The sobol sensitivity analysis of the pressure, stresses, and displacement arising from poroelastic modelling of hard mechanical systems

The sobol sensitivity analysis of the pressure, stresses, and displacement arising from poroelastic modelling of hard mechanical 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 Article The sobol sensitivity analysis of the pressure, stresses, and displacement arising from poroelastic modelling of hard mechanical systems Hadi Asghari, Laura Miller, Raimondo Penta, Andrey Melnikov, Christos Spitas, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7472991/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 23 Dec, 2025 Read the published version in Scientific Reports → Version 1 posted 10 You are reading this latest preprint version Abstract We perform a sensitivity analysis to investigate the influence of material input parameters on the pressure, stresses, and displacement of an isotropic porous solid cylinder representing hard mechanical systems such as the bone. We model the system using the governing equations of Biot’s poroelasticity in cylindrical polar coordinates, where the solutions are found by enforcing radial boundary conditions. The sensitivity analysis is carried out on the solutions for the pressure, stress components and displacement using ranges of the investigated parameters representative of the bone. Our study finds that the time t * has the highest influence on the pressure, the stress components and displacements. We find that the Poisson ratio ν plays a greater role than shear µ in the pressure response, and the shear µ counts more than the other parameters in the radial and circumferential stresses. There are key joint interactions between the Biot’s coefficient α and the Poisson ratio ν, the non-dimensionalised radius R * of the bone, and the Biot’s modulus M when investigating interstitial pressure, which is a key value in bone remodelling and fracture healing. This study paves the way to a deeper understanding of the interplay of all the parameters that are necessary to capture the true behaviour of hard mechanical systems such as the bone and its potential remodelling. Physical sciences/Energy science and technology Physical sciences/Engineering Physical sciences/Materials science Earth and environmental sciences/Solid earth sciences Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 23 Dec, 2025 Read the published version in Scientific Reports → Version 1 posted Editorial decision: Revision requested 24 Sep, 2025 Reviews received at journal 23 Sep, 2025 Reviews received at journal 19 Sep, 2025 Reviewers agreed at journal 14 Sep, 2025 Reviewers agreed at journal 10 Sep, 2025 Reviewers invited by journal 10 Sep, 2025 Editor invited by journal 01 Sep, 2025 Editor assigned by journal 01 Sep, 2025 Submission checks completed at journal 29 Aug, 2025 First submitted to journal 27 Aug, 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-7472991","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":514981713,"identity":"53f02558-cae4-40c4-83a6-1cbea01278a7","order_by":0,"name":"Hadi Asghari","email":"","orcid":"","institution":"Nazarbayev University","correspondingAuthor":false,"prefix":"","firstName":"Hadi","middleName":"","lastName":"Asghari","suffix":""},{"id":514981714,"identity":"ebc14ef3-8354-4a08-a213-090d882cacab","order_by":1,"name":"Laura Miller","email":"","orcid":"","institution":"University of Strathclyde","correspondingAuthor":false,"prefix":"","firstName":"Laura","middleName":"","lastName":"Miller","suffix":""},{"id":514981715,"identity":"0a98d6e2-c91d-4693-b4d4-b8fd269dbd06","order_by":2,"name":"Raimondo Penta","email":"data:image/png;base64,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","orcid":"","institution":"University of Glasgow","correspondingAuthor":true,"prefix":"","firstName":"Raimondo","middleName":"","lastName":"Penta","suffix":""},{"id":514981716,"identity":"ef92c879-ce55-4bcf-afb7-a13828bef1cd","order_by":3,"name":"Andrey Melnikov","email":"","orcid":"","institution":"Nazarbayev University","correspondingAuthor":false,"prefix":"","firstName":"Andrey","middleName":"","lastName":"Melnikov","suffix":""},{"id":514981717,"identity":"693e2733-f4d1-411a-b617-6baf4554fbff","order_by":4,"name":"Christos Spitas","email":"","orcid":"","institution":"University of Nottingham","correspondingAuthor":false,"prefix":"","firstName":"Christos","middleName":"","lastName":"Spitas","suffix":""},{"id":514981718,"identity":"f4fa086f-c9e5-4384-a5ad-3043ca31681c","order_by":5,"name":"JoséJos´José Merodio","email":"","orcid":"","institution":"Universidad Politecnica de Madrid","correspondingAuthor":false,"prefix":"","firstName":"JoséJos´José","middleName":"","lastName":"Merodio","suffix":""}],"badges":[],"createdAt":"2025-08-27 15:08:46","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7472991/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7472991/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41598-025-28109-z","type":"published","date":"2025-12-23T15:57:53+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":99172324,"identity":"abd23be6-1aa7-40e2-a34b-29dc50a6d3c4","added_by":"auto","created_at":"2025-12-29 16:07:52","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1388516,"visible":true,"origin":"","legend":"","description":"","filename":"SRHadietalfundingupdate28082025.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7472991/v1_covered_b5f73ce3-84fa-4e51-8b6f-27efc358278d.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"The sobol sensitivity analysis of the pressure, stresses, and displacement arising from poroelastic modelling of hard mechanical systems","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":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-7472991/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7472991/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"We perform a sensitivity analysis to investigate the influence of material input parameters on the pressure, stresses, and displacement of an isotropic porous solid cylinder representing hard mechanical systems such as the bone. We model the system using the governing equations of Biot’s poroelasticity in cylindrical polar coordinates, where the solutions are found by enforcing radial boundary conditions. The sensitivity analysis is carried out on the solutions for the pressure, stress components and displacement using ranges of the investigated parameters representative of the bone. Our study finds that the time t * has the highest influence on the pressure, the stress components and displacements. We find that the Poisson ratio ν plays a greater role than shear µ in the pressure response, and the shear µ counts more than the other parameters in the radial and circumferential stresses. There are key joint interactions between the Biot’s coefficient α and the Poisson ratio ν, the non-dimensionalised radius R * of the bone, and the Biot’s modulus M when investigating interstitial pressure, which is a key value in bone remodelling and fracture healing. This study paves the way to a deeper understanding of the interplay of all the parameters that are necessary to capture the true behaviour of hard mechanical systems such as the bone and its potential remodelling.","manuscriptTitle":"The sobol sensitivity analysis of the pressure, stresses, and displacement arising from poroelastic modelling of hard mechanical systems","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-09-17 06:28:56","doi":"10.21203/rs.3.rs-7472991/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-09-24T14:45:20+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-09-23T08:27:56+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-09-19T16:21:29+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"174074483338081646516035966538782043123","date":"2025-09-15T03:00:54+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"281249879461527118636095418324046144356","date":"2025-09-10T12:30:34+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-09-10T11:36:39+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2025-09-01T10:52:51+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-09-01T07:45:35+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-08-29T11:29:56+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2025-08-27T14:52:34+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"8975c9f9-5ffd-42e2-8e1d-927168026da1","owner":[],"postedDate":"September 17th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":54697549,"name":"Physical sciences/Energy science and technology"},{"id":54697550,"name":"Physical sciences/Engineering"},{"id":54697551,"name":"Physical sciences/Materials science"},{"id":54697552,"name":"Earth and environmental sciences/Solid earth sciences"}],"tags":[],"updatedAt":"2025-12-29T16:01:20+00:00","versionOfRecord":{"articleIdentity":"rs-7472991","link":"https://doi.org/10.1038/s41598-025-28109-z","journal":{"identity":"scientific-reports","isVorOnly":false,"title":"Scientific Reports"},"publishedOn":"2025-12-23 15:57:53","publishedOnDateReadable":"December 23rd, 2025"},"versionCreatedAt":"2025-09-17 06:28:56","video":"","vorDoi":"10.1038/s41598-025-28109-z","vorDoiUrl":"https://doi.org/10.1038/s41598-025-28109-z","workflowStages":[]},"version":"v1","identity":"rs-7472991","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7472991","identity":"rs-7472991","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}