Mathematical and numerical study of detachment with frictional contact and adhesion in a two-mass system

Mathematical and numerical study of detachment with frictional contact and adhesion in a two-mass system | 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 Mathematical and numerical study of detachment with frictional contact and adhesion in a two-mass system Sangmin Chun, Jeongho Ahn This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8477225/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 11 Mar, 2026 Read the published version in Zeitschrift für angewandte Mathematik und Physik → Version 1 posted 7 You are reading this latest preprint version Abstract This work presents mathematical and numerical analyses of a two mass-spring-damper system with frictional resistance and interfacial adhesion. The proposed model extends an existing detachment model to a more realistic setting and leads to modified steady states and adhesion-dependent detachment behavior. The motion of two masses, governed by Coulomb's law of dry friction and bonding fields, is described by a highly nonlinear system of ordinary differential equations. We prove the convergence of approximations in both the continuous and discrete cases, as well as the uniqueness of solutions. To handle the inherent non-smoothness of friction and adhesion and the associated nonlinearity, stable numerical schemes are constructed using appropriate regularization and the Newton-Raphson method. Numerical simulations illustrate the onset and propagation of detachment processes and support the theoretical predictions, providing new insights into the system. Nonlinear differential equation system Detachment Frictional contact Adhesion Existence and uniqueness Numerical schemes Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 11 Mar, 2026 Read the published version in Zeitschrift für angewandte Mathematik und Physik → Version 1 posted Editorial decision: Accepted 23 Feb, 2026 Reviews received at journal 23 Feb, 2026 Reviewers agreed at journal 06 Jan, 2026 Reviewers invited by journal 05 Jan, 2026 Editor assigned by journal 05 Jan, 2026 Submission checks completed at journal 05 Jan, 2026 First submitted to journal 29 Dec, 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. 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-8477225","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":570010624,"identity":"70713121-4ed1-41a8-b6e3-df480b2afcd5","order_by":0,"name":"Sangmin Chun","email":"","orcid":"","institution":"Chung-Ang University","correspondingAuthor":false,"prefix":"","firstName":"Sangmin","middleName":"","lastName":"Chun","suffix":""},{"id":570010627,"identity":"b3703ea4-24c7-4f29-81c3-22eb85a0b67f","order_by":1,"name":"Jeongho Ahn","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAv0lEQVRIiWNgGAWjYBACxgYeBoYPcC4bkVoYZzAwSEBUE6OFgYGHgZmHJC3M7WePPbapqavjn998gOFD2WEiHNaTl26cc+ywhMQxtgTGGeeI0dKQYyadw3ZAguEYjwEzbxsxWvrfmElb/KuTkD/G/4H5L1FaZgBtYWxjljA4BgwHRuK0vDGT7O07LLnxWJrBwZ5z6YS1GPbnmEn8+FbHL3f48MMHP8qsidDSgMQ5QFg9EMgTpWoUjIJRMApGNgAAsWw2yIxBemkAAAAASUVORK5CYII=","orcid":"","institution":"Arkansas State University","correspondingAuthor":true,"prefix":"","firstName":"Jeongho","middleName":"","lastName":"Ahn","suffix":""}],"badges":[],"createdAt":"2025-12-30 04:23:28","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8477225/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8477225/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s00033-026-02754-4","type":"published","date":"2026-03-11T15:57:47+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":99660501,"identity":"4511456f-2938-48d0-8556-0f50cfe478b4","added_by":"auto","created_at":"2026-01-07 03:41:58","extension":"json","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":3495,"visible":true,"origin":"","legend":"","description":"","filename":"c3c215a93b1847d5a9dc72eb630cfc00.json","url":"https://assets-eu.researchsquare.com/files/rs-8477225/v1/f6b518bd0e9e9c98473bc78d.json"},{"id":104739394,"identity":"db89004a-ea42-450b-aeec-9bd227faa52d","added_by":"auto","created_at":"2026-03-16 16:05:34","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2610494,"visible":true,"origin":"","legend":"","description":"","filename":"ZAMPpub.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8477225/v1_covered_e8b603da-d0d1-47bc-a7a7-3cf9d5540e90.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Mathematical and numerical study of detachment with frictional contact\nand adhesion in a two-mass system","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":"Nonlinear differential equation system, Detachment, Frictional contact, Adhesion, Existence and uniqueness, Numerical schemes","lastPublishedDoi":"10.21203/rs.3.rs-8477225/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8477225/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"This work presents mathematical and numerical analyses of a two mass-spring-damper\nsystem with frictional resistance and interfacial adhesion. The proposed\nmodel extends an existing detachment model to a more realistic setting\nand leads to modified steady states and adhesion-dependent detachment\nbehavior. The motion of two masses, governed by Coulomb's law of dry\nfriction and bonding fields, is described by a highly nonlinear system\nof ordinary differential equations. We prove the convergence of approximations\nin both the continuous and discrete cases, as well as the uniqueness\nof solutions. To handle the inherent non-smoothness of friction and\nadhesion and the associated nonlinearity, stable numerical schemes\nare constructed using appropriate regularization and the Newton-Raphson\nmethod. Numerical simulations illustrate the onset and propagation\nof detachment processes and support the theoretical predictions, providing\nnew insights into the system.","manuscriptTitle":"Mathematical and numerical study of detachment with frictional contact\nand adhesion in a two-mass system","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-01-07 03:41:54","doi":"10.21203/rs.3.rs-8477225/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Accepted","date":"2026-02-23T16:57:23+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-02-23T09:02:17+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"37385882012552232948044703514338109567","date":"2026-01-06T07:10:04+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-01-05T18:00:16+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-01-05T13:53:50+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2026-01-05T12:57:47+00:00","index":"","fulltext":""},{"type":"submitted","content":"Zeitschrift für angewandte Mathematik und Physik","date":"2025-12-30T04:20:23+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":"2fed5642-0fe5-47d5-873b-748d5b5e0ef4","owner":[],"postedDate":"January 7th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2026-03-16T16:02:29+00:00","versionOfRecord":{"articleIdentity":"rs-8477225","link":"https://doi.org/10.1007/s00033-026-02754-4","journal":{"identity":"zeitschrift-fur-angewandte-mathematik-und-physik","isVorOnly":false,"title":"Zeitschrift für angewandte Mathematik und Physik"},"publishedOn":"2026-03-11 15:57:47","publishedOnDateReadable":"March 11th, 2026"},"versionCreatedAt":"2026-01-07 03:41:54","video":"","vorDoi":"10.1007/s00033-026-02754-4","vorDoiUrl":"https://doi.org/10.1007/s00033-026-02754-4","workflowStages":[]},"version":"v1","identity":"rs-8477225","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8477225","identity":"rs-8477225","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}