Modeling of Shape Memory Polymer Behavior Using Generalized Maxwell Model with Time-Temperature Superposition: Experiments, Parameter Identification, and Finite Element Validation

Modeling of Shape Memory Polymer Behavior Using Generalized Maxwell Model with Time-Temperature Superposition: Experiments, Parameter Identification, and Finite Element Validation | 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 Modeling of Shape Memory Polymer Behavior Using Generalized Maxwell Model with Time-Temperature Superposition: Experiments, Parameter Identification, and Finite Element Validation Mingkun Li, Longbin Liu, Shaozhe Ding, Haosen Chang, Xingfu Cui This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6959409/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 The modeling of the mechanical behavior of shape memory polymers (SMPs) is crucial for their engineering applications. This paper proposes a viscoelastic constitutive model based on the Generalized Maxwell Model combined with the Time-Temperature Superposition Principle (TTSP) to quantitatively predict the thermomechanical response of SMPs throughout the full shape memory cycle (loading–cooling–unloading–recovery). By decoupling the instantaneous elastic modulus and the normalized relaxation modulus, and considering the effect of temperature on the instantaneous modulus as well as the scaling of relaxation times, the model effectively resolves the simulation of stress increase during cooling caused by the growth of elastic modulus. The parameters of the Generalized Maxwell Model at different temperatures were determined through stress relaxation experiments, and the time-scaling factors were fitted using the Williams-Landel-Ferry (WLF) equation. Based on the fitted parameters, a three-dimensional constitutive model was implemented in ABAQUS, and finite element simulations of the full shape memory cycle under both uniaxial tension and bending deformation were conducted. Results demonstrate that the model accurately captures the stress growth due to increased elastic modulus during cooling, the shape fixity effect after unloading at low temperature, and the release of viscoelastic strain during the heating recovery process. The simulation results for both uniaxial and bending deformations are consistent with expected phenomena, validating the model's applicability under complex stress states. This study provides an efficient and reliable numerical tool for the intelligent structural design and controllable deformation analysis of SMPs. Physical sciences/Engineering/Mechanical engineering Physical sciences/Materials science/Theory and computation Physical sciences/Materials science/Structural materials Shape memory polymer Generalized Maxwell model Time-temperature superposition principle Finite element analysis Viscoelastic constitutive model 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. 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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-6959409","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":493834440,"identity":"67b109d5-f9a9-4866-82a8-c334576ed10d","order_by":0,"name":"Mingkun Li","email":"","orcid":"","institution":"National University of Defense Technology","correspondingAuthor":false,"prefix":"","firstName":"Mingkun","middleName":"","lastName":"Li","suffix":""},{"id":493834444,"identity":"de00b4e9-ac17-4fb4-8c03-54e7120a48b5","order_by":1,"name":"Longbin Liu","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAuElEQVRIiWNgGAWjYBACPiBmBjH4mZkPPyBKCxtMi2Q7W5oBaVoMzvMoSBCnhb338OvCNjt548M8DAYMNTbRhLXwnEuzntmWbLjtMO+BBwzH0nIbCGqRyDEz5m1jZtx2mC/BgLHhMNFa6u03N/MYSBCrxfgxb9vhxA3MRGvhOWPGPOPc8eQZh4GBnECMX/jZe4w/F5RV2/b3Hz784EONDWEtYLfBmQlEKAcB5g9EKhwFo2AUjIKRCgDQqjgWYBYrpAAAAABJRU5ErkJggg==","orcid":"","institution":"National University of Defense Technology","correspondingAuthor":true,"prefix":"","firstName":"Longbin","middleName":"","lastName":"Liu","suffix":""},{"id":493834449,"identity":"b0fd4ca3-a4b0-4edb-8a4b-001767a57249","order_by":2,"name":"Shaozhe Ding","email":"","orcid":"","institution":"National University of Defense Technology","correspondingAuthor":false,"prefix":"","firstName":"Shaozhe","middleName":"","lastName":"Ding","suffix":""},{"id":493834452,"identity":"8a676b2a-d879-40dc-8df2-462ee95303fa","order_by":3,"name":"Haosen Chang","email":"","orcid":"","institution":"National University of Defense Technology","correspondingAuthor":false,"prefix":"","firstName":"Haosen","middleName":"","lastName":"Chang","suffix":""},{"id":493834454,"identity":"15013382-b7b8-45d2-8def-d7bd129a8e53","order_by":4,"name":"Xingfu Cui","email":"","orcid":"","institution":"National University of Defense Technology","correspondingAuthor":false,"prefix":"","firstName":"Xingfu","middleName":"","lastName":"Cui","suffix":""}],"badges":[],"createdAt":"2025-06-23 19:08:15","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6959409/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6959409/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":91026686,"identity":"2e0ef325-db59-4d01-8a3d-1e7889cf7504","added_by":"auto","created_at":"2025-09-10 20:46:31","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2002004,"visible":true,"origin":"","legend":"","description":"","filename":"ModelingofShapeMemoryPolymerBehaviorUsingGeneralizedMaxwellModelwithTimeTemperatureSuperpositionEn.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6959409/v1_covered_94825f5e-39ef-49f1-99c9-1609848b3b86.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Modeling of Shape Memory Polymer Behavior Using Generalized Maxwell Model with Time-Temperature Superposition: Experiments, Parameter Identification, and Finite Element Validation","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":"Shape memory polymer, Generalized Maxwell model, Time-temperature superposition principle, Finite element analysis, Viscoelastic constitutive model","lastPublishedDoi":"10.21203/rs.3.rs-6959409/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6959409/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe modeling of the mechanical behavior of shape memory polymers (SMPs) is crucial for their engineering applications. This paper proposes a viscoelastic constitutive model based on the Generalized Maxwell Model combined with the Time-Temperature Superposition Principle (TTSP) to quantitatively predict the thermomechanical response of SMPs throughout the full shape memory cycle (loading\u0026ndash;cooling\u0026ndash;unloading\u0026ndash;recovery). By decoupling the instantaneous elastic modulus and the normalized relaxation modulus, and considering the effect of temperature on the instantaneous modulus as well as the scaling of relaxation times, the model effectively resolves the simulation of stress increase during cooling caused by the growth of elastic modulus. The parameters of the Generalized Maxwell Model at different temperatures were determined through stress relaxation experiments, and the time-scaling factors were fitted using the Williams-Landel-Ferry (WLF) equation. Based on the fitted parameters, a three-dimensional constitutive model was implemented in ABAQUS, and finite element simulations of the full shape memory cycle under both uniaxial tension and bending deformation were conducted. Results demonstrate that the model accurately captures the stress growth due to increased elastic modulus during cooling, the shape fixity effect after unloading at low temperature, and the release of viscoelastic strain during the heating recovery process. The simulation results for both uniaxial and bending deformations are consistent with expected phenomena, validating the model's applicability under complex stress states. This study provides an efficient and reliable numerical tool for the intelligent structural design and controllable deformation analysis of SMPs.\u003c/p\u003e","manuscriptTitle":"Modeling of Shape Memory Polymer Behavior Using Generalized Maxwell Model with Time-Temperature Superposition: Experiments, Parameter Identification, and Finite Element Validation","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-08-05 03:45:36","doi":"10.21203/rs.3.rs-6959409/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":"f11efedf-d8fd-4316-8cfd-5e0a2b42ed78","owner":[],"postedDate":"August 5th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":52446675,"name":"Physical sciences/Engineering/Mechanical engineering"},{"id":52446676,"name":"Physical sciences/Materials science/Theory and computation"},{"id":52446677,"name":"Physical sciences/Materials science/Structural materials"}],"tags":[],"updatedAt":"2025-09-10T20:38:22+00:00","versionOfRecord":[],"versionCreatedAt":"2025-08-05 03:45:36","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6959409","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6959409","identity":"rs-6959409","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}