Geometrical and Material Nonlinear Effects in Granular Micromechanics: Effects of Grain-Pair Tangential Plasticity and Induced Anisotropy

Geometrical and Material Nonlinear Effects in Granular Micromechanics: Effects of Grain-Pair Tangential Plasticity and Induced Anisotropy | 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 Geometrical and Material Nonlinear Effects in Granular Micromechanics: Effects of Grain-Pair Tangential Plasticity and Induced Anisotropy Nurettin Yilmaz, Luca Placidi, Anil Misra This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7601693/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 15 Apr, 2026 Read the published version in Continuum Mechanics and Thermodynamics → Version 1 posted 11 You are reading this latest preprint version Abstract Granular materials undergoing large deformations exhibit nonlinearity arising from both geometrical and material effects. Here we extend the earlier Granular Micromechanics Approach (GMA)-based continuum models by enriching the grain-pair elastic energy functional and dissipation potential with new tangential terms and a coupling between normal and tangential parameters to better describe these nonlinear effects. These new terms are expected to better represent various deformation mechanisms that grains experience including grain crushing, rearrangement, rotation/rolling, sliding, loss of lateral support, neighborhood densification and strain localization. The elastic energy of a generic grain-pair direction of the GMA is reformulated consisting of a complete quadratic and quartic (duffing) dependencies on normal and tangential relative displacements to capture various nuances of material nonlinearity. Further, the grain-pair dissipation potential formulation is modified by introducing (i) plastic dissipation in the tangential direction and (ii) coupling between the plastic dissipation in tension and compression. It is shown that the coupling of this nonlinear elastic and the damage-plastic behavior yields an apparent molecular-type, such as Lennard-Jones type, potential for the granular system. The GMA framework is exploited to link the grain-scale behavior to the macroscopic response. In this framework, the evolution of grain-scale dissipation parameters is obtained using a hemi-variational principle. To motivate the adoption of GMA framework, we present a brief review of grain-scale deformation mechanisms that lead to the emergent dissipative macroscale behavior and the evolution of induced anisotropy. The enriched model is used to simulate one-dimensional compression of elasto-frictional granular media. Classical behavior of lateral earth pressure coefficient, the ratio of lateral to axial stress, is predicted by the model.The obtained results are expounded with the aid of the evolution of two sets of parameters during the compaction process, one at the grain-scale and the other at the emergent macroscale. At the grain scale, we investigate the directional evolution of elastic energy, damage and plasticity. At the macroscale, we follow the evolution of macroscale induced anisotropy by considering the eigenvalues and harmonic decomposition of equivalent stiffness. one-dimensional compression tangential plasticity induced anisotropy granular micromechanics damage and plasticity mechanics variational-based model material nonlinearity harmonic decomposition Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 15 Apr, 2026 Read the published version in Continuum Mechanics and Thermodynamics → Version 1 posted Editorial decision: Revision requested 14 Mar, 2026 Reviews received at journal 13 Mar, 2026 Reviews received at journal 13 Mar, 2026 Reviewers agreed at journal 25 Feb, 2026 Reviewers agreed at journal 23 Feb, 2026 Reviews received at journal 10 Oct, 2025 Reviewers agreed at journal 15 Sep, 2025 Reviewers invited by journal 15 Sep, 2025 Editor assigned by journal 15 Sep, 2025 Submission checks completed at journal 15 Sep, 2025 First submitted to journal 12 Sep, 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-7601693","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":515507496,"identity":"a9787fd1-cd43-4805-acff-dc9d623ba89d","order_by":0,"name":"Nurettin Yilmaz","email":"","orcid":"","institution":"Florida International University","correspondingAuthor":false,"prefix":"","firstName":"Nurettin","middleName":"","lastName":"Yilmaz","suffix":""},{"id":515507497,"identity":"58181bdc-b7a2-41fe-bd3a-47d1f17a9da4","order_by":1,"name":"Luca Placidi","email":"","orcid":"","institution":"Telematic University Pegaso","correspondingAuthor":false,"prefix":"","firstName":"Luca","middleName":"","lastName":"Placidi","suffix":""},{"id":515507498,"identity":"8111e8b1-b1e5-4b98-8a08-be615465b771","order_by":2,"name":"Anil Misra","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAsklEQVRIiWNgGAWjYJCCA0Asx94MYrKRoMWY5zApWkAgsecAsVr4Z3cnHvy5xy69h53HgOFD2WHCWiTunN1wmOdZcm4PM48B44xzRGhhuJG74TDDAebc/UAtzLxtRGiRB2o5+ONAfToPSMtfYrQYALUc4DlwOAGshZEYLYYgh/EcOG7Yw8xWcLDnXDphLXI3cjd//HGgWp6H//DGBz/KrAlrQQEHSFQ/CkbBKBgFowAXAADXtzuVlDVGBQAAAABJRU5ErkJggg==","orcid":"","institution":"Florida International University","correspondingAuthor":true,"prefix":"","firstName":"Anil","middleName":"","lastName":"Misra","suffix":""}],"badges":[],"createdAt":"2025-09-12 14:53:21","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7601693/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7601693/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s00161-026-01476-2","type":"published","date":"2026-04-15T15:58:36+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":91942244,"identity":"2c52a21b-c1ea-4725-9231-97f005fe8e19","added_by":"auto","created_at":"2025-09-23 04:17:57","extension":"json","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":6107,"visible":true,"origin":"","legend":"","description":"","filename":"654ff74fc8824f0c923aef6ba5f092fb.json","url":"https://assets-eu.researchsquare.com/files/rs-7601693/v1/a4e8116777ddae3d5a8c95fb.json"},{"id":107351085,"identity":"ea63dade-6e68-4964-8fa3-ea4c796416cf","added_by":"auto","created_at":"2026-04-20 16:09:14","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3895537,"visible":true,"origin":"","legend":"","description":"","filename":"CMATPaper.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7601693/v1_covered_757aa7e7-f668-43b0-a684-8cee090ebdcd.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Geometrical and Material Nonlinear Effects in Granular Micromechanics: Effects of Grain-Pair Tangential Plasticity and Induced Anisotropy","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":"continuum-mechanics-and-thermodynamics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"cmat","sideBox":"Learn more about [Continuum Mechanics and Thermodynamics](http://link.springer.com/journal/161)","snPcode":"161","submissionUrl":"https://submission.nature.com/new-submission/161/3","title":"Continuum Mechanics and Thermodynamics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"one-dimensional compression, tangential plasticity, induced anisotropy, granular micromechanics, damage and plasticity mechanics, variational-based model, material nonlinearity, harmonic decomposition","lastPublishedDoi":"10.21203/rs.3.rs-7601693/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7601693/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Granular materials undergoing large deformations exhibit nonlinearity arising from both geometrical and material effects. 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