Topology Optimisation of Multiple Scales in Thermoelasticity

Topology Optimisation of Multiple Scales in Thermoelasticity | 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 Topology Optimisation of Multiple Scales in Thermoelasticity João Dias-de-Oliveira, Mafalda Gonçalves, Joaquim Pinho-da-Cruz, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8651336/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 9 You are reading this latest preprint version Abstract The design of multifunctional materials and structures that combine tailored mechanical performance with thermal behaviour is a central challenge in engineering, particularly in the context of the rapid development of additive manufacturing technologies. While topology optimisation provides a powerful computational framework to address this challenge, its extension to heterogeneous materials and multiscale systems remains non-trivial, especially when thermal and mechanical effects interact. In this work, a multiscale topology optimisation framework is presented for mechanical, thermal, and thermoelastic problems. The approach integrates asymptotic expansion homogenisation within a hierarchical formulation. Both fully coupled thermoelastic formulations and decoupled multiobjective strategies are investigated, allowing the relative influence of mechanical stiffness and thermal conductivity to be controlled through weighting factors. All problems are solved using an in-house developed numerical platform. The results demonstrate that the proposed framework provides accurate and robust solutions for single-scale, multiscale, and inverse homogenisation problems. While purely mechanical and thermal cases converge reliably, fully coupled thermoelastic formulations exhibit pronounced instabilities associated with the non-monotonic nature of their sensitivities. These findings motivate the adoption of decoupled multiobjective formulations as a stable and physically meaningful alternative for multiscale design. Overall, the proposed methodology establishes a computationally efficient and versatile basis for the multiscale optimisation of heterogeneous materials, with particular relevance to the design of additively manufactured multifunctional structures operating under combined thermal and mechanical conditions. topology optimization thermoelasticty multiobjective multiscale asymptotic expansion homogenisation heterogeneous materials Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 17 Feb, 2026 Reviews received at journal 14 Feb, 2026 Reviews received at journal 13 Feb, 2026 Reviewers agreed at journal 10 Feb, 2026 Reviewers agreed at journal 05 Feb, 2026 Reviewers invited by journal 03 Feb, 2026 Editor assigned by journal 28 Jan, 2026 Submission checks completed at journal 28 Jan, 2026 First submitted to journal 28 Jan, 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-8651336","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":585568514,"identity":"364eaa1d-9473-473d-9a56-a27752bc966f","order_by":0,"name":"João Dias-de-Oliveira","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAnElEQVRIiWNgGAWjYBACxgbmBgaGCtK0MAK1nAExmUnQxMDYRooW5vaDjY955x2WZ5DuP0CkHT2JzYYztx02bJA5TLSzEtskPm47zNggkUyslv6H7T8S5xy2J0HLjMQ2ho8NhxNJ0fKwWXLGsfTkNpnDBsRpMexPPviZp8batl+68QGRWhqgDDYJIt3FIA9nEa1lFIyCUTAKRhwAAN46K94ymKFEAAAAAElFTkSuQmCC","orcid":"","institution":"University of Aveiro","correspondingAuthor":true,"prefix":"","firstName":"João","middleName":"","lastName":"Dias-de-Oliveira","suffix":""},{"id":585568515,"identity":"8f6db0dc-c84d-4899-a349-edc9dc855cc4","order_by":1,"name":"Mafalda Gonçalves","email":"","orcid":"","institution":"Institute of Mechanical Engineering and Industrial Mangement","correspondingAuthor":false,"prefix":"","firstName":"Mafalda","middleName":"","lastName":"Gonçalves","suffix":""},{"id":585568516,"identity":"d102b66c-a951-47ba-a56a-8a588d0dcfd1","order_by":2,"name":"Joaquim Pinho-da-Cruz","email":"","orcid":"","institution":"University of Aveiro","correspondingAuthor":false,"prefix":"","firstName":"Joaquim","middleName":"","lastName":"Pinho-da-Cruz","suffix":""},{"id":585568517,"identity":"59c08930-67c3-4a35-bdf8-cb5c97c3c6c8","order_by":3,"name":"Filipe Teixeira-Dias","email":"","orcid":"","institution":"University of Edinburgh","correspondingAuthor":false,"prefix":"","firstName":"Filipe","middleName":"","lastName":"Teixeira-Dias","suffix":""}],"badges":[],"createdAt":"2026-01-20 16:54:11","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8651336/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8651336/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":102295236,"identity":"73956457-e44d-4e20-ad5d-fb7684fe2efc","added_by":"auto","created_at":"2026-02-10 10:10:10","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2799952,"visible":true,"origin":"","legend":"","description":"","filename":"ThElpaperv12.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8651336/v1_covered_e81c09c2-2361-4763-8a0e-6c9c7a333aa8.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Topology Optimisation of Multiple Scales in Thermoelasticity","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":"discover-materials","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"dime","sideBox":"Learn more about [Discover Materials](https://www.springer.com/journal/43939)","snPcode":"","submissionUrl":"","title":"Discover Materials","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Discover Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"topology optimization, thermoelasticty, multiobjective, multiscale, asymptotic expansion homogenisation, heterogeneous materials","lastPublishedDoi":"10.21203/rs.3.rs-8651336/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8651336/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe design of multifunctional materials and structures that combine tailored mechanical performance with thermal behaviour is a central challenge in engineering, particularly in the context of the rapid development of additive manufacturing technologies. 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