5720923","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5720923","identity":"rs-5720923","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}